Type Ia Supernova Magnitude Step from the local Dark Matter Environment
  Residuals in the Hubble diagram at optical wavelengths and host galaxy
stellar mass are observed to correlate in Type Ia supernovae (SNe Ia)
(`magnitude step'). Among possible progenitor channels for the associated
explosions, those based on dark matter (DM) have attracted significant
attention, including our recent proposal that `normal' SNe Ia from bare
detonations in sub-Chandrasekhar white dwarf stars are triggered by the passage
of asteroid-mass primordial black holes (PBHs): the magnitude step could then
originate from a brightness dependence on stellar properties, on DM properties,
or both. Here, we present a method to estimate the local DM density and
velocity dispersion of the environment of SN Ia progenitors. We find a
luminosity step of $0.52\pm 0.11\,$mag corresponding to bins of high vs low DM
density in a sample of 222 low-redshift events from the Open Supernova Catalog.
We investigate whether the magnitude step can be attributed to local DM
properties alone, assuming asteroid-mass PBHs. Given the inverse correlation
between SN Ia brightness and PBH mass, an intriguing explanation is a
spatially-inhomogeneous PBH mass function. If so, a strong mass segregation in
the DM density-dependent PBH mass scale is needed to explain the magnitude
step. While mass segregation is observed in dense clusters, it is unlikely to
be realized on galactic scales. Therefore, if DM consists of asteroid-mass
PBHs, the magnitude step is more likely to exist, and dominantly to be
attributed to local stellar properties.
