Stellar property statistics of massive haloes from cosmological hydrodynamics simulations: common kernel shapes

We study stellar property statistics, including satellite galaxy occupation, of haloes in three cosmological hydrodynamics simulations: BAHAMAS + MACSIS, IllustrisTNG, and Magneticum Pathfinder. Applying localized linear regression, we extract halo mass-conditioned normalizations, slopes, and intrinsic covariance for (i) N-sat, the number of stellar mass-thresholded satellite galaxies within radius R-200c of the halo; (ii) M-star,M-tot, the total stellar mass within that radius, and (iii) M-star,M-BCG, the gravitationally bound stellar mass of the central galaxy within a 100 kpc radius. The parameters show differences across the simulations, in part from numerical resolution, but there is qualitative agreement for the N-sat-M-star,M-BCG correlation. Marginalizing over M-halo, we find the N-sat kernel, p(ln N-sat vertical bar M-halo,M- z) to be consistently skewed left in all three simulations, with skewness parameter gamma = -0.91 +/- 0.02, while the M-star,M-tot kernel shape is closer to lognormal. The highest resolution simulations find gamma similar or equal to -0.8 for the z = 0 shape of the M-star,M-BCG kernel. We provide a Gaussian mixture fit to the low-redshift N-sat kernel as well as local linear regression parameters tabulated for M-halo > 10(13.5) M-circle dot in all simulations.