Modeling the Kinematics of Central and Satellite Galaxies Using Normalizing Flows

Galaxy clustering contains information on cosmology, galaxy evolution, and the relationship between galaxies and their dark matter hosts. On small scales, the detailed kinematics of galaxies within their host halos determines the galaxy clustering. In this paper, we investigate the dependence of the central and satellite galaxy kinematics on $\boldsymbol{\theta}$, the intrinsic host halo properties (mass, spin, concentration), cosmology ($\Omega_{\textrm{m}}$, $\sigma_8$), and baryonic feedback from active galactic nuclei and supernovae ($A_{\rm AGN1}$, $A_{\rm AGN2}$, $A_{\rm SN1}$, $A_{\rm SN2}$). We utilize 2,000 hydrodynamic simulations in CAMELS run using IllustrisTNG and SIMBA galaxy formation models. Focusing on central and satellite galaxies with $M>10^9M_\ast$, we apply neural density estimation (NDE) with normalizing flows to estimate their $p(\Delta r|\boldsymbol{\theta})$ and $p(\Delta v|\boldsymbol{\theta})$, where $\Delta r$ and $\Delta v$ are the magnitudes of the halo-centric spatial and velocity offsets. With NDE, we accurately capture the dependence of galaxy kinematics on each component of $\boldsymbol{\theta}$. For central galaxies, we identify significant spatial and velocity biases dependent on halo mass, concentration, and spin. For satellite distributions, we find significant deviations from an NFW profile and evidence that they consist of distinct orbiting and infalling populations. However, we find no significant dependence on $\boldsymbol{\theta}$ besides a weak dependence on host halo spin. For both central and satellite galaxies, there is no significant dependence on cosmological parameters and baryonic feedback. These results provide key insights for improving the current halo occupation distribution (HOD) models. This work is the first in a series that will re-examine and develop HOD frameworks for improved modeling of galaxy clustering at smaller scales.