The detection of Quasinormal Mode of Pop III Binary Black Hole merger with final $M \sim 60M_\odot$ and $a/M \sim 0.7$ would confirm the strong gravity space-time around $\sim 2M$ which is only $\sim 1.17$ times the event horizon radius

摘要

Recent population synthesis simulations of Pop III stars suggest that theevent rate of coalescence of $\sim 30M_\odot$--$30M_\odot$ binary black holescan be high enough for the detection by the second generation gravitationalwave detectors. The frequencies of chirp signal as well as quasinormal modesare near the best sensitivity of these detectors so that it would be possibleto confirm Einstein's general relativity. Using the WKB method, we suggest thatfor the typical value of spin parameter $a/M\sim 0.7$ from numerical relativityresults of the coalescence of binary black holes, the strong gravity of theblack hole space-time at around the radius $2M$, which is just $\sim 1.17$times the event horizon radius, would be confirmed as predicted by generalrelativity. The expected event rate with the signal-to-noise ratio $> 35$needed for the determination of the quasinormal mode frequency with themeaningful accuracy is $0.17$--$7.2$~${\rmevents~yr^{-1}~(SFR_p/(10^{-2.5}~M_\odot~yr^{-1}~Mpc^{-3}))} \cdot (\rm[f_b/(1+f_b)]/0.33)$ where ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value ofthe Pop III star formation rate and the fraction of binaries, respectively. Asfor the possible optical counter part, if the merged black hole of mass $M\sim60M_\odot$ is in the interstellar matter with $n\sim 100~{\rm cm^{-3}}$ and theproper motion of black hole is $\sim 1~{\rm km~s^{-1}}$, the luminosity is$\sim 10^{40}~{\rm erg~ s^{-1}}$ which can be detected up to $\sim 300~{\rmMpc}$, for example, by Subaru-HSC and LSST with the limiting magnitude 26.