Dark-matter-induced transients over cosmic time: The role of star formation history profiles

The dark matter (DM) conundrum is one of the most intriguing due to its resistance in direct detection experiments. In recent years, attempts to identify non-gravitational signatures as the result of DM traversing or accumulating within stars have attracted a lot of attention. These calculations are usually evaluated at the order-of-magnitude level for stellar populations where the DM density is highest, such as galactic centers. However, if the signature implies the destruction of the host star, their population could have been diminished over a Hubble time in the most DM-dense regions, unless replenished by star formation. This circumstance exemplifies the need for galactic star formation history profiles when deriving DM-induced transient rates, in particular for predicting the host-offset distribution. Here, we combine theoretical and empirical scaling relations of galaxy structure, star formation, and stellar initial mass function to construct a simple and efficient framework that permits us to estimate the target population formation rate and mass function within galactocentric radial zones across galaxy stellar masses and cosmic time. In a companion paper, we apply the framework to the hypothesis that DM in the form of primordial black holes accounts for the ignition of normal type Ia supernovae when colliding with white dwarf stars.