Semianalytical Models for the Formation of Disk Galaxies. I. Constraints from the Tully‐Fisher Relation

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We present new semianalytical models for the formation of disk galaxies with the purpose of investigating the origin of the near-infrared Tully-Fisher (TF) relation. The models assume that disks are formed by cooling of the baryons inside dark halos with realistic density profiles and that the baryons conserve their specific angular momentum. Adiabatic contraction of the dark halo is taken into account, as well as a recipe for bulge formation based on a self-regulating mechanism that ensures disks to be stable. Only gas with densities above the critical density given by Toomre's stability criterion is considered eligible for star formation. A Schmidt law is assumed to prescribe the rate at which this gas is transformed into stars. The introduction of the star formation threshold density proves an essential ingredient of our models and yields gas mass fractions that are in excellent agreement with observations. Finally, a simple recipe for supernovae feedback is included. We emphasize the importance of extracting the proper luminosity and velocity measures from the models, something that has often been ignored in the past. We use the zero point of the K-band TF relation to place stringent constraints on cosmological parameters. In particular, we rule out a standard cold dark matter universe, in which disk galaxies are too faint to be consistent with observations. The TF zero point, in combination with nucleosynthesis constraints on the baryon density, and with constraints on the normalization of the power spectrum, requires a matter density Ω0 0.3. The observed K-band TF relation has a slope that is steeper than simple predictions based on dynamical arguments suggest. Taking the stability related star formation threshold densities into account steepens the TF relation and decreases its scatter. However, in order for the slope to be as steep as observed, further physics are required. We argue that the characteristics of the observed near-infrared TF relation do not reflect systematic variations in stellar populations, or cosmological initial conditions. In fact, feedback seems an essential ingredient in order to explain the observed slope of the K-band TF relation. Finally, we show that our models provide a natural explanation for the small amount of scatter that makes the TF relation useful as a cosmological distance indicator.