HZ_exo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculations from Martínez-Rodríguez et al. (2019)\n",
    "## https://arxiv.org/abs/1910.12054"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "from astropy.table import Table, Column, vstack\n",
    "import astropy.io.fits as pyfits\n",
    "from astropy.io import ascii\n",
    "import os\n",
    "import re\n",
    "import csv\n",
    "\n",
    "from scipy import integrate, interpolate, optimize\n",
    "import matplotlib.patches as patches\n",
    "import matplotlib.gridspec as gridspec\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "import matplotlib.ticker\n",
    "\n",
    "from shapely.geometry import Point\n",
    "from shapely.geometry.polygon import Polygon\n",
    "from descartes import PolygonPatch\n",
    "import matplotlib.path as mplPath\n",
    "\n",
    "matplotlib.rcParams['mathtext.fontset'] = 'cm' # computer modern\n",
    "matplotlib.rcParams['font.family'] = 'STIXGeneral'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "pathw = os.getcwd() + '/'\n",
    "path_data = os.getcwd() + '/Input_tables/'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Tsun = 5778. #K\n",
    "Msun = 1.98E30 # kg\n",
    "Lsun = 3.828E26 # W\n",
    "Rsun = 6.957E8 # m\n",
    "One_AU = 149597870700. #m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hector/anaconda2/lib/python2.7/site-packages/ipykernel_launcher.py:8: RuntimeWarning: invalid value encountered in power\n",
      "  \n"
     ]
    },
    {
     "data": {
      "image/png": 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pT3+avr6+zJo1q+k40FWMYAEA9BgbDMPEUbAAAHqMDYZh4ihYAAA9RsGCiaNgAQD0kK1bt2bVqlVJTBGEiWCRixartWZoaGiv582YMWMS0gAA/LyHHnooGzduzOte97rMmTOn6TjQdkZzL78nClaLrVy5Mn19fXs9r9Y6CWkAAH7evHnz8uUvfzmbN29uOgq0pdHcy+9JcaPfWqWUUX2gPncAAGg/pZTRnrqi1vqaBxmNYLXYkiVLsmzZsqZjAAAAYzA4ODiq83Y30qVgtVgpxfNVAEBbGhoayic/+cn09/fnQx/60L78pB56xnjv5a0iCADQI+677758/vOfz2//9m8rVzBBFCwAgB4xsv/Vqaee2nAS6F4KFgBAj1i+fHkSGwzDRFKwAAB6hBEsmHgKFgBAD3jllVdy7733ZsqUKVm8eHHTcaBrKVgAAD1g9erV2bp1a44//vjsv//+TceBrmWZdgCAHjA0NJTTTz89S5YsaToKdDUFCwCgB5x99tm58847m44BXc8UQQAAgBZRsAAAutwrr7ySBx98MMPDw01Hga6nYAEAdLm77rorb3nLW3LOOec0HQW6noIFANDlRva/estb3tJwEuh+ChYAQJdbvnx5EhsMw2RQsAAAupyCBZNHwQIA6GJr167NmjVrMmvWLFMEYRIoWAAAXWzk+avFixdn2jRboMJEU7AAALrYSMHq7+9vOAn0Bj/GAADoYp/85Cdz6aWXZvbs2U1HgZ6gYAEAdLHp06dn8eLFTceAnmGKIAAAQIsoWAAAXeo73/lOzj333HzpS19qOgr0DAULAKBL3Xrrrbn55pvz+OOPNx0FeoaCBQDQpUY2GD7ttNMaTgK9Q8ECAOhCw8PDrxasU089teE00DusIthitdYMDQ3t9bwZM2ZMQhoAoFc9+uijWb9+fRYsWJD58+c3HQc6xmju5fdEwWqxlStXpq+vb6/n1VonIQ0A0KvuvvvuJKYHwr4azb38npgiCADQhUYKlumBMLmMYLXYkiVLsmzZsqZjAAA97sILL8ymTZty3nnnNR0FOsrg4OCoztvdSFcxVa21+vv768DAQNMxAACACVRKWVFr7d/5uCmCAAAALaJgAQB0mWXLluWqq67KM88803QU6DkKFgBAl/nzP//z/OIv/mK+/vWvNx0Feo6CBQDQZUY2GLZEO0w+BQsAoIts2LAh999/f6ZNm5aTTz656TjQcxQsAIAusnLlytRac+KJJ2bmzJlNx4Geo2ABAHQR0wOhWQoWAEAXufvuu5Mkp556asNJoDcpWAAAXWTTpk2ZOnWqggUNmdZ0AAAAWudb3/pWNm7c6PkraIiCBQDQZfbbb7+mI0DPMkUQAKBLrFu3LrXWpmNAT1OwAAC6xAc+8IHMmTMnt99+e9NRoGeZIggA0AWGh4dz99135+WXX84xxxzTdBzoWUawAAC6wKOPPpqXX3458+fPz4IFC5qOAz1LwQIA6AIj+1+dfvrpDSeB3qZgAQB0gbvuuitJctpppzWcBHqbggUA0AVGRrAULGiWggUA0OE2bdqU1atXp5SS/v7+puNAT7OKIABAh5s+fXpuvfXWPPTQQznwwAObjgM9TcECAOhwU6dOzemnn26BC2gDpggCAAC0iIIFANDhPvKRj+Qzn/lMNmzY0HQU6Hml1tp0hq7S399fBwYGmo4BAPSIF198MYcddlhmzpyZ9evXZ/r06U1Hgp5QSllRa33NqjJGsAAAOtjy5cuTJEuWLFGuoA0oWAAAHWxkg2ELXEB7ULAAADqYDYahvShYAAAdqtb6asEyggXtQcECAOhQa9asyfPPP5/DDz88xxxzTNNxgNhoGACgYw0PD+dXfuVXMnv27JRSmo4DRMFquVprhoaG9nrejBkzJiENANDN3vjGN+bLX/5y0zGgq4zmXn5P7IPVYqWUUX2gPncAAGg/+zAabB8sAIBuMTg4mKuvvjo/+clPmo4C7MAUwRZbsmRJli1b1nQMAKDLrVq1Ku973/vylre8Jffff3/TcaBrDA4Ojuq8vr6+XR5XsFqslOL5KgBgwt15551Jkre97W0NJ4HuMt57eVMEAQA60F133ZXE/lfQbhQsAIAOpGBBe1KwAAA6zE9/+tOsWbMm+++/f44//vim4wA7ULAAADrMyOhVf39/pk3zSD20EwULAKDDPPbYYymlWOAC2pCNhlusv7+/DgwMNB0DAOhy69evz9DQUObMmdN0FOhJpZRdbjRsTBkAoAMdeOCBTUcAdsEUQQCADrJ169aYgQTtS8ECAOggX/nKVzJ//vz8wR/8QdNRgF1QsAAAOsidd96ZZ599NlOmuI2DduRfJgBABxlZot0KgtCeFCwAgA7xs5/9LPfdd1+mTZuWJUuWNB0H2AUFCwCgQyxfvjzDw8M58cQTM2vWrKbjALugYAEAdIg777wzSbJ06dKGkwC7o2ABAHQIBQvan42GAQA6xKc//emceeaZOfvss5uOAuyGggUA0CFOO+20nHbaaU3HAPbAFEEAAIAWMYIFANAB/uf//J/56U9/mg9/+MN5wxve0HQcYDcULACADvAXf/EXWbFiRc466ywFC9qYKYIAAG1u48aNueeeezJlypT09/c3HQfYAwULAKDNrVixIlu2bMmJJ56Y2bNnNx0H2AMFCwCgzS1btixJ8ra3va3hJMDeKFgAAG1uZINhBQvan4IFANDGaq2vjmAtXbq04TTA3lhFEACgjb3yyis599xz8/DDD2fRokVNxwH2QsECAGhj++23X772ta81HQMYJVMEAQAAWkTBAgBoY7feemuef/75pmMAo2SKIABAmxocHMwFF1yQzZs3Z926dTnggAOajgTsxR4LVillTZKjJ+jaJcmaWuuxE/T+AAAdbeXKlRkaGsrxxx+vXEGH2NsI1j/UWl8/URcvpdw0Ue8NANDpbDAMncczWAAAbeqOO+5Ikrz97W9vOAkwWnsrWJ+f4OtP9PsDAHSkHTcYVrCgc+yxYNVavzmRF5/o9wcA6FRPPvlkfvKTn+SQQw7Jm970pqbjAKNkiiAAQBv64Q9/mCRZunRppkxxywadYkKXaS+lHJzkyiRHJalJnkryjVrryxN5XQCATnfZZZdl7dq1efllt03QSSasYJVSPpzkdUn+ptb6xPZjC5P8einliVrr1ybq2k2qtWZoaGiv582YMWMS0gAAnezQQw/NoYce2nQM6CmjuZffk1JrbVGUHd60lF9O8nyt9bu7+fpFSQ6vtf5Nyy/esFLKqD7QifjcAYDuUGtNKaXpGNCT9uHf3opaa//OB1s+obeUMjfJ3N2VqySptX4vybxSyuGtvj4AQKe75ZZbsnDhwnzqU59qOgqwjyZiiuAvJfmznQ+WUmbXWn+2w6E/T/Ir6bKl2pcsWfLqkqoAAGOxbNmyPPXUU1m/fn3TUaDnDA4Ojuq8vr6+XR6fiIJ1QK113Y4HSik3JHl7KeWcWuvdSVJrfbmUMnsCrt+oUornqwCAcRnZYHjp0qUNJ4HeM957+YlY83NXDxe9IcnMJPNHcS4AQM+ywTB0tokYwSqllFJ/fhWHc5K8efuzVyMnTUkydQKuDwDQsR577LG88MILOeKII/L617++6TjAPpqIEawbkrx7xwO11id3LFfbvTvJjRNwfQCAjjUyerV06VIrCUIHannBqrXenm3PWx20u3NKKYcmeUet9Y5WXx8AoJONPH9leiB0ponaaPg/JfndUsqXaq337viFUsoJSf7PJNYdBQDYyUc/+tEcffTRufTSS5uOAozBhGw0nLz6jNVHkrwxyabth6cneTzJV2qtWyfkwg3r7++vAwMDTccAAAAmUClllxsNT9QIVmqtw0m+NFHvDwAA0G4mrGABALBvrrrqqjz++OO58sors2jRoqbjAGMwqoJVSjmg1rphrBcZ7+sBAHrBX/7lX+Z73/tejj32WAULOtRoVxH87jivc904Xw8A0NWGh4d/bol2oDONtmAdNc7rLBzn6wEAutr999+f9evX5+ijj85RR4331gtoymifwVpYSvmTJM+O4RrzMv6CBgDQ1W6//fYkyRlnnNFwEmA89mWRi18b4zVKkolZCx4AoEvYYBi6w2gL1mCS25OMZaGKI5OcPobXAQD0DCNY0B1GW7CWJPmlJDOTfKvWeutoL1BKmZqxTS0EAOgJQ0NDOeWUUzJt2rSccMIJTccBxmFUBavW+mCSz5ZSpiW5vJTyh0meTvLVWutP9vLaraWUH40/KgBAd5oxY0auuuqqpmMALbBPGw3XWrck+UaSb5RS5if55VLKvCS3ZNvI1pbdvPTfjC8mAABA+xvtMu2vUWv9Sa3192utv5nkxST/tZTyO6WU43dx7srxhAQA6GZ33HFHXn755aZjAC2wTyNYu1NrvTnJzaWUA5N8sJTyb5KsTvK/aq1jWRgDAKAnvPLKKznnnHMyPDycl19+ObNnz246EjAOYx7B2pVa6/pa6xdrrf9XkieT3FtK+XIpxXI4AAC7sGLFimzevDnHH3+8cgVdoCUjWCO2rxh4eZKPJLl4+/v/i2xbqv2SVl4LAKAbjCzPbv8r6A4tKVjbn7v6l0k+nGROtm0u/JMkf5XkL2utj7XiOgAA3cYGw9BdxlywRp63yrZi1Z9tpWpzkm8m+csk19Vah1sREgCgG9VaXy1YNhiG7rDPBauUcl62lar3ZtvGwyXJA9lWqv661vp8SxMCAHSpRx99NC+88EKOPPLIvP71r286DtACoypYpZSjk/zq9l+vy7ZStSHJl5J8qdZ6115e/ze11g+PKykAQJdZvXp1km2jV6WUhtMArTDaEaxHkkzPtmJ1a7aNVn291rpxby8s275bnD/mhAAAXeoDH/hAzjnnnGzYYFcb6BajLVgzkizLtmL1WJKapH8UP2kpSa5McsRYAwIAdLMjjjgiRxzhVgm6xb48g/XDJEdt/zVaU5Kctk+JAAB6QK3VtEDoQqMtWE/VWn99LBcopfy3bFuyHQCA7a655pr85m/+Zv7Vv/pX+dSnPtV0HKBFpozyvKfGeoFa64YkD4719QAA3ei2227LmjVr8rOf/azpKEALjbZgXTzO61wwztcDAHSV22+/PUnyjne8o+EkQCvtsWCVUq5Iklrr+vFcZHevH3l/AIBe8sorr2T58uUppWTp0qVNxwFaaG8jWL8xwdef6PcHAGg7AwMD2bx5c9761rfm4IMPbjoO0EKjnSIIAECLmB4I3Wtvqwi+oZSydYKuXZL8wwS9NwBA27rtttuSKFjQjfZYsGqtx0xSDgCAnvHJT34y/f39Ofvss5uOArTYvmw0DABAC5x11lk566yzmo4BTADPYAEAALSIESwAgEn0R3/0R9m8eXM++MEPZv78+U3HAVpMwQIAmER/+Id/mDVr1uT8889XsKALmSIIADBJnn766axZsyYHHHBATjjhhKbjABNgVAWrlHLAeC4y3tcDAHSDkf2vli5dmqlTpzacBpgIox3B+u44r3PdOF8PANDxbDAM3W+0BeuocV5n4ThfDwDQ8UY2GD7jjDMaTgJMlNEucrGwlPInSZ4dwzXmZfwFDQCgo23YsCGrV6/OtGnTcvrppzcdB5gg+7KK4K+N8RolSR3jawEAusJLL72Uyy+/PENDQ9l///2bjgNMkNEWrMEktyfZMIZrHJnEj2kAgJ529NFH5+qrr246BjDBRluwliT5pSQzk3yr1nrraC9QSpmasU0tBAAA6CijWuSi1vpgrfWzST6V5PBSyh+WUj5RStnr7ni11q1JfjTOnAAAHWtoaCh///d/n5/97GdNRwEm2L48g5Va65Yk30jyje3l6pdLKfOS3JJtI1tbdvPSfzO+mJ2j1pqhoaG9njdjxoxJSAMAtIOBgYG8853vzFvf+tbce++9TccB9mA09/J7sk8Fa0e11p8k+f0kKaWck+S/llL+Mcn/qrXev9O5K8cTspOsXLkyfX19ez2vVut+AECvGFme/e1vf3vDSYC9Gc29/J6MuWDtqNZ6c5KbSykHJvlgKeXfJFmdbWVrLAtjAAB0jVtv3fb4+plnntlwEmCitaRgjai1rk/yxSQppVyU5N5Sys1J/rzWensrr9WulixZkmXLljXWXLJuAAAgAElEQVQdAwBoE8PDw7n99m23QQoWtL/BwcFRnbe7ka6WFqztKwZenuQjSS7e/v7/ItuWar+klddqV6UUz1cBAK964IEH8tJLL+Woo47K0Ucf3XQcYC/Gey/fkoJVSjk+yb9M8uEkc7Jtc+GfJPmrJH9Za32sFdcBAOg0O04PLKU0nAaYaGMuWCPPW2VbserPtlK1Ock3k/xlkutqrcOtCAkA0KkefPDBJKYHQq8o+7qaXSnlvGwrVe/Nto2HS5IHsq1U/XWt9flWh+wk/f39dWBgoOkYAEAbefrpp7PffvvlkEMOaToK0CKllBW11v6dj49qBKuUcnSSX93+63XZVqo2JPlSki/VWu/ay+v/ptb64X3MDADQFRYsWNB0BGCSjHaK4CNJpmdbsbo120arvl5r3bi3F5Ztk43PH3NCAIAOtWXLlkyb1tI1xYA2N9p/8TOSLMu2YvVYkpqkfxQPapYkVyY5YqwBAQA61cc+9rHcdNNN+fznP5+LL7646TjAJNiXH6n8MMlR23+N1pQkp+1TIgCALnHrrbfmkUceyUEHHdR0FGCSjLZgPVVr/fWxXKCU8t+ybcl2AICe8cILL+SBBx7IzJkzc8oppzQdB5gkU0Z53lNjvUCtdUOSB8f6egCATnTbbbclSZYuXTrujUuBzjHagjXeScMXjPP1AAAd5ZZbbkmSnHXWWQ0nASbTqApWrXX9eC4y3tcDAHQaBQt602hHsAAAGKX169dn1apVmTZtWt72trc1HQeYRDZmAABosb6+vlx77bX50Y9+lP3226/pOMAkUrAAAFqsr6/PvlfQo0wRBAAAaBEFCwCghV555ZX84i/+Yv74j/84tdam4wCTTMECAGihu+++O1dddVX+4i/+IqWUpuMAk0zBAgBoIcuzQ29TsAAAWkjBgt6mYAEAtMjmzZtzxx13JEnOPPPMhtMATVCwAABaZOXKldm4cWOOO+64HHHEEU3HARqgYAEAtMjI9ECjV9C7FCwAgBY59thj8653vSsXXXRR01GAhhT7M7RWf39/HRgYaDoGAAAwgUopK2qt/TsfN4IFAADQIgoWAEAL3H333fnBD36QTZs2NR0FaJCCBQDQAr//+7+fc845J1/96lebjgI0SMECABin4eHh/OAHP0iSnH322Q2nAZqkYAEAjNMDDzyQtWvXZv78+Tn22GObjgM0SMECABinHUevSikNpwGapGABAIzTSME655xzmg0CNE7BAgAYh1qr56+AVylYAADj8Nxzz6Wvry9HHnlk3vSmNzUdB2jYtKYDAAB0srlz5+aJJ57I2rVrPX8FGMECABivUkrmzJnTdAygDShYAABjVGvN2rVrm44BtBEFCwBgjB577LHMmTMn5513XtNRgDahYAEAjNHI6oGHHHJIw0mAdqFgAQCMkeXZgZ0pWAAAY2D/K2BXFCwAgDH4h3/4h/z4xz/OIYcckhNOOKHpOECbULAAAMZgZPTqzDPPzJQpbqmAbXw3AAAYg5tvvjlJcu655zYbBGgr05oOAADQiT73uc/lve99bxYvXtx0FKCNKFgAAGNw6KGH5oorrmg6BtBmTBEEAABoEQULAGAffeITn8iHPvSh3HfffU1HAdqMggUAsA9qrbnqqqvyta99LVu3bm06DtBmFCwAgH2wZs2aPPnkkzn00EPtfwW8hoIFALAPRpZnP/vss+1/BbyG7woAAPtgpGCdc845jeYA2pOCBQAwSrVWGwwDe6RgAQCM0uOPP54f//jHOeyww3L88cc3HQdoQzYaBgAYpf322y+/8zu/k61bt3r+CtilUmttOkNX6e/vrwMDA03HAAAAJlApZUWttX/n4370AgAA0CIKFgDAKDz55JP5vd/7vaxYsaLpKEAbU7AAAEbhe9/7Xj71qU/lv/yX/9J0FKCNKVgAAKNw0003JbH/FbBnChYAwF7UWvP9738/SXLeeec1nAZoZwoWAMBePPTQQ3nuuedy5JFH5s1vfnPTcYA2pmABAOzFyOjVueeem1JKw2mAdqZgAQDsxcjzV6YHAnujYAEA7MXhhx+eww8/XMEC9qrUWpvO0FX6+/vrwMBA0zEAgBYbuWcyRRBIklLKilpr/87HpzURBgCg0yhWwGiYIggAsAfLly/P+vXrm44BdAgFCwBgN7Zs2ZILLrgghx56aJ577rmm4wAdQMECANiNVatWZf369TnmmGNy5JFHNh0H6AAKFgDAbozsf2X1QGC0FCwAgN0Y2f/q3HPPbTgJ0CkULACAXRgaGsqtt96aRMECRs8y7S1Wa83Q0NBez5sxY8YkpAEAxmr58uXZuHFj3vzmN2fu3LlNxwEmyWju5fdEwWqxlStXpq+vb6/n2eAZANrbqlWrknj+CnrNaO7l96S40W+tUsqoPlCfOwC0v2effTabN2/OwoULm44CTJJ92FR8Ra21f+eDRrBabMmSJVm2bFnTMQCAFjA1EHrP4ODgqM7b3UiXgtVipRTPVwFAh9u8eXOmT5/edAygAeO9l7eKIADATj772c/mDW94Q77+9a83HQXoMAoWAMBOvv/972fNmjU54IADmo4CdBgFCwBgBy+//HJWrFiRadOm5cwzz2w6DtBhFCwAgB3cfPPNGR4eztve9rbsv//+TccBOoyCBQCwgxtvvDFJcv755zecBOhEChYAwA6+//3vJ1GwgLFRsAAAtnvmmWfywAMPZL/99svpp5/edBygA9kHCwBgu8MOOyw33HBDnnzySftaAmOiYAEAbDdjxgxTA4FxMUUQAACgRRQsAIAkjz/+eC6//PJ86UtfajoK0MEULACAJDfccEOuueaafPe73206CtDBFCwAgPzT/lfnnXdew0mATqZgAQA9b3h42P5XQEsoWABAz/vhD3+YF154IQsXLsyiRYuajgN0MAULAOh5N9xwQ5LkggsuSCml4TRAJ1OwAICeN1KwLrzwwoaTAJ3ORsMAQM973/vel+nTp1vgAhi3UmttOkNX6e/vrwMDA03HAAAAJlApZUWttX/n46YIAgAAtIiCBQD0tP/xP/5HbrzxxmzevLnpKEAX8AwWANCzXnrppfzmb/5mpk6dmhdffDHTp09vOhLQ4YxgAQA96+abb87w8HCWLl2a2bNnNx0H6AIKFgDQs3bc/wqgFRQsAKBn2f8KaDUFCwDoSU8++WQeeeSRHHjggenvf81KywBjomABAD3pxhtvTJKce+65mTbNul9AayhYAEBPGh4ezjHHHOP5K6ClSq216Qxdpb+/vw4MDDQdAwAYpa1bt2bq1KlNxwA6TCllRa31NfOLjWABAD1NuQJaScECAHrOgw8+mGeffbbpGEAXUrAAgJ7zG7/xG5k3b16+/e1vNx0F6DIKFgDQU1555ZXccsstSZLTTz+94TRAt1GwAICectttt2VwcDCLFy/O4Ycf3nQcoMsoWABAT7n++uuTJO985zsbTgJ0IwULAOgpf//3f58kufDCCxtOAnQjBQsA6BnPPfdc7rnnnsyaNStnnHFG03GALqRgAQA9Y9WqVZk6dWrOOuuszJw5s+k4QBea1nQAAIDJcvHFF2ft2rVZu3Zt01GALqVgAQA95aCDDspBBx3UdAygS5kiCAD0hMHBwQwPDzcdA+hyChYA0BP+5E/+JHPnzs2f/umfNh0F6GIKFgDQE66//vo8//zzOeCAA5qOAnQxBQsA6HqDg4P5wQ9+kCS54IILGk4DdDMFCwDoerfffnteeeWVnHDCCZk7d27TcYAupmABAF3ve9/7XpLkoosuajgJ0O0ULACg6ylYwGRRsACArvbss8/mnnvuyaxZs/KOd7yj6ThAl7PRMADQ1Q4//PDcfffdefTRRzNz5sym4wBdTsECALra1KlTc+qpp+bUU09tOgrQA0wRBAAAaBEFCwDoWqtXr87ZZ5+dL37xi01HAXqEggUAdK3rrrsut9xySwYGBpqOAvQIBQsA6FqWZwcmm4IFAHSlDRs25Pbbb8+UKVNy/vnnNx0H6BEKFgDQlW666aZs2bIlp59+eg455JCm4wA9QsECALqS6YFAExQsAKArjRSsd77znQ0nAXqJjYYBgK4zPDycz372s7n55pttMAxMqlJrbTpDV+nv76+WggUAgO5WSllRa+3f+bgpggAAAC2iYAEAXWVoaCgf//jH861vfStm6gCTTcECALrKbbfdli984Qv5zGc+k1JK03GAHqNgAQBd5bvf/W6S5OKLL244CdCLFCwAoKtcd911SZJLLrmk4SRAL1KwAICu8dRTT+W+++7L/vvvnzPOOKPpOEAPUrAAgK4xMj3w/PPPz4wZMxpOA/QiBQsA6BojBcv0QKAp05oOAADQKieddFIefvjhXHTRRU1HAXpUsT9Ea/X399eBgYGmYwAAABOolLKi1tq/83FTBAEAAFpEwQIAusLXvva1PPbYY03HAHqcZ7AAgI733HPP5UMf+lBmzpyZl156KTNnzmw6EtCjjGABAB3ve9/7XpLk3HPPVa6ARilYAEDHG1me3eqBQNMULACgo23duvXVgnXppZc2nAbodQoWANDR7rrrrrz00kt54xvfmEWLFjUdB+hxChYA0NG+853vJDF6BbQHBQsA6GgbN27MrFmzFCygLZRaa9MZukp/f38dGBhoOgYA9JRNmzZl6tSpmT59etNRgB5RSllRa+3f+bh9sACAjmdpdqBdmCIIAHSs++67L0NDQ03HAHiVggUAdKTNmzfnjDPOyGGHHZYXXnih6TgASRQsAKBD3XHHHVm/fn0WLlyYOXPmNB0HIImCBQB0qOuuuy5JcskllzScBOCfKFgAQEey/xXQjhQsAKDj/PjHP869996b2bNn5x3veEfTcQBepWABAB3nu9/9bpLk/PPPT19fX8NpAP6JggUAdJy77747iemBQPsptdamM3SV/v7+OjAw0HQMAOhqtdY8/PDDOeKII3LooYc2HQfoQaWUFbXW/p2PT2siDADAeJRSctxxxzUdA+A1TBEEADrKxo0bm44AsFsKFgDQMWqtOemkk3LKKafk6aefbjoOwGuYIggAdIyHH344jz32WA477LDMnTu36TgAr2EECwDoGNdee22S5JJLLsnUqVMbTgPwWgoWANAxRgrWu971roaTAOyaggUAdIR169bl1ltvzdSpU3PRRRc1HQdglxQsAKAjXH/99dmyZUvOOOOMHHLIIU3HAdglBQsA6Ajf+c53kpgeCLQ3qwgCAB3h85//fN797nenv7+/6SgAu6VgAQAd4cADD8yVV17ZdAyAPTJFEAAAoEUULACg7V100UX55V/+5Tz77LNNRwHYIwULAGhrTz/9dK6//vp84xvfyMEHH9x0HIA9UrAAgLY2srnwhRdemJkzZzacBmDPFCwAoK1dc801SZJ3v/vdDScB2DsFCwBoWxs3bswNN9yQxP5XQGdQsACAtnXjjTdm06ZNOfXUUzNv3rym4wDslYIFALStkemBl112WcNJAEbHRsMAQNv6+Mc/nqOOOirvf//7m44CMCoKFgDQtk444YSccMIJTccAGDVTBAEAAFpEwQIA2tJHP/rR/N7v/V7Wr1/fdBSAUSu11qYzdJX+/v46MDDQdAwA6GhPPfVUFi5cmP322y9r1661wTDQdkopK2qt/TsfN4IFALSda6+9Nkly4YUXKldAR1GwAIC2M7I8+7vf/e6GkwDsGwULAGgrGzduzI033pgkede73tVwGoB9o2ABAG3lhhtuyKZNm3Lqqadm3rx5TccB2CcKFgDQVv7u7/4uSXLFFVc0nARg39loGABoK5dddlk2bNiQ97znPU1HAdhnlmkfpVLKzCR9tdZ1ezrPMu0AAND9LNM+RqWUKaWUX0nySJJTm84DAAC0LwVr7+Yk+UGShU0HAYBu95nPfCbf/va3s2XLlqajAIyJZ7D2otb60yQppTQdBQC62qOPPprf/d3fzcEHH5yf/vSnTccBGJOuG8Ha/qwUANBhvvWtbyXZtvfV9OnTG04DMDZdM4JVSjkgyceS/Nskh+/mnKOT/MckTyU5KMncJJ+otT4xWTkBgF0bWZ798ssvbzgJwNh1RcEqpZyT5Jwkn0wyazfnvC7JsiT/vtb65e3H/nWSO0op/bXWZyYlLADwGi+88EJuv/32TJ8+PRdffHHTcQDGrCsKVq315iQ3l1IuTPL23Zz2R0mGk3xlh2N/nuT/S/IHST5cSvm/k/zn7V/bUms9eAxZMjQ0tK8v260ZM2a07L0AoF1de+21GR4ezgUXXJADDzyw6ThAF2rlPfqedEXB2sHmXR0spcxPclmSv6k7bPxVa91aSrkpyQdKKb9Ra/2jbCtiY7Zy5cr09fWN5y1+jn3KAOgFI89fXXHFFQ0nAbpVK+/R96TrFrnYjaVJSpKHd/G1h5JMz+5HvlJK6ZXPCQAasWTJkhx//PG57LLLmo4CMC7dNoK1O0dv//2FXXzt+e2/H7urF5ZSjkjyf2z/zw+VUp6utT64uwstWbIky5YtG3NQAOhFn/70p/PpT3+66RhAFxscHGzp++1uRKxXCtbIwhe7mng58knP3tULt++D9Z/zT89m7VEpxXNTAADQZibrHr1Xpr6NjFztalONkWP/OElZAIDttm7dmi984QtZs2ZN01EAWqJXCtbIEuyH7eJrc7b//tgkZQEAtrvzzjvz8Y9/POeff76FnYCu0CsF685sW6J90S6+9gtJtia5fVITAQD55je/mSR5z3vek1JKw2kAxq8nClat9fkk1yY5d8fj21cHPC/Jt2qtLzaRDQB6Va01V199dZJtBQugG3RbwZqdJKWUXT1r9VtJDi2lfHiHYx/d/ppPTEI2AGAHDzzwQH70ox9lzpw5efvbd7tbCkBH6YpVBEspS5O8K8mS7Yf+pJTy7Vrr342cU2t9pJTy9iT/sZSyJNvK5YIkb6u1/mjSQwNAjxuZHnjZZZdl2rSuuCUB6I6CVWtdlmRZks/s5bz7k7x/UkIBAHu04/NXAN2i26YIAgAdYGhoKEcddVTmzJmTCy+8sOk4AC3TFSNYAEBnmTFjRq6++ups3rw506fv6tFpgM5kBAsAaIxyBXQbBQsAmFTr1q3L9ddfn6GhoaajALScggUATKpvf/vbueiii3LllVc2HQWg5RQsAGBSjWwubHELoBspWADApNm4cWOuu+66JMl73/vehtMAtJ6CBQBMmuuvvz4bN27MqaeemoULFzYdB6DlLNPeYrXWUT20O2PGjElIAwDt5Rvf+EaS5H3ve1/DSQB2bbwL8JRaa4uikCSllFF9oD53AHrN5s2bc8QRR+Tll1/Oww8/nDe96U1NRwJ4jVLKaE9dUWvt3/mgESwAYFI88cQTmTNnThYsWKBcAV3LCFaLnXLKKXXZsmV7Pc8UQQB6Ua01L774Yg477LCmowDs0minCPb19RnBmkillBlJBkf+W4ECmBxDQ0Pp6+tLkgwODvr+2+ZKKcoVdIlu/f473j+HVQQBgAn39NNP56mnnmo6BsCEU7AAgAn33//7f8/ChQvzuc99rukoABNKwQIAJlSt9dXl2U8//fSG0wBMLAULAJhQ99xzT9asWZO5c+dm6dKlTccBmFAKFgAwoUZGr97znvdkyhS3HkB3810OAJhQ//t//+8kyXvf+96GkwBMPAULAJgwDz74YB544IEccsghOffcc5uOAzDhFCwAYMKsXr06M2bMyBVXXJHp06c3HQdgwpVaa9MZusKOGw1300ZrAO2uWze67Cbr16/Phg0bsmDBgqajAC3U699/Sykraq39Ox83gkVPGRoaSiklpZQMDQ01HWfSdNqfu13yTnaOibzeRLx3q96zXf6+mTgHHnhgDj/88J78e+60/7/bJa/vv5Pznu3y991tFCwAYEL8+Mc/zpYtW5qOATCpFCwAYEJceeWVmTt3blauXNl0FIBJo2ABAC33xBNPZPny5dm0aVPe/OY3Nx0HYNIoWABAy41sLnzppZdm1qxZDacBmDwKFgDQcn/7t3+bJHn/+9/fcBKAyaVgAQAt9fTTT+eOO+7IzJkzc+mllzYdB2BSKVgAQEtdffXVSZKLL744s2fPbjgNwOSa1nSAbjSafQR6bSM2AHrHHXfckcT0QKAzjXdPMAVrAhxwwAF7PafWOglJAGDyffWrX81v/dZvZdGiRU1HAdhnfX1943p9caPfWqWU0X6gKyY0CAAAMBanjPK8F2qth+980AhW642q8tZaxzf2CAAAtFwpZVTP8uzuft4IFgAAQItYRRAAAKBFFCwAAIAWUbAAAABaRMECAABoEQULAACgRRQsAACAFlGwAAAAWkTBAqAnlVJmllIOajoHAN1FwWpAKeXsUso9pZQNpZTrSylHN50JoFeUUqaUUn4lySNJTm06D0A3K6UsKKX8/+3da4wdZR3H8e+PUqChCOGiXEW5pNUgMQ0qoAlYEDFgoFErFPESUMEoMcb6ghdSEqJGQiIYBYMaICFEvHMJYAJWjUKMikEDgiC0cqsIhQASufTvizPHHtez292zs3t2T7+f5GT2zDwzz3/74tn8+jwzc2mSs5NcleSQYdc00wxYsyzJq4EzgNOBDwBLgO8OtShJ2rrsDvwC2G/YhUjSKEsS4Drgx1V1KfAV4Pok2w63spllwJp9xwCfqaq7qupmYA3wjuGWJElbj6r6R1U9NOw6JGkrcCzwRmAtQFXdDbwEnDzEmmacAWsSkuzQ1rWq6pqqeqZn1+PA+rauL0mjps0xWJI0NdMcg98OPFhVL/bsuw9YPr2q5raRnp6briQ7AZ8GPgfsMU6b1wLnAw8DOwN7Aqurat0ku1kGXDb9aiVptMzSGCxJ6qOlMXhP4Jkxpz0N7DsTNc8VBqxxJDkaOBr4ArBonDb7A7cD51bVFc2+s4DfJDmsqh7bQh87AocCp7VWuCSNgNkYgyVJ/bU4Br9MZ0lgr5FfQTfyv+CgqmptVa0B7pyg2SXAJuDKnn2X0/l3vRAgyTlJnms+T485fzVwTlW93F7lkjT/zdIYLEnqo60xGHiMzsxWr12AR9updG4yYG3Z2NQNQJK9gfcCt1VVdfdX1SvAz4GVSXarqkuqanHz2aXn/E8AV1fVhub7djP6W0jS/DQjY7AkaVKmNQY3Px+QpDdzLKV56MWoMmAN7gggwL19jv0FWAgc2e/E5v0rLwALkixNchSwaqYKlaQRNPAYDJ13Yc1QXZK0NZjsGHw7sI7OckOSLAV2BK6flSqHxHuwBtd9OfA/+xx7otkeOPZAkuOB7wALxhxa2l5pkjTyBhqD4b/vIzyz+Xpakkeq6p6W65OkUTapMbiqKslJwBeTvAF4K3BiVT0/G0UOiwFrcN0b/l7sc+zfzXbx2APNu6/8d5ek6RloDIbOe7CALzUfSdLUTXoMrqoHgI80+74xw3XNCS6RGFw3sS/sc6y7b6TTuSQNkWOwJA2PY/AEDFiD6z7+d7c+x3ZvtvfPUi2StLVxDJak4XEMnoABa3B30Hk05cF9ji0BXgF+PasVSdLWwzFYkobHMXgCBqwBVdUTwI3AO3v3N0+mWg5cV1VPDaM2SRp1jsGSNDyOwRMzYG3ZYoAk/daYfh7YNcmHevad0ZyzehZqk6RR5xgsScPjGDwAn2Y3jiRHACcAy5pd30xyQ1X9tNumqu5LciRwfpJldALrPsDhzRNTJEkDcAyWpOFxDJ6e9Lx8WZIkSZI0DS4RlCRJkqSWGLAkSZIkqSUGLEmSJElqiQFLkiRJklpiwJIkSZKklhiwJEmSJKklBixJkiRJaokBS5IkSZJaYsCSJEmSpJYYsCRJkiSpJQYsSZIkSWqJAUuSJEmSWmLAkiRJkqSWGLAkSZIkqSUGLEmSJElqiQFLkiRJklpiwJIkqZHkoSRrm8+KYdczniQreup8aNj1SJI2S1UNuwZJkuaEJFVVmUL7PYBVVXXxDJa1pRqmVLMkaWY5gyVJ0uA+BnwtyZu21DDJkiR3JNmQpHo+TyX5bZIjetouSvK7JM/1tNuY5NYZ/W0kSdPmDJYkSY0BZrDuBN4MfLmqzp3kOdsANwLHA38GllXVS+O0XQzcCjwCfLBfO2ewJGlucQZLkqQBJFlKJ1wBnDrZ86pqE7Ch+frkeOGqafsccAtw/UTtJElzhwFLkqTBrAJ+2Pz8ut4lfi3bBLjcRJLmCQOWJEmDOQVYDTzYfJ/0LJYkaXQZsCRJmqIkbwE2VtWDwLXN7pVJFgyxLEnSHGDAkiSNjCSHJbkoyY+S3JbkriTfTnJAy12dyuZg1d2+Bljecj+SpHnGgCVJGglJ9gZ+BRwDnFJVy4HDgV2APyZ5W0v9bAOsBL4PUFV/AP7aHF7VRh+SpPnLgCVJGhU7NNs9gYUAVfUv4OPA9sAlLfVzFLC+qtb37OvOYq1Isn1L/UiS5iEDliRpJFTV34B9gIOq6vme/RuBx4FlLXW1is2Bqut7zXZn4ISW+pEkzUMGLEnSyKiqp4CXk5yc5OvNfVi/pHN/1LbTvX6ShcAKmuWBPf3+Cbin+erTBCVpKzbtPzaSJM0VSU4HLgIeA74KrKmqJ5M8BOzfQhfHAwuAq5OMPdZdonhikp2q6tkJrvNCs53M3+HtgBenVKUkaWgMWJKkkZDkHOBi4AbgfVU1E6FkFfDZqrqyT//7AOvpBK0VwFUTXKf77qzdJtHnfsBNU6xTkjQkqfLl8JKk+S/Jw3TuwVpaVfeOOfYosFdVJclxAFX1sz7XqKr6v6mp5tiOwAPAgb33eI1pcwtwHHBzVb1nglqX0FlSuAnYeYLrbQPcDRw6XmCcqGZJ0uzzHixJ0qh4VbPd0LszycF0nizYtTew1wDXP4lOcOobhhpXNNtjk+wxXqMmAF5DZ7nhygmudyZw7QzNxkmSZoABS5I0Kq5utuc1Mz/dd2N9C7ix+f564EDg/qlcOMn+wBo6gWgiNwFFZ4O7N4IAAAEkSURBVAn+WVto+0ng98AFSfbt0+dRwPuBC6ZSqyRpuFwiKEkaCU2oOhv4KJ3ZrIeBp4HzgI3AT4BFwOVVdfE41/if5XZJDgJ+ABzC5nD1d+DDVbW2p90i4FbgYGD3nkveD9xbVSeO098OwIV0ZscuA+5qan83nf8E/dQWHpbhEkFJmmMMWJIkNYYVVpLsCryLzpMOnwVuG3sf2QTnGrAkaQ4xYEmS1JiPYWU+1ixJo8x7sCRJkiSpJQYsSZIkSWqJAUuSJEmSWmLAkiRps3VJ1jafFcMuZjxJVnTrBNYNux5J0mY+5EKSJEmSWuIMliRJkiS1xIAlSZIkSS0xYEmSJElSSwxYkiRJktQSA5YkSZIktcSAJUmSJEktMWBJkiRJUkv+A/k3sDVOjEEjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Figure 11 from Barnes+17: https://arxiv.org/pdf/1708.02981.pdf\n",
