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Tully-Fisher Relation and its Implications for Halo Density Profile and Self-interacting Dark Matter

We show that the Tully-Fisher relation observed for spiral galaxies can be explained in the current scenario of galaxy formation without invoking subtle assumptions, provided that galactic-sized dark haloes have shallow, core-like central profiles, with a core radius proportional to halo circular velocity. In such a system, both disk and halo contribute significantly to the maximum rotation of the disk, and the interaction between the disk and halo components acts to reduce the scatter in the Tully-Fisher relation. With model parameters chosen in plausible ranges, the model can well accommodate the zero-point, slope, scatter of the observed Tully-Fisher relation, as well as the large range of disk sizes. The model predicts that LSB disks obey a Tully-Fisher relation similar to that of normal disks, if disk mass-to-light ratio is properly taken into account. The halo profile required by the Tully-Fisher relation is as shallow as that required by the rotation curves of faint disks, but much shallower than that predicted by conventional CDM models. Our results cannot be explained by some of the recent proposals for resolving the conflict between conventional CDM models and the rotation-curve shapes of faint galaxies. If dark matter self-interaction (either scattering or annihilation) is responsible for the shallow profile, the observed Tully-Fisher relation requires the interaction cross section σ_X to satisfy <σ_{X}|v|>/m_{X}~10^{-16} cm^3/s/GeV.