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.