Rates of Superluminous Supernovae at z~0.2
  We calculate the volumetric rate of superluminous supernovae (SLSNe) based on
5 events discovered with the ROTSE-IIIb telescope. We gather light curves of 19
events from the literature and our own unpublished data and employ crude
k-corrections to constrain the pseudo-absolute magnitude distributions in the
rest frame ROTSE-IIIb (unfiltered) band pass for both the hydrogen poor
(SLSN-I) and hydrogen rich (SLSN-II) populations. We find that the peak
magnitudes of the available SLSN-I are narrowly distributed ($M = -21.7 \pm
0.4$) in our unfiltered band pass and may suggest an even tighter intrinsic
distribution when the effects of dust are considered, although the sample may
be skewed by selection and publication biases. The presence of OII features
near maximum light may uniquely signal a high luminosity event, and we suggest
further observational and theoretical work is warranted to assess the possible
utility of such SN 2005ap-like SLSN-I as distance indicators. Using the
pseudo-absolute magnitude distributions derived from the light curve sample, we
measure the SLSN-I rate to be about (32^{+77}_{-26}) events Gpc^{-3} yr^{-1}
h_{71}^{3} at a weighted redshift of z = 0.17, and the SLSN-II rate to be about
(151^{+151}_{-82}) events Gpc^{-3} yr^{-1} h_{71}^{3} at z = 0.15. Given that
the exact nature and limits of these populations are still unknown, we discuss
how it may be difficult to distinguish these rare SLSNe from other transient
phenomena such as AGN activity and tidal disruption events even when multi-band
photometry, spectroscopy, or even high resolution imaging are available.
Including one spectroscopically peculiar event, we determine a total rate for
SLSN-like events of (199^{+137}_{-86}) events Gpc^{-3} yr^{-1} h_{71}^{3} at z
= 0.16.