    "\n",
    "a_TD = np.logspace(np.log10(0.1), np.log10(1.5), 100)\n",
    "M_TD = np.logspace(np.log10(0.01), np.log10(1.5), 100)\n",
    "\n",
    "\n",
    "CTL_TD = 5.0E-1*(a_TD + 0.65)**((3.8-0.7)/(0.48-0.19))\n",
    "CPL_TD = 1.0E0*(a_TD - 0.28)**((1.5-0.7)/(0.48-0.19))\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,9))\n",
    "\n",
    "\n",
    "ax.plot(a_TD, CTL_TD, 'k--', lw=2.0);\n",
    "#ax.plot(a_TD, CPL_TD, 'k-', lw=2.0);\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$\\rm{a \\, [AU]}$',fontsize = 25, labelpad=10);\n",
    "ax.tick_params(axis='x', which='major', pad=10)\n",
    "ax.set_ylabel(r'$\\rm{M \\, [M_{\\odot}]}$',fontsize = 25, labelpad=10)\n",
    "ax.tick_params(axis='y', which='major', pad=5)\n",
    "\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(20);\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(20); \n",
    "            \n",
    "            \n",
    "ax.tick_params(which='both', width=2.05);\n",
    "ax.tick_params(which='major', length=20);\n",
    "ax.tick_params(which='minor', length=10);\n",
    "ax.set_xlim(0.01, 1.5);\n",
    "#ax.set_xticks([6400, 6500, 6600]);\n",
    "ax.minorticks_on();\n",
    "ax.set_xscale('log');\n",
    "ax.set_yscale('log');\n",
    "ax.set_ylim(0.08, 1.5);\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "\n",
    "# For the legend\n",
    "#l = plt.legend(loc=1, bbox_to_anchor=(0.97, 0.32), frameon=True, shadow=True,\\\n",
    "#               title=r'$\\rm{273 \\, < \\, T_{surf} \\, [K] \\, < \\, 373}$', labelspacing=1.0)\n",
    "#setp(l.get_texts(), fontsize=21) \n",
    "#setp(l.get_title(), fontsize=21)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig('Tidallocking.pdf', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Assume MS stars: L \\propto M**3.5\n",
    "idxMS = 3.5\n",
    "L_TD = (M_TD)**idxMS\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,9))\n",
    "\n",
    "\n",
    "ax.plot(a_TD, CTL_TD**idxMS, 'k--', lw=2.0);\n",
    "ax.plot(a_TD, CPL_TD**idxMS, 'k-', lw=2.0);\n",
    "\n",
    "\n",
    "ax.plot()\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$\\rm{a \\, [AU]}$',fontsize = 25, labelpad=10);\n",
    "ax.tick_params(axis='x', which='major', pad=10)\n",
    "ax.set_ylabel(r'$\\rm{L \\, [L_{\\odot}]}$',fontsize = 25, labelpad=10)\n",
    "ax.tick_params(axis='y', which='major', pad=5)\n",
    "\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(20);\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(20); \n",
    "            \n",
    "            \n",
    "ax.tick_params(which='both', width=2.05);\n",
    "ax.tick_params(which='major', length=20);\n",
    "ax.tick_params(which='minor', length=10);\n",
    "ax.set_xlim(0.01, 1.5);\n",
    "#ax.set_xticks([6400, 6500, 6600]);\n",
    "ax.minorticks_on();\n",
    "ax.set_xscale('log');\n",
    "ax.set_yscale('log');\n",
    "ax.set_ylim(1.E-4, 1.E0);\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "\n",
    "# For the legend\n",
    "#l = plt.legend(loc=1, bbox_to_anchor=(0.97, 0.32), frameon=True, shadow=True,\\\n",
    "#               title=r'$\\rm{273 \\, < \\, T_{surf} \\, [K] \\, < \\, 373}$', labelspacing=1.0)\n",
    "#setp(l.get_texts(), fontsize=21) \n",
    "#setp(l.get_title(), fontsize=21)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "#fig.savefig('Tidallocking.pdf', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Habitable zones from radiative transfer calculations: rationale "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "HZ: Liquid water on planet's surface (273 < T [K] < 373)\n",
    "\n",
    "\n",
    "\n",
    "Caldwell (1992): equation for radiative balance:\n",
    "\n",
    "(1 - A) * pi * R_{2}**2 * S = f * 4 * pi * R_{2}**2 * sigma * T_{eq,2}**2\n",
    "\n",
    "\n",
    "A: albedo\n",
    "\n",
    "R2: planet's radius\n",
    "\n",
    "S = L / (4*pi*a**2) [power per surface unit]\n",
    "\n",
    "T_{eq,2} = function(A, L1, a) [planet's effective temperature]\n",
    "\n",
    "f: either 0.5 (planet tidally locked) or 1.0 (normal rotation)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "Surface temperature: depends on optical depth\n",
    "\n",
    "T_{surf,2}**4 = T_{eq,2}**4 * (1 + 2/3 * tau)\n",
    "\n",
    "Usually, 0.1 <= tau <= 10,100  (tau = 1 would be realistic, close to Earth's)\n",
    "\n",
    "Greenhouse effect on Solar System:\n",
    "\n",
    "Planet     Tsurf     A     Teff     Ttop     tau\n",
    "Venus       750     0.77    227     ~230     160\n",
    "Earth       288     0.30    256     ~250     0.80\n",
    "Mars        230     0.15    216     ~220     0.38\n",
    "\n",
    "\n",
    "0.8 <= M_{planet} [M_{\\oplus}] <= 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Some definitions\n",
    "\n",
    "npoints = 1000\n",
    "\n",
    "loglmin = np.log10(2.E-4)\n",
    "loglmax = np.log10(0.2)\n",
    "\n",
    "L = np.logspace(loglmin, loglmax, npoints)\n",
    "f = np.array([0.25, 0.5, 0.75, 1.0])\n",
    "A = np.array([0., 0.5])\n",
    "a = np.logspace(-3, 1, npoints)\n",
    "tau = np.array([0.01, 1.0])\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def Lum(R = [], Teff = []):\n",
    "    \n",
    "    import numpy as np\n",
    "    sigma = 5.670367E-8 #W*m−2*K−4\n",
    "    \n",
    "    return 4 * np.pi * R**2 * sigma * Teff**4\n",
    "\n",
    "\n",
    "\n",
    "def Seff(L = [], a = []):\n",
    "    \n",
    "    import numpy as np\n",
    "    \n",
    "    return L * 1. / (4. * np.pi * a**2)\n",
    "\n",
    "\n",
    "\n",
    "def Teff(A = [], Seff = [], f = []):\n",
    "    \n",
    "    import numpy as np\n",
    "    sigma = 5.670367E-8 #W*m−2*K−4\n",
    "    \n",
    "    return np.power( ( (1 - A) * Seff / (4. * f * sigma)  ), 1./4.)\n",
    "\n",
    "\n",
    "\n",
    "def Tsurf(Teff = [], tau = []):\n",
    "\n",
    "    return Teff * np.power( (1 + 2./3. * tau), 1./4.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "742 230\n",
      "283 255\n",
      "231 218\n",
      "\n",
      "\n",
      "1.99 2.97\n",
      "0.70 1.04\n",
      "0.70 1.04\n"
     ]
    }
   ],
   "source": [
    "#### Example: Solar System\n",
    "\n",
    "aref = np.logspace(-3, 2, 1000)\n",
    "\n",
    "tau_Venus = 160\n",
    "tau_Earth = 0.80\n",
    "tau_Mars = 0.38\n",
    "\n",
    "albedo_Venus = 0.77\n",
    "albedo_Earth = 0.30\n",
    "albedo_Mars = 0.15\n",
    "\n",
    "\n",
    "#--------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "\n",
    "Seff_Venus = Seff(Lsun, 0.7*One_AU) \n",
    "Seff_Earth = Seff(Lsun, 1.0*One_AU)\n",
    "Seff_Mars = Seff(Lsun, 1.5*One_AU)\n",
    "\n",
    "Teff_Venus = Teff(albedo_Venus, Seff_Venus, 1.0)\n",
    "Teff_Earth = Teff(albedo_Earth, Seff_Earth, 1.0)\n",
    "Teff_Mars = Teff(albedo_Mars, Seff_Mars, 1.0)\n",
    "\n",
    "Tsurf_Venus = Tsurf(Teff_Venus, 160)\n",
    "Tsurf_Earth = Tsurf(Teff_Earth, 0.80)\n",
    "Tsurf_Mars = Tsurf(Teff_Mars, 0.38)\n",
    "\n",
    "\n",
    "#--------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "\n",
    "Seff_SS = Seff(Lsun, aref*One_AU)\n",
    "\n",
    "Teff_SS_Venuslike = Teff(albedo_Venus, Seff_SS, aref)\n",
    "Tsurf_SS_Venuslike = Tsurf(Teff_SS_Venuslike,tau_Venus)\n",
    "\n",
    "Teff_SS_Earthlike = Teff(albedo_Earth, Seff_SS, aref)\n",
    "Tsurf_SS_Earthlike = Tsurf(Teff_SS_Earthlike,tau_Earth)\n",
    "\n",
    "Teff_SS_Marslike = Teff(albedo_Mars, Seff_SS, aref)\n",
    "Tsurf_SS_Marslike = Tsurf(Teff_SS_Marslike,tau_Mars)\n",
    "\n",
    "\n",
    "amin_Venuslike = aref[ np.where( (Tsurf_SS_Venuslike >= 273) & (Tsurf_SS_Venuslike <= 373) ) [0] ] [0]\n",
    "amax_Venuslike = aref[ np.where( (Tsurf_SS_Venuslike >= 273) & (Tsurf_SS_Venuslike <= 373) ) [0] ] [-1]\n",
    "\n",
    "amin_Earthlike = aref[ np.where( (Tsurf_SS_Earthlike >= 273) & (Tsurf_SS_Earthlike <= 373) ) [0] ] [0]\n",
    "amax_Earthlike = aref[ np.where( (Tsurf_SS_Earthlike >= 273) & (Tsurf_SS_Earthlike <= 373) ) [0] ] [-1]\n",
    "\n",
    "amin_Marslike = aref[ np.where( (Tsurf_SS_Marslike >= 273) & (Tsurf_SS_Marslike <= 373) ) [0] ] [0]\n",
    "amax_Marslike = aref[ np.where( (Tsurf_SS_Marslike >= 273) & (Tsurf_SS_Marslike <= 373) ) [0] ] [-1]\n",
    "\n",
    "\n",
    "#--------------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "\n",
    "print \"%.0f\"%Tsurf_Venus, \"%.0f\"%Teff_Venus\n",
    "print \"%.0f\"%Tsurf_Earth, \"%.0f\"%Teff_Earth\n",
    "print \"%.0f\"%Tsurf_Mars, \"%.0f\"%Teff_Mars\n",
    "print ''\n",
    "print ''\n",
    "print \"%.2f\"%amin_Venuslike, \"%.2f\"%amax_Venuslike\n",
    "print \"%.2f\"%amin_Earthlike, \"%.2f\"%amax_Earthlike\n",
    "print \"%.2f\"%amin_Marslike, \"%.2f\"%amax_Marslike"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Seff_Mdwarf = np.zeros(( len(L), len(a) ))\n",
    "\n",
    "Teff_Mdwarf = np.zeros(( np.concatenate((np.shape(Seff_Mdwarf), np.shape(A), np.shape(f)), axis=0) ))\n",
    "\n",
    "Tsurf_Mdwarf = np.zeros(( np.concatenate((np.shape(Teff_Mdwarf), np.shape(tau)), axis=0) ))\n",
    "\n",
    "\n",
    "for i, lum in enumerate(L):\n",
    "    \n",
    "    for j, dist in enumerate(a):\n",
    "        \n",
    "        Seff_Mdwarf[i][j] = Seff(lum*Lsun, dist*One_AU)\n",
    "            \n",
    "        for k, alb in enumerate(A):\n",
    "            \n",
    "            for l, fact in enumerate(f):\n",
    "                \n",
    "                Teff_Mdwarf[i][j][k][l] = Teff(alb, Seff_Mdwarf[i][j], fact)\n",
    "                \n",
    "                for m, ta in enumerate(tau):\n",
    "                \n",
    "                    Tsurf_Mdwarf[i][j][k][l][m] = Tsurf(Teff_Mdwarf[i][j][k][l], ta)           "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "wh_tau_min = np.where(tau == np.min(tau)) [0][0]\n",
    "wh_tau_max = np.where(tau == np.max(tau)) [0][0]\n",
    "\n",
    "wh_albedo_min = np.where(A == np.min(A)) [0][0]\n",
    "wh_albedo_max = np.where(A == np.max(A)) [0][0]\n",
    "\n",
    "wh_factor_half = np.where(f == 0.5) [0][0]\n",
    "wh_factor_all = np.where(f == 1.0) [0][0]\n",
    "\n",
    "\n",
    "# IHZ and OHZ will be determined by:\n",
    "# Tsurf,min(A=0.5,f=1.0,tau=0.01) \n",
    "# Tsurf,max(A=0.0,f=0.5,tau=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "Tsurf_Mdwarf_IHZ = np.zeros(( len(L), len(a) ))\n",
    "Tsurf_Mdwarf_OHZ = np.zeros(( len(L), len(a) ))\n",
    "\n",
    "\n",
    "##### HZ parameters. In the end, for each luminosity, find low and high limits for the semimajor axis #####\n",
    "\n",
    "\n",
    "# Inner limit HZ\n",
    "HZ_Mdwarf_IHZ = np.zeros(len(L), dtype=int)\n",
    "HZ_Seff_Mdwarf_IHZ = np.zeros(len(L), dtype=int)\n",
    "HZ_a_Mdwarf_IHZ = np.zeros(len(L))\n",
    "HZ_Lumstar_Mdwarf_IHZ = np.zeros(len(L))\n",
    "\n",
    "# Outer limit HZ\n",
    "HZ_Mdwarf_OHZ = np.zeros(len(L), dtype=int)\n",
    "HZ_Seff_Mdwarf_OHZ = np.zeros(len(L), dtype=int)\n",
    "HZ_a_Mdwarf_OHZ = np.zeros(len(L))\n",
    "HZ_Lumstar_Mdwarf_OHZ = np.zeros(len(L))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "for i, lum in enumerate(L):\n",
    "    \n",
    "    for j, dist in enumerate(a):\n",
    "        \n",
    "        # All the planets are tidally locked, according to the models by Barnes+17...\n",
    "        # Change these two as desired\n",
    "        Tsurf_Mdwarf_IHZ[i][j] = Tsurf_Mdwarf[i][j][wh_albedo_max][wh_factor_half][wh_tau_min]\n",
    "        Tsurf_Mdwarf_OHZ[i][j] = Tsurf_Mdwarf[i][j][wh_albedo_min][wh_factor_half][wh_tau_max]\n",
    "        \n",
    "        \n",
    "        \n",
    "    HZ_Mdwarf_IHZ[i] = np.where( (Tsurf_Mdwarf_IHZ[i] >= 273) & (Tsurf_Mdwarf_IHZ[i] <= 373) ) [0][0]\n",
    "    HZ_Mdwarf_OHZ[i] = np.where( (Tsurf_Mdwarf_OHZ[i] >= 273) & (Tsurf_Mdwarf_OHZ[i] <= 373) ) [0][-1]\n",
    "    \n",
    "    HZ_Seff_Mdwarf_IHZ[i] =  Seff_Mdwarf[i][HZ_Mdwarf_IHZ[i]]\n",
    "    HZ_Seff_Mdwarf_OHZ[i] =  Seff_Mdwarf[i][HZ_Mdwarf_OHZ[i]]\n",
    "    \n",
    "    HZ_a_Mdwarf_IHZ[i] =  a[HZ_Mdwarf_IHZ[i]]\n",
    "    HZ_a_Mdwarf_OHZ[i] =  a[HZ_Mdwarf_OHZ[i]]\n",
    "    \n",
    "    HZ_Lumstar_Mdwarf_IHZ[i] = HZ_Seff_Mdwarf_IHZ[i] * 4 * np.pi * (HZ_a_Mdwarf_IHZ[i]*One_AU)**2 / Lsun\n",
    "    HZ_Lumstar_Mdwarf_OHZ[i] = HZ_Seff_Mdwarf_OHZ[i] * 4 * np.pi * (HZ_a_Mdwarf_OHZ[i]*One_AU)**2 / Lsun\n",
    "    \n",
    "    \n",
    "\n",
    "    \n",
    "    \n",
    "### Final interpolations ###\n",
    "knd = 'linear'\n",
    "#knd = 'quadratic'\n",
    "#knd = 'cubic'\n",
    "\n",
    "HZ_interp_aLum_Mdwarf_IHZ = interpolate.interp1d(HZ_a_Mdwarf_IHZ, HZ_Lumstar_Mdwarf_IHZ, kind = knd)\n",
    "HZ_interp_aLum_Mdwarf_OHZ = interpolate.interp1d(HZ_a_Mdwarf_OHZ, HZ_Lumstar_Mdwarf_OHZ, kind = knd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00371620564065\n"
     ]
    }
   ],
   "source": [
    "### ROCHE LIMIT: \n",
    "### http://adsabs.harvard.edu/abs/1974ApJ...191..577A\n",
    "\n",
    "# d = r * ( 2 * M/m )**1/3 = R * ( 2 * rhoM/rhom )**1/3\n",
    "\n",
    "def Roche_solid(r, M, m): # au\n",
    "    \n",
    "    return r * ( 2 * M/m )**(1./3.) * 1./One_AU\n",
    "\n",
    "\n",
    "\n",
    "REarth = 6.3781366E6 # m\n",
    "MEarth = 5.98E24 # kg\n",
    "\n",
    "print Roche_solid(REarth, Msun, MEarth) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SS planets\n",
    "\n",
    "a_SS = np.array([0.39, 0.72, 1.00, 1.52, 5.20, 9.55, 19.22, 30.11])\n",
    "m_SS = np.array([0.0553, 0.815, 1.00, 0.11, 317.8, 95.2, 14.6, 17.2])\n",
    "r_SS = np.array([0.38, 0.95, 1.00, 0.53, 10.97, 9.14, 3.98, 3.87])\n",
    "color_SS = np.array(['black', 'darkkhaki', 'deepskyblue', 'crimson', \n",
    "                     'darkgoldenrod', 'chocolate', 'turquoise', 'cadetblue'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mass-radius forecasting for the exoplanets. Already included in final table"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "#M_R relation for the exoplanets: Chen-Kipping forecasting\n",
    "\n",
    "def m_r(r = []):\n",
    "    \n",
    "    r = np.asarray([r])\n",
    "    \n",
    "    m_forecast = np.asarray([1.0E-20]*len(r)) \n",
    "    \n",
    "    for ri, rr in enumerate(r):\n",
    "        \n",
    "            m_forecast[ri] = \\\n",
    "            mr.Rstat2M(rr, std=0.1, unit='Earth', sample_size=1000, grid_size=1e3, classify='No')[0]\n",
    "            \n",
    "            \n",
    "    return m_forecast\n",
    "\n",
    "\n",
    "\n",
    "def r_m(m = []):\n",
    "    \n",
    "    m = np.asarray([m])\n",
    "    \n",
    "    r_forecast = np.asarray([1.0E-20]*len(m)) \n",
    "    \n",
    "    for mi, mm in enumerate(m):\n",
    "        \n",
    "            r_forecast[mi] = mr.Mstat2R(mm, std=0.1, unit='Earth', sample_size=1000, classify='No')[0]\n",
    "            \n",
    "            \n",
    "    return r_forecast"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "r_MR = np.linspace(0.5, 50, 1000) \n",
    "r_MR_interp = interpolate.interp1d(r_MR, [m_r(i)[0] for i in r_MR])(r_MR)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10,7))\n",
    "plt.xlabel(r'$R \\, [R_{\\oplus}]$', fontsize=15, labelpad=10);\n",
    "plt.ylabel(r'$M \\, [M_{\\oplus}]$', fontsize=15, labelpad=10);\n",
    "plt.xscale('log');\n",
    "plt.yscale('log');\n",
    "plt.xticks(size=13)\n",
    "plt.yticks(size=13)\n",
    "plt.axvline(1.0, color='red', lw=1.5, ls='dashed', alpha=0.75);\n",
    "plt.axvline(1.5, color='red', lw=1.5, ls='dashed', alpha=0.75);\n",
    "plt.axvline(3.87, color='red', lw=1.5, ls='dashed', alpha=0.75);\n",
    "    \n",
    "\n",
    "plt.plot(r_MR, r_MR_interp, color='black', lw=1.5);\n",
    "    \n",
    "#plt.yscale('log');    \n",
    "plt.tight_layout()\n",
    "plt.savefig('MR_interp_ChenKipping.jpg', bbox_to_inches = 'tight')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "m_MR = np.linspace(0.5, 1000, 1000) \n",
    "m_MR_interp = interpolate.interp1d(m_MR, [r_m(i)[0] for i in m_MR])(m_MR)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(10,7))\n",
    "plt.xlabel(r'$M \\, [M_{\\oplus}]$', fontsize=15, labelpad=10);\n",
    "plt.ylabel(r'$R \\, [R_{\\oplus}]$', fontsize=15, labelpad=10);\n",
    "plt.xscale('log');\n",
    "plt.yscale('log');\n",
    "plt.xticks(size=13)\n",
    "plt.yticks(size=13)\n",
    "plt.axvline(1.0, color='red', lw=1.5, ls='dashed', alpha=0.75);\n",
    "plt.axvline(3.86, color='red', lw=1.5, ls='dashed', alpha=0.75);\n",
    "plt.axvline(17.2, color='red', lw=1.5, ls='dashed', alpha=0.75);\n",
    "    \n",
    "\n",
    "plt.plot(m_MR, m_MR_interp, color='black', lw=1.5);\n",
    "    \n",
    "#plt.yscale('log');    \n",
    "plt.tight_layout()\n",
    "plt.savefig('RM_interp_ChenKipping.jpg', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolate to find k2, Q and lambda (gyration radius) using values for small, rocky planets, Neptune and Jupiter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5042016806722688 -0.4563025210084033\n",
      "\n",
      "4.845660074896766 14.019147865877494\n",
      "4.43090652852999 24.60037134436068\n",
      "\n",
      "-0.0588235294117647 0.4582352941176471\n",
      "0.0033850493653032362 0.21686600846262336\n"
     ]
    }
   ],
   "source": [
    "r_kQ = np.array([1.5, 3.88, 10.97]) # Limit for Rocky (Barnes), Neptune, Jupiter\n",
    "k_arr = np.array([0.3, 1.5, 1.5 + 1.E-4])\n",
    "Q_arr = np.array([2, 4, 6]) # log\n",
    "lambda_arr = np.array([0.37, 0.23, 0.254]) \n",
    "\n",
    "\n",
    "fit_k = np.polyfit(r_kQ[:-1], k_arr[:-1], 1)\n",
    "\n",
    "fit_Q_1 = np.polyfit(np.log10(r_kQ[:-1]), Q_arr[:-1], 1)\n",
    "fit_Q_2 = np.polyfit(np.log10(r_kQ[-2:]), Q_arr[-2:], 1)\n",
    "\n",
    "fit_lambda_1 = np.polyfit(r_kQ[:-1], lambda_arr[:-1], 1)\n",
    "fit_lambda_2 = np.polyfit(r_kQ[-2:], lambda_arr[-2:], 1)\n",
    "\n",
    "\n",
    "print fit_k[0], fit_k[1]\n",
    "print ''\n",
    "print fit_Q_1[0], 10**fit_Q_1[1]\n",
    "print fit_Q_2[0], 10**fit_Q_2[1]\n",
    "print ''\n",
    "print fit_lambda_1[0], fit_lambda_1[1]\n",
    "print fit_lambda_2[0], fit_lambda_2[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Interpolate to generate k2/Q/lambda-R relations for the exoplanets\n",
    "\n",
    "def k2_r(r = []):\n",
    "    \n",
    "    r = np.asarray([r])\n",
    "    \n",
    "    k2r = np.asarray([1.0E-20]*len(r)) \n",
    "    \n",
    "    for ri, rr in enumerate(r):\n",
    "        \n",
    "    \n",
    "        if rr <= 1.5:\n",
    "        \n",
    "            k2r[ri] = 0.3\n",
    "            \n",
    "            \n",
    "        elif ((rr > 1.5) & (rr <= 3.87)):\n",
    "        \n",
    "            k2r[ri] = fit_k[1] + rr * fit_k[0]\n",
    "            \n",
    "    \n",
    "        else:\n",
    "        \n",
    "            k2r[ri] = 1.5\n",
    "            \n",
    "            \n",
    "    return k2r\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def Q_r(r = []):\n",
