Bondi-Hoyle-Lyttleton Accretion in a Reactive Medium: Detonation Ignition and a Mechanism for SNe Ia

Detonation initiation in a reactive medium can be achieved by an externally created shock wave. Supersonic flow onto a gravitating center, known as Bondi-Hoyle-Lyttleton (BHL) accretion, is a natural shock wave creating process, but, to our knowledge, a reactive medium has never been considered in the literature. Here, we conduct an order of magnitude analysis to investigate under which conditions the shock-induced reaction zone recouples to the shock front. We derive three semi-analytical criteria for self-sustained detonation ignition. We apply these criteria to the special situation where a primordial black hole (PBH) of asteroid mass traverses a carbon-oxygen white dwarf (WD). Since detonations in carbon-oxygen WDs are supposed to produce normal thermonuclear supernovae (SNe Ia), the observed SN Ia rate constrains the fraction of dark matter (DM) in the form of PBHs as $\log_{10}(f_{\rm pbh})< 0.8 \log_{10}(m_{\rm bh}/{\rm g})-18$ in the range $10^{21}-10^{22}$g ($10^{20}-10^{22}$g) from a conservative (optimistic) analysis. Most importantly, these encounters can account for both the rate and the median explosion mass of normal sub-Chandrasekhar SNe Ia if a significant fraction of DM is in the form of PBHs with mass $10^{23}$g.