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 9 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 &gt; 10 14 M ⊙ , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">200</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> </mml:msub> <mml:mi>tanh</mml:mi> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> with M 0 ≈ 5 × 10 13 M ⊙ . This relation is qualitatively similar to stellar mass–halo mass relations derived from abundance matching, but exhibits less scatter.