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.