Dark and luminous matter in the NGC 3992 group of galaxies, II. The   dwarf companions UGC 6923, UGC 6940, UGC 6969, and the Tully-Fisher relation
  Detailed neutral hydrogen observations have been obtained of the large barred spiral galaxy NGC 3992 and its three small companion spiral galaxies, UGC 6923, UGC 6940, and UGC 6969. Contrary to the large galaxy, for the companions the HI distribution ends quite abruptly at the optical edges. Velocity fields have been constructed from which rotation curves have been derived. Assuming a reasonable M/L ratio, a decomposition of these rotation curves generates nearly equal dark matter halos. When comparing the position-velocity diagrams of the two brightest galaxies, UGC 6923 and UGC 6969, it is obvious that the rotation curve of the latter has a shape closer to solid body than the former, yet the same maximum rotational level is reached. This is likely generated by the equal dark matter halos in combination with UGC 6923 being a factor five more luminous than UGC 6969 and so its luminous matter gives a higher contribution to the rotation in the inner regions. An NFW-CDMLambda dark halo is consistent with the observed rotation curve of UGC 6923 but not consistent with the rotation curve of UGC 6969. If the NGC 3992 group is part of the Ursa Major cluster, then the I-band M/L ratio of NGC 3992 has to be at least 1.35 times as large as that of the average spiral galaxy in the cluster. On the other hand, equal M/L ratios can be achieved when the NGC 3992 group is placed more than 3 Mpc behind the cluster. Both possibilities can explain why NGC 3992 appears to be 0.43 magnitudes too faint for its rotation. 
Roelof Bottema