Why do people choose 0.2 as the value of linking length in the friends-of-friends algorithm? The friends-of-friends algorithm (hereafter FOF) is commonly used to find halos in cosmological simulations. And FOF depends on only one parameter, linking length, $l_\mathrm{link}=b \left(\frac{V_u}{N}\right)^{1/3}$, where $V_u$ is the volume of the simulation box, and $N$ is the number of dark matter particles.
In most literature, the value of $b$ is set at 0.2. What does $b\approx 0.2$ mean physically?
The friends-of-friends (FOF) algorithm (Huchra &amp; Geller 1982; Press &amp; Davis 1982, Davis et al. 1985) for finding groups of particles can be used for various numerical problems, not just cosmology, and linking lengths may vary between these problems. The larger the values you use for $b$ (the linking length in terms of the mean interparticle distance), the more particles you will include in your group of particles. Since the density falls off with distance from the center of the group, this means that the average density will be smaller for larger values of $b$.
In cosmological applications of the FOF algorithm, particle groups are called halos, and experience shows that using $b = 0.2$ result in an average enclosed overdensity of close to $\Delta = 180$ times the average &quot;global&quot; density. This value of 180 equals the virial overdensity predicted by the spherical collapse model in the Einstein-De Sitter cosmology (see e.g. Mo et al. 2010). Also, the value of 180, or perhaps 200, is also typically the overdensity used for another popular halo finder, the so-called spherical overdensity algorithm.
That $b=0.2$ results in $\Delta \simeq 180$ is actually only true for an isothermal density profile; the exact value will depend on the actual profile and halo concentration $c$. Surhud et al. (2011) offer an analytical solution to the overdensity as a function of $b$ and $c$.