The Ursa Major Cluster of Galaxies. V. HiRotation Curve Shapes and the Tully‐Fisher Relations

The Tully-Fisher relations for a complete sample of spirals in the Ursa Majorcluster is investigated. The merits of combining B, R, I and K' photometry withHI rotation curves (RCs) have been exploited. In addition to the corrected HIglobal profile widths W_{R,I}^i, the HI RCs allow direct measurements of themaximum rotation Vmax and the amplitudes Vflat of the outer flat parts. Thedynamical state of the gas disks could also be determined in detail. For largegalaxy samples, the M^{b,i}_R - Log(W_{R,I}^i) correlation in conjunction withstrict selection criteria is preferred for distance determinations with a 7%accuracy. Galaxies with rising RCs at the last measured point liesystematically on the low velocity side of the TF-relation. Galaxies withpartly declining RCs (Vmax>Vflat) tend to lie on the high velocity side whenusing W_{R,I}^i or Vmax. These trends are eliminated when Vflat is used. TheM^{b,i}_B - Log(2Vflat) residuals correlate consistently with morphology,color, surface brightness and gas mass fraction. These correlations are absentfor 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 intrinsicscatter of zero. The tightness of the near-IR correlation is preserved whenconverting 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. Thetightness of the near-IR and baryonic correlations suggests that theTF-relation reflects a correlation between the dark matter halo mass, indicatedby Vflat, and the total baryonic mass Mbar where Mbar~Vflat^4. The distributionof the baryons inside halos of similar mass is irrelevant for this relation.Comment: 24 pages, 9 tables, 9 figures. Accepted for publication in the Astrophysical Journa