    "    \n",
    "    r = np.asarray([r])\n",
    "    \n",
    "    Qr = np.asarray([1.0E-20]*len(r)) \n",
    "    \n",
    "    for ri, rr in enumerate(r):\n",
    "        \n",
    "    \n",
    "        if rr <= 1.5:\n",
    "        \n",
    "            Qr[ri] = 1.E2\n",
    "            \n",
    "            \n",
    "        elif ((rr > 1.5) & (rr <= 3.88)):\n",
    "        \n",
    "            Qr[ri] = 10**fit_Q_1[1] * rr**fit_Q_1[0]\n",
    "            \n",
    "            \n",
    "        elif ((rr > 3.88) & (rr <= 10.97)):\n",
    "        \n",
    "            Qr[ri] = 10**fit_Q_2[1] * rr**fit_Q_2[0]\n",
    "            \n",
    "    \n",
    "        else:\n",
    "        \n",
    "            Qr[ri] = 1.E6\n",
    "            \n",
    "            \n",
    "    return Qr\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "def lambda_r(r = []):\n",
    "    \n",
    "    r = np.asarray([r])\n",
    "    \n",
    "    lambdar = np.asarray([1.0E-20]*len(r)) \n",
    "    \n",
    "    for ri, rr in enumerate(r):\n",
    "        \n",
    "    \n",
    "        if rr <= 1.5:\n",
    "        \n",
    "            lambdar[ri] = 0.37\n",
    "            \n",
    "            \n",
    "        elif ((rr > 1.5) & (rr <= 3.88)):\n",
    "        \n",
    "            lambdar[ri] = fit_lambda_1[1] + rr * fit_lambda_1[0]\n",
    "            \n",
    "            \n",
    "        elif ((rr > 3.88) & (rr <= 10.97)):\n",
    "        \n",
    "            lambdar[ri] = fit_lambda_2[1] + rr * fit_lambda_2[0]\n",
    "            \n",
    "    \n",
    "        else:\n",
    "        \n",
    "            lambdar[ri] = 0.254\n",
    "            \n",
    "            \n",
    "    return lambdar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,7))\n",
    "\n",
    "plt.xlabel(r'$R \\, [R_{\\oplus}]$', fontsize=15, labelpad=10);\n",
    "plt.ylabel(r'$k_{2}$', fontsize=15, labelpad=10);\n",
    "\n",
    "plt.xticks(size=13)\n",
    "plt.yticks(size=13)\n",
    "    \n",
    "    \n",
    "plt.scatter(r_kQ[:-1], k_arr[:-1]); \n",
    "plt.plot(r_kQ[:-1], fit_k[1] + r_kQ[:-1]*fit_k[0], color='black');\n",
    "\n",
    "\n",
    "r_k2Qplot = np.linspace(0.5, 15., 1000)\n",
    "for i in r_k2Qplot:\n",
    "    plt.scatter(i, k2_r(i), color='red', s=1);\n",
    "    \n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.savefig('k2r.jpg', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,7))\n",
    "\n",
    "plt.xlabel(r'$\\log \\, R \\, [R_{\\oplus}]$', fontsize=15, labelpad=10);\n",
    "plt.ylabel(r'$\\log \\, Q$', fontsize=15, labelpad=10);\n",
    "\n",
    "plt.xticks(size=13)\n",
    "plt.yticks(size=13)\n",
    "    \n",
    "    \n",
    "plt.scatter(np.log10(r_kQ), Q_arr); \n",
    "plt.plot(np.log10(r_kQ[:-1]), fit_Q_1[1] + np.log10(r_kQ[:-1])*fit_Q_1[0], color='black');\n",
    "plt.plot(np.log10(r_kQ[-2:]), fit_Q_2[1] + np.log10(r_kQ[-2:])*fit_Q_2[0], color='black');\n",
    "\n",
    "for i in r_k2Qplot:\n",
    "    plt.scatter(np.log10(i), np.log10(Q_r(i)), color='red', s=1);\n",
    "    \n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.savefig('Qr.jpg', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,7))\n",
    "\n",
    "plt.xlabel(r'$R \\, [R_{\\oplus}]$', fontsize=15, labelpad=10);\n",
    "plt.ylabel(r'$\\lambda$', fontsize=15, labelpad=10);\n",
    "\n",
    "plt.xticks(size=13)\n",
    "plt.yticks(size=13)\n",
    "    \n",
    "    \n",
    "plt.scatter(r_kQ, lambda_arr); \n",
    "plt.plot(r_kQ[:-1], fit_lambda_1[1] + r_kQ[:-1]*fit_lambda_1[0], color='black');\n",
    "plt.plot(r_kQ[-2:], fit_lambda_2[1] + r_kQ[-2:]*fit_lambda_2[0], color='black');\n",
    "\n",
    "\n",
    "for i in r_k2Qplot:\n",
    "    plt.scatter(i, lambda_r(i), color='red', s=1);\n",
    "    \n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.savefig('lambdar.jpg', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load tables with stellar and planetary data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['ID', 'Name', 'Alt. name', 'Karmn', 'RA_J2015.5', 'DE_J2015.5', 'd_pc', 'ed_pc', 'Ref_d', 'SpT', 'SpTnum', 'FUV_mag', 'eFUV_mag', 'NUV_mag', 'eNUV_mag', 'Ref19', 'u_mag', 'eu_mag', 'Ref20', 'BT_mag', 'eBT_mag', 'Ref21', 'B_mag', 'eB_mag', 'Ref22', 'g_mag', 'eg_mag', 'Ref23', 'BPmag', 'e_BPmag', 'Ref_24', 'VT_mag', 'eVT_mag', 'Ref25', 'V_mag', 'eV_mag', 'Ref26', 'Gmag', 'e_Gmag', 'Ref_27', 'r_mag', 'er_mag', 'Ref28', 'i_mag', 'ei_mag', 'Ref29', 'RPmag', 'e_RPmag', 'Ref_30', 'J_mag', 'eJ_mag', 'H_mag', 'eH_mag', 'Ks_mag', 'eKs_mag', 'Qflag_2M', 'Ref31', 'W1_mag', 'eW1_mag', 'W2_mag', 'eW2_mag', 'W3_mag', 'eW3_mag', 'W4_mag', 'eW4_mag', 'Qflag_W', 'Ref32', 'K', 'M_Ben16', 'M_Del00', 'M_adopted', 'Source', 'M_mann', 'eM_mann', 'Model', 'Teff', 'logg', 'Meta.', 'Lbol', 'Lberr']\n",
      "\n",
      "['ID', 'Name', 'Planet', 'a_au', '+a_au', '-a_au', 'P_day', '+P_day', '-P_day', 'Mod', 'M_earth', '+M_earth', '-M_earth', 'M_earth_est', 'R_earth', '+R_earth', '-R_earth', 'R_earth_est', 'Detection', 'True M&R', 'Mass_determination', 'Reference', 'Ref', 'bibitem', 'Potential HZ', 'M_star (MSun)', 'eM_star (Msun)', 'est_a (au)', 'e_a (au)', 'Lbol', 'Lberr', 'Seff', 'e_Seff', 'Teq', 'e_Teq']\n"
     ]
    }
   ],
   "source": [
    "star_prop = Table.read(path_data + 'hmr18.stars.v16.csv', format='ascii.csv')\n",
    "planet_prop = Table.read(path_data + 'hmr18.planets.v19.csv', format='ascii.csv')\n",
    "\n",
    "print star_prop.colnames\n",
    "print ''\n",
    "print planet_prop.colnames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "planet_name = planet_prop['Name']\n",
    "planet_char = planet_prop['Planet']\n",
    "planet_a = planet_prop['a_au']\n",
    "planet_M = planet_prop['M_earth_est']\n",
    "planet_R =planet_prop['R_earth_est']\n",
    "\n",
    "star_name = star_prop['Name']\n",
    "# Detection methods: RV (Radial Velocity), PT (Primary Transit), X (RV+PT)\n",
    "planet_detect = planet_prop['Detection']\n",
    "star_L = planet_prop['Lbol']\n",
    "star_M = np.zeros(len(star_L))\n",
    "star_Teff = np.zeros(len(star_L))\n",
    "\n",
    "\n",
    "\n",
    "for s, ss in enumerate(planet_name):\n",
    "    \n",
    "    for n, nn in enumerate(star_prop['Name']):\n",
    "        \n",
    "        if ss == nn:\n",
    "            \n",
    "            star_M[s] = star_prop['M_mann'][n]\n",
    "            star_Teff[s] = star_prop['Teff'][n]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Habitable zones from radiative transfer (not used in the paper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "### HABITABLE, BOIL AND FREEZE POLYGONS\n",
    "\n",
    "# Start from low, left vertex of the HZ and move counterclockwise\n",
    "\n",
    "bla = np.where(np.isfinite(HZ_interp_aLum_Mdwarf_IHZ(HZ_a_Mdwarf_IHZ))==True)\n",
    "\n",
    "v0x = np.log10(np.min(HZ_a_Mdwarf_IHZ[bla]))\n",
    "v0y = np.log10(np.min(HZ_interp_aLum_Mdwarf_IHZ(HZ_a_Mdwarf_IHZ[bla])))\n",
    "\n",
    "v3x = np.log10(np.max(HZ_a_Mdwarf_IHZ[bla]))\n",
    "v3y = np.log10(np.max(HZ_interp_aLum_Mdwarf_IHZ(HZ_a_Mdwarf_IHZ[bla])))\n",
    "\n",
    "\n",
    "bla = np.where(np.isfinite(HZ_interp_aLum_Mdwarf_OHZ(HZ_a_Mdwarf_OHZ))==True)\n",
    "\n",
    "v1x = np.log10(np.min(HZ_a_Mdwarf_OHZ[bla]))\n",
    "v1y = np.log10(np.min(HZ_interp_aLum_Mdwarf_OHZ(HZ_a_Mdwarf_OHZ[bla])))\n",
    "\n",
    "v2x = np.log10(np.max(HZ_a_Mdwarf_OHZ[bla]))\n",
    "v2y = np.log10(np.max(HZ_interp_aLum_Mdwarf_OHZ(HZ_a_Mdwarf_OHZ[bla])))\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "polygon_habitable = Polygon([(v0x, v0y), (v1x, v1y), (v2x, v2y), (v3x, v3y)])\n",
    "\n",
    "polygon_boil = Polygon([(-4, v0y), (v0x, v0y), (v3x, v3y), (-4, v3y)])\n",
    "\n",
    "polygon_freeze = Polygon([(v1x, v1y), (2, v1y), (2, v2y), (v2x, v2y)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "wh_habitable = []\n",
    "wh_boil = []\n",
    "wh_freeze = []\n",
    "\n",
    "color_pl = []\n",
    "\n",
    "\n",
    "for i in range(len(planet_a)):\n",
    "    \n",
    "    if polygon_habitable.contains(Point(np.log10(planet_a[i]), np.log10(star_L[i]))):\n",
    "        \n",
    "        color_pl.append('forestgreen')\n",
    "        wh_habitable.append(i)\n",
    "        \n",
    "    elif polygon_boil.contains(Point(np.log10(planet_a[i]), np.log10(star_L[i]))):\n",
    "        \n",
    "        color_pl.append('red')\n",
    "        wh_boil.append(i)\n",
    "        \n",
    "    elif polygon_freeze.contains(Point(np.log10(planet_a[i]), np.log10(star_L[i]))):\n",
    "        \n",
    "        color_pl.append('blue')\n",
    "        wh_freeze.append(i)\n",
    "        \n",
    "        \n",
    "        \n",
    "# Avoid plotting problems\n",
    "color_pl = np.asarray(color_pl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 10))\n",
    "\n",
    "habitable_patch = PolygonPatch(polygon_habitable, color='forestgreen', alpha=0.25)\n",
    "ax.add_patch(habitable_patch)\n",
    "\n",
    "boil_patch = PolygonPatch(polygon_boil, color='red', alpha=0.25)\n",
    "ax.add_patch(boil_patch)\n",
    "\n",
    "freeze_patch = PolygonPatch(polygon_freeze, color='blue', alpha=0.25)\n",
    "ax.add_patch(freeze_patch)\n",
    "\n",
    "ax.scatter(np.log10(planet_a[wh_habitable]), np.log10(star_L[wh_habitable]), color='forestgreen')\n",
    "ax.scatter(np.log10(planet_a[wh_boil]), np.log10(star_L[wh_boil]), color='red')\n",
    "ax.scatter(np.log10(planet_a[wh_freeze]), np.log10(star_L[wh_freeze]), color='blue')\n",
    "\n",
    "#ax.set_xscale('log')\n",
    "#ax.set_yscale('log')\n",
    "\n",
    "ax.set_xlabel(r'$a \\, \\rm{[au]}$',fontsize = 13);\n",
    "ax.set_ylabel(r'$L \\, \\rm{[L_{\\odot}]}$',fontsize = 13);\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "53\n",
      "124\n",
      "28\n"
     ]
    }
   ],
   "source": [
    "print len(wh_habitable)\n",
    "print len(wh_boil)\n",
    "print len(wh_freeze)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LHS 1140\tb\n",
      "YZ Cet\td\n",
      "GJ 96\tb\n",
      "CD-23 1056\tb\n",
      "LP 413-32 B\tb\n",
      "LPM 178\tc\n",
      "HG 8-15\td\n",
      "LP 834-042\tb\n",
      "LP 834-042\td\n",
      "LEHPM 3808\td\n",
      "LP 776-27\tb\n",
      "LP 776-27\tc\n",
      "Kapteyn's star\tb\n",
      "BD-06 1339\tc\n",
      "Luyten's star\tb\n",
      "NGC 2632 JS 597\tc\n",
      "LTT 3758\tc\n",
      "K2-239\tc\n",
      "K2-239\td\n",
      "Innes' star\tb\n",
      "PM J11293-0127\tc\n",
      "PM J11293-0127\td\n",
      "PM J11302+0735\tb\n",
      "Ross 1003\tb\n",
      "LP 613-39\tb\n",
      "FI Vir\tb\n",
      "K2-152\tb\n",
      "Proxima Centauri\tb\n",
      "HO Lib\tc\n",
      "K2-286\tb\n",
      "HD 147379\tb\n",
      "MCC 767\tb\n",
      "V2306 Oph\tc\n",
      "HD 156384 C\tc\n",
      "HD 156384 C\te\n",
      "HD 156384 C\tf\n",
      "CD-51 10924\te\n",
      "CD-44 11909\tb\n",
      "Kepler-235\te\n",
      "Kepler-52\td\n",
      "Kepler-155\tc\n",
      "V1428 Aql\tb\n",
      "LSPM J1930+4149\tb\n",
      "Kepler-54\td\n",
      "Kepler-186\tf\n",
      "Kepler-267\td\n",
      "HD 204961\tc\n",
      "IL Aqr\tb\n",
      "IL Aqr\tc\n",
      "2MUCD 12171\tc\n",
      "2MUCD 12171\td\n",
      "2MUCD 12171\te\n",
      "2MUCD 12171\tf\n"
     ]
    }
   ],
   "source": [
    "for h, hh in enumerate(planet_name[wh_habitable]):\n",
    "    print hh + '\\t' +  planet_char[wh_habitable][h]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GX And\tb\n",
      "K2-149\tb\n",
      "CD-44 170\tb\n",
      "LHS 1140\tc\n",
      "2MASS J01021226-6145216\tb\n",
      "BD+61 195\tb\n",
      "YZ Cet\tb\n",
      "YZ Cet\tc\n",
      "K2-150\tb\n",
      "K2-151\tb\n",
      "BD-17 400\tb\n",
      "BD-17 400\tc\n",
      "BD-21 784\tb\n",
      "LPM 178\tb\n",
      "Melotte 25 VA 50\tb\n",
      "HG 8-15\tb\n",
      "HG 8-15\tc\n",
      "LP 834-042\te\n",
      "LEHPM 3808\tb\n",
      "LEHPM 3808\tc\n",
      "LP 358-499\tb\n",
      "LP 358-499\tc\n",
      "LP 358-499\td\n",
      "HD 285968\tb\n",
      "LP 656-38\tb\n",
      "LP 892-26\tb\n",
      "NGTS-1\tb\n",
      "HATS-6\tb\n",
      "BD-06 1339\tb\n",
      "PM J06168+2435\tb\n",
      "Luyten's star\tc\n",
      "LP 424-4\tb\n",
      "NGC 2632 JS 183\tb\n",
      "K2-146\tb\n",
      "NGC 2632 JS 597\tb\n",
      "K2-117\tb\n",
      "K2-117\tc\n",
      "BD+48 1829\tb\n",
      "LTT 3758\tb\n",
      "K2-239\tb\n",
      "LP 905-36\tb\n",
      "Lalande 21185\tb\n",
      "K2-22\tb\n",
      "PM J11293-0127\tb\n",
      "PM J11302+0735\tc\n",
      "CD-31 9113\tb\n",
      "Ross 905\tb\n",
      "K2-153\tb\n",
      "K2-137\tb\n",
      "K2-154\tb\n",
      "K2-154\tc\n",
      "Ross 1020\tb\n",
      "HD 122303\tb\n",
      "K2-240\tb\n",
      "K2-240\tc\n",
      "HO Lib\tb\n",
      "HO Lib\td\n",
      "MCC 759\tb\n",
      "USco J161014.7-191909\tb\n",
      "V2306 Oph\tb\n",
      "LHS 3275\tb\n",
      "BD+11 3149\tb\n",
      "BD+11 3149\tc\n",
      "HD 156384 C\tb\n",
      "CD-46 11540\tb\n",
      "CD-51 10924\td\n",
      "BD+18 3421\tb\n",
      "Kepler-83\tb\n",
      "Kepler-83\tc\n",
      "Kepler-83\td\n",
      "Kepler-446\tb\n",
      "Kepler-446\tc\n",
      "Kepler-446\td\n",
      "Kepler-303\tb\n",
      "Kepler-303\tc\n",
      "Kepler-617\tb\n",
      "Kepler-236\tb\n",
      "Kepler-236\tc\n",
      "Kepler-235\tb\n",
      "Kepler-235\tc\n",
      "Kepler-235\td\n",
      "Kepler-52\tb\n",
      "Kepler-52\tc\n",
      "Kepler-155\tb\n",
      "Kepler-138\tb\n",
      "Kepler-138\tc\n",
      "Kepler-138\td\n",
      "LSPM J1928+4437\tb\n",
      "LSPM J1928+4437\tc\n",
      "LSPM J1928+4437\td\n",
      "Kepler-49\tb\n",
      "Kepler-49\tc\n",
      "Kepler-49\td\n",
      "Kepler-49\te\n",
      "Kepler-45\tb\n",
      "Kepler-231\tb\n",
      "Kepler-231\tc\n",
      "Kepler-54\tb\n",
      "Kepler-54\tc\n",
      "Kepler-252\tb\n",
      "Kepler-252\tc\n",
      "Kepler-32\tb\n",
      "Kepler-32\tc\n",
      "Kepler-32\td\n",
      "Kepler-32\te\n",
      "Kepler-32\tf\n",
      "Kepler-125\tb\n",
      "Kepler-125\tc\n",
      "Kepler-186\tb\n",
      "Kepler-186\tc\n",
      "Kepler-186\td\n",
      "Kepler-186\te\n",
      "Kepler-445\tb\n",
      "Kepler-445\tc\n",
      "Kepler-445\td\n",
      "Kepler-267\tb\n",
      "Kepler-267\tc\n",
      "LP 819-052\tb\n",
      "LP 700-6\tb\n",
      "K2-21\tb\n",
      "K2-21\tc\n",
      "LHS 3844\tb\n",
      "IL Aqr\td\n",
      "2MUCD 12171\tb\n"
     ]
    }
   ],
   "source": [
    "for h, hh in enumerate(planet_name[wh_boil]):\n",
    "    print hh + '\\t' +  planet_char[wh_boil][h]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BD-17 400\td\n",
      "LPM 178\td\n",
      "LP 834-042\tc\n",
      "Wolf 1539\tb\n",
      "LP 656-38\tc\n",
      "Kapteyn's star\tc\n",
      "HD 42581\tb\n",
      "LP 844-8\tb\n",
      "LP 844-8\tc\n",
      "BD+02 2098\tb\n",
      "CD-31 9113\tc\n",
      "Ross 1003\tc\n",
      "LP 804-27\tb\n",
      "V2306 Oph\td\n",
      "BD+25 3173\tb\n",
      "HD 156384 C\td\n",
      "HD 156384 C\tg\n",
      "CD-51 10924\tb\n",
      "CD-51 10924\tc\n",
      "BD+68 946\tb\n",
      "CD-44 11909\tc\n",
      "Barnard's star\tb\n",
      "HD 204961\tb\n",
      "BD-05 5715\tb\n",
      "BD-05 5715\tc\n",
      "IL Aqr\te\n",
      "2MUCD 12171\tg\n",
      "2MUCD 12171\th\n"
     ]
    }
   ],
   "source": [
    "for h, hh in enumerate(planet_name[wh_freeze]):\n",
    "    print hh + '\\t' +  planet_char[wh_freeze][h]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Filled circles for transit and empty circles for radial velocity\n",
    "\n",
    "\n",
    "#Radial Velocity\n",
    "#Primary Transit\n",
    "wh_RV = np.where(planet_detect == 'RV')[0]\n",
    "wh_PT = np.where( (planet_detect == 'PT') | (planet_detect == 'X')  | (planet_detect == 'PT+RV') )[0]\n",
    "\n",
    "\n",
    "\n",
    "wh_habitable_RV = sorted(list(set(wh_habitable).intersection(wh_RV)))\n",
    "wh_habitable_PT = sorted(list(set(wh_habitable).intersection(wh_PT)))\n",
    "\n",
    "wh_boil_RV = sorted(list(set(wh_boil).intersection(wh_RV)))\n",
    "wh_boil_PT = sorted(list(set(wh_boil).intersection(wh_PT)))\n",
    "\n",
    "wh_freeze_RV = sorted(list(set(wh_freeze).intersection(wh_RV)))\n",
    "wh_freeze_PT = sorted(list(set(wh_freeze).intersection(wh_PT)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Habitable zones from [Kopparapu+14](https://ui.adsabs.harvard.edu/abs/2014ApJ...787L..29K/abstract)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "path_data_Kop = os.getcwd() + '/data_Kop/'\n",
    "\n",
    "# Table 1 from http://adsabs.harvard.edu/abs/2014ApJ...787L..29K (Kopparapu +14)\n",
    "# See also http://adsabs.harvard.edu/abs/2013ApJ...765..131K (Kopparapu +13)\n",
    "# The coefficients are as follows. The columns, i, are arranged according to\n",
    "# the HZ limits given in the paper.\n",
    "#\n",
    "# i = 1 --> Recent Venus\n",
    "# i = 2 --> Runaway Greenhouse\n",
    "# i = 3 --> Maximum Greenhouse\n",
    "# i = 4 --> Early Mars\n",
    "# i = 5 --> Runaway Greenhouse for 5 ME\n",
    "# i = 6 --> Runaway Greenhouse for 0.1 ME\n",
    "# First row: S_effSun(i)\n",
    "# Second row: a(i)\n",
    "# Third row:  b(i)\n",
    "# Fourth row: c(i)\n",
    "# Fifth row:  d(i)\n",
    "HZ_coeff = np.genfromtxt(path_data_Kop + 'HZ_coefficients.dat')\n",
    "S_effSun = HZ_coeff[0]\n",
    "a_coeff = HZ_coeff[1]\n",
    "b_coeff = HZ_coeff[2]  \n",
    "c_coeff = HZ_coeff[3]  \n",
    "d_coeff = HZ_coeff[4]  \n",
    "\n",
    "# Habitable zone 'fluxes' S_eff [Sun]\n",
    "Seff_HZs = np.genfromtxt(path_data_Kop + 'HZs.dat')\n",
    "Teff = Seff_HZs[:,0]\n",
    "\n",
    "\n",
    "\n",
    "Seff_HZs_interp = []\n",
    "\n",
    "for i in range(6):\n",
    "    \n",
    "    Seff_HZs_interp.append(interpolate.interp1d(Teff, Seff_HZs[:,i + 1], kind='linear'))\n",
    "    \n",
    "    \n",
    "L_Lsun_interp = interpolate.interp1d(np.sort(star_prop['Teff']), np.sort(star_prop['Lbol']), kind='linear')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "### HABITABLE, BOIL AND FREEZE POLYGONS\n",
    "### IHZ: Recent Venus\n",
    "### OHZ: Maximum Greenhouse\n",
    "\n",
    "# Start from low, left vertex of the HZ and move counterclockwise\n",
    "\n",
    "HZ_a_Mdwarf_IHZ = np.sqrt(L_Lsun_interp(np.asarray(np.sort(star_prop['Teff'])))\n",
    "                          /Seff_HZs_interp[0](np.asarray(np.sort(star_prop['Teff']))))\n",
    "\n",
    "v0x = np.log10(np.min(HZ_a_Mdwarf_IHZ))\n",
    "v0y = np.log10(np.min(L_Lsun_interp(np.asarray(np.sort(star_prop['Teff'])))))\n",
    "\n",
    "v3x = np.log10(np.max(HZ_a_Mdwarf_IHZ))\n",
    "# Problems with Kepler-155, maxL\n",
    "v3y = np.log10(np.max(L_Lsun_interp(np.asarray(np.sort(star_prop['Teff']))))) + 0.001\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "HZ_a_Mdwarf_OHZ = np.sqrt(L_Lsun_interp(np.asarray(np.sort(star_prop['Teff'])))\n",
