The Impact of Baryonic Effects on the Dynamical Masses Inferred Using Satellite Kinematics

TL;DR

This work develops an analytical framework to quantify how baryons modify dynamical masses inferred from satellite kinematics, incorporating stars, gas, and adiabatic dark-matter response for halos in the $10^{12}-10^{15}\,M_\odot$ range. The model is calibrated against EAGLE simulations and integrated into BASILISK to produce a baryonic correction function for $\sigma_{\rm ap}$, revealing that baryons can reduce observed velocity dispersions by a few percent, with larger effects at lower halo masses and when strong feedback ejects baryons. The key contributions are (i) a flexible, physically-motivated mass model including ejected baryons and a diffuse stellar component, (ii) a calibrated adiabatic-response treatment of DM, and (iii) a practical correction for satellite-kinematics analyses that shifts inferred halo masses by up to ~0.3 dex at fixed luminosity, underscoring implications for cosmological parameter inferences and feedback-process constraints.

Abstract

Satellite kinematics offers a powerful method to infer dynamical halo masses and has been demonstrated to yield tight constraints on the galaxy-halo connection. However, previous studies have assumed that the halos in which the satellites orbit are composed solely of dark matter, neglecting the role of baryons. Here, we develop an analytical model incorporating stars, gas, and the adiabatic response of dark matter to assess the impact of baryonic effects on the inference from satellite kinematics. The model covers halos in the mass range $10^{12}-10^{15}M_\odot$ and is tuned to agree with well-established observational scaling relations. In addition, the model uses simple functional forms for the mass fractions of ejected baryons and diffuse halo stars, calibrated to the median trends in the EAGLE hydrodynamical simulations. We find that baryonic effects mainly result in a reduction of the satellite line-of-sight velocity dispersion due to the ejection of baryons and the resulting response of the dark matter halo. The effect is minimal (less than 1%) for the most massive halos, but reaches ~5-6% for halos in the mass range $10^{12}-10^{13}M_\odot$, and up to 8% in extreme cases. We propose a simple formalism for correcting the satellite line-of-sight velocity dispersion for baryonic effects, and for marginalizing over the uncertainties. We integrate this correction function into BASILISK, a Bayesian hierarchical inference method applied to satellite kinematics data extracted from large redshift surveys, and find that this shifts central galaxies to higher inferred halo masses at fixed luminosity by up to ~0.3 dex. In a forthcoming work, we demonstrate that these few-percent level baryonic effects can have a non-negligible impact on the inference of cosmological parameters, motivating a novel approach to constraining the efficiency of feedback processes associated with galaxy formation.

Figures (9)

