foftools - galaxy group identification using the friends-of-friends algorithm.

This package was written to include a variety of computational tools for performing friends-of-friends group identification analyses, especially as related to the RESOLVE/ECO surveys (Kannappan et al. 2011, Moffett et al. 2015).

Using foftools

There are two key functions in the package:

1. the fof.fast_fof function, an implementation of the friends-of-friends algorithm (Huchra & Geller, 1982; Berlind et al. 2006).
2. the fof.fast_pfof function, an implementation of the probability friends-of-friends algorithm (Liu et al. 2009). The library also includes a number of functions for computing the properties of the groups, such as their multiplicities, radii or velocity dispersions, and total masses.

The Friends-of-Friends Algorithm

Our FoF code works by following the process described in Berlind et al. (2006). In this approach, two galaxies are considered friends if the perpendicular and line-of-sight comoving distances between them are each less than a characteristic linking length. The perpendicular and line-of-sight linking lengths are products of the mean separation between galaxies with the perpendicular and line-of-sight linking constants. In general, linking lengths are optimized with mock catalogs, but Duarte & Mamon (2014) provide several recommendations for different scientific purposes.

Our implementation of the FoF algorithm is the fof.fast_fof function. It can be called as:

fof.fast_fof(ra, dec, cz, bperp, blos, s)

Here ra, dec, and cz are iterables that represent the coordinates of galaxies to be included in the group-finding. The bperp and blos parameters are the dimensionless linking factors that optimize the mean separation between galaxies, s, to identify groups. The fast_fof function will return a NumPy array containing a group identification number for every input galaxy. The algorithm will also accept s as an iterable of equivalent length as ra.

Note: The FoF algorithm will run helper functions for calculating the perpendicular and line-of-sight comoving distances between galaxies. The foftools package defaults to a LambdaCDM cosmology with H0 = 100.0, OmegaM = 0.3, and OmegaDE = 0.7. These can be modified in the source.

The Probability Friends-of-Friends Algorithm

The package includes an implementation of the probability friends-of-friends algorithm (Liu et al. 2008) for volume-limited data sets. This algorithm presents a modification to the traditional friends-of-friends linking criteria. In PFoF, galaxies are modeled with probability distribution functions, and satisfaction of the line-of-sight linking criterion is given probabilistically. Our implementation models the galaxy PDFs with Gaussian distributions whose centroids are the galaxies' measured redshifts and whose standard deviations are the errorbars on the galaxies' redshifts. The routine can be called from

fof.fast_pfof(ra, dec, cz, czerr, perpll, losll, Pth)

This function follows the same input scheme as foftools.fast_fof, but requires an additional input array czerr that represents the error bars on individual galaxy redshift velocities. The perpll and losll are the on-sky and line-of-sight linking lengths in Mpc/h and km/s respectively. The last parameter, Pth, is the threshold probability used to construct to a group catalog from PFoF's friendship probabilities.

The PFoF algorithm is very computationally-expensive; the supporting functions require Numba's @njit decorator to improve integration speed for galaxy friendship probabilities.