The Ursa Major Cluster of Galaxies. V ; HI Rotation Curve Shapes and the Tully-Fisher Relations

The Tully-Fisher relations for a complete sample of spirals in the Ursa Major cluster is investigated. The merits of combining B, R, I and K' photometry with HI rotation curves (RCs) have been exploited. In addition to the corrected HI global profile widths W_{R,I}^i, the HI RCs allow direct measurements of the maximum rotation Vmax and the amplitudes Vflat of the outer flat parts. The dynamical state of the gas disks could also be determined in detail. For large galaxy samples, the M^{b,i}_R - Log(W_{R,I}^i) correlation in conjunction with strict selection criteria is preferred for distance determinations with a 7% accuracy. Galaxies with rising RCs at the last measured point lie systematically on the low velocity side of the TF-relation. Galaxies with partly declining RCs (Vmax>Vflat) tend to lie on the high velocity side when using W_{R,I}^i or Vmax. These trends are eliminated when Vflat is used. The M^{b,i}_B - Log(2Vflat) residuals correlate consistently with morphology, color, surface brightness and gas mass fraction. These correlations are absent for the near-IR M^{b,i}_K' - Log(2Vflat) residuals. The tightest correlation (Xred=1.1) is found for the M^{b,i}_K' - Log(2Vflat) relation with a slope of -11.3 +/- 0.5 and a total scatter of 0.26^m with a most likely intrinsic scatter of zero. The tightness of the near-IR correlation is preserved when converting it into a baryonic TF-relation which has a slope of -10.0 for (Mgas/L_K')=1.6 while a zero intrinsic scatter remains most likely. The tightness of the near-IR and baryonic correlations suggests that the TF-relation reflects a correlation between the dark matter halo mass, indicated by Vflat, and the total baryonic mass Mbar where Mbar~Vflat^4. The distribution of the baryons inside halos of similar mass is irrelevant for this relation.