Baryonic Imprints on DM Halos: the concentration-mass relation and its dependence on halo and galaxy properties

The halo concentration-mass relation has ubiquitous use in modeling the matter field for cosmological and astrophysical analyses, and including the imprints from galaxy formation physics is tantamount to its robust usage. Many analyses, however, probe the matter around halos selected by a given halo/galaxy property -- rather than by halo mass -- and the imprints under each selection choice can be different. We employ the CAMELS simulation suite to quantify the astrophysics and cosmology dependence of the concentration-mass relation, $c_{\rm vir}-M_{\rm vir}$, when selected on five properties: (i) velocity dispersion, (ii) formation time, (iii) halo spin, (iv) stellar mass, and (v) gas mass. We construct simulation-informed nonlinear models for all properties as a function of halo mass, redshift, and six cosmological/astrophysical parameters, with a mass range $M_{\rm vir} \in [10^{11}, 10^{14.5}] M_\odot/h$. There are many mass-dependent imprints in all halo properties, with clear connections across different properties and non-linear couplings between the parameters. Finally, we extract the $c_{\rm vir}-M_{\rm vir}$ relation for subsamples of halos that have scattered above/below the mean property-$M_{\rm vir}$ relation for a chosen property. Selections on gas mass or stellar mass have a significant impact on the astrophysics/cosmology dependence of $c_{\rm vir}$, while those on any of the other three properties have a significant (mild) impact on the cosmology (astrophysics) dependence. We show that ignoring such selection effects can lead to errors of $\approx 25\%$ in baryon imprint modelling of $c_{\rm vir}$. Our nonlinear model for all properties is made publicly available.