Far-ultraviolet Irradiated Rotational Evolution model for low mass stars (FIREstars)

Author: Julia Roquette

This package, which is part of the research presented in Roquette et al. (2021), includes a compilation of tools for computing rotational evolution models of stars evolving under the irradiation of far-ultraviolet radiation. The package can be used to derive the rotational evolution of stars in the mass range 0.1-1.3.

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Installation

This package requires a Python3 installation with astropy, matplotlib, numpy, pandas and scipy.

To install, first clone this repository:

git clone https://github.com/juliaroquette/FIREstars.git

Next, use a terminal to access the repository directory and use pip to install:

pip install .

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Rotational Evolution model: SpinEvolution.py

The module SpinEvolution.py contains a class SpinEvolutionCode which comprises all tools to be used for modelling the rotational evolution of stars. Research notes on the implementation of this class can be found in the jupyter-notebook jupyter/SpinEvolutionModel.ipynb. The model implemented here is based on three assumptions:

1. Disk-locking: During the early-PMS phase, stars with disks are locked to their disks and remain with constant rotation. The duration of the disk-locking phase is parametrised using FUV-irradiated disk-dissipation models by Winter et al. (2020) and a tool for reading and using disk-models is implemented as part of FUVfunctions.py. See notes on jupyter/FUV_TauD.ipynb.

2. Internal Structure: The internal structure of stars is described by the stellar evolution models of Baraffe et al. (2015). Tools for reading these models are implemented in StarEvolution.py. See notes on jupyter/StellarEvolution_BHAC15.ipynb.

3. Magnetised Winds: At all ages, stars are subject to a wind-torque. The wind-torque adopted is the one by Matt et al. (2015).

Usage:

from FIREstars.SpinEvolution import SpinEvolutionCode

Initialize the class by providing an initial time for the model, t0, in years.

spin = SpinEvolutionCode(t0)

Following initialization, the rotational evolution is estimated by spin.dOmegadt:

time, omega = spin.dOmegadt(M, Omega0, t, tau_d=0, e=0.01, wind=True, structure=True, snapshot=False, breakup=True)

Where:

• M: is the stellar mass in .
• Omega0 is the initial rotation rate, in .
• t is one or multiple ages for model calculation:
  • If snapshot=True, t must be an array or list of ages at which snapshot values of the model will be saved.
  • Otherwise if snapshot=False, t must be the final age in the model.
• tau_d is the disk-locking duration (in years) set as zero as default.
• e is a tolerance factor which defines the size of the time-step in foward-step Euler-method. For example, in the default e=0.01, the model is estimating using time-steps large enough to increase in 1% in each step.
• wind turns on/off the wind-torque.
• structure turns on/off the structure term.
• snapshot sets the way in which the model's outputs are returned: - If snapshot=False (default) the model will return pairs of and at each time-step required for running the model with a tolerance factor e. - If snapshot=True, and are returned only for pre-defined timesteps provided inputed in the array t.
• breakup if set to True, the spin evolution model has a condition that prevents stars from rotating faster than the break-up limit.

Example 1: Spin evolution of a star from 0.5 Myr to 4.5 Gyr, with a disk-lifetime of 5 Myr and an initial rotational period of 8 d.

First, to transform the period of 8 d to and vice-versa, SpinEvolution.py includes the functions period2omega and omega2period:

from FIREstars.SpinEvolution import  SpinEvolutionCode, period2omega
spin = SpinEvolutionCode(0.5e6)
time, omega = spin.dOmegadt(1.0, period2omega(8.), [4.5e9], tau_d=5e6)

Example 2: Rotational period of a star at the ages 10 Myr, 120 Myr and 4.5 Gyr, considering a disk-lifetime of 5 Myr and an initial rotational period of 8 d at the age 1 Myr.

from FIREstars.SpinEvolution import  SpinEvolutionCode, period2omega
spin = SpinEvolutionCode(1e6)
time, omega = spin.dOmegadt(1.0, period2omega(8.), [10e6, 120e6, 4.5e9], tau_d=5e6, snapshot=true)

Further usage

Break-up Limit:

SpinEvolution can also be used to estimate the break-up limit as a function of age.

Example 3: breakup limit for a at the ages 10 Myr and 1Gyr.

spin = SpinEvolutionCode(1e6)
omega_crit = spin.get_BreakUp(1., [10e6, 1e9])

Saturation limit:

Similarly, the saturation limit used in the wind-torque can also be tracked.

Example 4: saturation limit for a at the ages 10 Myr and 1Gyr.

 spin = SpinEvolutionCode(1e6)
 omega_sat = spin.get_SaturationLimit1., [10e6, 1e9])

Rotational Evolution in Period-Mass space

The class SpinEvolutionCode also includes a tool for calculating "isogyrochrones" (see notes in jupyter/PeriodMassDiagrams.ipynb). Isogyrochrones are rotation tracks in period-mass space, in which the rotation of stars in the whole mass range 0.1-1.3 is evolved from a common set of initial conditions to a given age.

spin = SpinEvolutionCode(t0)
mass, period = spin.isogyrochrone(initial_period, time, fuv=False, tau_d=False,
                                  dm=0.025, e=0.01, tau_vis=1.0, wind=True,
                                  structure=True, breakup=True, initial_age=False,
                                  get_breakup_limit=False)

Where:

• initial_period is the rotational period at the time t0.
• time provide a single or multiple ages (in years) at which the isogyrochrones will be estimated.
• fuv set as False for a model ignoring the environment. Otherwise, fuv is the local far-ultraviolet flux in Habing flux units ().
• tau_vis sets the viscous timescale in the disk-dissipation model (see notes in jupyter/FUV_TauD.ipynb). Possible values are 1, 2 or 5 Myr.
• initial_age if True, includes the isogyrochrone ate the age t0.
• get_breakup_limit if True returns an isogyrochrone with the break-up limit.
• tau_d is set as False if using the keyword fuv. Otherwise, tau_d sets a common disk-lockig duration for all the stars in the isogyrochrone.
• The remaining keywords are the same as in dOmegadt

Example 5: Creates an isogyrochrone at the age of 15 Myrs, for stars with initial rotation of 8 d at an age of 1 Myr, which are evolving under an FUV-flux of 1,000. Using steps of and considering a disk with viscosity timescale of 1 Myr.

spin = SpinEvolutionCode(1e6)
mass, period = spin.isogyrochrone(8., 15e6, fuv=1000., dm=0.05, e=0.01, tau_vis=1.0)

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