Stellar Property Statistics of Massive Halos from Cosmological
  Hydrodynamics Simulations: Common Kernel Shapes
  We study stellar property statistics, including satellite galaxy occupation,
of massive halo populations realized by three cosmological hydrodynamics
simulations: BAHAMAS + MACSIS, TNG300 of the IllustrisTNG suite, and Magneticum
Pathfinder. The simulations incorporate independent sub-grid methods for
astrophysical processes with spatial resolutions ranging from $1.5$ to $6$ kpc,
and each generates samples of $1000$ or more halos with $M_{\rm halo}>
10^{13.5} M_{\odot}$ at redshift $z=0$. Applying localized, linear regression
(LLR), we extract halo mass-conditioned statistics (normalizations, slopes, and
intrinsic covariance) for a three-element stellar property vector consisting
of: i) $N_{sat}$, the number of satellite galaxies with stellar mass,
$M_{\star, \rm sat} > 10^{10} M_{\odot}$ within radius $R_{200c}$ of the halo;
ii) $M_{\star,\rm tot}$, the total stellar mass within that radius, and; iii)
$M_{\star,\rm BCG}$, the gravitationally-bound stellar mass of the central
galaxy within a $100 \, \rm kpc$ radius. Scaling parameters for the three
properties with halo mass show mild differences among the simulations, in part
due to numerical resolution, but there is qualitative agreement on property
correlations, with halos having smaller than average central galaxies tending
to also have smaller total stellar mass and a larger number of satellite
galaxies. Marginalizing over total halo mass, we find the satellite galaxy
kernel, $p(\ln N_{sat}\,|\,M_{\rm halo},z)$ to be consistently skewed left,
with skewness parameter $\gamma = -0.91 \pm 0.02$, while that of $\ln
M_{\star,\rm tot}$ is closer to log-normal, in all three simulations. The
highest resolution simulations find $\gamma \simeq -0.8$ for the $z=0$ shape of
$p(\ln M_{\star,\rm BCG}\,|\,M_{\rm halo},z)$ and also that the fractional
scatter in total stellar mass is below $10\%$ in halos more massive than
$10^{14.3} M_{\odot}$.
