The host galaxy and late-time evolution of the Super-Luminous Supernova
  PTF12dam
  Super-luminous supernovae of type Ic have a tendency to occur in faint host
galaxies which are likely to have low mass and low metallicity. PTF12dam is one
of the closest and best studied super-luminous explosions that has a broad and
slowly fading lightcurve similar to SN 2007bi. Here we present new photometry
and spectroscopy for PTF12dam from 200-500 days (rest-frame) after peak and a
detailed analysis of the host galaxy (SDSS J142446.21+461348.6 at z = 0.107).
Using deep templates and image subtraction we show that the full lightcurve can
be fit with a magnetar model if escape of high-energy gamma rays is taken into
account. The full bolometric lightcurve from -53 to +399 days (with respect to
peak) cannot be fit satisfactorily with the pair-instability models. An
alternative model of interaction with a dense CSM produces a good fit to the
data although this requires a very large mass (~ 13 M_sun) of hydrogen free
CSM. The host galaxy is a compact dwarf (physical size ~ 1.9 kpc) and with M_g
= -19.33 +/- 0.10, it is the brightest nearby SLSN Ic host discovered so far.
The host is a low mass system (2.8 x 10^8 M_sun) with a star-formation rate
(5.0 M_sun/year), which implies a very high specific star-formation rate (17.9
Gyr^-1). The remarkably strong nebular lines provide detections of the [O III]
\lambda 4363 and [O II] \lambda\lambda 7320,7330 auroral lines and an accurate
oxygen abundance of 12 + log(O/H) = 8.05 +/- 0.09. We show here that they are
at the extreme end of the metallicity distribution of dwarf galaxies and
propose that low metallicity is a requirement to produce these rare and
peculiar supernovae.