    "                          /Seff_HZs_interp[2](np.asarray(np.sort(star_prop['Teff']))))\n",
    "\n",
    "v1x = np.log10(np.min(HZ_a_Mdwarf_OHZ))\n",
    "v1y = np.log10(np.min(L_Lsun_interp(np.asarray(np.sort(star_prop['Teff'])))))\n",
    "\n",
    "v2x = np.log10(np.max(HZ_a_Mdwarf_OHZ))\n",
    "# Problems with Kepler-155, maxL\n",
    "v2y = np.log10(np.max(L_Lsun_interp(np.asarray(np.sort(star_prop['Teff']))))) + 0.001\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "polygon_habitable = Polygon([(v0x, v0y), (v1x, v1y), (v2x, v2y), (v3x, v3y)])\n",
    "\n",
    "polygon_boil = Polygon([(-4, v0y), (v0x, v0y), (v3x, v3y), (-4, v3y)])\n",
    "\n",
    "polygon_freeze = Polygon([(v1x, v1y), (2, v1y), (2, v2y), (v2x, v2y)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "wh_habitable = []\n",
    "wh_boil = []\n",
    "wh_freeze = []\n",
    "\n",
    "color_pl = []\n",
    "\n",
    "\n",
    "for i in range(len(planet_a)):\n",
    "    \n",
    "    if polygon_habitable.contains(Point(np.log10(planet_a[i]), np.log10(star_L[i]))):\n",
    "        \n",
    "        color_pl.append('forestgreen')\n",
    "        wh_habitable.append(i)\n",
    "        \n",
    "    elif polygon_boil.contains(Point(np.log10(planet_a[i]), np.log10(star_L[i]))):\n",
    "        \n",
    "        color_pl.append('red')\n",
    "        wh_boil.append(i)\n",
    "        \n",
    "    elif polygon_freeze.contains(Point(np.log10(planet_a[i]), np.log10(star_L[i]))):\n",
    "        \n",
    "        color_pl.append('blue')\n",
    "        wh_freeze.append(i)\n",
    "        \n",
    "        \n",
    "        \n",
    "# Avoid plotting problems\n",
    "color_pl = np.asarray(color_pl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 10))\n",
    "\n",
    "habitable_patch = PolygonPatch(polygon_habitable, color='forestgreen', alpha=0.25)\n",
    "ax.add_patch(habitable_patch)\n",
    "\n",
    "boil_patch = PolygonPatch(polygon_boil, color='red', alpha=0.25)\n",
    "ax.add_patch(boil_patch)\n",
    "\n",
    "freeze_patch = PolygonPatch(polygon_freeze, color='blue', alpha=0.25)\n",
    "ax.add_patch(freeze_patch)\n",
    "\n",
    "ax.scatter(np.log10(planet_a[wh_habitable]), np.log10(star_L[wh_habitable]), color='forestgreen')\n",
    "ax.scatter(np.log10(planet_a[wh_boil]), np.log10(star_L[wh_boil]), color='red')\n",
    "ax.scatter(np.log10(planet_a[wh_freeze]), np.log10(star_L[wh_freeze]), color='blue')\n",
    "\n",
    "#ax.set_xscale('log')\n",
    "#ax.set_yscale('log')\n",
    "\n",
    "ax.set_xlabel(r'$a \\, \\rm{[au]}$',fontsize = 13);\n",
    "ax.set_ylabel(r'$L \\, \\rm{[L_{\\odot}]}$',fontsize = 13);\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33\n",
      "146\n",
      "26\n"
     ]
    }
   ],
   "source": [
    "print len(wh_habitable)\n",
    "print len(wh_boil)\n",
    "print len(wh_freeze)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LHS 1140\tb\n",
      "GJ 96\tb\n",
      "CD-23 1056\tb\n",
      "LP 413-32 B\tb\n",
      "LPM 178\tc\n",
      "LP 834-042\tb\n",
      "LP 834-042\td\n",
      "LP 776-27\tc\n",
      "Kapteyn's star\tb\n",
      "BD-06 1339\tc\n",
      "Luyten's star\tb\n",
      "Innes' star\tb\n",
      "PM J11293-0127\td\n",
      "PM J11302+0735\tb\n",
      "Ross 1003\tb\n",
      "LP 613-39\tb\n",
      "Proxima Centauri\tb\n",
      "HD 147379\tb\n",
      "V2306 Oph\tc\n",
      "HD 156384 C\tc\n",
      "HD 156384 C\te\n",
      "HD 156384 C\tf\n",
      "CD-44 11909\tb\n",
      "CD-44 11909\tc\n",
      "V1428 Aql\tb\n",
      "Kepler-186\tf\n",
      "HD 204961\tc\n",
      "IL Aqr\tb\n",
      "IL Aqr\tc\n",
      "2MUCD 12171\td\n",
      "2MUCD 12171\te\n",
      "2MUCD 12171\tf\n",
      "2MUCD 12171\tg\n"
     ]
    }
   ],
   "source": [
    "for h, hh in enumerate(planet_name[wh_habitable]):\n",
    "    print hh + '\\t' +  planet_char[wh_habitable][h]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GX And\tb\n",
      "K2-149\tb\n",
      "CD-44 170\tb\n",
      "LHS 1140\tc\n",
      "2MASS J01021226-6145216\tb\n",
      "BD+61 195\tb\n",
      "YZ Cet\tb\n",
      "YZ Cet\tc\n",
      "YZ Cet\td\n",
      "K2-150\tb\n",
      "K2-151\tb\n",
      "BD-17 400\tb\n",
      "BD-17 400\tc\n",
      "BD-21 784\tb\n",
      "LPM 178\tb\n",
      "Melotte 25 VA 50\tb\n",
      "HG 8-15\tb\n",
      "HG 8-15\tc\n",
      "HG 8-15\td\n",
      "LP 834-042\te\n",
      "LEHPM 3808\tb\n",
      "LEHPM 3808\tc\n",
      "LEHPM 3808\td\n",
      "LP 358-499\tb\n",
      "LP 358-499\tc\n",
      "LP 358-499\td\n",
      "HD 285968\tb\n",
      "LP 776-27\tb\n",
      "LP 656-38\tb\n",
      "LP 892-26\tb\n",
      "NGTS-1\tb\n",
      "HATS-6\tb\n",
      "BD-06 1339\tb\n",
      "PM J06168+2435\tb\n",
      "Luyten's star\tc\n",
      "LP 424-4\tb\n",
      "NGC 2632 JS 183\tb\n",
      "K2-146\tb\n",
      "NGC 2632 JS 597\tb\n",
      "NGC 2632 JS 597\tc\n",
      "K2-117\tb\n",
      "K2-117\tc\n",
      "BD+48 1829\tb\n",
      "LTT 3758\tb\n",
      "LTT 3758\tc\n",
      "K2-239\tb\n",
      "K2-239\tc\n",
      "K2-239\td\n",
      "LP 905-36\tb\n",
      "Lalande 21185\tb\n",
      "K2-22\tb\n",
      "PM J11293-0127\tb\n",
      "PM J11293-0127\tc\n",
      "PM J11302+0735\tc\n",
      "CD-31 9113\tb\n",
      "Ross 905\tb\n",
      "FI Vir\tb\n",
      "K2-152\tb\n",
      "K2-153\tb\n",
      "K2-137\tb\n",
      "K2-154\tb\n",
      "K2-154\tc\n",
      "Ross 1020\tb\n",
      "HD 122303\tb\n",
      "K2-240\tb\n",
      "K2-240\tc\n",
      "HO Lib\tb\n",
      "HO Lib\tc\n",
      "HO Lib\td\n",
      "K2-286\tb\n",
      "MCC 759\tb\n",
      "USco J161014.7-191909\tb\n",
      "MCC 767\tb\n",
      "V2306 Oph\tb\n",
      "LHS 3275\tb\n",
      "BD+11 3149\tb\n",
      "BD+11 3149\tc\n",
      "HD 156384 C\tb\n",
      "CD-46 11540\tb\n",
      "CD-51 10924\td\n",
      "CD-51 10924\te\n",
      "BD+18 3421\tb\n",
      "Kepler-83\tb\n",
      "Kepler-83\tc\n",
      "Kepler-83\td\n",
      "Kepler-446\tb\n",
      "Kepler-446\tc\n",
      "Kepler-446\td\n",
      "Kepler-303\tb\n",
      "Kepler-303\tc\n",
      "Kepler-617\tb\n",
      "Kepler-236\tb\n",
      "Kepler-236\tc\n",
      "Kepler-235\tb\n",
      "Kepler-235\tc\n",
      "Kepler-235\td\n",
      "Kepler-235\te\n",
      "Kepler-52\tb\n",
      "Kepler-52\tc\n",
      "Kepler-52\td\n",
      "Kepler-155\tb\n",
      "Kepler-155\tc\n",
      "Kepler-138\tb\n",
      "Kepler-138\tc\n",
      "Kepler-138\td\n",
      "LSPM J1928+4437\tb\n",
      "LSPM J1928+4437\tc\n",
      "LSPM J1928+4437\td\n",
      "Kepler-49\tb\n",
      "Kepler-49\tc\n",
      "Kepler-49\td\n",
      "Kepler-49\te\n",
      "LSPM J1930+4149\tb\n",
      "Kepler-45\tb\n",
      "Kepler-231\tb\n",
      "Kepler-231\tc\n",
      "Kepler-54\tb\n",
      "Kepler-54\tc\n",
      "Kepler-54\td\n",
      "Kepler-252\tb\n",
      "Kepler-252\tc\n",
      "Kepler-32\tb\n",
      "Kepler-32\tc\n",
      "Kepler-32\td\n",
      "Kepler-32\te\n",
      "Kepler-32\tf\n",
      "Kepler-125\tb\n",
      "Kepler-125\tc\n",
      "Kepler-186\tb\n",
      "Kepler-186\tc\n",
      "Kepler-186\td\n",
      "Kepler-186\te\n",
      "Kepler-445\tb\n",
      "Kepler-445\tc\n",
      "Kepler-445\td\n",
      "Kepler-267\tb\n",
      "Kepler-267\tc\n",
      "Kepler-267\td\n",
      "LP 819-052\tb\n",
      "LP 700-6\tb\n",
      "K2-21\tb\n",
      "K2-21\tc\n",
      "LHS 3844\tb\n",
      "IL Aqr\td\n",
      "2MUCD 12171\tb\n",
      "2MUCD 12171\tc\n"
     ]
    }
   ],
   "source": [
    "for h, hh in enumerate(planet_name[wh_boil]):\n",
    "    print hh + '\\t' +  planet_char[wh_boil][h]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BD-17 400\td\n",
      "LPM 178\td\n",
      "LP 834-042\tc\n",
      "Wolf 1539\tb\n",
      "LP 656-38\tc\n",
      "Kapteyn's star\tc\n",
      "HD 42581\tb\n",
      "LP 844-8\tb\n",
      "LP 844-8\tc\n",
      "BD+02 2098\tb\n",
      "CD-31 9113\tc\n",
      "Ross 1003\tc\n",
      "LP 804-27\tb\n",
      "V2306 Oph\td\n",
      "BD+25 3173\tb\n",
      "HD 156384 C\td\n",
      "HD 156384 C\tg\n",
      "CD-51 10924\tb\n",
      "CD-51 10924\tc\n",
      "BD+68 946\tb\n",
      "Barnard's star\tb\n",
      "HD 204961\tb\n",
      "BD-05 5715\tb\n",
      "BD-05 5715\tc\n",
      "IL Aqr\te\n",
      "2MUCD 12171\th\n"
     ]
    }
   ],
   "source": [
    "for h, hh in enumerate(planet_name[wh_freeze]):\n",
    "    print hh + '\\t' +  planet_char[wh_freeze][h]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Filled circles for transit and empty circles for radial velocity\n",
    "\n",
    "\n",
    "#Radial Velocity\n",
    "#Primary Transit\n",
    "wh_RV = np.where(planet_detect == 'RV')[0]\n",
    "wh_PT = np.where( (planet_detect == 'PT') | (planet_detect == 'X')  | (planet_detect == 'PT+RV') )[0]\n",
    "\n",
    "\n",
    "\n",
    "wh_habitable_RV = sorted(list(set(wh_habitable).intersection(wh_RV)))\n",
    "wh_habitable_PT = sorted(list(set(wh_habitable).intersection(wh_PT)))\n",
    "\n",
    "wh_boil_RV = sorted(list(set(wh_boil).intersection(wh_RV)))\n",
    "wh_boil_PT = sorted(list(set(wh_boil).intersection(wh_PT)))\n",
    "\n",
    "wh_freeze_RV = sorted(list(set(wh_freeze).intersection(wh_RV)))\n",
    "wh_freeze_PT = sorted(list(set(wh_freeze).intersection(wh_PT)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "z_lines = 1\n",
    "z_points = 2\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12,9))\n",
    "\n",
    "scale_factor = 20\n",
    "corrfactor = 1./2.5\n",
    "\n",
    "\n",
    "\n",
    "# HZ\n",
    "ax.plot(HZ_a_Mdwarf_IHZ, \\\n",
    "         L_Lsun_interp(np.asarray(np.sort(star_prop['Teff']))), color='red', lw=2.0, zorder=z_lines)\n",
    "\n",
    "\n",
    "ax.plot(HZ_a_Mdwarf_OHZ, \\\n",
    "         L_Lsun_interp(np.asarray(np.sort(star_prop['Teff']))), color='blue', lw=2.0, zorder=z_lines)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Tidal locking models, Roche limit\n",
    "\n",
    "ax.plot(a_TD, CTL_TD**idxMS, 'k--', lw=2.0);\n",
    "#ax.plot(a_TD, CPL_TD**idxMS, 'k-', lw=2.0);\n",
    "\n",
    "ax.plot(Roche_solid(REarth, Msun*(L_TD)**(1./3.5), MEarth), L_TD, color='grey', lw = 2.0, ls = 'dashed')\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Planets\n",
    "\n",
    "\n",
    "# Sort bubbles by decreasing mass to plot little ones on top\n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "boil_inds = planet_M[wh_boil].argsort()[::-1]\n",
    "\n",
    "for h in boil_inds:\n",
    "    \n",
    "    if ((planet_detect[wh_boil][h] == 'PT') |\\\n",
    "        (planet_detect[wh_boil][h] == 'X')  | (planet_detect[wh_boil][h] == 'PT+RV')):\n",
    "        \n",
    "        ax.scatter(planet_a[wh_boil][h], star_L[wh_boil][h], color='red', edgecolor='red',\\\n",
    "           lw=1.5, s=scale_factor*(planet_M[wh_boil][h])**(corrfactor), zorder=z_points);\n",
    "        \n",
    "    else:\n",
    "        \n",
    "        ax.scatter(planet_a[wh_boil][h], star_L[wh_boil][h], color='white', edgecolor='red',\\\n",
    "           lw=1.5, s=scale_factor*(planet_M[wh_boil][h])**(corrfactor), zorder=z_points);\n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "fre_inds = planet_M[wh_freeze].argsort()[::-1]\n",
    "\n",
    "for h in fre_inds:\n",
    "    \n",
    "    if ((planet_detect[wh_freeze][h] == 'PT') |\\\n",
    "        (planet_detect[wh_freeze][h] == 'X')  | (planet_detect[wh_freeze][h] == 'PT+RV')):\n",
    "        \n",
    "        ax.scatter(planet_a[wh_freeze][h], star_L[wh_freeze][h], color='blue', edgecolor='blue',\\\n",
    "           lw=1.5, s=scale_factor*(planet_M[wh_freeze][h])**(corrfactor), zorder=z_points);\n",
    "        \n",
    "    else:\n",
    "        \n",
    "        ax.scatter(planet_a[wh_freeze][h], star_L[wh_freeze][h], color='white', edgecolor='blue',\\\n",
    "           lw=1.5, s=scale_factor*(planet_M[wh_freeze][h])**(corrfactor), zorder=z_points);\n",
    "        \n",
    "        \n",
    "        \n",
    "        \n",
    "hab_inds = planet_M[wh_habitable].argsort()[::-1]\n",
    "\n",
    "for h in hab_inds:\n",
    "    \n",
    "    if ((planet_detect[wh_habitable][h] == 'PT') |\\\n",
    "        (planet_detect[wh_habitable][h] == 'X')  | (planet_detect[wh_habitable][h] == 'PT+RV')):\n",
    "        \n",
    "        ax.scatter(planet_a[wh_habitable][h], star_L[wh_habitable][h], color='forestgreen', edgecolor='forestgreen',\\\n",
    "           lw=1.5, s=scale_factor*(planet_M[wh_habitable][h])**(corrfactor), zorder=z_points);\n",
    "        \n",
    "    else:\n",
    "        \n",
    "        ax.scatter(planet_a[wh_habitable][h], star_L[wh_habitable][h], color='white', edgecolor='forestgreen',\\\n",
    "           lw=1.5, s=scale_factor*(planet_M[wh_habitable][h])**(corrfactor), zorder=z_points);\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# SS planets\n",
    "\n",
    "for ipl in range(8):\n",
    "    ax.scatter(a_SS[ipl], 1.0, color=color_SS[ipl], edgecolor=color_SS[ipl], s=scale_factor*(m_SS[ipl])**(corrfactor),\\\n",
    "               zorder=z_points);\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "\n",
    "#ax.set_xlabel(r'$\\rm{a \\, [au]}$',fontsize = 25, labelpad=10);\n",
    "ax.set_xlabel(r'$a \\, \\rm{[au]}$',fontsize = 25, labelpad=10);\n",
    "ax.tick_params(axis='x', which='major', pad=10)\n",
    "#ax.set_ylabel(r'$\\rm{L \\, [L_{\\odot}]}$',fontsize = 25, labelpad=10)\n",
    "ax.set_ylabel(r'$L \\, \\rm{[L_{\\odot}]}$',fontsize = 25, labelpad=10)\n",
    "ax.tick_params(axis='y', which='major', pad=5)\n",
    "\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(20);\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(20); \n",
    "            \n",
    "            \n",
    "ax.tick_params(which='both', width=2.05);\n",
    "ax.tick_params(which='major', length=20);\n",
    "ax.tick_params(which='minor', length=10);\n",
    "#ax.set_xlim(7.0E-4, 4.5E1);\n",
    "ax.set_xlim(7.0E-4, 7.0E1);\n",
    "ax.minorticks_on();\n",
    "ax.set_xscale('log');\n",
    "ax.set_yscale('log');\n",
    "ax.set_ylim(7.E-5, 2.5E0);\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "ax.text(1.9E-3, 1.25E-4, r'$\\rm{Roche \\,\\, limit \\,\\, Terran \\,\\, planet}$', color='grey', fontsize=16)\n",
    "ax.text(2.3E-1, 1.25E-4, r'$\\rm{Tidal \\,\\, locking \\,\\, boundary}$', color='black', fontsize=16)\n",
    "\n",
    "\n",
    "ax.text(5.E0, 2.90E-4, r'$\\rm{Closer \\,\\, than \\,\\, inner \\,\\, HZ}$', color='red', fontsize=16)\n",
    "ax.text(5.E0, 1.90E-4, r'$\\rm{In \\,\\, the \\,\\, HZ}$', color='forestgreen', fontsize=16)\n",
    "ax.text(5.E0, 1.25E-4, r'$\\rm{Beyond \\,\\, the \\,\\, outer \\,\\, HZ}$', color='blue', fontsize=16)\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('HZ_plot_paper.pdf', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exomoon calculations from [Piro+18a](https://ui.adsabs.harvard.edu/abs/2018AJ....156...54P/abstract) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "dEarthMoon = 3.84399E8 # m\n",
    "\n",
    "# Maximum and minimum allowed distances for the exomoon\n",
    "\n",
    "# Max: Eq 1 from Piro+18a\n",
    "f = 0.49\n",
    "acrit = f * (planet_a * One_AU) * ( planet_M * MEarth / (3. *  star_M * Msun ) )**(1./3.) / dEarthMoon\n",
    "\n",
    "###################################################################################################################################\n",
    "\n",
    "# Min: Eq 32 from Piro+18a\n",
    "#Rm = 0.462 * (1 + Mp/Mm)**-1/3 * at\n",
    "#rhoMoon = 3.34E3 # kg/m3\n",
    "rhoMoon_example = 2.5E3 # kg/m3 Typical density ~ 2-3 g/cm3\n",
    "\n",
    "\n",
    "at = 1.34 * (planet_M * MEarth / rhoMoon_example)**(1./3.) / dEarthMoon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### Our tables have periods already. This is a check using Kepler's third law ####\n",
    "\n",
    "\n",
    "#### P0 will be given by Kepler's third law, assuming tidal locking for the planets ####\n",
    "#### A few of them might not be tidally locked, but they will receive no special treatment ####\n",
    "\n",
    "G = 6.673E-11 # N m2 kg-2\n",
    "T = 2 * np.pi * np.sqrt( (planet_a * One_AU) **3 / (G* (star_M*Msun + planet_M*MEarth) ) ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.log10(T / 3600.), color='blue', alpha=0.25);\n",
    "plt.hist(np.log10(planet_prop['P_day'] *24.), color='red', alpha=0.25);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exomoon's fate: will it fall back into the exoplanet or will it be stripped away?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "#If a_m > a_{crit,m} then the moon is eventually stripped\n",
    "#If a_m < a_{crit,m} then the moon eventually falls back into the planet\n",
    "\n",
    "# Eq 30 from Piro+18a\n",
    "\n",
    "MMoon = 7.346E22 # kg \n",
    "G = 6.673E-11 # N m2 kg-2\n",
    "h_to_s = 3600.\n",
    "d_to_s = 86400.\n",
    "\n",
    "P0 = planet_prop['P_day'] # Switch to 3h if desired\n",
    "\n",
    "lambda_r_sample = np.zeros(len(planet_R))\n",
    "\n",
    "for i, el in enumerate(planet_R):\n",
    "    \n",
    "    lambda_r_sample[i] = lambda_r(el)\n",
    "\n",
    "###################################################################################################################################\n",
    "\n",
    "am = 4 * np.pi**2 * lambda_r_sample**2 * (planet_M * MEarth) * (planet_R * REarth) **4 / \\\n",
    "(G * MMoon**2 * (P0 * d_to_s)**2 ) * 1 / dEarthMoon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# List intersections\n",
    "\n",
    "wh_moon_strip = list(np.where(am > acrit)[0])\n",
    "wh_moon_fall = list(np.where(am < acrit)[0])\n",
    "\n",
    "\n",
    "wh_habitable_moon_strip = sorted(list(set(wh_habitable).intersection(wh_moon_strip)))\n",
    "wh_habitable_moon_fall = sorted(list(set(wh_habitable).intersection(wh_moon_fall)))\n",
    "wh_habitable_PT_moon_strip = sorted(list(set(wh_habitable_PT).intersection(wh_moon_strip)))\n",
    "wh_habitable_PT_moon_fall = sorted(list(set(wh_habitable_PT).intersection(wh_moon_fall)))\n",
    "wh_habitable_RV_moon_strip = sorted(list(set(wh_habitable_RV).intersection(wh_moon_strip)))\n",
    "wh_habitable_RV_moon_fall = sorted(list(set(wh_habitable_RV).intersection(wh_moon_fall)))\n",
    "\n",
    "wh_boil_moon_strip = sorted(list(set(wh_boil).intersection(wh_moon_strip)))\n",
    "wh_boil_moon_fall = sorted(list(set(wh_boil).intersection(wh_moon_fall)))\n",
    "wh_boil_PT_moon_strip = sorted(list(set(wh_boil_PT).intersection(wh_moon_strip)))\n",
    "wh_boil_PT_moon_fall = sorted(list(set(wh_boil_PT).intersection(wh_moon_fall)))\n",
    "wh_boil_RV_moon_strip = sorted(list(set(wh_boil_RV).intersection(wh_moon_strip)))\n",
    "wh_boil_RV_moon_fall = sorted(list(set(wh_boil_RV).intersection(wh_moon_fall)))\n",
    "\n",
    "\n",
    "wh_freeze_moon_strip = sorted(list(set(wh_freeze).intersection(wh_moon_strip)))\n",
    "wh_freeze_moon_fall = sorted(list(set(wh_freeze).intersection(wh_moon_fall)))\n",
    "wh_freeze_PT_moon_strip = sorted(list(set(wh_freeze_PT).intersection(wh_moon_strip)))\n",
