The little galaxy that could: Kinematics of Camelopardalis B

We present deep, high velocity resolution (1.6 km/s) GMRT HI as well as optical data for the faint (M_B ~ -10.9) galaxy Camelopardalis B. We find that the HI in the galaxy has a regular velocity field, consistent with rotational motion. The implied kinematical major axis is well aligned with the major axis of both the HI and optical images. Cam B is the faintest known galaxy with such relatively well behaved kinematics. From the HI velocity field we derive a rotation curve for the galaxy. The peak (inclination corrected) rotation velocity is only 7km/s, comparable to the observed velocity dispersion. After correcting the observed rotation velocities for random motions (the "asymmetric drift" correction) we find a corrected peak rotation velocity of ~ 20 km/s. On fitting mass models to corrected rotation curve we find that the kinematics of Cam B is well fit with a modified isothermal halo with central density $\rho_0$ approximately 12.0 $M_\odot$ pc$ ^{-3}$. This derived central density has only a very weak dependence on the assumed M/L ratio of the stellar disk. We also find that the corrected rotation curve cannot be fit with an NFW halo regardless of the assumed M/L ratio. We compile from the literature a sample of galaxies with rotation curves obtained from HI synthesis observations. From this sample (which has an absolute magnitude range of ~ 12) we find (i) that Cam B lies on the Tully-Fisher relation defined by these galaxies, provided we use the corrected rotation velocity, and (ii) a weak trend for increasing halo central density with decreasing galaxy size. Such a trend is expected in hierarchical models of halo formation.