Observations of SN 2015F suggest a correlation between the intrinsic
  luminosity of Type Ia supernovae and the shape of their light curves >900
  days after explosion
  The late-time light curves of Type Ia supernovae (SNe Ia), observed $>900$
days after explosion, present the possibility of a new diagnostic for SN Ia
progenitor and explosion models. First, however, we must discover what physical
process (or combination of processes) leads to the slow-down of the late-time
light curve relative to a pure $^{56}$Co decay, as observed in SNe 2011fe,
2012cg, and 2014J. We present Hubble Space Telescope observations of SN 2015F,
taken $\approx 600-1040$ days past maximum light. Unlike those of the three
other SNe Ia, the light curve of SN 2015F remains consistent with being powered
solely by the radioactive decay of $^{56}$Co. We fit the light curves of these
four SNe Ia in a consistent manner and measure possible correlations between
the light curve stretch - a proxy for the intrinsic luminosity of the SN - and
the parameters of the physical model used in the fit (e.g., the mass ratio of
$^{56}$Co and $^{57}$Co produced in the explosion, or the time at which
freeze-out sets in). We propose a new, late-time Phillips-like correlation
between the stretch of the SNe and the shape of their late-time light curves,
which we parametrize as the difference between their pseudo-bolometric
luminosities at 600 and 900 days: $\Delta L_{900} = {\rm
log}(L_{600}/L_{900})$. This model-independent correlation provides a new way
to test which physical process lies behind the slow-down of SN Ia light curves
$>900$ days after explosion, and, ultimately, fresh constraints on the various
SN Ia progenitor and explosion models.
