Possible confirmation of the existence of ergoregion by the Kerr quasinormal mode in gravitational waves from Pop III massive black hole binary

The existence of the ergoregion of the Kerr space-time has not been confirmed observationally yet. We show that the confirmation would be possible by observing the quasinormal mode in gravitational waves. As an example, using the recent population synthesis results of Pop III binary black holes, we find that the peak of the final merger mass ($M_f$) is about $50~\rm M_{\odot}$, while the fraction of the final spin $q_f = a_f/M_f > 0.7$ needed for the confirmation of a part of ergoregion is $\sim 77\%$. To confirm the frequency of the quasinormal mode, ${\rm SNR} > 35$ is needed. The standard model of Pop III population synthesis tells us that the event rate for the confirmation of more than $50\%$ of the ergoregion by the second generation gravitational wave detectors is $\sim 2.3$ ${\rm events\ yr^{-1}\ (SFR_p/(10^{-2.5}\ M_\odot yr^{-1}\ Mpc^{-3}))} \cdot (\rm [f_b/(1+f_b)]/0.33)$ where ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Pop III star formation rate and the fraction of binaries, respectively.Comment: Accepted for publication in PTEP. Comments welcom

Gravitational wave quasinormal mode from Population III massive black hole binaries in various models of population synthesis

Focusing on the remnant black holes after merging binary black holes, we show that ringdown gravitational waves of Population III binary black holes mergers can be detected with the rate of $5.9-500~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for various parameters and functions. This rate is estimated for the events with SNR$>8$ for the second generation gravitational wave detectors such as KAGRA. Here, ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Population III star formation rate and the fraction of binaries, respectively. When we consider only the events with SNR$>35$, the event rate becomes $0.046-4.21~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$. This suggest that for remnant black hole's spin $q_f>0.95$ we have the event rate with SNR$>35$ less than $0.037~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$, while it is $3-30~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for the third generation detectors such as Einstein Telescope. If we detect many Population III binary black holes merger, it may be possible to constrain the Population III binary evolution paths not only by the mass distribution but also by the spin distribution.Comment: Submitted to PTEP. comments welcom

One-Leader and Multiple-Follower Stackelberg Games with Private Information

July 2014. Revised August 201

薄膜エレクトロニクスのための有機半導体材料の分子配向制御

京都大学0048新制・課程博士博士(工学)甲第21785号工博第4602号新制||工||1717(附属図書館)京都大学大学院工学研究科物質エネルギー化学専攻(主査)教授 村田 靖次郎, 教授 大江 浩一, 教授 中村 正治学位規則第4条第1項該当Doctor of Philosophy (Engineering)Kyoto UniversityDGA

Dirac pairs on Jacobi algebroids

We define Dirac pairs on Jacobi algebroids, which is a generalization of Dirac pairs on Lie algebroids introduced by Kosmann-Schwarzbach. We show the relationship between Dirac pairs on Lie and on Jacobi algebroids, and that Dirac pairs on Jacobi algebroids characterize several compatible structures on Jacobi algebroids