  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 \sigma_X to satisfy
<\sigma_{X}|v|>/m_{X}~10^{-16} cm^3/s/GeV.

Astrophysics