• Figure 1: Left: Fraction of stellar mass in the central galaxy relative to the total DMO halo mass. The fiducial model follows the stellar–halo mass relation of Moster2013. For comparison, we overplot the empirical SHMRs of Moster2013, Behroozi2013 and RodriguezPuebla2017, as indicated, which are in excellent agreement with each other. The red shaded band marks 0.2 dex scatter around the relation of Moster2013, which, based on estimates of the scatter in the SHMR, indicates the band that is expected to enclose about 68 percent of all galaxies. The gray points indicate relaxed halos from the EAGLE simulation, which underpredict the observed relation at low halo masses. Middle: Fraction of stellar mass in the diffuse stellar component as a function of halo mass, defined as $f_{\mathrm{\ast, diffuse}} = M_{\rm \ast, diffuse}/(f_{\rm b}M_{\mathrm{DMO}})$, where $M_{\rm \ast, diffuse}$ is the total stellar mass within the virial radius minus the central galaxy mass. The solid pink curve is a fit to the EAGLE data of the form of equation (\ref{['eq:methodology:fdiffuse']}). Right: Fraction of ejected baryonic mass as a function of halo mass, defined as $f_{\mathrm{eject}} = M_{\rm eject}/(f_{\rm b}M_{\mathrm{DMO}})$, where $M_{\rm eject}$ is determined through equation (\ref{['eq:methodology:feject']}). The solid brown curve is a fit to the EAGLE data of the form of equation (\ref{['eq:methodology:fgas']}). The shaded bands in the middle and right panels indicate the 16th–84th percentile ranges, computed in ten equally spaced bins in halo mass.
• Figure 1: The aperture velocity dispersion ratio, $\sigma_{\rm ap}/\sigma_{\rm ap, DMO}$, as a function of halo mass, while varying many parameters in the halo model (see text). In each panel, the fiducial model is shown in black. If no baryonic corrections were applied to $\sigma_{\rm ap}$, the ratio would remain at $\sigma_{\rm ap}/\sigma_{\rm ap, DMO}=1$, indicated with the black dotted line in each panel. The gray area indicates the extreme scenarios discussed in Section \ref{['sec:results:variations_from_fiducial']} and Fig. \ref{['fig:results:finalplot']}. Notably, all variations fall within this region, showing the minor impact of these parameters compared to these extreme scenarios.
• Figure 1: The impact of baryons on the fourth-order moment of satellite kinematics. We show results for three halo masses: $M_{\mathrm{DMO}} = 10^{12.5} M_{\odot}$ (top), $10^{13.5} M_{\odot}$ (middle), and $10^{14.5} M_{\odot}$ (bottom). The panels display the line-of-sight velocity dispersion $\sigma_{\mathrm{los}}$ (left), the projected fourth velocity moment $\langle v_{\mathrm{los}}^4 \rangle$ (middle), and the line-of-sight kurtosis $\kappa_{\mathrm{los}} \equiv \langle v_{\mathrm{los}}^4 \rangle / \sigma_{\mathrm{los}}^4$ (right). Black curves represent the DMO model. Blue and green curves show the fiducial baryonic model without ($\nu=0$) and with ($\nu=1$) adiabatic halo response, respectively. While the central galaxy strongly suppresses $\kappa_{\mathrm{los}}$ in the inner halo ($R_{\mathrm{p}} \lesssim 0.1 r_{200}$), the baryonic models converge to the DMO kurtosis profile in the radial range probed by the satellite kinematics analysis ($R_{\rm min} < R_{\rm p} < R_{\rm max}$, gray shaded region).
• Figure 2: Left: Analytical density profiles for two halos of mass $M_{\rm DMO} = 10^{12.5}\mathrm{M}_{\odot}$ (top) and $M_{\rm DMO} = 10^{13.5}\mathrm{M}_{\odot}$ (bottom) for our fiducial model. We show the different components of the model; the total DMO profiles (black), dark matter in the baryonic model with no adiabatic response ($\nu=0$) (gray), the central galaxy (red dashed), diffuse stellar component (light pink dashed), total stellar component (red solid), gas (light blue) and total profile in the baryon model (blue). Middle: The corresponding enclosed mass profiles for the same two halos. Right: The line-of-sight velocity dispersion for both the DMO model (black) and the baryonic model (blue), which are obtained from their corresponding density (equiv. mass) profiles. We highlight the region where satellites are selected in Basilisk, between the minimum radius ($R_{\mathrm{min}}$ = 55$\hbox{$^{\prime\prime}$}$ due to fibre collisions) and maximum radius ($R_{\mathrm{max}}$ = 0.375 $R_{\mathrm{vir}}$) as the gray shaded area. The integrated aperture velocity dispersion is computed over the radial range [$R_{\mathrm{min}}, R_{\mathrm{max}}$] for both the baryonic model ($\sigma_{\mathrm{ap}}$) and DMO model ($\sigma_{\mathrm{ap,DMO}}$). The ratio of the integrated velocity dispersion between the two models is indicated in the lower left corner.
• Figure 3: Comparison between the fiducial halo model and EAGLE halos of similar mass. We show the density profiles for two halos of mass $M_{\rm DMO} = 10^{12.5}\mathrm{M}_{\odot}$ (left) and $M_{\rm DMO} = 10^{13.5}\mathrm{M}_{\odot}$ (right). Solid lines represent the components of our halo model: dark matter (gray), total stellar mass (central + diffuse) (red), gas (light blue), and total density profile (blue). To quantify the halo-to-halo variation in EAGLE halos, we compute the central 95% spread in density in bins of $r/r_{200}$ for two stacks of EAGLE halos whose median DMO masses match the model: $10^{12.25}<M_{\rm DMO}/\>{\rm M_{\odot}}<10^{12.85}$ (480 halos, left panel) and $10^{13.3}<M_{\rm DMO}/\>{\rm M_{\odot}}<10^{13.9}$ (31 halos, right panel). This spread is shown as shaded regions in matching colors for each component. In the main panels, the analytical model does not include halo response ($\nu=0$). The insets in the lower-left corner zoom in on the inner dark matter density profiles: the gray curve shows the $\nu=0$ model (as in the main panel), while the green curve includes adiabatic response ($\nu=1$).