We present observations and interpretation of the Type IIn supernova SN
2008am discovered by the ROTSE Supernova Verification Project (RSVP). SN 2008am
peaked at approximately -22.3 mag at a redshift of z=0.2338, giving it a peak
luminosity of 3 x 10^{44}erg/s and making it one of the most luminous
supernovae ever observed. The total radiated energy is ~ 2 x 10^{51} erg.
Photometric observations in the ultraviolet, optical and infrared bands
(J,H,Ks) constrain the SED evolution. We obtained six optical spectra of the
supernova, five on the early decline from maximum light and a sixth nearly a
year later plus a very late-time spectrum (~2 yr) of the host galaxy. The
spectra of SN 2008am show strong Balmer-line and He I lambda 5876A emission
with intermediate widths (~25A) in the first ~40 days after optical maximum. We
examine a variety of models for the line wings and conclude that multiple
scattering is most likely, implying that our spectra contain no specific
information on the bulk flow velocity. We examine a variety of models for the
ROTSE light curve subject to the rise time and the nature of the spectra,
including radioactive decay, shocks in optically-thick and optically-thin
circumstellar media (CSM) and a magnetar. The most successful model is one for
which the CSM is optically-thick and in which diffusion of forward
shock-deposited luminosity gives rise to the observed light curve. Diffusion of
the shock-deposited energy from the forward shock is found to be important to
account for the rising part of the light curve. Although there are differences
in detail, SN 2008am appears to be closely related to other super-luminous Type
IIn supernovae, SN 2006gy, SN 2006tf and perhaps SN 2008iy, that may represent
the deaths of very massive LBV-type progenitors and for which the luminosity is
powered by the interaction of the ejecta with a dense circumstellar medium.Comment: 58 pages, 14 figure