Dark Matter Halos of Disk Galaxies: Constraints from the Tully‐Fisher Relation

Abstract

We investigate structural properties of dark matter halos of disk galaxies, using a well-defined sample of 81 disk-dominated galaxies from the SDSS redshift survey. We model the mass-velocity (TF) and fundamental plane (FP) relations of these galaxies, using the observed stellar mass M * , disk scale length R d , and optical Hα rotation velocity at 2.2 R d . We calculate model galaxy populations, defined by the distribution of the stellar disk-to-total mass fraction, m d , and include the effect of adiabatic contraction. We find that models with constant m d underpredict the intrinsic scatter of the TF and FP relations and predict an (unobserved) strong correlation between TF residuals, even with the full range of halo concentration scatter. Introducing a scatter of m d and allowing the mean value ##IMG## [http://ej.iop.org/images/0004-637X/671/2/1115/eq-00007.gif] {\overline{m}_{d}} to scale with the stellar surface density significantly improves observational match and reduces the predicted residual correlation enough to be consistent with the data. The distribution of angular momentum parameters required to match the observed scale lengths is an output of the models and is narrower than that predicted for halo spin parameters. However, our best-fit models with a Kroupa stellar IMF overproduce the galaxy stellar mass function and predict the virial mass-to-light ratios lower than those inferred from galaxy-galaxy weak lensing and satellite dynamics. We suggest three possible solutions to these problems: (1) ignoring the effects of adiabatic contraction, (2) adopting a "light" stellar IMF with M * / L lower by 0.15 dex, or (3) considering the lower halo concentrations expected for a low power spectrum normalization σ 8 ≈ 0.74. In combination with our proposed correlation of ##IMG## [http://ej.iop.org/images/0004-637X/671/2/1115/eq-00010.gif] {\overline{m}_{d}} with surface density, any of these solutions yields acceptable residual correlations and relieves most of the observational tension between the TF relation and the galaxy stellar mass function.