XRF 100316D / SN 2010bh and the nature of gamma ray burst supernovae

We present ground-based and HST optical and infrared observations of XRF 100316D / SN 2010bh. It is seen that the optical light curves of SN 2010bh evolve at a faster rate than the archetype GRB-SN 1998bw, but at a similar rate to SN 2006aj, a supernova that was spectroscopically linked with XRF 060218, and at a similar rate to non-GRB associated type Ic SN 1994I. We estimate the rest-frame extinction of this event from our optical data to be E(B-V)=0.18 +/- 0.08 mag. We find the V-band absolute magnitude of SN 2010bh to be M_{V}=-18.62 +/- 0.08, which is the faintest peak V-band magnitude observed to-date for a spectroscopically-confirmed GRB-SNe. When we investigate the origin of the flux at t-t_{o}=0.598 days, it is shown that the light is not synchrotron in origin, but is likely coming from the supernova shock break-out. We then use our optical and infrared data to create a quasi-bolometric light curve of SN 2010bh which we model with a simple analytical formula. The results of our modeling imply that SN 2010bh synthesized a nickel mass of M_{Ni}=0.10 +/- 0.01 M_{\odot}, ejected M_{ej}=2.24 +/- 0.08 M_{\odot} and has an explosion energy of E_{k}=1.39 +/- 0.06 x 10^{52} erg (where the quoted errors are statistical only; we discuss the potential sources of the systematic errors in the text). Finally, for a sample 20 GRB-SNe we check for a correlation between the stretch factors and luminosity factors in the R band and conclude that no statistically-significant correlation exists.