Self-regulating galaxy formation as an explanation for the Tully-Fisher relation

Using three-dimensional hydrodynamical simulations of galaxy formation with supernova feedback and a multiphase medium, we derive theoretical relation s analogous to the observed Tully-Fisher (TF) relations in various photomet ric bands. This paper examines the influence of self-regulation mechanisms including supernova feedback on galaxy luminosities and the TF relation in three cosmological scenarios: CDM, Lambda CDM, and BSI (broken scale invari ance). Technical questions such as dependence on resolution, galaxy-finding algorithms, and assignment procedure for circular velocity are critically examined. The luminosity functions in the B and K bands are quite sensitive to supernova feedback at the faint end studied here. We find that the fain t end of the B-band luminosity function (-18 less than or equal to M-B less than or equal to -15) is alpha approximate to -(1.5-1.9). This slope is st eeper than the Stromlo-Automatic Plate Measuring Facility estimate but in r ough agreement with the recent ESO Slice Project estimates. The galaxy cata logs derived from our hydrodynamic simulations lead to an acceptably small scatter in the theoretical TF relation amounting to Delta M = 0.2-0.4 in th e I band and increasing by 0.1 mag from the I band to the B band. Our resul ts give strong evidence that the tightness of the TF relation cannot be att ributed to supernova feedback alone. However, although eliminating supernov a feedback affects the scatter only moderately (Delta M = 0.3-0.6), it does influence the slope of the TF relation quite sensitively. With supernova f eedback, L proportional to V-c(3-3.5) (the exponent depending on the degree of feedback). Without it, L proportional to V-c(2) as predicted by the vir ial theorem with constant MIL and radius independent of luminosity. The TF relation reflects the complex connection between depths of galaxy potential wells and the supply of gas for star formation. Hydrodynamic simulations p rovide direct information on this connection and its dependence on modeling parameters. Because of the small number of phenomenological parameters in our approach, it can serve as a useful laboratory for testing various hypot heses and gaining insight into the physics responsible for the scatter, slo pe, and amplitude of the TF relation.