Self‐regulating Galaxy Formation as an Explanation for the Tully‐Fisher Relation

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Abstract
Using three-dimensional 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, 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 faint end of the B-band luminosity function (-18≤MB≤-15) is α≈-(1.5-1.9). This slope is steeper than the Stromlo-Automatic Plate Measuring Facility estimate but in rough agreement with the recent ESO Slice Project estimates. The galaxy catalogs derived from our hydrodynamic simulations lead to an acceptably small scatter in the theoretical TF relation amounting to ΔM=0.2-0.4 in the I band and increasing by 0.1 mag 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 affects the scatter only moderately (ΔM=0.3-0.6), it does influence the slope of the TF relation quite sensitively. With supernova feedback, L∝V3-3.5c (the exponent depending on the degree of feedback). Without it, L∝V2c as predicted by the virial theorem with constant M/L 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 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 a useful laboratory for testing various hypotheses and gaining insight into the physics responsible for the scatter, slope, and amplitude of the TF relation.
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