Collisions of Primordial Black Holes with the Moon
PBH Mass constraints
The Moon as a PBH Detector
200 \rm \, km/s
R_b \approx \frac{G M}{v^2}
Ejecta Blanket
High Pressure Phase of Silica
Classical Ejecta Blankets
v \propto m^{-\beta}
1>\beta>\frac{1}{2}
r \propto v^2 \propto m^{-2\beta}
\sigma \propto \frac{m}{r^2} \propto r^{-2-\frac{1}{2 \beta}}
-2.5> \frac{d \ln \sigma}{d \ln r} > -3
PBH Ejecta Blankets
m = \rho_0 x^3
v \approx \sqrt{\frac{E}{m}} \approx x^{-1} \approx m^{-1/3}
\sigma \propto \frac{m}{r^2} \propto r^{-2-\frac{1}{2 \beta}}
\frac{d \ln \sigma}{d \ln r} = -3.5
E \approx \rho_0 R_b^2 x v_i^2
Crater Size
Strength Regime
Gravity Regime
R \approx R_i \left(\frac{\rho v_i^2}{Y}\right)^{1/6\beta}
R \approx R_i \left(\frac{v_i^2}{g R_i}\right)^{1/\left(6\beta+1\right)}
R \approx \left(\frac{v_i^2 R_b^2}{g}\right)^{1/3} \approx 100 \left(\frac{v_i}{200 \, \rm \frac{km}{s}}\right)^{2/3} \left(\frac{R_b}{1 \, \rm cm}\right)^{2/3} \left(\frac{g}{2 \, \rm \frac{m}{s^2}}\right)^{-1/3} \, \rm m
Regular Craters
PBH
Rate
N \approx 0.1 \left(\frac{\rho_{DM}}{8 \cdot 10^{-25} \, \rm g/cm^3}\right) \left(\frac{m_i}{10^{19} \, \rm g}\right)^{-1} \left(\frac{v_i}{200 \, \rm km/s}\right)
Simulations: Regular Crater
Simulations: PBH
Conclusion
Possibility of a past PBH - moon collision
Different ejecta blanket
Pyrite like silica phase
Low probability, but can be raised by including other rocky bodies