Dynamical Constraints on Disk Galaxy Formation

The rotation curves of disk galaxies exhibit a number of striking regularities. The amplitude of the rotation is correlated with luminosity (Tully-Fisher), the shape of the rotation curve is well predicted by the luminous mass distribution, and the magnitude of the mass discrepancy increases systematically with decreasing centripetal acceleration. These properties indicate a tight connection between light and mass, and impose strong constraints on theories of galaxy formation. 1. Some Important Properties There are many systematic properties of the dynamics of spiral galaxies which galaxy formation theory must explain. These include (at least) 1. the luminosity–rotation velocity relation (Tully & Fisher 1977), 2. the utility of maximum disk in high surface brightness galaxies (van Albada & Sancisi 1986; Sellwood 1999), 3. the surface brightness–enclosed mass-to-light ratio relation (Zwaan et al. 1995; McGaugh & de Blok 1998), 4. the luminosity–rotation curve shape relation (Rubin et al. 1985; Persic & Salucci 1991), 5. the mass discrepancy–acceleration relation (Sanders 1990; McGaugh 1999), and 6. the MOND (Milgrom 1983) phenomenology (Begeman et al. 1991; Sanders 1996; de Blok & McGaugh 1998). The properties listed above are interrelated, and their meaning open to interpretation. I will attempt here to take an empirical approach illustrating the general requirements imposed on theory by the data. 2. The Baryonic Mass–Rotation Velocity Relation The relation between galaxy luminosity and line width is well known (the TullyFisher relation). This important property (1) is illustrated in Fig. 1. Common lore has it that the Tully-Fisher relation is a reflection of an underlying relation between total mass and rotation velocity. Presumably, luminosity