Response of dark matter halos to condensation of baryons: cosmological simulations and improved adiabatic contraction model

TL;DR

This study tests adiabatic contraction (AC) in cosmological halos using high-resolution simulations that include gas cooling and star formation. It finds that the standard AC prediction $M(r) r = const$ overpredicts the inner DM compression, and introduces a modified invariant $M(bar r) r = const$ based on orbit-averaged radii, which better reproduces the simulated DM profiles with typical residuals of 10–20%. The approach leverages orbit analyses and analytic fitting functions to translate complex baryon-induced contraction into practical prescriptions. The work improves interpretation of inner-halo density profiles and has implications for observational constraints and dark matter annihilation estimates, showing that baryonic physics leaves a lasting imprint on DM structure even through hierarchical mergers.

Abstract

The cooling of gas in the centers of dark matter halos is expected to lead to a more concentrated dark matter distribution. The response of dark matter to the condensation of baryons is usually calculated using the model of adiabatic contraction, which assumes spherical symmetry and circular orbits. In contrast, halos in the hierarchical structure formation scenarios grow via multiple violent mergers and accretion along filaments, and particle orbits in the halos are highly eccentric. We study the effects of the cooling of gas in the inner regions of halos using high-resolution cosmological simulations which include gas dynamics, radiative cooling, and star formation. We find that the dissipation of gas indeed increases the density of dark matter and steepens its radial profile in the inner regions of halos compared to the case without cooling. For the first time, we test the adiabatic contraction model in cosmological simulations and find that the standard model systematically overpredicts the increase of dark matter density in the inner 5% of the virial radius. We show that the model can be improved by a simple modification of the assumed invariant from M(r)r to M(r_av)r, where r and r_av are the current and orbit-averaged particle positions. This modification approximately accounts for orbital eccentricities of particles and reproduces simulation profiles to within 10-20%. We present analytical fitting functions that accurately describe the transformation of the dark matter profile in the modified model and can be used for interpretation of observations.

Figures (7)

• Figure 1: Mass profile of one of the clusters as a function of physical radius. The solid and dotted lines show the profiles of dark matter and baryons (stars+gas) in the adiabatic ( thin) and cooling ( thick) runs, respectively. The dashed curve shows the prediction of the standard adiabatic contraction model, while dot-dashed curve shows the improved model. The profiles are truncated at four resolution elements of the simulation. Top panel: relative mass difference between the adiabatic contraction model and the DM profile in the CSF simulation. The dashed line is prediction of the standard AC model, while dot-dashed line shows our modified model.
• Figure 2: Density profile of the cluster shown in Figure \ref{['fig:cl6_m']}, with the same line types. In order to emphasize the differences at small radii, we plot the combination $\rho(r)r^2$ which is roughly constant for isothermal distributions. Physical radius is shown in $h^{-1}$ kpc ( bottom axis) and as a fraction of the virial radius, $r_{\rm vir}$ ( top axis).
• Figure 3: Density profile in the galaxy formation run at $z=4$ as a function of physical radius. Lines types are as in Figure \ref{['fig:cl6_m']}.
• Figure 4: Fractional differences of the mass profiles predicted by the adiabatic contraction models and the simulation profiles for eight clusters ( top eight panels) and one galaxy formation run (the bottom panel). Dashed lines correspond to the standard model and dot-dashed lines show our modified model, eq. (\ref{['eq:modified']}). The cluster in the top panel is experiencing a merger event with a comparable mass cluster, which can be seen as an excursion of the profile at $r \sim 0.2 r_{\rm vir}$.
• Figure 5: The effect of gas cooling on the mass profile at different epochs for the cluster shown in Figures \ref{['fig:cl6_m']} and \ref{['fig:cl6_den']}. Thin and thick lines show the profiles at $z=4$ and $z=0.18$, respectively: dotted lines --- profiles for baryons (gas$+$stars) in the CSF run; dot-dashed lines --- profiles of DM in the adiabatic run; solid lines --- DM profiles in the CSF run.