    "wh_freeze_PT_moon_fall = sorted(list(set(wh_freeze_PT).intersection(wh_moon_fall)))\n",
    "wh_freeze_RV_moon_strip = sorted(list(set(wh_freeze_RV).intersection(wh_moon_strip)))\n",
    "wh_freeze_RV_moon_fall = sorted(list(set(wh_freeze_RV).intersection(wh_moon_fall)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exomoon migration timescale (taumig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Consider k2, Q and tau for arbitrary planets (i.e., not assuming they are rocky)\n",
    "\n",
    "# Eq 25 from Piro +18a\n",
    "\n",
    "k2_Earth = 0.3\n",
    "tau_Earth = 638 #s\n",
    "Q_Earth = 12.0\n",
    "\n",
    "\n",
    "k2_r_sample = np.zeros(len(planet_R))\n",
    "\n",
    "for i, el in enumerate(planet_R):\n",
    "    \n",
    "    k2_r_sample[i] = k2_r(el)\n",
    "    \n",
    "    \n",
    "    \n",
    "Q_r_sample = np.zeros(len(planet_R))\n",
    "\n",
    "for i, el in enumerate(planet_R):\n",
    "    \n",
    "    Q_r_sample[i] = Q_r(el)\n",
    "    \n",
    "    \n",
    "\n",
    "\n",
    "# If a_m > a_{crit,m} when the moon is eventually stripped, better use a_{crit,m} to estimate tau_mig than a_m\n",
    "\n",
    "am[wh_moon_strip] = acrit[wh_moon_strip]\n",
    "taumig = 2.5E11 * (k2_Earth / k2_r_sample) * (Q_r_sample / Q_Earth) * \\\n",
    "(MMoon / MMoon)**(-1.0) * (planet_R)**(-5.0) * (am)**(8.0) # yr"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "# Plot all the exomoons in our sample, not just those with am > at\n",
    "\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(7,5))\n",
    "\n",
    "scale_factor = 60\n",
    "corrfac = 20\n",
    "#colma = 'gist_rainbow'\n",
    "colma = 'gist_rainbow'\n",
    "\n",
    "\n",
    "# Some lists might be empty (try except)\n",
    "# Problems when trying to set edgecolor (black by default) to colormap facecolor in filled circles (PT)\n",
    "# facecolors='None' for empty circles with colormap edgecolor (RV)\n",
    "\n",
    "\n",
    "try:\n",
    "    \n",
    "        ax.scatter(at[wh_habitable_PT_moon_strip], \n",
    "                   acrit[wh_habitable_PT_moon_strip],\n",
    "                   s = scale_factor*np.log10(planet_M[wh_habitable_PT_moon_strip]*corrfac),\n",
    "                   c=np.log10(taumig[wh_habitable_PT_moon_strip]),\n",
    "                   vmin=np.floor(np.log10(np.min(taumig[wh_habitable]))),\n",
    "                   vmax=np.ceil(np.log10(np.max(taumig[wh_habitable]))),\n",
    "                   cmap=colma, zorder=z_points, marker='o', lw=0.1);\n",
    "\n",
    "        PT_strip = ax.scatter(at[wh_habitable_PT_moon_strip], \n",
    "                              acrit[wh_habitable_PT_moon_strip],\n",
    "                              s = scale_factor*np.log10(planet_M[wh_habitable_PT_moon_strip]*corrfac),\n",
    "                              c=np.log10(taumig[wh_habitable_PT_moon_strip]),\n",
    "                              facecolors='None',\n",
    "                              vmin=np.floor(np.log10(np.min(taumig[wh_habitable]))),\n",
    "                              vmax=np.ceil(np.log10(np.max(taumig[wh_habitable]))),\n",
    "                              cmap=colma, zorder=z_points, marker='o');\n",
    "        \n",
    "        PT_strip.set_facecolor('none')\n",
    "\n",
    "except ValueError:\n",
    "\n",
    "        pass\n",
    "\n",
    "try:\n",
    "\n",
    "        RV_strip = ax.scatter(at[wh_habitable_RV_moon_strip], \n",
    "                              acrit[wh_habitable_RV_moon_strip],\n",
    "                              s = scale_factor*np.log10(planet_M[wh_habitable_RV_moon_strip]*corrfac),\n",
    "                              c=np.log10(taumig[wh_habitable_RV_moon_strip]),\n",
    "                              facecolors='None',\n",
    "                              vmin=np.floor(np.log10(np.min(taumig[wh_habitable]))),\n",
    "                              vmax=np.ceil(np.log10(np.max(taumig[wh_habitable]))),\n",
    "                              cmap=colma, zorder=z_points, marker='o');\n",
    "        \n",
    "        RV_strip.set_facecolor('none')\n",
    "\n",
    "except ValueError:\n",
    "\n",
    "        pass\n",
    "\n",
    "try:\n",
    "    \n",
    "        ax.scatter(at[wh_habitable_PT_moon_fall], \n",
    "                   acrit[wh_habitable_PT_moon_fall],\n",
    "                   s = scale_factor*np.log10(planet_M[wh_habitable_PT_moon_fall]*corrfac),\n",
    "                   c=np.log10(taumig[wh_habitable_PT_moon_fall]),\n",
    "                   vmin=np.floor(np.log10(np.min(taumig[wh_habitable]))),\n",
    "                   vmax=np.ceil(np.log10(np.max(taumig[wh_habitable]))),\n",
    "                   cmap=colma, zorder=z_points, marker='D', lw=0.1);\n",
    "\n",
    "        PT_fall = ax.scatter(at[wh_habitable_PT_moon_fall], \n",
    "                             acrit[wh_habitable_PT_moon_fall],\n",
    "                             s = scale_factor*np.log10(planet_M[wh_habitable_PT_moon_fall]*corrfac),\n",
    "                             c=np.log10(taumig[wh_habitable_PT_moon_fall]),\n",
    "                             facecolors='None',\n",
    "                             vmin=np.floor(np.log10(np.min(taumig[wh_habitable]))),\n",
    "                             vmax=np.ceil(np.log10(np.max(taumig[wh_habitable]))),\n",
    "                             cmap=colma, zorder=z_points, marker='D');\n",
    "        \n",
    "        PT_fall.set_facecolor('none')\n",
    "\n",
    "except ValueError:\n",
    "\n",
    "        pass\n",
    "\n",
    "try:\n",
    "\n",
    "        RV_fall = ax.scatter(at[wh_habitable_RV_moon_fall], \n",
    "                             acrit[wh_habitable_RV_moon_fall],\n",
    "                             s = scale_factor*np.log10(planet_M[wh_habitable_RV_moon_fall]*corrfac),\n",
    "                             c=np.log10(taumig[wh_habitable_RV_moon_fall]),\n",
    "                             facecolors='None',\n",
    "                             vmin=np.floor(np.log10(np.min(taumig[wh_habitable]))),\n",
    "                             vmax=np.ceil(np.log10(np.max(taumig[wh_habitable]))),\n",
    "                             cmap=colma, zorder=z_points, marker='D');\n",
    "        \n",
    "        RV_fall.set_facecolor('none')\n",
    "\n",
    "except ValueError:\n",
    "\n",
    "        pass\n",
    "\n",
    "\n",
    "    \n",
    "    \n",
    "\n",
    "\n",
    "# For the colorbar\n",
    "\n",
    "sc = ax.scatter(1.E11 + at[wh_habitable], acrit[wh_habitable], \n",
    "                s = scale_factor*np.log10(planet_M[wh_habitable]*corrfac),\n",
    "                c=np.log10(taumig[wh_habitable]), vmin=np.floor(np.log10(np.min(taumig[wh_habitable]))),\n",
    "                vmax=np.ceil(np.log10(np.max(taumig[wh_habitable]))), cmap=colma, zorder=z_points, marker='o');\n",
    "\n",
    "\n",
    "cbar = fig.colorbar(sc)#, orientation = 'horizontal')\n",
    "cbar.set_label(r'$\\mathrm{\\log} \\, \\tau_{\\mathrm{mig},m} \\, [\\mathrm{yr}]}$',\\\n",
    "               rotation=270, fontsize = 14, labelpad=25)\n",
    "\n",
    "\n",
    "\n",
    "ax.plot((1.E-2, 1.E0), (1.E-2, 1.E0), color='black', ls='dashed', lw=1.5, zorder=z_lines)\n",
    "\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$a_{\\rm{Roche}} \\, [a_{\\rm{M}}]$',fontsize = 17, labelpad=10)\n",
    "ax.tick_params(axis='x', which='major', pad=5)\n",
    "ax.set_ylabel(r'$a_{\\mathrm{crit},m} \\, [a_{\\rm{M}}]$',fontsize = 17, labelpad=5);\n",
    "ax.tick_params(axis='y', which='major', pad=10)\n",
    "\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(13);\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(13); \n",
    "            \n",
    "            \n",
    "ax.tick_params(which='both', width=1.75);\n",
    "ax.tick_params(which='major', length=12);\n",
    "ax.tick_params(which='minor', length=6);\n",
    "\n",
    "ax.set_xscale('log');\n",
    "ax.set_yscale('log');\n",
    "\n",
    "ax.set_xlim(1.E-2, 1.E0);\n",
    "ax.set_ylim(1.E-2, 1.E1);\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "\n",
    "# For the legend\n",
    "\n",
    "ax.scatter(1.35E-2, 6.0E0, s=80, color='black', marker='o')\n",
    "ax.scatter(1.35E-2, 3.5E0, s=80, color='black', marker='D')\n",
    "\n",
    "ax.text(1.6E-2, 5.3E0, r'$\\rm{Moon \\ stripped \\ away}$', fontsize=13)\n",
    "ax.text(1.6E-2, 3.1E0, r'$\\rm{Moon \\ falls \\ back}$', fontsize=13)\n",
    "\n",
    "ax.text(2.7E-1, 3.0E-2, r'$\\mathrm{M}_{m} = \\, 1.0 \\, \\mathrm{M_{M}}$', fontsize=13)\n",
    "ax.text(2.7E-1, 1.7E-2, r'$\\rm{P_{0} = \\, P_{orb}}$', fontsize=13)\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('Moon_dist_range_stripfall_taumig.pdf', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 17, 75, 76, 83, 178, 200, 201, 202, 203]\n",
      "[]\n",
      "[15, 20, 26, 28, 39, 42, 48, 51, 71, 92, 102, 105, 112, 114, 115, 123, 124, 147, 186]\n",
      "[16, 80, 194, 195]\n"
     ]
    }
   ],
   "source": [
    "print wh_habitable_PT_moon_fall\n",
    "\n",
    "print wh_habitable_PT_moon_strip\n",
    "\n",
    "print wh_habitable_RV_moon_fall\n",
    "\n",
    "print wh_habitable_RV_moon_strip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hector/anaconda2/lib/python2.7/site-packages/numpy/core/fromnumeric.py:688: UserWarning: Warning: 'partition' will ignore the 'mask' of the MaskedColumn.\n",
      "  a.partition(kth, axis=axis, kind=kind, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "\n",
    "\n",
    "#ax.hist(planet_prop['P_day'][wh_boil], bins=fd(planet_prop['P_day'][wh_boil]), color='red', alpha=0.5);\n",
    "#ax.hist(planet_prop['P_day'][wh_habitable], bins=fd(planet_prop['P_day'][wh_habitable]), color='forestgreen', alpha=0.5);\n",
    "#ax.hist(planet_prop['P_day'][wh_freeze], bins=fd(planet_prop['P_day'][wh_freeze]), color='blue', alpha=0.5);\n",
    "\n",
    "\n",
    "ax.hist(planet_prop['P_day'][wh_boil], \\\n",
    "        bins=10 ** np.linspace(np.log10(min(planet_prop['P_day'][wh_boil])),\\\n",
    "                               np.log10(max(planet_prop['P_day'][wh_boil])), 9), color='red',\\\n",
    "        edgecolor='black', alpha=0.5);\n",
    "\n",
    "ax.hist(planet_prop['P_day'][wh_habitable], \\\n",
    "        bins=10 ** np.linspace(np.log10(min(planet_prop['P_day'][wh_habitable])),\\\n",
    "                               np.log10(max(planet_prop['P_day'][wh_habitable])), 6), color='forestgreen',\\\n",
    "        edgecolor='black', alpha=0.5);\n",
    "\n",
    "ax.hist(planet_prop['P_day'][wh_freeze], \\\n",
    "        bins=10 ** np.linspace(np.log10(min(planet_prop['P_day'][wh_freeze])),\\\n",
    "                               np.log10(max(planet_prop['P_day'][wh_freeze])), 9), color='blue',\\\n",
    "        edgecolor='black', alpha=0.5);\n",
    "\n",
    "#ax.set_xlim(0., 150.);\n",
    "\n",
    "ax.set_xlabel(r'$\\rm{P_{orb} \\, [d]}$', fontsize=23, labelpad=5);\n",
    "ax.set_ylabel(r'$\\rm{Counts}$', fontsize=23, labelpad=10);\n",
    "ax.tick_params(axis='both', which='major', labelsize=17, length=14, width=1.75, pad = 7);\n",
    "#ax.tick_params(which='both', width=1.75);\n",
    "#ax.tick_params(which='major', length=12);\n",
    "ax.tick_params(which='minor', length=6, width=1.3);\n",
    "\n",
    "\n",
    "ax.axvline(np.median(planet_prop['P_day'][wh_boil]), color='red', lw=1.5, ls='dashed')\n",
    "ax.axvline(np.median(planet_prop['P_day'][wh_habitable]), color='forestgreen', lw=1.5, ls='dashed')\n",
    "ax.axvline(np.median(planet_prop['P_day'][wh_freeze]), color='blue', lw=1.5, ls='dashed')\n",
    "\n",
    "\n",
    "ax.set_xscale('log');\n",
    "ax.set_xlim(0.1, 2.E4);\n",
    "ax.set_ylim(0., 53);\n",
    "ax.set_xticks([0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000])\n",
    "ax.set_xticklabels([r'$\\rm{0.2}$', r'$\\rm{0.5}$', r'$\\rm{1}$', r'$\\rm{2}$', r'$\\rm{5}$', r'$\\rm{10}$',\\\n",
    "                    r'$\\rm{20}$', r'$\\rm{50}$', r'$\\rm{100}$', r'$\\rm{200}$', r'$\\rm{500}$',\\\n",
    "                    r'$\\rm{1e3}$', r'$\\rm{2e3}$', r'$\\rm{5e3}$', r'$\\rm{1e4}$'], fontsize=22)\n",
    "\n",
    "\n",
    "#ax.set_yticklabels([r'$\\rm{0}$', r'$\\rm{5}$', r'$\\rm{10}$', r'$\\rm{15}$',\\\n",
    "#                    r'$\\rm{20}$', r'$\\rm{25}$', r'$\\rm{30}$', r'$\\rm{35}$', r'$\\rm{40}$'], fontsize=22)\n",
    "#ax.set_yscale('log');\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "\n",
    "ax.text(1.5E-1, 48., r'$\\rm{Closer \\,\\, than \\,\\, inner \\,\\, HZ}$', color='red', fontsize=20)\n",
    "ax.text(1.5E-1, 45., r'$\\rm{In \\,\\, the \\,\\, HZ}$', color='forestgreen', fontsize=20)\n",
    "ax.text(1.5E-1, 42., r'$\\rm{Beyond \\,\\, the \\,\\, outer \\,\\, HZ}$', color='blue', fontsize=20)\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.savefig('Porb_log.pdf', bbox_to_inches = 'tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "planet_name_finalan = []\n",
    "planet_a_finalan = []\n",
    "P0_finalan = []\n",
    "star_M_finalan = []\n",
    "planet_M_finalan = []\n",
    "planet_R_finalan = []\n",
    "at_finalan = []\n",
    "acrit_finalan = []\n",
    "am_finalan = []\n",
    "taumig_finalan = []\n",
    "\n",
    "k2_finalan = []\n",
    "Q_finalan = []\n",
    "lambda_finalan = []\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "for h, hh in enumerate(planet_name):\n",
    "\n",
    "    \n",
    "    if ( (taumig[h] >= 1.E8) and (h in wh_habitable) ) :\n",
    "        \n",
    "        \n",
    "        planet_name_finalan.append(hh + ' ' +  planet_char[h])\n",
    "        planet_a_finalan.append(planet_a[h])\n",
    "        P0_finalan.append(P0[h]) \n",
    "        star_M_finalan.append(star_M[h])\n",
    "        planet_M_finalan.append(planet_M[h]) \n",
    "        planet_R_finalan.append(planet_R[h]) \n",
    "        at_finalan.append(at[h])\n",
    "        acrit_finalan.append(acrit[h]) \n",
    "        am_finalan.append(am[h]) \n",
    "        taumig_finalan.append(taumig[h])\n",
    "        k2_finalan.append(k2_r_sample[h])\n",
    "        Q_finalan.append(Q_r_sample[h])\n",
    "        lambda_finalan.append(lambda_r_sample[h])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name \b Planet \b a \b P0 \b M* \b Mp \b Rp \b at \b acrit \b am \b taumig\n",
      "----------------------------------------------------------------\n",
      "CD-23 1056 b 0.25 \b 53 \b 0.62 \b 114.0 \b 13.1 \b 0.23 \b 2.72 \b 2.72 \b 32934\n",
      "Ross 1003 b 0.17 \b 41 \b 0.35 \b 96.7 \b 11.9 \b 0.21 \b 2.08 \b 2.08 \b 5903\n",
      "IL Aqr b 0.21 \b 61 \b 0.34 \b 760.9 \b 13.1 \b 0.43 \b 5.36 \b 5.36 \b 7356120\n",
      "IL Aqr c 0.13 \b 30 \b 0.34 \b 241.5 \b 13.7 \b 0.29 \b 2.29 \b 2.29 \b 6610\n"
     ]
    }
   ],
   "source": [
    "print 'Name', '\\b', 'Planet', '\\b', 'a', '\\b', 'P0', '\\b', 'M*', '\\b', 'Mp', '\\b', 'Rp',\\\n",
    "'\\b', 'at', '\\b', 'acrit', '\\b', 'am', '\\b', 'taumig'\n",
    "\n",
    "print ('----------------------------------------------------------------')\n",
    "\n",
    "for h, hh in enumerate(planet_name_finalan):\n",
    "\n",
    "            print hh,\\\n",
    "        \"%.2f\" % planet_a_finalan[h], '\\b', \"%.0f\" % P0_finalan[h], '\\b', \"%.2f\" % star_M_finalan[h],'\\b',\\\n",
    "        \"%.1f\" % planet_M_finalan[h], '\\b', \"%.1f\" % planet_R_finalan[h], '\\b',\\\n",
    "        \"%.2f\" % at_finalan[h], '\\b', \"%.2f\" % acrit_finalan[h], '\\b', \"%.2f\" % am_finalan[h], '\\b',\\\n",
    "        \"%.0f\" % (1.E-9*taumig_finalan[h])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exomoon detection by radial velocity or transit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def detect_moon_pt(r = [], R = []):\n",
    "    \n",
    "    '''\n",
    "    m_0 - m_transit = Delta m = -2.5 * log(L_0/L_transit)\n",
    "    \n",
    "    returns m_0 - m_transit\n",
    "    '''\n",
    "    \n",
    "    import numpy as np\n",
    "    \n",
    "    r = np.asarray(r)\n",
    "    R = np.asarray(R)\n",
    "    \n",
    "    return 2.5 * np.log10(1 - r**2/R**2)\n",
    "\n",
    "\n",
    "\n",
    "def detect_moon_rv(a = [], m = [], M = []):\n",
    "    \n",
    "    '''\n",
    "    K = (2 * pi * G / P)**(1/3) * m * sin(i) / (m + M)**(2/3) * 1 / (1 - e**2)**(1/2)\n",
    "    \n",
    "    P = 2 * pi * ( a**3 / ( G * (m+M) ) )**(1/2) ->\n",
    "    \n",
    "    (2* pi * G / P)**(1/3) = (G / a)**(1/2) * (m + M)**(1/6) ->\n",
    "    \n",
    "    K = (G / a)**(1/2) * m * sin(i) / (m+M)**(1/2) * 1 / (1 - e**2)**(1/2)\n",
    "    \n",
    "    returns K/sin(i), i.e., an upper limit for K, assuming zero eccentricity\n",
    "    '''\n",
    "    \n",
    "    a = np.asarray(a)\n",
    "    m = np.asarray(m)\n",
    "    M = np.asarray(M)\n",
    "    \n",
    "    G = 6.674E-11 # N*kg–2*m2. \n",
    "    \n",
    "    return (G / a)**(1./2.) * m / (m+M)**(1./2.)\n",
    "\n",
    "\n",
    "\n",
    "def moon_period(a = [], m = [], M = []):\n",
    "    \n",
    "    '''\n",
    "    K = (2 * pi * G / P)**(1/3) * m * sin(i) / (m + M)**(2/3) * 1 / (1 - e**2)**(1/2)\n",
    "    \n",
    "    P = 2 * pi * ( a**3 / ( G * (m+M) ) )**(1/2) ->\n",
    "    \n",
    "    (2* pi * G / P)**(1/3) = (G / a)**(1/2) * (m + M)**(1/6) ->\n",
    "    \n",
    "    K = (G / a)**(1/2) * m * sin(i) / (m+M)**(1/2) * 1 / (1 - e**2)**(1/2)\n",
    "    \n",
    "    returns K/sin(i), i.e., an upper limit for K, assuming zero eccentricity\n",
    "    '''\n",
    "    \n",
    "    import numpy as np\n",
    "    \n",
    "    a = np.asarray(a)\n",
    "    m = np.asarray(m)\n",
    "    M = np.asarray(M)\n",
    "    \n",
    "    G = 6.674E-11 # N*kg–2*m2. \n",
    "    \n",
    "    return 2 * np.pi * ( a**3 / ( G * (m+M) ) )**(1./2.) * 1./d_to_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "27.3\n"
     ]
    }
   ],
   "source": [
    "print \"%.1f\" % moon_period(dEarthMoon, MMoon, MEarth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Greatest possible changes in magnitude / radial velocity\n",
    "\n",
    "\n",
    "mass_Ganymede = 148.19E21 # kg\n",
    "mass_Titania = 3.53E21 # kg\n",
    "\n",
    "radius_Ganymede = 2634.10E3/REarth # REarth\n",
    "radius_Titania = 788.40E3/REarth # REarth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CD-23 1056 b 0.28 11.53 11.53 0.28\n",
      "Ross 1003 b 0.28 8.34 8.34 0.28\n",
      "IL Aqr b 0.28 12.34 12.34 0.28\n",
      "IL Aqr c 0.28 6.11 6.11 0.28\n"
     ]
    }
   ],
   "source": [
    "for h, hh in enumerate(planet_M_finalan):\n",
    "        \n",
    "    print planet_name_finalan[h],\\\n",
    "    \"%.2f\" % moon_period(at_finalan[h]*dEarthMoon, mass_Ganymede, hh*MEarth),\\\n",
    "    \"%.2f\" % moon_period(acrit_finalan[h]*dEarthMoon, mass_Titania, hh*MEarth),\\\n",
    "    \"%.2f\" % moon_period(acrit_finalan[h]*dEarthMoon, mass_Ganymede, hh*MEarth),\\\n",
    "    \"%.2f\" % moon_period(at_finalan[h]*dEarthMoon, mass_Titania, hh*MEarth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CD-23 1056 b 0.03 4.97\n",
