Variations On Tully-Fischer

The Baryonic Tully-Fischer relation (a tight correlation between ordinary matter and inferred total mass) holds much more tightly than a parallel correlation considering only ordinary matter in stars.

We combine data for extragalactic systems to quantify a relation between the observed baryonic mass Mb and the enclosed dynamical mass M200 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)>10^14M⊙, 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) ≈ 5 × 10^13 M⊙. 

This relation is qualitatively similar to stellar mass-halo mass relations derived from abundance matching, but exhibits less scatter.

Stacy McGaugh, Tobias Mistele, Francis Duey, Konstantin Haubner, Federico Lelli, Jim Schombert, Pengfei Li, "The Baryonic Mass-Halo Mass Relation of Extragalactic Systems" arXiv:2603.06479 (March 6, 2026) (Accepted for publication in the Astrophysical Journal).