Secondary Dependence of Baryonic Effects on the Density Profile of Dark Matter Halos
Baryonic physics is anticipated to be a major source of systematic uncertainty in current and future large-scale cosmological surveys. We investigate how baryonic effects on halo density profiles vary with secondary halo properties at fixed halo mass, using the large-volume MillenniumTNG hydrodynamical simulation and its dark matter-only counterpart. We focus on the impact of halo concentration and large-scale environment on the ratio of density profiles of matched halos in the hydrodynamical and dark matter-only simulations. At redshift $z = 0.0$, we find a strong dependence on halo concentration, especially at lower halo mass ($12.5 < \log(M_h/h^{-1}M_{\odot}) < 13.0$), where more concentrated halos exhibit weaker inner enhancement and stronger intermediate-radius suppression at fixed halo mass, with variations reaching $\sim 15\%$ at small scales and decreasing toward larger scales. This trend weakens and reverses at higher halo mass. In contrast, the secondary dependence on large-scale environment is weaker ($\sim 2\%$) and largely scale-independent, with halos in denser regions exhibiting slightly weaker intermediate suppression. By separating internal profile redistribution from total mass suppression, we show that concentration impacts both components, whereas the environmental dependence is primarily associated with an overall mass shift. These secondary dependencies persist at $ z = 0.5$ and correlate with variations in internal baryonic properties. We examine additional halo properties, including halo spin and velocity dispersion, and find significant secondary dependence. Overall, our results highlight the important role of secondary halo properties in modulating baryonic effects on halo density profiles, with potential implications for future modeling efforts.