      "Ross 1003 b 0.04 5.55\n",
      "IL Aqr b 0.01 1.40\n",
      "IL Aqr c 0.03 3.02\n"
     ]
    }
   ],
   "source": [
    "for h, hh in enumerate(planet_M_finalan):\n",
    "        \n",
    "    print planet_name_finalan[h],\\\n",
    "    \"%.2f\" % detect_moon_rv(acrit_finalan[h]*dEarthMoon, mass_Titania, hh*MEarth),\\\n",
    "    \"%.2f\" % detect_moon_rv(at_finalan[h]*dEarthMoon, mass_Ganymede, hh*MEarth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Name', 'L_hmr', 'eL_hmr', 'L_lit', 'eL_lit', 'M_hmr', 'eM_hmr', 'M_lit', 'eM_lit', 'Ref', 'Ref_L', 'Ref_M', 'Comments']\n"
     ]
    }
   ],
   "source": [
    "Lcomp = Table.read(path_data + 'hmr18.LM_comparison.v05.csv', format='ascii.csv')\n",
    "\n",
    "print Lcomp.colnames\n",
    "\n",
    "Lours = Lcomp['L_hmr']\n",
    "eLours = Lcomp['eL_hmr']\n",
    "\n",
    "Llit = Lcomp['L_lit']\n",
    "eLlit = Lcomp['eL_lit']\n",
    "\n",
    "\n",
    "Mours = Lcomp['M_hmr']\n",
    "eMours = Lcomp['eM_hmr']\n",
    "\n",
    "Mlit = Lcomp['M_lit']\n",
    "eMlit = Lcomp['eM_lit']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "xeq = np.linspace(1.E0, 3.E3, 10000)\n",
    "yeq = np.linspace(1.E0, 3.E3, 10000)\n",
    "yp20per = yeq*1.2\n",
    "ym20per = yeq*0.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "\n",
    "\n",
    "#sc_l = ax.scatter(Lours, Llit, s = 100, color='black', edgecolor='black', zorder=z_points, marker='o');\n",
    "\n",
    "ax.errorbar(Lours, Llit, xerr=eLours, yerr=eLlit, color = 'black', ecolor='black',\n",
    "            fmt='o', markersize=10, zorder=z_points, elinewidth=1.0, lw=1.0);\n",
    "\n",
    "\n",
    "ax.plot(xeq, yeq, color='grey', lw=1.5, ls='dashed');\n",
    "# \\pm 20%\n",
    "ax.plot(xeq, yp20per, color='darkorchid', lw=1.5, ls='dashed');\n",
    "ax.plot(xeq, ym20per, color='darkorchid', lw=1.5, ls='dashed');\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$L \\,\\, \\rm{[10^{-4} \\, L_{\\odot}] \\ (This \\ work)}$', fontsize=23, labelpad=5);\n",
    "ax.set_ylabel(r'$L \\,\\, \\rm{[10^{-4} \\, L_{\\odot}] \\ (Literature)}$', fontsize=23, labelpad=10);\n",
    "ax.tick_params(axis='both', which='major', labelsize=17, length=14, width=1.75, pad = 7);\n",
    "#ax.tick_params(which='both', width=1.75);\n",
    "#ax.tick_params(which='major', length=12);\n",
    "ax.tick_params(which='minor', length=6, width=1.3);\n",
    "\n",
    "\n",
    "ax.set_xscale('log');\n",
    "ax.set_yscale('log');\n",
    "ax.set_xlim(1.E0, 2.5E3);\n",
    "ax.set_ylim(1.E0, 2.5E3);\n",
    "#ax.set_xticks([0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000])\n",
    "#ax.set_xticklabels([r'$\\rm{0.2}$', r'$\\rm{0.5}$', r'$\\rm{1}$', r'$\\rm{2}$', r'$\\rm{5}$', r'$\\rm{10}$',\\\n",
    "#                    r'$\\rm{20}$', r'$\\rm{50}$', r'$\\rm{100}$', r'$\\rm{200}$', r'$\\rm{500}$',\\\n",
    "#                    r'$\\rm{1e3}$', r'$\\rm{2e3}$', r'$\\rm{5e3}$', r'$\\rm{1e4}$'], fontsize=22)\n",
    "\n",
    "\n",
    "#ax.set_yticklabels([r'$\\rm{0}$', r'$\\rm{5}$', r'$\\rm{10}$', r'$\\rm{15}$',\\\n",
    "#                    r'$\\rm{20}$', r'$\\rm{25}$', r'$\\rm{30}$', r'$\\rm{35}$', r'$\\rm{40}$'], fontsize=22)\n",
    "#ax.set_yscale('log');\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.savefig('Lcomp_log.pdf', bbox_to_inches = 'tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "xeq = np.linspace(0., 0.8, 10000)\n",
    "yeq = np.linspace(0., 0.8, 10000)\n",
    "yp20per = yeq*1.2\n",
    "ym20per = yeq*0.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/hector/anaconda2/lib/python2.7/site-packages/numpy/core/numeric.py:501: UserWarning: Warning: converting a masked element to nan.\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10,7))\n",
    "\n",
    "\n",
    "#sc_l = ax.scatter(Lours, Llit, s = 100, color='black', edgecolor='black', zorder=z_points, marker='o');\n",
    "\n",
    "ax.errorbar(Mours, Mlit, xerr=eMours, yerr=eMlit, color = 'black', ecolor='black',\n",
    "            fmt='o', markersize=10, zorder=z_points, elinewidth=1.0, lw=1.0);\n",
    "\n",
    "\n",
    "ax.plot(xeq, yeq, color='grey', lw=1.5, ls='dashed');\n",
    "# \\pm 20%\n",
    "ax.plot(xeq, yp20per, color='darkorchid', lw=1.5, ls='dashed');\n",
    "ax.plot(xeq, ym20per, color='darkorchid', lw=1.5, ls='dashed');\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$M \\,\\, \\rm{[M_{\\odot}] \\ (This \\ work)}$', fontsize=23, labelpad=5);\n",
    "ax.set_ylabel(r'$M \\,\\, \\rm{[M_{\\odot}] \\ (Literature)}$', fontsize=23, labelpad=10);\n",
    "ax.tick_params(axis='both', which='major', labelsize=17, length=14, width=1.75, pad = 7);\n",
    "#ax.tick_params(which='both', width=1.75);\n",
    "#ax.tick_params(which='major', length=12);\n",
    "ax.tick_params(which='minor', length=6, width=1.3);\n",
    "\n",
    "\n",
    "ax.set_xlim(0.025, 0.8);\n",
    "ax.set_ylim(0.025, 0.8);\n",
    "#ax.set_xticks([0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, 2000, 5000, 10000])\n",
    "#ax.set_xticklabels([r'$\\rm{0.2}$', r'$\\rm{0.5}$', r'$\\rm{1}$', r'$\\rm{2}$', r'$\\rm{5}$', r'$\\rm{10}$',\\\n",
    "#                    r'$\\rm{20}$', r'$\\rm{50}$', r'$\\rm{100}$', r'$\\rm{200}$', r'$\\rm{500}$',\\\n",
    "#                    r'$\\rm{1e3}$', r'$\\rm{2e3}$', r'$\\rm{5e3}$', r'$\\rm{1e4}$'], fontsize=22)\n",
    "\n",
    "\n",
    "#ax.set_yticklabels([r'$\\rm{0}$', r'$\\rm{5}$', r'$\\rm{10}$', r'$\\rm{15}$',\\\n",
    "#                    r'$\\rm{20}$', r'$\\rm{25}$', r'$\\rm{30}$', r'$\\rm{35}$', r'$\\rm{40}$'], fontsize=22)\n",
    "#ax.set_yscale('log');\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.savefig('Mcomp.pdf', bbox_to_inches = 'tight');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "#ID, star, planet, star_M [MSun] ,planet_M [MEarth], planet_R [REarth], planet_a [au], Porb [d], \n",
    "#at, acrit, am, taumig [Gyr], k2, Q, lambda\n",
    "\n",
    "\n",
    "with open('./Output_tables/PHZ_parameters_P0.csv', 'w') as f:\n",
    "    \n",
    "    row = csv.writer(f)\n",
    "    \n",
    "    for p, pp in enumerate(planet_name[wh_habitable]):\n",
    "        row.writerow([ planet_prop[wh_habitable]['ID'][p],\n",
    "                      pp, \n",
    "                      planet_prop[wh_habitable]['Planet'][p],\n",
    "                      \"%.4f\" % star_M[wh_habitable][p] ,\n",
    "                      \"%.4f\" % planet_M[wh_habitable][p], \n",
    "                      \"%.4f\" % planet_R[wh_habitable][p],\n",
    "                      \"%.4e\" % planet_a[wh_habitable][p], \n",
    "                      \"%.4f\" % planet_prop['P_day'][wh_habitable][p],\n",
    "                      \"%.4e\" % at[wh_habitable][p], \n",
    "                      \"%.4e\" % acrit[wh_habitable][p], \n",
    "                      \"%.4e\" % am[wh_habitable][p],\n",
    "                      \"%.4e\" % (1.E-9*taumig[wh_habitable][p]),\n",
    "                      \"%.4f\" % k2_r_sample[wh_habitable][p], \n",
    "                      \"%.4e\" % Q_r_sample[wh_habitable][p],\n",
    "                      \"%.4f\" % lambda_r_sample[wh_habitable][p] ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LHS 1140\tb\n",
      "PM J11293-0127\td\n",
      "PM J11302+0735\tb\n"
     ]
    }
   ],
   "source": [
    "wh_PTRV = np.where(planet_detect == 'PT+RV' )[0]\n",
    "wh_habitable_PTRV = sorted(list(set(wh_habitable).intersection(wh_PTRV)))\n",
    "\n",
    "for h, hh in enumerate(planet_name[wh_habitable_PTRV]):\n",
    "    \n",
    "    print hh + '\\t' +  planet_char[wh_habitable_PTRV][h]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot exomoons with am > at"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "Wh_habitable = list(np.where(am[wh_habitable] - at[wh_habitable] > 0.)[0])\n",
    "\n",
    "\n",
    "Wh_habitable_PT_moon_strip = \\\n",
    "list(np.where(am[wh_habitable_PT_moon_strip] - at[wh_habitable_PT_moon_strip] > 0.)[0])\n",
    "\n",
    "Wh_habitable_RV_moon_strip = \\\n",
    "list(np.where(am[wh_habitable_RV_moon_strip] - at[wh_habitable_RV_moon_strip] > 0.)[0])\n",
    "\n",
    "\n",
    "Wh_habitable_PT_moon_fall = \\\n",
    "list(np.where(am[wh_habitable_PT_moon_fall] - at[wh_habitable_PT_moon_fall] > 0.)[0])\n",
    "\n",
    "Wh_habitable_RV_moon_fall = \\\n",
    "list(np.where(am[wh_habitable_RV_moon_fall] - at[wh_habitable_RV_moon_fall] > 0.)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CD-23 1056 b \t2.72e+00  2.26e-01 3.29e+04 YES\n",
      "LP 834-042 b \t3.64e-01  1.34e-01 1.25e-02 YES\n",
      "BD-06 1339 c \t3.82e-01  1.75e-01 1.39e-02 YES\n",
      "Ross 1003 b \t2.08e+00  2.14e-01 5.90e+03 YES\n",
      "IL Aqr b \t5.36e+00  4.26e-01 7.36e+06 YES\n",
      "IL Aqr c \t2.29e+00  2.90e-01 6.61e+03 YES\n"
     ]
    }
   ],
   "source": [
    "##### Check in which cases am < at\n",
    "\n",
    "for i, el in enumerate(at[wh_habitable]):\n",
    "    \n",
    "    \n",
    "    if np.heaviside(am[wh_habitable][i] - el, 0) == 1.0:\n",
    "    \n",
    "        print planet_name[wh_habitable][i] + ' ' + planet_char[wh_habitable][i],\\\n",
    "        '\\t', \"%.2e\" % am[wh_habitable][i], '' ,\"%.2e\" % el, \"%.2e\" % (1.E-9 * taumig[wh_habitable][i]), 'YES'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LHS 1140 b \t2.35e-03  8.77e-02 3.26e-19 NO\n",
      "GJ 96 b \t3.72e-02  1.26e-01 1.56e-10 NO\n",
      "LP 413-32 B b \t1.65e-03  7.41e-02 1.10e-20 NO\n",
      "LPM 178 c \t1.52e-02  8.83e-02 2.59e-13 NO\n",
      "LP 834-042 d \t5.47e-03  9.17e-02 6.92e-17 NO\n",
      "LP 776-27 c \t1.42e-02  8.66e-02 1.62e-13 NO\n",
      "Kapteyn's star b \t1.38e-03  7.86e-02 1.90e-21 NO\n",
      "Luyten's star b \t1.90e-03  6.64e-02 5.55e-20 NO\n",
      "Innes' star b \t3.94e-02  1.00e-01 3.84e-10 NO\n",
      "PM J11293-0127 d \t1.50e-03  1.04e-01 6.89e-21 NO\n",
      "PM J11302+0735 b \t9.55e-03  9.49e-02 7.10e-15 NO\n",
      "LP 613-39 b \t1.76e-02  8.39e-02 1.06e-12 NO\n",
      "Proxima Centauri b \t6.89e-04  5.05e-02 7.51e-23 NO\n",
      "HD 147379 b \t5.34e-02  1.36e-01 2.63e-09 NO\n",
      "V2306 Oph c \t3.99e-03  7.02e-02 1.35e-17 NO\n",
      "HD 156384 C c \t2.28e-03  7.28e-02 1.31e-19 NO\n",
      "HD 156384 C e \t1.68e-04  6.49e-02 1.97e-28 NO\n",
      "HD 156384 C f \t3.73e-04  6.49e-02 1.35e-25 NO\n",
      "CD-44 11909 b \t8.82e-03  7.64e-02 5.69e-15 NO\n",
      "CD-44 11909 c \t5.36e-03  9.59e-02 5.27e-17 NO\n",
      "V1428 Aql b \t3.67e-03  1.07e-01 1.88e-18 NO\n",
      "Kepler-186 f \t9.48e-06  5.51e-02 6.19e-38 NO\n",
      "HD 204961 c \t3.83e-03  8.18e-02 5.68e-18 NO\n",
      "2MUCD 12171 d \t4.33e-04  3.41e-02 9.46e-24 NO\n",
      "2MUCD 12171 e \t7.18e-04  4.18e-02 2.22e-22 NO\n",
      "2MUCD 12171 f \t8.07e-04  4.86e-02 3.09e-22 NO\n",
      "2MUCD 12171 g \t8.19e-04  5.31e-02 2.28e-22 NO\n"
     ]
    }
   ],
   "source": [
    "##### Check in which cases am > at\n",
    "\n",
    "for i, el in enumerate(at[wh_habitable]):\n",
    "    \n",
    "    \n",
    "    if np.heaviside(am[wh_habitable][i] - el, 0) == 0.0:\n",
    "    \n",
    "        print planet_name[wh_habitable][i] + ' ' + planet_char[wh_habitable][i],\\\n",
    "        '\\t', \"%.2e\" % am[wh_habitable][i], '' ,\"%.2e\" % el, \"%.2e\" % (1.E-9 * taumig[wh_habitable][i]), 'NO'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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r7jbGQzPmQa+hcFURWLEAyufgKVoTkqH2r45k/ZyTgzA3nIf7f4OvK0H1nDvy3xfd3ZUkRie40d39kBPd3SKyF6iGo2d5GPCSqmY9K5UfWUvaGOO5GfNgwMuwejH0exbuaAl79wU6Kt/JnweW3ABjjsFbxyG7xs7qs/DAHvj4+hydoH3FT7dgVQFqAwdF5CkvhO0Vdk3aGOOZ1AT95edQo6rjAY5EnZNb1DcUgDWV4B97YFocPBMFHYpBoZS2T7I6Vsh6/yR8e96xuMbdQdGDGnI8uCZdQkTSN8EnqeqkDM+huhm4T0SqA/8TkWWq6vwczj5iSdoY474rE3SqZ7s4fub0RF0uP3xf5a9k3OcQlMrn+GQ9mghl88OzUTC7LBS269DuSr1P2g0nXO16V9XtIvIZUBqwJG2MCVGZJehUuSVR5xG47yrH449ER3JOVIjKC6XzOlbCMh7xx33SIhKe7lp0OLDNx6d0iiVpY4zrskvQqXJLok5VPK/jYbzKg5Z0lkQkBrgauBdoLCLlgEXAjGAZPGZ/TT6kqmzYsIF69epdNoOXMSHN2QSdKrclauN1vmpJq+pGIHWxgUU+OIXHLEmn8PZkJqpKnz59eOutt+jVqxcTJkywRG1Cn6sJOpUl6hzH35OZ5JS5uF1lSdoHUhP0pEmTUFUmTXIMJrREbUKauwk6lSVq46bcPHe3JekU0dHReGMyk/QJ+vx5x5qx58+fz1WJ+syZMxQoUID8+fNf9twZCxYsYPXq1Tz99NNUqVLFq7EYDxw5Cp2eg+WfuZegUz3bBX7YCl17O5K9CVmZ9TL64vMtNydpm8zEizJK0KlSE3WfPn1wZpa3ZcuW8eCDDxIREZHhl4fFixcjIjzxxBOsW7fOa+8hM4cPH6Znz5507tyZjz/+ONNyn332GVWrVmXt2rWXPXfWAw88wE8//cShQ4c8jtmd85tMlCoJI4fAM/3hkAd3pSxYCl8sh7Evei82k+P5alrQUGAtaS/JKkGncqVF3bx5cwoWLEhkZCSTJ08mJubyW/1Onz4NwIgRI/xybWjs2LHcfffdXH311cTHx2darm3btnzxxRd/e+6svHnzUrp0aY9izSgW4wWDezt+pnZXX+vi72nBUvhnP1g6G+rU8n58JseylrTxiDMJOpWrLeqnnnqKOXPmcOHCX3cD7N69m8qVK3sctyvi4uK46qqraNCgAXfeeWeWZdN/+Qh0136gz5/jDO4NnTs4ErUrLWpL0Ma4xVrSXrBhwwbeeustp5IuOBL1W2+9RYcOHbjllluyLFuhQgVq1apFbGwsHTp0AGDz5s20atXqsnJLly5lx44dFC9enN9++42+ffsSGRmZ6b4vv/ySfv360bNnT0qVKsW2bdsoWLAgQ4YM+VsMS5YsYevWrcyaNYtjx47xyCOPMH78eIoXL84vv/xC/fr1admyZbbve9u2baxbt45ixYqxZs0aHnroIRo3bpxh2S+++IKjR49y/Phxzp8/z4ABAwAyPe+8efP46aefKFeuHFu2bGHcuHHky5cvrb4zZ85QqVIlYmJieP3116lRo0a28ZpMuNqitgRtPJSbR3ejqvZQpW7duuqu5ORk7d27txYqVEhx/D1l+ShUqJD27t1bk5OTs6x3xYoVumfPHp0+fbrec889qqqamJio8+fP10uXLimge/bs0S1btuj999+fdtz69eu1TZs2qqpZ7nv88ce1d+/eqqoaFxenERERmcbSqVMnXbFihaqqnjx5UiMjIzUxMVEvXbqkUVFReurUqQzLpn/+3HPP6Z49e1RVdfv27bpmzZpMzzV9+vS07S5duuicOXMyPe+GDRu0Vq1ampycrMnJyVqvXj09duzYZedftWqVzpo1K8t/b+Oi0W+oVrlF9eChzMvELlEtWV110w/+i8sEFLBRvfz5fDV19VnU5YcvYvH3w1rSXiAiTJgwASDbLu9ChQrRvXt3l0Z5t2nThp49e7J//35+/fVXmjRpctn+2bNnc+ONN6Zt16xZk88//5xTp05luS8sLIybbroJgKJFi3L27Fmn4ilevDhfffUVU6ZMISIigjx58hAXF5fWcs9M69atqVevHrfccgudOnXikUceybRs0aJF057HxMQwb9482rVrl+F5Z8+eze2335727/ndd99dVtfy5cv597//zbfffuvU+zNOyq5F7WYL+mICbNkNf56DwuFQvRwUtXUpcrXc3JK2a9Jekpqou3fvTqFChTIs406CBihYsCDt2rVj6tSpnDhxgqioqMv2nz9/nosXL6ZtJyYmoqokJiZmuQ8gLMz1Sf937txJ9+7dadiwIe3bt097vwkJWf83qlixIjt37qRbt2689dZbTg/qOn/+PElJSZmeNz4+nqSkpEyPr169Ovfccw8jR4508h0ap2V2jdqNBP37ERg8Cco+At3GwegZ0PtdKN8euo6Fzb/66D2YoOenpSqDkiVpL8oqUbuToJOTk3H0HjkGkE2aNIlrrrnmb+Xat29/2W1aGzZsoFmzZpQoUSLLfe5atGgRd9xxBzVq1CAhIYHjx4+jqsyZMyfL49544w3y5ctHy5Yt+eijj9i1a1emZU+ePJn2fP369XTs2DHT85YqVYoVK1Zw6ZLjv+XOnTv5+eef046vXLkyL7/8Mp999hk//PCD2+/bZOLKRO1Ggl74DcR0hwsJsPod+OFj+OpNWD8RfpkOFUrDA4Pg1RnZL91scp7UlrTdgpWLeWta0Iy6vt1J0EuXLmXkyJFERkYydOhQGjVqRL169WjSpAk///wzH3zwAQDDhw+nR48e9OrVi7FjxxIREcGBAweYOXMmAPXr189wX2xsLGvWrOHgwYPUqVOHGTNmADBgwABee+21y+JcuHAha9asIS4uDnB0v7/88sssXLiQc+fOMXDgQMaMGcPAgQOJjY1l7dq1nDt3ju+//z7tefny5SlcuHDaF40DBw7QrVu3DN97iRIlKFq0KDNnzuTQoUPcdttttGnThr1792Z63vLly9O3b19uvvlm8uXLx+OPP54Wy8WLF3n99deJioqiZcuWTJgwgdatW7v0ezXZSO36btDc0V/tQoL+z3fw9HhYNhZiqv19f8niMKQjdG4O9/aDvGHQv4MXYzdu8fe0oDmlZewqUftaCkCBAgU0o/tzbe5uY1wwZRbUqQm1bnKq+IWLUK4dzB8BjWpmX/7AMbi5K3zzLlS1WUUDKrMk/fvvv29SF9dwzk4xidGmuD4j5ALE67H4myXpFDExMeqNaUHTU7VVsIzJyozlMH05/Gec88cMnuToFn/jOd/FZdwn4v3EGCkx2siNJL00ByRpuybtQyLCLbfcYgnamExMXATPZH+L/WWefhCm/cfRCje5Q24eOGbXpI0xAfPjLmha27VjypeGohGw/zhULpN5ud/Owpz9cDhlsr7S4dChLNxQOPNjTHCyW7CMMSYALiRAwQKuH1ewAMRn0pJecwJarIZb/gdHLkClCKgc4Xhe70vHvjUnPIvbGH+xlrQxJmCKFYFjcVDm73cWZkoVjp9yHHulT/bCwC0wOho+awgFr5gG4LWaMHsftFkLY2vCE+U9id74S24e3W1J2hgTMC3qw+z/uXZL1VeboWQxKHP15a8vOgSDt8KqO6BqJjOUFQyDp26AhlFw5yoomh/+ca378Rv/sO5uY4wJgGdawvsLYfdZ+OFP2HUWLiVnfcz7CxzHpR+PmZgMz26GeQ0yT9DpVbsKPm0Az212HGuCmw0cM8YYPzuZACvzwpGWcPNyKF8MziZCfBJ0Kwfdy0OZgpcfM38VrN8OUwdf/vriw1C2EDRyYSK920rA9YVgyWF46DqP347xodzc3W0taWOM3606ATW+gp/PQGxDKB0LLXbCjqbwv4Zw6hLUXglzDjjKq8In/4YeE+CL0VDkiunxP/wNnqnoehzPVISJv3n6boyv2bSgxhjjJ2v/gLYbYG4M3JlyXXnNO/DEaCj3CHR9ALo2hQerw+Nb4D/r4dsFkC8vrHgTbrzh73X+/KdrrehUt5WAIT959HaMH/iyJS0i0cA2Vc18lZ4AsiRtjPGbxGTosBGm3vxXggYoURSWjoVte2HiQmj3kmOpygKlYNZd8PnzcP/Nl1+HTu980t9HcjujYBicT3TnnRh/8tXAMRG5FfgKiAKSUl6rC3RX1ad9cEqXWZI2xvjN4qNwXTi0KJXx/hrl4e1el7/22Cb4NRJaZDFxX9F8cCIBrgl3LZ6TCY4R3ia4+aolrarrReR46raIFAXuANy4e9837Jq0McZvJu6FZzLors7KszfAB3uyLnNPSfh0v+vxfLrfcawJbsn47Zp0W2C+p/F6kyVpY4zf/Pgn3OHiteMGxWBfvGPUd2Z6VIRJv2V/+1Z6l5Idx/RwY8CZ8S8PbsEqISIb0z26Z3YOEWkLxKacLmhYd7cxxm/ik6CQi9eORSA8j+PYzK471ywKVYrA+F9hUAZrUmdk/K+OY6IjXYvHhJQTLqyC9STwOFAIqCYifVV1vO9Cc44l6RRbt27NcH1Ud9eTNsb8XbH8cPSi46ez4pPgXBJclc2n1fRboOFXUCQvPFsp67Lv7YL3d8HaO52Pw1wus/WkfcEf90mragsAESkPvBQMCRqsu9sY40ctSsKsA64dM/cg3HsN5M3m06pMIVjZFN7ZBc2+dkwTmpSu4zJJHa81+9pRZtUdjmNMaEjM4/ojOyISA1wN3Ovr+N0lqkHV/R4wMTExunGj64uKG2Oct+003L0W9t4L+Z34EFWFW7+GF6tmPiL8SheSYN5+eH83/H7+r6Up95yD8oXgmUrwcBkId+OWLZM9EdnkQhezc3XmiVHyu/H5fNH7sfibdXcbY/ymxlVQrxj0+Qneic78vudUE3bDxWS4z4UR2OFhjtWtnijvmBP8SMp60qXCoWKEu5GbgBLAnVvlMlnONJRYkjbG+NW0OnDHGuixBcbdCBEZfApdTILXdsHk32H17RCWTTLPTMUIS8w5ggD5Ah1EYFiSNsb4VWQ+WHkb/PNHKLscHisDba+FYvngbBIsOQIf74NaV8Ha2+HagtnXaXI4d1vSOYAlaWOM312VD2bFwP54mLQXBm+D04mOVnX9Yo4kXs2JJSdNLmEtaWOM8b/rC8Ir1R0PYzKVB2tJG2OMMUHJWtLGGGNMkLIkbYwxxgSpXDxwzGYcM8YYY4KUtaSNMcYEN+vuNsYYY4JULu7utiRtjDEmuFlL2hhjjAlS1pI2xhhjgpS1pI0xxpggZUnaGJMrfbsZIotA9cqBjsSYzNm0oMaYXGf51/BoT8ibF/4zDWrVCHRExmTMWtLGmFxl+dfwWC9Y8BEcPgbNnrBEbYKXDRwzxuQaqQk6dhI0qvfX65aoTbCylrQxJlfILEE/3MLx0xK1MUHFkrQxuUVmCTqVJWoTrKy7O2cQkYLA88D3QAlVnR7gkIwJDtkl6FSWqE0wsu7uHON5YJWqrhGRT0RksarGBTooYwLK2QSdyhK1CTaWpIOXiIQD7VT1k3Sv3Q/EAMeACsAgVU0G6gGTU4odAWoBK/0asDHBxNUEncoStQkmPuzuFpFoYJuqJvnmDJ4J6vWkReQG4G1g/BWvvQ+MVtWJQDjQPWV3PkBTniuOX60xudM3G9xL0KkebgHvvOxI1L/+5v34jHFWakva1Ud21YrcCnwL5BORoiLyloh8KSIDfPAu3BLULWlV3SMis4DW6V7uBGxQ1cSU7S+BUcBEYCOOlvVR4DrgB2fPtXXrVsqXL+90bHv37nW6rDEBkUdABJKT3a8jKcnxAZknqL/PGx9y9nMxMTGR8+fP+yYIH7WkVXW9iBxP2ayA45IpwHJgrPfP6LpQ/J9XCziQbns/UENE8gFvAveISDNgpV2PNrlawxiY/Ta07QFfr3f9+DmL4PkR8N+ZUKm818MzOUNycjJxcXEcPHiQU6dO+eYk7rekS4jIxnSP7n+v3EFVN6dcNm0IfOSbN+K6oG5JZyICOJtu+wyOLxtRqnoEGOFOpdHR0WzcuNEL4RkTRO5q9Fei/uwDaHyrc8elT9A3VfVtjCaoZdZrqKq8/fbbjBgxgjNnztCpUydGjhzJ9ddf7/0g3J+7+4SqxjhbWEQqAE8C9UUt39rlAAAgAElEQVRkoapecOusXhSKLek/gMLptgvjuP78R2DCMSbIpU/UzrSoLUEbJ4gIa9asoU6dOmzevJmpU6dSpkwZH50Mn1yTvpKq/qaqXYD1QLQXIvdYKLakNwN10m2XAbaraoInlWZ2TdquPZscwdkWtSVok4W1a9cycOBAPvzwQ+6//35UFRGhZcuWvj2x/yczOQUExWjJUGxJzwFuFZHULxh3A1MDF44xISK7FrUlaJOJXbt20bZtW2677TZ2797NwYMHAUdr2i98N7o7BrgauFdEXhaRySLSAliqqie9/0ZcF9QtaRG5DmgLFBORVsAyVf1dRPoAL4nIvpSib3p6LrsmbXKFzFrUlqBNJgYOHMiECRMoUKAAI0aMoE+fPhQuXDjTXka/JW4vUNWN/HX5dFEgY8lMUCdpVT0IPJfySP/658DnAQnKmFB3ZaI+dNQStLlMQkIC+fM7+pfDwsLo0qULL730EqVKlQpMQDbjmDEmV0lN1K2fhnx5LUEbwHE71axZsxgyZAgfffQRzZo1Y9SoUYFvHdsCG8YGjplc565GsOwTuCoCqlYMdDQmwL766iv69+/P5s2bqVOnDpGRkUDm3deuTP7kMWtJG2NypXq1Ah2BCQJPPfUUU6ZMoWzZssyYMYMOHTqQJ5hmmbOWtLGBY8aY3OTo0aNERUWRN29eGjduTLVq1ejZsyfh4eFOHe/XgWMh2pIWkeaquiyL/Q+o6uKs6rAkbYwxuci5c+cYP348Y8eOZfz48Tz99NN07tw50GFlzf0ZxwJthIjcksk+AdqJyP9UNT6zCrJN0iLyKlDSzQBTAzmkqkM9qMMYY4wHkpKSmDp1Ki+88AKHDx+mTZs23HnnnYEOyzkh2pIGkvlrZcYrKTCbbFZrdKYlXVtVm7sY2GVE5AtPjvcHGzhmjMnJHn30UebNm0eDBg347LPPaNiwoUf12cAxp7yIY1XGx4HzwDRV3elKBc6MDFjpelx/87UX6jDGGOOCH374gT///BOAHj168Omnn7JmzRqPE7TfpQ4cc/UReInAFKAUcC0wU0QauVJBti1pVX3Nvdguq+N1T+vwNRs4ZozJKfbv38+wYcOYPn06w4YNY8SIETRt2tSr57CBY05poKq1078gIkOAb5ytwKMx9iKS6f0bWe0zxhjjfadPn2bIkCFUqVKFuXPn0r9/f/r06RPosHKzIxm8ti+D1zLl6ejuniLySSb7OgFdPKzfGGOMk3r06MGsWbN47LHHGDVqFOXKlQt0SN4RuvdJlxGRPKqanO61Cq5U4GmSvh+onvL8yj6O8h7WbYwxJguqysKFC6lZsyYVKlTgxRdf5PnnnycmJibQoXlX6HZ3rwS2ichPwCWgKtDTlQo8TdK3AjVwDDNfo6rnUneIyP95WLcxxphMrF+/nv79+7N69Wqef/55JkyYQJUqVQIdlm+EaEtaVVekrOD4OJAADFVVl9ap9ihJq+o+YJ+I5AFuE5EI4Iiqfq+q73hSt7/ZLVjGmFCwZ88eBg8ezNy5c7nmmmuYOHEiXbr4/8qi3YKVMREpDAwBtqjqXFXdLiIvAzcCca7W55UZx1L621enBHitiLwHbFfVd71RvzHGGIcJEyawaNEiXnjhBfr370+RIkUCHZLvhVCSBv4JLAFuFZHFwO/AXUAEkF9EuqnqQmcrE9XMJkNxjYhUxjFQ7BFgHTBRVVd7pXI/iImJUbsFyxgTbC5evMh7771H/fr1adiwISdPnuTChQtcd911gQ4tQyKySVW9elFcYmKU9W58Puf1fizZSUnCH4njXrSfgPeAeap6IuW1wao62tn6PL0FK1xEnhCRr4G5wEGgjqo+Bmz3pG5jjMnNVJW5c+dSvXp1+vbtS2xsLABRUVFBm6B9KizZ9UdgnANQRwv4Io7pP/+84jWnedrdvR34N9BXVTdcsa8/MNDD+o0xJtdZs2YNffr04bvvvqNmzZosX76ce+65J9BhBZDiGHcVEgoDiEgUjilB/wNsFJGzQBSwypXKPE3SW4BvgRoiUj3d64Jj5LcxxhgXrVu3joMHDzJlyhQ6duxIWFhYoEMKMMVxB1NIiBCR24BmwNeq+puI3Ak0BXYAdVypzKNr0iLSSFUznN5MRBqrasjM2W3XpI0xgXL8+HFefvllbrvtNjp06MDFixdJSkqiUKFCgQ7NZb65Jl1b2fiVGwdGBeKadCFgKI6R3G+qamK6ffmAyara0dn6PL0FKy1Bi0hH4BtV3ZOyL2QSNNgtWMYY/4uPj+fNN9/k1Vdf5fz581xzzTUAFChQIMCRZc+vt2CFEFU9jyNJZ7TvEuB0ggY3k7SI9MLR97BaVbemvLwUaC4i7VR1jDv1GmNMbrFw4UKee+45Dhw4wEMPPcSYMWOoVq1aoMMKUr67Ji0i0cA2VU3yyQk85G5LugQwCFAROYNjRY+vgZ8Bj9aeDhRbBcsY4w/JycnkyZOHxMRESpcuzcyZM2ncuHGgw3KZX1fB8tE1aRG5FfgKiEqZhORDHOOpvgaeVG/do/zX+dqq6meuHOPuLVj5cEwSXhRoB3yPIznPAb50s05jjMmxfvrpJ5o3b86oUaMAaN26Nd9++21IJmj/S21Ju/rIplbV9cDxlM17gadwrEdRF7jFm+8gxW4Rcamn2d0kfVpV96vqeVX9UlVfUtW7gaeBk27WaYwxOc6hQ4fo2rUrtWrV4ttvv6V48eKAo8WZJ49HU1XkIqktaVcflBCRjeke3bM4ySJVjVfVi8A2vJDLRCRWRIaKSA0AVf0ex8JUTnO3u7uciNyvqkvTv6iqc0VkOLDIzXqNMSbHmD59Ov/85z+5dOkSvXr1YujQoURFRQU6rBDkdnf3CWdHd6tqAjgm6QIOqOoud054hf7A7cAzIhIJ7MZxr7TT3E3SLwKrUla6mgusUtU9KUHkwqlwjDHGITExkfPnz3PVVVdRvXp1HnjgAUaPHk3FihUDHVoI8+tkJu1w5DiPpST6XcAUgJTFqB51pQ63+lpU9QjQEDiE40L7LhGJBw7jGERmjDG5iqqyZMkSatWqxfPPPw9ATEwMc+fOtQTtMbe7u10iIvcDS1X1rIiU80ro6aQsRuXSKPJsk7SI1MzkZCdVtQtQCvgH8BhQSVWnZ1BHtCtBGWNMKNm8eTN33XUXDzzwAJcuXeLBBx8MdEg5jG+StIjEAFcD94pIexyNzhUish1o4fW34RDvSmFnurvHkMWFblWNw7EsV1ZG4UjkQcsmMzHGuONf//oX3bp1o0SJErzzzjs8/fTT5MsXOusqusu/k5n4prtbVTeSMtd2ijneqFdEHlPVmem2n1LVySmbTVypy5kkXVJEJuOYj9ude8YEKOnGccYYE5T+/PNP4uLiKF++PPfddx+DBw9m4MCBREZGBjq0HCqk5u4GeFVEuuIIvCSOAWOTAVT1jCsVZZukVbWuOxGGGpvMxBiTnYSEBCZOnMiIESOoVasW//vf/yhTpgyjRzu9PHCO4d/JTJIJoVWwANqq6nepGyLygLsVeboKljHG5Hiqyueff86gQYPYtWsXd955J+PGjQt0WCZ4dRWRginP8+Po4l7sTkWWpI0xJhv/+te/6N69OzfeeCNLliyhefPmPmoxmoyFXHd3ZRxLUyqOwdVuz8RpSdoYYzKwe/dujh07RoMGDXj00UfJmzcvHTt2JG9e+9j0v5BL0gNUdUPqhoi4Pdzf/tqMMSadkydP8sorr/D+++9z0003sWnTJgoXLsyTTz4Z6NByMb9OZuINr4vIipTn+YFiwBfuVGRJ2hhjgAsXLvDOO+8watQozpw5Q5cuXXj55ZetWzsohFxL+hcgNUlfBLa4W5HXkrSIhAGFVPWMiNwNqKr+z1v1G2OML8XGxjJgwADuv/9+xo4dy4033hjokEyakEvS81X169QNEakiIonAHqCGqv7sbEXebElPwnFPdUEczfq8gCVpY0zQWrlyJUePHqVdu3a0a9eO66+/nkaNGgU6LPM3IdfdPV1EtqXbLgb0Ac4CQ3Fh/m5vJunPVXWJiBTAMbvYRS/WbYwxXrN9+3YGDhzIF198Qa1atXj44YfJkyePJeigFRotaRFpBtQC2uBIzHtxrIL1P1X9JaWY7xfYyEReESmmqhdV9VNVteUqjTFB5ejRo/To0YPo6GhWrVrFq6++yrp162xd56CX2pJ29eF3xYH3gAnASqA+jkTdwd0KvdmSvhd4V0SWAv/F8c0hzov1+5TN3W1Mzrdjxw7+9a9/0aNHD4YPH87VV18d6JBClv/n7g7+ljRwGscCGvtTxmf9AXwNlHa3Qm8m6ZU4+twbAnfjWBWrlRfrN8YYlyQlJTFt2jQOHDjACy+8QJMmTfj999+59tprAx2acUnIJOkIoBKO0d0A3wEfAT+6W6E3k3S8ql7EMex8RXaFg43N3W1MzrJ8+XL69evH1q1buf322xkyZAhhYWGWoL3Ev3N3h4zdOBqorwOo6n6gg4j0d7dCb16IqSMiM0XkfhEp5MV6jTHGaTt37qRZs2Y0a9aMc+fOMW/ePFatWkVYWFigQzNuS11gI7ivSavqRlV9kStyq6q+7m6d3kzSccBM4B7gGxGxgWPGGL9RdaykKyL8+OOPTJgwgW3btvHwww/n9tZdDpDa3e3qw79EpK6INAG8lv+82d29FohS1ecBRMQWVjXG+NyZM2d47bXX2LlzJ3PnzqVSpUrs27eP/PnzBzo04zWhcU1aVTelPL3NW3V6rSWtqptUdXm67T+9Vbcxxlzp0qVLfPDBB1SqVIlRo0YRFhZGQoKji9MSdE4TMrdgeZ3N3W2MCTlbt27l4Ycf5pdffqFx48YsXryYevXqBTos4zOh0ZL2BbuD3xgTMuLj4wG4/vrrKVGiBAsXLmTlypWWoHO80GpJp1ybDhOR60WksSd1+aQlLY5RGnfjuKl7Q8qtWcYY45a9e/cyZMgQtm3bxqZNmyhatCjffPNNoMMyfhNyLekGwGAc3xQO4JjQxC2+aklXwDEt2jrgbrslyxjjjri4OPr370/VqlVZsGABDzzwAJcuhdSHtfGK0BjdnUpV31XVtkAPHIOq3eaTlrSq7gaiUzaX+OIcxpicbevWrTRt2pS4uDg6d+7MiBEjKFOmTKDDMgHhu1WwRCQa2KaqSRltu1nnAByN1LXAMU/i81pLWkQeTPl5lYg8LiLtvFW3MSZ3UFX27NkDQLVq1WjdujXff/89kydPtgSdq/mmJS0itwLfAvky2vbAIuBWYDEurnp1JY9b0iJSNuVpNRFJnZ90PdDR07qNMbnHmjVr6NevH3v27GHnzp0UKVKEjz76KNBhmaDgm2vSqrpeRI5ntu1BvTuAHcA4EbnHk7q80d1dG/g/4HqgOSA4+iUme6FuY0wO9+uvvzJo0CBiY2O59tprGT16NIUK2TAW4xUlRCT9ogyTVHWSr08qIi8CUTha1MU8qcvjJK2qi0RkFdBAVf/taX3GmNxj+/bt1KxZk/DwcEaMGEGfPn0oXLhwoMMyQSd17m6XnVDVGC8H44yfgY1AYxxTZrvNKwPHUmYXC+kEbetJG+Mf8fHxfPfddzRp0oRq1arx+uuv06FDB0qWLBno0IwLbD3pzKnqZyJSTFWneVqXRwPHRKRoys9wESl7xWOEp8EZY3KO5ORkpk+fTtWqVWnWrBnHjx9HROjdu7claJON0JrMBEBVPWpBp/K0Jf2TiDQEbgTeAfbhuCYNjnulh3tYv9/YetLG+M5XX31Fv379+P7776lbty7Tpk3j6quvDnRYxgP+XU/aNy1pEYkBrgbuBRZdue31E7rB0yRdSVUviEg+4CngW1VNABCRZh5HZ4wJeXv37uWee+6hTJkyzJw5k/bt25Mnj81IbFzhs9HdG4HCmW0HA4+StKpeSPm5W0RGA9uAEym7t3oYmzEmRB0+fJjFixfTrVs3ypcvz5IlS2jatCnh4eGBDs2EJN9NZuJNInIf4Oq1m6NZDbr25oxjC4A6IvIrjqF4zwCDvFi/MSbInT17lvHjx/P6669z6dIlmjdvTpkyZbjvvvsCHZoJaSEzcOwe4G0cATurN1kMvPZmkn4d+JXLr0lbkjYmF0hMTGTKlCkMHz6cI0eO0LZtW1599VWbJcx4Scgk6UWq+rsrB4jIwqz2ezNJd1fVpelObNekjckl4uLi6Nu3L9HR0Xz++ec0aNAg0CGZHCU0urtVdZWIPAtEqurojMqIyJOqOiX9MVnV6bXRG+kTdMr2f7xVtzEm+Hz//ff07t0bVeXqq69m48aNfPPNN5agjQ+E1CpYRYHNV74oIoVFpCswypXKvLnARh8ReSrleU0RaeKtuo0xwWP//v106tSJunXrMmPGDH777TcAqlSp4qPbb4wJKb8DO1M3RKS2iLyf8nozHJeFnebN+yCOAl8CqOoWHN8mjDE5xLlz5xgyZAhVqlRh7ty5DBgwgF27dlGxYsVAh2ZyvNCZzERVZwAVRaSniKwDPsMxh0gNVX0YeNiV+rx5TTqfqu5Lt32dF+s2xgRYWFgYc+bMoW3btowcOZJy5coFOiSTa4TMwDEAVHU5sFxEvgDuw3HHU+rylwVcqcubSbqYiEzGMbF4TWC7F+s2xviZqrJgwQLef/99Fi1aRMGCBfnxxx8pUqRIoEMzuYzgXrIKdFpX1T3AByISBjwgIu2Ap4Gqztbhze7uE8AuoCLwlaqO8WLdxhg/Wr9+PY0bN6Z169YcPHiQAwcOAFiCNgEhQH43HsFCVZNUdaGqTgB+dOVYt5K0iPQSkWdEJDrdy0tx9LvvU9VP3KnXGBNYZ8+epV27dtSvX5+dO3cyceJEtmzZQuXKlQMdmsnFBEdfsauPINXJlcLudneXwDFRiYrIGeAb4GscXd3N3azTGBMgiYmJ5M2bl8KFC/PHH38wfPhw+vXrZy1nExRSW9KhRkSaq+qyK16+C1jsbB3uJul8OGYUOwk0BBrhSM4vAM+7Wacxxs8uXrzIu+++y1tvvcWGDRsoWbIky5cvt1upTFBJbUmHoBEicku67TCgJX5I0qdVdX/K8y9THqRcFI93s05jjJ+oKnPnzmXw4MHs3buX++67j/h4x39dS9Am2IRwks7LX/N4Fwbq4kKCTq3AHeVE5P4MZhmbKyLDCZJ1OI0xf3fhwgWaNm3K+vXrqVWrFv/973+5++67Ax2WMZkK1e5u4ENVnZj+BRHp5UoF7o7ufhF4Q0SWiUhnEbkh5eSR2P3RxgSlY8eOARAeHs5tt93G1KlT2bRpkyVoE/RCdeBYBgm6HdDVlTrcStKqegTHtehDwIfALhGJBw7jGERmjAkSx44d49lnn+X6669ny5YtAIwfP55OnToRFhYW4OiMyV6o3IKVOjV2ZlR1LpD+GnW2x7g9mYmqngS6iEg/oAEQDnyrqofcrdMY4z3nz5/njTfe4LXXXuP8+fM8/fTTlC5dOtBhGZOTNRSRpOwKpRv3oTgavJMzK+vxjGOqGofjHmljTJC4dOkStWvXZufOnbRs2ZIxY8ZQtarTkxwZE1RCaODYEBwNVlf8O6ud3pwW1BgTYN999x316tUjX7589O/fn2rVqnH77bcHOixjPBIqSVpVj3m7Tm9OCxo0RKSOiDwd6DiM8ZetW7fSvHlzbr31Vv7zH8dS7t26dbMEbXKEPITGNWlfyHFJWv7q7LeZz0yOd+jQIbp06ULt2rVZv34948eP54477gh0WMZ4VaiO7vaGoO3uFpFwoF36ecBF5H4gBjiGY8azQaqanP44VVUR+cOvwRoTAMnJyTRu3Jj9+/fTu3dvhg4dSvHixQMdljFe58v7pFPWoNimqtkO+AqEoEzSKfddDwZaA5+ke+19oJKqJorI20B3YGKmFRmTwyQmJjJ79mzat29Pvnz5+PDDD7nhhhuoUKFCoEMzxmd8dU1aRG4FvgKiUnphXwQ2A9WBMVc2AgMhKJO0qu4RkVk4knSqTsAGVU1M2f4SGAVMFJEOOKZbW6eq890559atWylfvrzT5ffu3evOaYxxi6qyZMkSBgwYwPbt2ylQoACPPPIId911V6BDMzmcK5+LvuKrJK2q60XkeMpmN+CgqsaKSCngYWCuD07rklC6Jl0LOJBuez9QQ0TyqepsVe2XLkE3AK4XkZJ+j9IYL9u0aRN33nknDz74IElJScTGxvLwww8HOixj/MaDyUxKiMjGdI/uWZymPvBDyvMfgBZefyNuCMqWdCYigLPpts/g+JIRBRxJX1BVZwOzXak8OjqajRs3ehqjMV6lqnTr1o39+/fz7rvv0r17d/LlyylDYkwocLXX0BcLtHjQkj6hqjFOli2FI6+Q8jMoGnmhlKT/wLGKSKrCOGZrsUFiJkc5deoU48ePp0+fPhQrVozZs2dTqlQpIiMjAx2aMQHhpwU2TuJoDJLy84TvT5m9UOru3szli3eUAbarakKA4jHGqxISEnj77bepVKkSo0aN4t//dkxEVLVqVUvQxvjechyXVQFqpmwHXCi1pOcAPUQkb8rgsbuBqd6qPLOBYzZAzPjD/PnzGTRoELt27eLuu+/m9ddfp3bt2oEOy5hM+XNAmQ9Hd8cAVwP3AtOAESLyCFAWx0jvgAvKJC0i1wFtgWIi0gpYpqq/i0gf4CUR2ZdS9M2ABWmMF02bNo3w8HCWLVtGs2bNfHJdz5hQlTrjmLep6kYuv4w6LOXnPB+czi2iqoGOISjExMSoDRwz/rJr1y6GDRvGK6+8QuXKlfnjjz+IjIy0pSNNyBORTS4M1nJK6RjRTm58PL8meD0Wfwula9LGhLwTJ07Qq1cvatSoweLFi/nxxx8BKF68uCVoYzKRm6cFtSRtjJ+8+eabVKpUiXfffZcnn3ySnTt30rZt20CHZUzQ8+A+6ZAXlNekA8EGjhlfUNW068t79+6lUaNGvPbaa9x4440BjswYz+SEgWOhwFrSxvjIihUrqFevHitXrgRg3LhxLF682BK0MS6ylrSxGceM12zbto2BAweyePFiypYtS3x8PAB589p/N5NzZNbLGGQzjoU8a0kb40WDBw8mOjqar7/+mjFjxrBjxw6aN7elzY3xRG4eOGZf7Y3x0Llz5wgPDycsLIwyZcrw7LPPMnz4cEqUKBHo0IzJEfw0LWhQsiSdwgaOGVclJSUxdepUXnjhBUaPHk3nzp159tlnAx2WMX4RDEtY5gbW3W2Mi1SVf//739x888107dqVcuXKUa1atUCHZUyOZd3dxgaOGac988wzTJw4kQoVKjBv3jzatm1r03iaXMefA8d8NS1oKLAkbYwTDhw4QNGiRYmIiOAf//gH1apVo0ePHuTPn1s/OozxHxvdbYzJ0OnTpxk6dCiVK1dm3LhxADRv3pxevXpZgjbGT6y72xhzmUuXLvHRRx/x0ksvcfz4cR599FE6d+4c6LCMyZVsdLex0d3mMj169ODjjz+mSZMmjBs3jpiYkF5Ixxivs2lB/cOStDEpvvvuO6699lrKlClDz549eeihh3jggQdsUJgxAWYtaWOju3OxPXv2MGTIEObMmUOPHj14//33qVmzJjVr1gx0aMYELZsW1D8sSZtcKy4ujlGjRvHOO+8QFhbGsGHDGDBgQKDDMsZcwZK0MbnQ8OHDee+99+jcuTOvvPIK1113XaBDMsZkwLq7jckFVJV58+ZRuXJl6tSpw9ChQ+nWrZt1axsT5HJzS9rukza5wjfffEODBg1o3749H3zwAQClSpWyBG2MCWqWpE2O9uuvv9K6dWtuv/129u/fz5QpU5g4cWKgwzLGuCC1u9vVR05g3d0p7D7pnOnTTz/lv//9LyNHjuT555+nUKFCgQ7JmBzB7pP2D0vSJkeJj4/nzTffpHr16rRs2ZLnn3+erl27UrJkyUCHZoxxkyVpY/dJh7jk5GRmzJjBsGHD2L9/P8899xwtW7akUKFC1no2xgdCfRUsEYkCugF7gdKq+oaXT+EVdk3ahLzVq1dTt25dOnXqRMmSJVm5ciXvvPNOoMMyxniJjxbYGASsU9U5QFURqeWD0D1mLWkT8vbv309cXByzZs2iXbt25Mlj3z2NyUk8uE+6hIik7yKdpKqTUp7fBMxMef4r0Bj40c0QfcaStAk5hw8fZvjw4VSrVo2+ffvSvn17WrduTXh4eKBDM8b4gAfXpE+oamar42wDmgA/4MiFQZkPrclhQsbZs2d56aWXqFSpEp988gmnT58GIE+ePJagjcnJFCTR9Uc2XgEqiEhf4E7gZ1+/DXcE5TcHY670xRdf0L17d44cOcIjjzzC6NGjqVixYqDDMsb4gwIJXq5S9RTQS0SKAw8Dy717Bu+wJG2ClqqSkJBAgQIFiIqKomLFisTGxlK/fv1Ah2aM8ScFLnm/WhEpAYwDuqmqD87gOUvSKWwyk+CyefNm+vfvT9WqVXn//fdp2LAhq1evtrWdjQkS/pzMxBdE5HqgDvCMqp4PdDyZsWvSJqjs27ePjh07UrduXX788Ueio6PT9lmCNiaXSu3udvWRVZWq+1V1YTAnaLCWdBqbzCTw5s6dS6dOnQAYOHAggwcPJjIyMsBRGWMy4s/JTHzV3R0KrCVtAiohIYFjx44BcMstt9C+fXt+/fVXxowZYwnauG3ZsmU8+OCDREREZPjle/HixYgITzzxBOvWrfNrbEePHqVNmzZZllm1ahWDBw/m448/5v/+7/+4ePHiZfuD+f35RGqSdvWRA1hL2gSEqhIbG8vAgQOpVKkSy5Yt44YbbmDq1KmBDs3kAM2bN6dgwYJERkYyefJkYmIuv1U29fa9ESNG+PXa6kcffcRPP/3Epk2bMi0THx9Pt27d2LJlC+Hh4bz22mu888479OvXL61MsL4/n/HB6O5QYS1p43fffvstt99+O23atCF//vw899xzgQ7J5FBPPfUUc+bM4cKFC2mv7d69m8qVKwcknm7dunzJjnIAABSfSURBVPH8889nWWblypWULVs27d7/hg0bEhsbm2HZYHt/PmMtaWP8Y9asWTz22GOUKlWKSZMm8eSTT5I3r/0ZGt+oUKECtWrVIjY2lg4dOgCOOwdatWrldp2HDh3i7bffzrJM586dqVatmlv179u3j6JFi6ZtFy1alB07dmRY1hfvLyglk2tb0vbpaHzu5MmTHDp0iOjoaB544AFGjRpFz549iYiICHRoJhfo0qULU6ZMoUOHDiQlJREWFuZRfddeey1jxozxUnR/d/Lkyctm0MufPz9nzpzJtLy3319QsoFjxnjfhQsXGDduHBUrVuSxxx5DVbnqqqsYMmSIJWjjN23atGHjxo3s37+flStX0qRJk0CHlKXIyEhUNW07Pj6eEiVKZFremfe3evVq6tWrx/z589NeO3HiBBUqVODDDz/07hvwBR/cghUqrCVtvC45OZk5c+YwZMgQfv/9d5o3b87YsWPtPmcTEAULFqRdu3ZMnTqVKlWqEBUVRWJi9hM7Z8aZ7u5OnTpRvXp1t+qvUqUKCxYsSNs+ceIEZcuWzbS8M+/v9ttvp3///kyfPj1tZPnOnTspW7Ysjz32mFtx+lUubklbkjZeN3/+fB577DFq167Nxx9/zF133RXokEwulJycnNYifeqpp2jdujXTpk3LsOyKFStYsGAB//jHPzh8+DD79++nadOmzJ8/n3Hjxl1W1lfd3cuXL+eGG26gcePGdO3alTNnzlCkSBFWrFhB69atPXp/AMWLFycyMpLff/+dcuXKeT1+n8rFSdq6u1OkTgt65cM4Z8eOHSxbtgyAVq1a8emnn7Jp0yZL0CYgli5dyrBhw3jmmWf45ptvqFevHvXq1aNJkyb8/PPP9O7dG4Dhw4ezbt06/r+9u4+uqjrzOP59gryF4cUOAwRaeW/Dm0EIS1gOGIaghEUXi5dpcbDIIFUZi1UYEUEpk1GEophKodSiKNaiXQytr7AoUjTYglgUBCRCRJkAYRYgjQpIIM/8cW80Cgl5uTf33NzfZ60s7jk5Z+/nZO3kYe+zzz6dO3fm6NGjZGRkkJKSQvPmzRkwYABHjhyJaFy//e1vmT17NoWFhUyfPp3c3Nwvv/fLX/6S119/nYYNG7J48WLmzp3L8uXLOXHixJfxVvf6St1888088cQTbN++nbS0tBpdy8X+Xkbtb2YCD3db2Xsfiaxhw4aekpJywX6t3V2xo0ePMnfuXH7zm9/QoUMH8vLy6ubEFanTioqKmDFjBsuWLeO+++5j0qRJNG3alAceeIBp06bFX8/zIjZs2EBmZiZDhw5l9uzZZGRkkJGRwcsvv1ytOSLlJeSPP/74bxW8w7la0ruav51T9fNsBBGPpbZpuDtMy4JWzalTp3j00UeZP38+Z86cYcqUKcyZM0cJWuLS1q1bGTp0KBCaXd2pUyf27NlD69atv1wYJJ5t3LiRZcuW0a5dO0aMGEGLFi3YvHkzBw8e5Nlnn+XWW2+tcplaFrR2qCcdlp6e7krSlffaa6+RmZnJqFGjmD9/Pt/97ndjHZKIBICZRb4n3dn87YeqEcsP1ZOWBLJ+/Xry8vKYOnUqQ4YMYceOHVx55ZWxDktE6roE7klr4phc0s6dO7n++uu5/vrrWbp0KcXFod8WJWgRqRUJvCyokrSU68iRI0yaNInevXuzbds2Fi1axLvvvkv9+vVjHZqIJJLSZUETcHa3hrulXCdPnuT5559n2rRpzJ49m8svvzzWIYlIIkrg4W4lafnSuXPnWL58OTt37mTp0qV069aNgoICJWcRiS29qlISmbvz4osv0qtXL6ZMmcLu3bs5ffo0gBK0iMSe7klLosrPz2fw4MGMHDkSd+ePf/wjmzZtonHjxrEOTUQkJIGTtIa7E1RJSQlJSUk0b96cw4cPs3TpUiZPnqxJYSISPAk83K0knWBOnjzJvHnz+Mtf/sIbb7xBy5Yt2bt3L0lJGlQRkcRiZinAj4D9wEDgHncP1H8H9Jc5QZw9e5acnBw6d+7Mww8/TJcuXTh16hSAErSIBFv0hrt/COS5+5pwLb0iHHmNqSedAD744AOGDx9Ofn4+mZmZLFy4kN69e8c6LBGRyonecPcm4AkzO0kore+ISi01oC5UHfbJJ58A0L59e3r06MHatWtZv369ErSIxJfq96RbmtnbZb5u+Vqx7u8CLwGrgL3ufq5WrqcK1JOug/bt28fMmTN56623yMvLIzk5mRdeeCHWYYnUmrVr17J06VI2bNjArFmzuOyyyzhx4gSFhYVkZ2fTsWPHOll3nVX9xUyOVfSCDTMbABQBVwHrzWy7uweqN60kHfbee+9d9P2o8fQ+6WPHjpGdnc2vfvUrGjZsyD333BOd18aJBFxWVhaNGzfmnXfe4f777/9y/y9+8Quuu+468vLyojYXI5Z116by3icdFdEb7r4a2OfuR81sBdCJgA15K0nXEfn5+fTp04fPPvuMH//4x8ydO5c2bdrEOiyRQElNTWX//v2cOHGCli1bJkzdcS96y4KuAmaa2WVAC+DXUamlBpSkw3r16kW8vU+6pKSE3bt306tXLzp16sTtt9/OjTfeSPfu3WMdmkggvfrqq4wdO7ZSSfLw4cM89thjFR4zceJEUlNTI153PChvlDEqo3elL9iIMHc/CtwV3vxD5GuoOSXpOLVx40buvvtu9u7dS35+Pm3atGHevHmxDkskUD799FOWLVsGQFFREX369CEnJ6dS57Zt25b58+fHpO7Nmzfj7gwcOLDa9dcpesGGxIs9e/YwY8YMXnnlFa644goef/xxWrVqFeuwRAKpfv363HbbbRf9XlFRETk5OVx11VUcP36ciRMn1lrdl5KWlsbUqVOVpEspSUs8OHToEGlpaTRp0oQFCxZwxx130KhRo1iHJRKXnnrqKfr160dWVhbf//73GT9+/NeWxa3McPdNN91Et27dIh5b06ZNI15mXNOyoBJUn3/+OevXr2fUqFG0a9eOFStWMGzYsDpzX0skVvbt28e1114LQLNmzSgoKPja41E1He6uyMGDB9mwYQPt27fn0KFDTJgwgVdffZUlS5YwcOBAMjMzOXDgAH/+85/Zs2cPGRkZ9OjRIyqxxIUE7knH/3MAddT58+dZvnw5Xbt2ZcyYMRw4cACAG2+8UQla5BLWrl3LokWLOHnyJNOnT2f//v0XHFNSUkK9evWA0O9bpB6Lqkzdc+bMYcSIEQwZMoRdu3axY8cOhg8fTsOGDZk5cybp6el07NiRwYMHM2HCBGbPnh2R2CT+qCcdMO7OunXrmDFjBrt27WLAgAGsXr1aCyCIVEFWVhZZWVkVHtO9e3eOHDlCz549OXbsGG3btq21uk+fPs25c6HFrYqLiykuDnUTmzVrdsGxX3zxBSUlJRGJLW5puFuC4vjx44wdO5aUlBRWr17N6NGjtSCJSBSMHz+exYsXc+bMGUaPHl2rr2ldsGABr7zyCqmpqaSmppKens5rr73Gnj172LVrFz179iQpKYnc3Fy2bt3KokWLai22QErg4W5z91jHEAjp6ekeq+ekCwoKWLlyJffeey9mxpYtW+jTpw8NGjSISTwiItVlZn+raCnO6khvYv52Nebn2d+IeCy1TfekY6ioqIhZs2bRtWtXsrOzef/99wHo37+/ErSISKnS4e6qftUBStIxUFxczJIlS+jSpQsPPfQQY8aMIS8vTyuFiYhcTPTeJx14uicdA8XFxcybN48ePXqwcOFC0tPjejRGRCS6orQsaDxQkq4lW7duZfHixTz55JMkJyezbds2UlJSNClMRORSEnjimIa7o+zDDz9k3Lhx9O/fnw0bNpCXlweEFkpQghYRqYQEHu5Wko6SM2fOMH36dFJTU3nppZe4//772bdvH7169Yp1aCIi8SWBJ45puBsws48iNZva3TEzGjRoQG5uLhMmTCA7OztiCyVI4urQoQNQ/isCRWIt3EYj3xPRcLfUlLvz3HPP0bdvX44fP05SUhKbN29m+fLlStAiIlItStIRkJubS//+/bnhhhs4f/48hYWFAHrWWUQkEhJ4uFtJugbOnj3LqFGjGDRoEIcOHWLFihVs3749sd9WIyISaQk8cUz3pKvh9OnTNG7cmAYNGtCiRQsefPBB7rzzTpKTk2MdmohI3VRSrxonnY94GLVNSboKTp06RU5ODo888ghvvvkmqamprFixItZhiYjUcQZU5/bh6UgHUuuUpCuhpKSEZ555hvvuu4+CggJGjhwZ2PvNsZoBHI16I1FmdcqoyjmVPbYyxyXS7O1YXGu06qxpudFuo1U5/lLHxa6NGlCdt5QpSQeKmXUA/hPoDfze3R+raZnnz5/nmmuuYevWrfTr149nn32WQYMG1bRYERGptOom6fhX1yaOpbj7T4AhwK01KejAgQMA1KtXjzFjxrBq1Sq2bNmiBC0iUuuSCA13V/Ur/gUySZtZIzO76Rv7hpvZHDO7zcx+bmYXxO7ufy2zWa2XQx8+fJjJkyfTpUsX/vSnPwFw9913M27cOJKSAvnjEhGp40p70lX9in+Byzpm1hF4DHjkG/uWAvPcfRnQCLilgmLGAbOqWvfPfvYzunbtysqVK/npT39K3759q1qEiIhEXOSTtJlNNLPdZva2meWb2eToxV99gbsn7e4HzOx3wOgyu28Ctrn7ufD2BuBBYJmZ3QD0Bf7q7v9jZpnhz4fMrIm7f16Zes+ePUt2djbJycm0atWKNWvWsGbNmnKPT4TJPSIipZPFAAoKCi7YV1bp9yOvurO7K7TD3XsAmNl/Ay9HuoJIMHePdQwXMLMMYLW7twxv/wH4yN3vCm9fRWg4u5G7F5c5byRwL/ARkAzc4e4fVbLO88C5Sx74lfeqcKyISLyq6lrcRe7+T5EMwMzWAS2rcWoj4EyZ7cfd/fGLlP+Eu99c3fiiKXA96XL8A/BZme1PCQ3V/yNQWLrT3V8AXqhOBe5enSflRUQkytx9WLTKNrPvAXnRKr+mAndPuhwngCZltpsQWijuRGzCERGROmI01ezc1YZ4SdLbgXZltr8NvO/udWQJdRERiZFUd1dPuoaeA642s9Lh+UzgqdiFIyIi8c7Mvg0cinUcFQncxDEza0do8tcUYCyw1t3PmNlooA9wEOgGzCg7aUxERKSuCVySDppoLDUqEg1m1gfo5+6/jnUsIqXMrDFwF/AO0NLdn4lxSHElXoa7YyliS42KRIuZWfhjVkwDEbnQXcDr7r4WyDSzy2MdUDxJmCQdy6VGRSqrBu1UTztIraliO+0H5Ic/FwJptRlrvEuIJB3LpUZFKitC7VQkqqrRTusTemSW8L+GVFpCJGl3PwD87hu7L7bU6O0AZnaDmT1sZmPC219barS24pbEUtN2KlIbqtpOCY1Adgp/bge8G/Ug65B4WXEsGtIILR9a6n+B7mZW391XAavg60uNmlkycAdQqfXARSKgUu00bADwHTNr7e5HazFGkXLbKZAD3GFmzYBN7v5JDOKLW4mcpKO+1KhIBFSqnQJcJGmL1JZy26m7FwLZMYmqDkiI4e5yaKlRiQdqpxIP1E6jJJGTtJYalXigdirxQO00ShI5SWupUYkHaqcSD9ROoyQh7kmHlxodC1xuZqMILTX6sZlNA+aa2cHwoTkxC1ISntqpxAO109qlZUFFREQCKpGHu0VERAJNSVpERCSglKRFREQCSklaREQkoJSkRUREAkpJWkREJKCUpEVERAJKSVpERCSglKRFREQCSklaREQkoJSkRUREAkpJWkREJKCUpEVERAJKSVpERCSglKRFREQCSklapI4xs+1mts7Mekep/Jnh8hdEo3wR+YqStEjds9Pdh7n7u9Eo3N3nu/swoHU0yheRryhJi4iIBJSStIiISEApSYuIiATUZbEOQCTozCwF+C/gINAUKAaOu/ujMQ2sCurCNYgkIiVpkQqYWUvgdWC6u79kZlcAHwJ3xjayyqsL1yCSqDTcLVKxBcABd38pvH0ccCDXzAaa2Ytm9p6ZTTazm83s52Y2tDoVmdl1ZjbDzJpHKviwcq8hXG/pdXxsZsnfiKm9mRWa2QozuyrCcYnIJagnLVIOM/sW8CNgSpndA4DPgPfcvcTMOgMj3H15+JxWwBEzS3X3fVWsciOhhPp74O81vgAufQ0A7p4bvo4jwL8CT5c5tjvwEfC0u78TiZhEpPLUkxYp3wCgPrCpzL6BwGZ3LynnnDbAUeBkVStz93NEKDmXUZVreAKYXLphZvWA8q5TRGqBetIi5WsEnHX3/DL7/hlYF77POzy8r7WZDSPU60wHrnT3Y6UnmNl/AMcAA9oCOe7uZjaNUDI/C7R290fCp/Q3s17AvwF3uXthuJx7gQKgHaEkuzkS1+DuKwHc/S0za2pm33P3POAa4M3K/KBEJDrUkxYp3xbAzexyADMbB/QDdgNZfJXAjrr7OndfFN4eUVqAmY0BrnD337v784RmVv+7md1AKJk/SejecNke9LHw/eOPgH8JlzMR+I67PwPkEBoWj+Q1lHoSmBT+3NTdP6tkPSISBUrSIuVw90PArcDPzWwucAa4i9A93u98o3daajvwgzLbgwkNf5c6AmQAgwglStz949J72mEF4X+/ABqEP18NJIV77BnA21G6hmeAH5jZt4HCytQhItGj4W6RCrj703x9IhWE7t2W5++Ehr0xs7bANkI911KdgK3A58CQ0p1mlubuOyoo9w3gandfFz7+g2hcg7t/YmZ/BWa7+5SLHSMitUdJWqSazGwgMBroaWaTwkPXzwEjzWw8UOTuT5tZMzP7Ufi0o+6+JHx+WzP7CXAIOBnuJXcCbjGzFYSGuv/PzDa5+yoz+5aZ3QKcAE4RetY5EtdxLTDJzHoAC4FfA2lmZsBUoCNwk5n9XTO8RWqXuXusYxCRCDKzp9x9Yl2pRySR6Z60iIhIQClJi9Q93c3sZTNLi0bh4VXRXiY0CU5EokjD3SIiIgGlnrSIiEhAKUmLiIgElJK0iIhIQClJi4iIBJSStIiISEApSYuIiASUkrSIiEhA/T/4mIA6LM0tMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7,5))\n",
    "\n",
    "scale_factor = 60\n",
    "corrfac = 20\n",
    "colma = 'gist_rainbow'\n",
    "#colma = 'winter'\n",
    "\n",
    "\n",
    "# http://matplotlib.org/examples/color/colormaps_reference.html\n",
    "# http://stackoverflow.com/questions/6063876/matplotlib-colorbar-for-scatter\n",
    "\n",
    "# Some lists might be empty (try except)\n",
    "# Problems when trying to set edgecolor (black by default) to colormap facecolor in filled circles (PT)\n",
    "# facecolors='None' for empty circles with colormap edgecolor (RV)\n",
    "\n",
    "\n",
    "try:\n",
    "    \n",
    "        ax.scatter(at[wh_habitable_PT_moon_strip][Wh_habitable_PT_moon_strip], \n",
    "                   acrit[wh_habitable_PT_moon_strip][Wh_habitable_PT_moon_strip],\n",
    "                   s = scale_factor*\n",
    "                   np.log10(planet_M[wh_habitable_PT_moon_strip][Wh_habitable_PT_moon_strip]*corrfac),\n",
    "                   c=np.log10(taumig[wh_habitable_PT_moon_strip][Wh_habitable_PT_moon_strip]),\n",
    "                   vmin=np.floor(np.log10(np.min(taumig[wh_habitable][Wh_habitable]))),\n",
    "                   vmax=np.ceil(np.log10(np.max(taumig[wh_habitable][Wh_habitable]))),\n",
    "                   cmap=colma, zorder=z_points, marker='o', lw=0.1);\n",
    "\n",
    "        PT_strip = ax.scatter(at[wh_habitable_PT_moon_strip][Wh_habitable_PT_moon_strip], acrit[wh_habitable_PT_moon_strip][Wh_habitable_PT_moon_strip], \\\n",
    "                        s = scale_factor*np.log10(planet_M[wh_habitable_PT_moon_strip][Wh_habitable_PT_moon_strip]*corrfac),\\\n",
    "                        c=np.log10(taumig[wh_habitable_PT_moon_strip][Wh_habitable_PT_moon_strip]), \\\n",
    "                        facecolors='None', \\\n",
    "                        vmin=np.floor(np.log10(np.min(taumig[wh_habitable][Wh_habitable]))), \\\n",
    "                        vmax=np.ceil(np.log10(np.max(taumig[wh_habitable][Wh_habitable]))), \\\n",
    "                        cmap=colma, zorder=z_points, marker='o');\n",
    "        \n",
    "        PT_strip.set_facecolor('none')\n",
    "\n",
    "except ValueError:\n",
    "\n",
    "        pass\n",
    "\n",
    "try:\n",
    "\n",
    "        RV_strip = ax.scatter(at[wh_habitable_RV_moon_strip][Wh_habitable_RV_moon_strip], \n",
    "                              acrit[wh_habitable_RV_moon_strip][Wh_habitable_RV_moon_strip],\n",
