The Baryonic Mass-Halo Mass Relation of Extragalactic Systems

Abstract

We combine data for extragalactic systems to quantify a relation between the observed baryonic mass $M_b$ and the enclosed dynamical mass $M_{200}$ inferred from kinematics or gravitational lensing. Our sample covers nine orders of magnitude in baryonic mass, including galaxies with kinematic or weak gravitational lensing data and groups and clusters of galaxies with new gravitational lensing data. For rich clusters with $M_b > 10^{14}\;\mathrm{M}_{\odot}$, the observed baryon fraction is consistent with the cosmic value, $f_b = 0.157$. For lower masses, the baryon fraction decreases systematically with mass. The variation is well described by $M_b/M_{200} = f_b \tanh(M_b/M_0)^{1/4}$ with $M_0 \approx 5 \times 10^{13}\;\mathrm{M}_{\odot}$. This relation is qualitatively similar to stellar mass-halo mass relations derived from abundance matching, but exhibits less scatter.

Figures (9)

• Figure 1: Conceptual elements of a galaxy: the stars (yellow/blue) and atomic gas (green) of NGC 6946 FTHINGS are shown embedded in an extended dark matter halo (black). The dark matter density decreases continuously with radius so the halo has no hard edge, but for convenience we adopt the common convention that the radius $r_{200}$ marks the boundary of the dark matter halo and the dividing line between the CGM and IGM (orange). The stars and gas illustrated here appear within $r < 20\;\mathrm{kpc}$ while $r_{200} \approx 220\;\mathrm{kpc}$ (not shown to scale).
• Figure 2: The observed flat velocity $V_f$ as it relates to the fitted $V_{\mathrm{200}}$ for pseudo-isothermal (left) and NFW (right) halos Li2020. Filled points have formal uncertainties less than 20% in $V_{\mathrm{200}}$; open points are less accurate fits. The solid line shows $V_f = V_{\mathrm{200}}$. The gray line in the right panel shows eq. 2a of KatzfV, which corresponds roughly to $f_v \approx 1.4$.
• Figure 3: The flat-equivalent circular velocity of extragalactic systems as a function of stellar mass (top) and baryonic mass (bottom). Data for rotationally supported galaxies are depicted by circles; squares represent pressure supported systems. The blue circles are galaxies with directly measured distances, $V_f$ from rotation curves, and stellar masses from WISE photometry from Duey_wiseiii. Green circles are gas rich galaxies trachstarkLeoProtSHIELDiorio2017KK153Namumba2025 not in Duey_wiseiii. Yellow points are Local Group galaxies, both spirals and dwarfs McG2021; gray squares are ultrafaint dwarfs OneLaw. Lensing results for early and late type galaxies indefinitelyflat are shown as pink squares and magenta circles, respectively. Red squares are clusters of galaxies Mistele_CLASH and purple squares are groups of galaxies (this work). The orange line is the BTFR (eq. \ref{['eq:btfr']}).
• Figure 4: The stellar mass fraction as a function of stellar mass (top) and the baryonic mass fraction as a function of baryonic mass (bottom). Data and symbols as in Fig. \ref{['fig:VMb']} with the additional distinction that large squares in the top panel represent the sum of the stellar mass of all galaxies in a group or cluster while small squares are the stellar mass of the brightest galaxy only. The horizontal line is the cosmic baryon fraction $f_b = 0.157$PlanckCosmology. The colored lines in the top panels show the stellar mass--halo mass relations from abundance matching given by Moster2013, Behroozi13, and KravtsovAM. The black line in the lower panel is eq. \ref{['eq:KMM']}.
• Figure 5: The baryonic mass fraction as a function of mass $M_{\mathrm{200}}$ with the equivalent $V_{\mathrm{200}}$ noted on the top axis. Data and symbols are the same as in figures \ref{['fig:M200']} and \ref{['fig:VMb']}. The top panels follow from using rotation curve fits to estimate halo mass as in Fig. \ref{['fig:M200']} for pseudo-isothermal (left) and NFW (right) halo models. The bottom panels follow from using the flat rotation speed as the halo mass estimator as in Fig. \ref{['fig:VMb']} with $f_v = 1.0$ (left) or $f_v = 1.4$ (right) for the kinematic data; the lensing data are unchanged.