A general framework to test gravity using galaxy clusters II: A
  universal model for the halo concentration in $f(R)$ gravity
  We present a novel fitting formula for the halo concentration enhancement in
chameleon $f(R)$ gravity relative to General Relativity (GR). The formula is
derived by employing a large set of $N$-body simulations of the Hu-Sawicki
$f(R)$ model which cover a wide range of model and cosmological parameters,
resolutions and simulation box sizes. The complicated dependence of the
concentration on halo mass $M$, redshift $z$, and the $f(R)$ and cosmological
parameters can be combined into a simpler form that depends only on a rescaled
mass $M/10^{p_2}$, with
$p_2\equiv1.5\log_{10}\left[|{\bar{f}_R(z)}|/(1+z)\right]+21.64$ and
$\bar{f}_R(z)$ the background scalar field at $z$, irrespective of the $f(R)$
model parameter. Our fitting formula can describe the concentration enhancement
well for redshifts $z\leq3$, nearly 7 orders of magnitude in $M/10^{p_2}$ and
five decades in halo mass. This is part of a series of works which aims to
provide a general framework for self-consistent and unbiased tests of gravity
using present and upcoming galaxy cluster surveys. The fitting formula, which
is the first quantitative model for the concentration enhancement due to
chameleon type modified gravity, is an important part in this framework and
will allow continuous exploration of the parameter space. It can also be used
to model other statistics such as the matter power spectrum.