    "                              s = scale_factor*\n",
    "                              np.log10(planet_M[wh_habitable_RV_moon_strip][Wh_habitable_RV_moon_strip]*corrfac),\n",
    "                              c=np.log10(taumig[wh_habitable_RV_moon_strip][Wh_habitable_RV_moon_strip]),\n",
    "                              facecolors='None',\n",
    "                              vmin=np.floor(np.log10(np.min(taumig[wh_habitable][Wh_habitable]))),\n",
    "                              vmax=np.ceil(np.log10(np.max(taumig[wh_habitable][Wh_habitable]))),\n",
    "                              cmap=colma, zorder=z_points, marker='o');\n",
    "        \n",
    "        RV_strip.set_facecolor('none')\n",
    "\n",
    "except ValueError:\n",
    "\n",
    "        pass\n",
    "\n",
    "try:\n",
    "    \n",
    "        ax.scatter(at[wh_habitable_PT_moon_fall][Wh_habitable_PT_moon_fall], \n",
    "                   acrit[wh_habitable_PT_moon_fall][Wh_habitable_PT_moon_fall],\n",
    "                   s = scale_factor*\n",
    "                   np.log10(planet_M[wh_habitable_PT_moon_fall][Wh_habitable_PT_moon_fall]*corrfac),\n",
    "                   c=np.log10(taumig[wh_habitable_PT_moon_fall][Wh_habitable_PT_moon_fall]),\n",
    "                   vmin=np.floor(np.log10(np.min(taumig[wh_habitable][Wh_habitable]))),\n",
    "                   vmax=np.ceil(np.log10(np.max(taumig[wh_habitable][Wh_habitable]))),\n",
    "                   cmap=colma, zorder=z_points, marker='D', lw=0.1);\n",
    "\n",
    "        PT_fall = ax.scatter(at[wh_habitable_PT_moon_fall][Wh_habitable_PT_moon_fall], \n",
    "                             acrit[wh_habitable_PT_moon_fall][Wh_habitable_PT_moon_fall],\n",
    "                             s = scale_factor*\n",
    "                             np.log10(planet_M[wh_habitable_PT_moon_fall][Wh_habitable_PT_moon_fall]*corrfac),\n",
    "                             c=np.log10(taumig[wh_habitable_PT_moon_fall][Wh_habitable_PT_moon_fall]),\n",
    "                             facecolors='None',\n",
    "                             vmin=np.floor(np.log10(np.min(taumig[wh_habitable][Wh_habitable]))),\n",
    "                             vmax=np.ceil(np.log10(np.max(taumig[wh_habitable][Wh_habitable]))),\n",
    "                             cmap=colma, zorder=z_points, marker='D');\n",
    "        \n",
    "        PT_fall.set_facecolor('none')\n",
    "\n",
    "except ValueError:\n",
    "\n",
    "        pass\n",
    "\n",
    "try:\n",
    "\n",
    "        RV_fall = ax.scatter(at[wh_habitable_RV_moon_fall][Wh_habitable_RV_moon_fall], \n",
    "                             acrit[wh_habitable_RV_moon_fall][Wh_habitable_RV_moon_fall],\n",
    "                             s = scale_factor*\n",
    "                             np.log10(planet_M[wh_habitable_RV_moon_fall][Wh_habitable_RV_moon_fall]*corrfac),\n",
    "                             c=np.log10(taumig[wh_habitable_RV_moon_fall][Wh_habitable_RV_moon_fall]),\n",
    "                             facecolors='None',\n",
    "                             vmin=np.floor(np.log10(np.min(taumig[wh_habitable][Wh_habitable]))),\n",
    "                             vmax=np.ceil(np.log10(np.max(taumig[wh_habitable][Wh_habitable]))),\n",
    "                             cmap=colma, zorder=z_points, marker='D');\n",
    "        \n",
    "        RV_fall.set_facecolor('none')\n",
    "\n",
    "except ValueError:\n",
    "\n",
    "        pass\n",
    "\n",
    "\n",
    "    \n",
    "    \n",
    "\n",
    "\n",
    "# For the colorbar\n",
    "\n",
    "sc = ax.scatter(1.E11 + at[wh_habitable][Wh_habitable], \n",
    "                acrit[wh_habitable][Wh_habitable], \n",
    "                s = scale_factor*np.log10(planet_M[wh_habitable][Wh_habitable]*corrfac),\n",
    "                c=np.log10(taumig[wh_habitable][Wh_habitable]), \n",
    "                vmin=np.floor(np.log10(np.min(taumig[wh_habitable][Wh_habitable]))),\n",
    "                vmax=np.ceil(np.log10(np.max(taumig[wh_habitable][Wh_habitable]))), \n",
    "                cmap=colma, zorder=z_points, marker='o');\n",
    "\n",
    "\n",
    "cbar = fig.colorbar(sc)#, orientation = 'horizontal')\n",
    "cbar.set_label(r'$\\mathrm{\\log} \\, \\tau_{\\mathrm{mig},m} \\, [\\mathrm{yr}]}$', \n",
    "               rotation=270, fontsize = 14, labelpad=25)\n",
    "#cbar.set_ticks([-16, -14, -12, -10, -8, -6, -4, -2, 0])\n",
    "#cbar.ax.tick_params(labelsize=60, pad = 25, gridOn = False, tick1On = True, tick2On = True)\n",
    "\n",
    "\n",
    "\n",
    "ax.plot((1.E-2, 1.E0), (1.E-2, 1.E0), color='black', ls='dashed', lw=1.5, zorder=z_lines)\n",
    "\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$a_{\\rm{Roche}} \\, [a_{\\rm{M}}]$',fontsize = 17, labelpad=10)\n",
    "ax.tick_params(axis='x', which='major', pad=5)\n",
    "ax.set_ylabel(r'$a_{\\mathrm{crit},m} \\, [a_{\\rm{M}}]$',fontsize = 17, labelpad=5);\n",
    "ax.tick_params(axis='y', which='major', pad=10)\n",
    "\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(13);\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(13); \n",
    "            \n",
    "            \n",
    "ax.tick_params(which='both', width=1.75);\n",
    "ax.tick_params(which='major', length=12);\n",
    "ax.tick_params(which='minor', length=6);\n",
    "\n",
    "ax.set_xscale('log');\n",
    "ax.set_yscale('log');\n",
    "\n",
    "ax.set_xlim(1.E-2, 1.E0);\n",
    "ax.set_ylim(1.E-2, 1.E1);\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "\n",
    "# For the legend\n",
    "\n",
    "ax.scatter(1.35E-2, 6.0E0, s=80, color='black', marker='o')\n",
    "ax.scatter(1.35E-2, 3.5E0, s=80, color='black', marker='D')\n",
    "\n",
    "ax.text(1.6E-2, 5.3E0, r'$\\rm{Moon \\ stripped \\ away}$', fontsize=13)\n",
    "ax.text(1.6E-2, 3.1E0, r'$\\rm{Moon \\ falls \\ back}$', fontsize=13)\n",
    "\n",
    "ax.text(2.7E-1, 3.0E-2, r'$\\mathrm{M}_{m} = \\, 1.0 \\, \\mathrm{M_{M}}$', fontsize=13)\n",
    "ax.text(2.7E-1, 1.7E-2, r'$\\rm{P_{0} = \\, P_{orb}}$', fontsize=13)\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('Moon_dist_range_stripfall_taumig.pdf', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tidal-locking timescale calculations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "def R_from_LTeff(L, Teff):\n",
    "    \n",
    "    sigma = 5.67E-8 # W m-2 K-4\n",
    "    Lsun = 3.828E26 # W\n",
    "    Rsun = 6.957E8\n",
    "    \n",
    "    R = np.sqrt( ( L * Lsun ) / ( 4 * np.pi * sigma * Teff**4 ) ) / Rsun\n",
    "    \n",
    "    return R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.65 19.66 114.00 4.01 6.80 23.54 7.60 6.40 4.80 53.00 2.89 9.90 11.10 8.43 96.70 5.83 1.27 24.70 3.41 3.80 2.70 2.70 4.40 8.70 12.20 1.65 5.40 760.90 241.50 0.39 0.72 1.13 1.48\n"
     ]
    }
   ],
   "source": [
    "for el in planet_M[wh_habitable]:\n",
    "    \n",
    "    print \"%.2f\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.43 4.74 13.06 1.70 2.52 5.14 2.63 2.43 1.98 8.42 1.45 3.13 1.51 2.38 11.94 2.25 1.07 5.28 1.66 1.78 1.47 1.42 1.92 2.81 3.40 1.17 2.16 13.10 13.66 0.77 0.92 1.04 1.13\n"
     ]
    }
   ],
   "source": [
    "for el in planet_R[wh_habitable]:\n",
    "    \n",
    "    print \"%.2f\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.30 1.50 1.50 0.40 0.81 1.50 0.87 0.77 0.54 1.50 0.30 1.12 0.31 0.74 1.50 0.68 0.30 1.50 0.38 0.44 0.30 0.30 0.51 0.96 1.26 0.30 0.63 1.50 1.50 0.30 0.30 0.30 0.30\n"
     ]
    }
   ],
   "source": [
    "for el in k2_r_sample[wh_habitable]:\n",
    "    \n",
    "    print \"%.2f\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.00e+02 2.43e+04 1.00e+06 1.83e+02 1.24e+03 3.48e+04 1.52e+03 1.04e+03 3.84e+02 3.10e+05 1.00e+02 3.53e+03 1.03e+02 9.36e+02 1.00e+06 7.13e+02 1.00e+02 3.92e+04 1.63e+02 2.29e+02 1.00e+02 1.00e+02 3.31e+02 2.09e+03 5.27e+03 1.00e+02 5.85e+02 1.00e+06 1.00e+06 1.00e+02 1.00e+02 1.00e+02 1.00e+02\n"
     ]
    }
   ],
   "source": [
    "for el in Q_r_sample[wh_habitable]:\n",
    "    \n",
    "    print \"%.2e\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.370 0.233 0.254 0.358 0.310 0.234 0.304 0.315 0.342 0.245 0.370 0.274 0.369 0.318 0.254 0.326 0.370 0.235 0.361 0.354 0.370 0.370 0.345 0.293 0.258 0.370 0.331 0.254 0.254 0.370 0.370 0.370 0.370\n"
     ]
    }
   ],
   "source": [
    "for el in lambda_r_sample[wh_habitable]:\n",
    "    \n",
    "    print \"%.3f\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.66e+01 3.15e-01 7.66e-03 4.17e+01 6.20e+00 2.20e-01 5.04e+00 7.39e+00 1.99e+01 2.47e-02 7.66e+01 2.17e+00 7.41e+01 8.18e+00 7.66e-03 1.07e+01 7.66e+01 1.95e-01 4.69e+01 3.34e+01 7.66e+01 7.66e+01 2.31e+01 3.66e+00 1.45e+00 7.66e+01 1.31e+01 7.66e-03 7.66e-03 7.66e+01 7.66e+01 7.66e+01 7.66e+01\n"
     ]
    }
   ],
   "source": [
    "for el in Q_r_sample[wh_habitable]: #tau [s]\n",
    "    \n",
    "    print \"%.2e\" % (12/el*638.),"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1824 0.5763 0.6174 0.5035 0.4054 0.4507 0.4507 0.4092 0.2787 0.6348 0.2946 0.3595 0.5506 0.4446 0.3456 0.3036 0.1238 0.6314 0.3022 0.3268 0.3268 0.3268 0.2743 0.2743 0.4745 0.5493 0.4404 0.3381 0.3381 0.0898 0.0898 0.0898 0.0898\n"
     ]
    }
   ],
   "source": [
    "for el in star_M[wh_habitable]:\n",
    "    \n",
    "    print \"%.4f\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2306 0.5535 0.6275 0.6208 0.4245 0.4517 0.4517 0.4237 0.2754 0.6390 0.3237 0.3856 0.5381 0.4419 0.3984 0.3000 0.1666 0.6849 0.3183 0.3325 0.3325 0.3325 0.2932 0.2932 0.4909 0.5236 0.4393 0.3699 0.3699 0.1236 0.1236 0.1236 0.1236\n"
     ]
    }
   ],
   "source": [
    "for el in R_from_LTeff(star_L[wh_habitable], star_Teff[wh_habitable]):\n",
    "    \n",
    "    print \"%.4f\" % el, # radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.087 0.291 0.250 0.164 0.125 0.143 0.194 0.129 0.168 0.457 0.091 0.119 0.208 0.143 0.166 0.091 0.049 0.319 0.089 0.125 0.213 0.156 0.080 0.176 0.336 0.432 0.163 0.214 0.134 0.021 0.028 0.037 0.045\n"
     ]
    }
   ],
   "source": [
    "for el in planet_a[wh_habitable]:\n",
    "    \n",
    "    print \"%.3f\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4 16 17 18 21 27 29 40 43 49 52 72 76 77 81 84 93 103 106 113 115 116 124 125 148 179 187 195 196 201 202 203 204\n"
     ]
    }
   ],
   "source": [
    "for el in planet_prop['ID'][wh_habitable]:\n",
    "    \n",
    "    print el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\" LHS 1140 \" \" GJ 96 \" \" CD-23 1056 \" \" LP 413-32 B \" \" LPM 178 \" \" LP 834-042 \" \" LP 834-042 \" \" LP 776-27 \" \" Kapteyn's star \" \" BD-06 1339 \" \" Luyten's star \" \" Innes' star \" \" PM J11293-0127 \" \" PM J11302+0735 \" \" Ross 1003 \" \" LP 613-39 \" \" Proxima Centauri \" \" HD 147379 \" \" V2306 Oph \" \" HD 156384 C \" \" HD 156384 C \" \" HD 156384 C \" \" CD-44 11909 \" \" CD-44 11909 \" \" V1428 Aql \" \" Kepler-186 \" \" HD 204961 \" \" IL Aqr \" \" IL Aqr \" \" 2MUCD 12171 \" \" 2MUCD 12171 \" \" 2MUCD 12171 \" \" 2MUCD 12171 \"\n"
     ]
    }
   ],
   "source": [
    "for el in planet_name[wh_habitable]:\n",
    "    \n",
    "    print '\"',el,'\"',"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\" b \" \" b \" \" b \" \" b \" \" c \" \" b \" \" d \" \" c \" \" b \" \" c \" \" b \" \" b \" \" d \" \" b \" \" b \" \" b \" \" b \" \" b \" \" c \" \" c \" \" e \" \" f \" \" b \" \" c \" \" b \" \" f \" \" c \" \" b \" \" c \" \" d \" \" e \" \" f \" \" g \"\n"
     ]
    }
   ],
   "source": [
    "for el in planet_char[wh_habitable]:\n",
    "    \n",
    "    print '\"',el,'\"',"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004425108 0.063856810 0.090805605 0.036404450 0.021697850 0.027579645 0.027579645 0.024274724 0.012805443 0.103932050 0.009900130 0.017896352 0.060347500 0.026395837 0.014989760 0.012170071 0.001536843 0.097754300 0.010823072 0.014945071 0.014945071 0.014945071 0.008118322 0.008118322 0.032581307 0.057127886 0.029206133 0.012926352 0.012926352 0.000537818 0.000537818 0.000537818 0.000537818\n"
     ]
    }
   ],
   "source": [
    "for el in star_L[wh_habitable]:\n",
    "    \n",
    "    print \"%.9f\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3100 3900 4000 3200 3400 3500 3500 3500 3700 4100 3200 3400 3900 3500 3200 3500 2800 3900 3300 3500 3500 3500 3200 3200 3500 3900 3600 3200 3200 2500 2500 2500 2500\n"
     ]
    }
   ],
   "source": [
    "for el in star_Teff[wh_habitable]:\n",
    "    \n",
    "    print \"%.0f\" % el,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['ID', 'Name', 'Planet', 'a_au', 'M_star', 'Lbol', 'Teff', 'M_planet', 'R_planet', 'tlock_CPL', 'tlock_CTL']\n"
     ]
    }
   ],
   "source": [
    "# tlock for the whole PHZ sample\n",
    "\n",
    "tlock_systems = Table.read(path_data + 'hmr18.planets_tlock.v08.csv', format='ascii.csv')\n",
    "print tlock_systems.colnames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LP 834-042 d 1.04e+08\n",
      "PM J11293-0127 d 2.33e+08\n",
      "HD 156384 C e 2.21e+08\n",
      "CD-44 11909 c 1.72e+08\n"
     ]
    }
   ],
   "source": [
    "for i, el in enumerate(tlock_systems['Name']):\n",
    "    \n",
    "    if tlock_systems['tlock_CPL'][i] > 1.E8:\n",
    "        \n",
    "        if tlock_systems['tlock_CPL'][i] < 1.E9:\n",
    "    \n",
    "            print el + ' ' + tlock_systems['Planet'][i], \"%.2e\"%tlock_systems['tlock_CPL'][i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GJ 96 b 1.74e+09\n",
      "CD-23 1056 b 8.15e+09\n",
      "BD-06 1339 c 1.30e+10\n",
      "Ross 1003 b 2.51e+09\n",
      "HD 147379 b 3.77e+09\n",
      "V1428 Aql b 3.15e+09\n",
      "Kepler-186 f 5.93e+09\n",
      "IL Aqr b 1.30e+10\n",
      "IL Aqr c 1.14e+09\n"
     ]
    }
   ],
   "source": [
    "for i, el in enumerate(tlock_systems['Name']):\n",
    "    \n",
    "    if tlock_systems['tlock_CPL'][i] > 8.E8:\n",
    "    \n",
    "        print el + ' ' + tlock_systems['Planet'][i], \"%.2e\"%tlock_systems['tlock_CPL'][i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7,5))\n",
    "\n",
    "\n",
    "ax.scatter(tlock_systems['tlock_CPL'], tlock_systems['tlock_CTL'], color='forestgreen', s=80);\n",
    "\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$\\mathrm{t_{lock} \\, (CPL)} \\, [\\mathrm{yr}]$',fontsize = 17, labelpad=10)\n",
    "ax.tick_params(axis='x', which='major', pad=5)\n",
    "ax.set_ylabel(r'$\\mathrm{t_{lock} \\, (CTL)} \\, [\\mathrm{yr}]$',fontsize = 17, labelpad=5);\n",
    "ax.tick_params(axis='y', which='major', pad=10)\n",
    "\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(13);\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(13); \n",
    "            \n",
    "            \n",
    "ax.tick_params(which='both', width=1.75);\n",
    "ax.tick_params(which='major', length=12);\n",
    "ax.tick_params(which='minor', length=6);\n",
    "\n",
    "ax.set_xscale('log');\n",
    "ax.set_yscale('log');\n",
    "\n",
    "ax.set_xlim(10.E2, 5.E10);\n",
    "ax.set_ylim(10.E2, 8.E10);\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "ax.plot((1.E2, 1.E11), (1.E2, 1.E11), color='darkgrey', lw=1.5, ls='dashed');\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('tlock_CPLCTL.pdf', bbox_to_inches = 'tight')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Limit for taumig using at, acrit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "taumig_at = 2.5E11 * (k2_Earth / k2_r_sample) * (Q_r_sample / Q_Earth) \\\n",
    "* (MMoon / MMoon)**(-1.0) * (planet_R)**(-5.0) * (at)**(8.0) # yr\n",
    "\n",
    "taumig_acrit = 2.5E11 * (k2_Earth / k2_r_sample) * (Q_r_sample / Q_Earth) \\\n",
    "* (MMoon / MMoon)**(-1.0) * (planet_R)**(-5.0) * (acrit)**(8.0) # yr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CD-23 1056 b BD-06 1339 c Ross 1003 b IL Aqr b IL Aqr c\n"
     ]
    }
   ],
   "source": [
    "for i, el in enumerate(taumig_at[wh_habitable]):\n",
    "    \n",
    "    if el >= 1.E4:\n",
    "        \n",
    "        print planet_name[wh_habitable][i] + ' ' +  planet_char[wh_habitable][i],\n",
    "        \"%.2e\"%el, \"%.2e\"%taumig_acrit[wh_habitable][i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7,5))\n",
    "\n",
    "\n",
    "ax.scatter(taumig_at[wh_habitable_PT], taumig_acrit[wh_habitable_PT],\n",
    "           s = scale_factor*np.log10(planet_M[wh_habitable_PT]*corrfac),\n",
    "           facecolor='forestgreen', edgecolor='forestgreen', zorder=z_points, marker='o', lw=0.1);\n",
    "\n",
    "\n",
    "ax.scatter(taumig_at[wh_habitable_RV], taumig_acrit[wh_habitable_RV],\n",
    "           s = scale_factor*np.log10(planet_M[wh_habitable_RV]*corrfac),\n",
    "           facecolor='w', edgecolor='forestgreen', zorder=z_points, marker='o', lw=1.0);\n",
    "\n",
    "\n",
    "\n",
    "ax.set_xlabel(r'$\\mathrm{\\tau_{\\mathrm{mig},m}} \\, (a_{\\mathrm{Roche}}) \\, [\\mathrm{yr}]$',\n",
    "              fontsize = 17, labelpad=10)\n",
    "ax.tick_params(axis='x', which='major', pad=5)\n",
    "\n",
    "ax.set_ylabel(r'$\\mathrm{\\tau_{\\mathrm{mig},m}} \\, (a_{\\mathrm{crit},m}) \\, [\\mathrm{yr}]$',\n",
    "              fontsize = 17, labelpad=5);\n",
    "ax.tick_params(axis='y', which='major', pad=10)\n",
    "\n",
    "\n",
    "for tick in ax.xaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(13);\n",
    "for tick in ax.yaxis.get_major_ticks():\n",
    "            tick.label.set_fontsize(13); \n",
    "    \n",
    "            \n",
    "            \n",
    "ax.tick_params(which='both', width=1.75);\n",
    "ax.tick_params(which='major', length=10);\n",
    "ax.tick_params(which='minor', length=6);\n",
    "\n",
    "ax.set_xscale('log');\n",
    "ax.set_yscale('log');\n",
    "\n",
    "\n",
    "\n",
    "# Minor log ticks disappear for broad range\n",
    "# https://stackoverflow.com/questions/45905135/matplotlib-missing-minor-ticks-on-y-axis-because-of-log-range-10-decades\n",
    "#locmaj = matplotlib.ticker.LogLocator(base=10.0, subs=(1.0, ), numticks=100)\n",
    "#ax.yaxis.set_major_locator(locmaj)\n",
    "\n",
    "#locmin = matplotlib.ticker.LogLocator(base=10.0, subs=np.arange(2, 10) * .1,\n",
    "#                                      numticks=20)\n",
    "#ax.yaxis.set_minor_locator(locmin)\n",
    "#ax.yaxis.set_minor_formatter(matplotlib.ticker.NullFormatter())\n",
    "plt.minorticks_off()\n",
    "\n",
    "\n",
    "\n",
    "ax.set_xlim(5.E0, 8.E7);\n",
    "ax.set_ylim(1.E2, 5.E17);\n",
    "\n",
    "ax.plot((1.E2, 1.E8), (1.E2, 1.E8), color='black', ls='dashed', lw=1.5, zorder=z_lines)\n",
    "ax.axhline(0.8E9, color='black', lw=1.5, ls='dotted', zorder=z_lines)\n",
    "\n",
    "\n",
    "ax.get_yaxis().set_tick_params(right = True, which='both', direction='in')\n",
    "ax.get_xaxis().set_tick_params(top = True, which='both', direction='in')\n",
    "\n",
    "\n",
    "\n",
    "fig.tight_layout()\n",
    "fig.savefig('taumig_acritaRoche.pdf', bbox_to_inches = 'tight')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}