Baryonic Tully-Fisher Relations

I describe the disk mass–rotation velocity relation which underpins the familiar luminosity–linewidth relation. Continuity of this relation favors nearly maximal stellar mass-to-light ratios. This contradicts the low mass-to-light ratios implied by the lack of surface brightness dependence in the same relation. 1. Searching for the Physical Basis of the Tully-Fisher Relation The Tully-Fisher (TF) relation (Tully & Fisher 1977) is well known. Yet why it works is not clear. A dizzying variety of distinct interpretations have been offered over the years (e.g., Aaronson, Mould, & Huchra 1979; Milgrom 1983; Walker 1999). There is no consensus even when the context is limited to that of NFW halos Widely divergent pictures have been offered, sometimes in successive papers by the same authors (e.g., Dalcanton, Spergel, & Summers 1995, 1997; van den Bosch & Dalcanton 2000; Mo, Mao & White 1998; Mo & Mao 2000; Steinmetz & Navarro 1999, Navarro & Steinmetz 2000). It is commonly assumed that mass scales with some power of rotation velocity, and that luminosity traces mass. The first piece of this common wisdom is questionable given the startling lack of dependence of the TF relation on surface brightness (Sprayberry et al. 1995; Zwaan et al. 1995). It matters not at all whether the luminous mass is concentrated or diffuse. This is commonly interpreted to mean that the mass in stars is insignificant. If stellar mass contributes noticeably to the rotation velocity, V 2 = GM/R surely demands some shift (McGaugh & de Blok 1998; Courteau & Rix 1999). Whether luminosity traces mass is a more tractable issue. I address this here in an empirical way using data which span the largest available dynamic range. This at least makes clear that the fundamental relation which needs explaining is one between rotation velocity and disk mass (McGaugh et al. 2000). 2. The Disk Mass–Rotation Velocity Relation Implicit in our presumption that light traces mass is the relation L = Υ ∗ f∗fdfbMtot, (1) where fb is the baryon fraction of the universe, fd is the fraction of the baryons associated with a particular galaxy which reside in the disk, f∗ is the fraction