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

Using 3D hydrodynamical simulations of galaxy formation with supernova feedback and a multiphase medium, we derive theoretical relations analogous to the observed Tully-Fisher (TF) relations in various photometric 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, ΛCDM and BSI (broken scale invariance)). Technical questions such as dependence on resolution, galaxy finding algorithms, 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 faint end of the B-band luminosity function (−18 ≤ MB ≤ −15) is α ≈ -(1.5 to 1.9). This slope is steeper than the Stromlo-APM estimate, but in rough agreement with the recent ESO Slice Project estimates. The galaxy catalogs derived from our hydrodynamical simulations lead to an acceptably small scatter in the theoretical TF relation amounting to ∆M = 0.2− 0.4 in the I band, and increasing by 0.1 magnitude from the I-band to the B-band. Our results give strong evidence that the tightness of the TF relation cannot be attributed to supernova feedback alone. However, although eliminating supernova feedback hardly affects the scatter, it does influence the slope of the TF relation quite sensitively. With supernova feedback, L ∝ V 3−3.5 c (depending on the strength of supernova feedback). Without it, L ∝ V 2 c as predicted by the virial theorem with constant M/L. The TF relation reflects the complex connection between depths of galaxy potential wells and the supply of gas for star formation. Hydrodynamic simulations provide 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