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

Abstract

Recent population synthesis simulations of Pop III stars suggest that the event rate of coalescence of $\sim 30M_{\odot }$--$30M_{\odot }$ binary black holes can be high enough for the detection by the second generation gravitational wave detectors. The frequencies of chirp signal as well as quasinormal modes are near the best sensitivity of these detectors so that it would be possible to confirm Einstein's general relativity. Using the WKB method, we suggest that for the typical value of spin parameter $a/M\sim 0.7$ from numerical relativity results of the coalescence of binary black holes, the strong gravity of the black 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 general relativity. The expected event rate with the signal-to-noise ratio $>35$ needed for the determination of the quasinormal mode frequency with the meaningful accuracy is $0.17$--$7.2$~$\mathrm{events}\mathrm{y}{\mathrm{r}}^{-1}(\mathrm{SF}{\mathrm{R}}_{\mathrm{p}}/(10^{-2.5}{\mathrm{M}}_{\odot }\mathrm{y}{\mathrm{r}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-3}))\cdot ([{\mathrm{f}}_{\mathrm{b}}/(1+{\mathrm{f}}_{\mathrm{b}})]/0.33)$ where $\mathrm{SF}{\mathrm{R}}_{\mathrm{p}}$ and ${\mathrm{f}}_{\mathrm{b}}$ are the peak value of the Pop III star formation rate and the fraction of binaries, respectively. As for the possible optical counter part, if the merged black hole of mass $M\sim 60M_{\odot }$ is in the interstellar matter with $n\sim 100\mathrm{c}{\mathrm{m}}^{-3}$ and the proper motion of black hole is $\sim 1\mathrm{km}{\mathrm{s}}^{-1}$, the luminosity is $\sim 10^{40}\mathrm{erg}{\mathrm{s}}^{-1}$ which can be detected up to $\sim 300\mathrm{Mpc}$, for example, by Subaru-HSC and LSST with the limiting magnitude 26.

17 pages, 13 figures, accepted to PRD