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, Lambda CDM and BSI (broken scale invariance)). The galaxy catalogs derived from our hydrodynamical simulations lead to an acceptably small scatter in the theoretical TF relation amounting to Delta 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 propto V_c^{3-3.5} (depending on the strength of supernova feedback). Without it, L propto V_c^{2} as predicted by the virial theorem with constant M/L. 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 leq M_B leq -15) has a slope that is steeper than the Stromlo-APM estimate, but in rough agreement with the recent ESO Slice Project estimates.
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