  A string of recent studies has debated the exact form and physical origin of
an evolutionary trend between the peak luminosity of Type Ia supernovae (SNe
Ia) and the properties of the galaxies that host them. We shed new light on the
discussion by presenting an analysis of ~200 low-redshift SNe Ia in which we
measure the separation of Hubble residuals (HR; as probes of luminosity)
between two host-galaxy morphological types. We show that this separation can
test the predictions made by recently proposed models, using an independently
and empirically determined distribution of each morphological type in
host-property space. Our results are partially consistent with the new HR--age
slope, but we find significant scatter in the predictions from different galaxy
catalogues. The inconsistency in age illuminates an issue in the current debate
that was not obvious in the long-discussed mass models: HR--host-property
models are strongly dependent on the methods employed to determine galaxy
properties. While our results demonstrate the difficulty in constructing a
universal model for age as a proxy for host environment, our results indeed
identify evolutionary trends between mass, age, morphology, and HR values,
encouraging (or requiring, if such trends are to be accounted for in
cosmological studies) further investigation.
