Comparing hierarchical black hole mergers in star clusters and active galactic nuclei

Star clusters (SCs) and active galactic nuclei (AGNs) are promising sites for the occurrence of hierarchical black hole (BH) mergers. We use simple models to compare hierarchical BH mergers in two of the dynamical formation channels. We find that the primary mass distribution of hierarchical mergers in AGNs is higher than that in SCs, with the peaks of $\sim$$50\,M_{\odot}$ and $\sim$$13\,M_{\odot}$, respectively. The effective spin ($\chi_{\rm eff}$) distribution of hierarchical mergers in SCs is symmetrical around zero as expected and $\sim$$50\%$ of the mergers have $|\chi_{\rm eff}|>0.2$. The distribution of $\chi_{\rm eff}$ in AGNs is narrow and prefers positive values with the peak of $\chi_{\rm eff}\ge0.3$ due to the assistance of AGN disks. BH hierarchical growth efficiency in AGNs, with at least $\sim$$30\%$ of mergers being hierarchies, is much higher than the efficiency in SCs. Furthermore, there are obvious differences in the mass ratios and effective precession parameters of hierarchical mergers in SCs and AGNs. We argue that the majority of the hierarchical merger candidates detected by LIGO-Virgo may originate from the AGN channel as long as AGNs get half of the hierarchical merger rate.Comment: 12 pages, 5 figures, 2 tables, accepted for publication in PHYS. REV. D; v2. add Figs. 4 and 5, showing mass-ratios and effective precession parameters, respectively; v3. delete an additional free parameter (maximum generation, $N_{\rm max}^{\rm G}$), replot Fig. 3 using the mergers detected by LIGO-Virgo, and add Yong Yuan as the third author of this manuscript; v4. add more details for SN

Understanding Simulations of Thin Accretion Disks by Energy Equation

We study the fluctuations of standard thin accretion disks by linear analysis of the time-dependent energy equation together with the vertical hydrostatic equilibrium and the equation of state. We show that some of the simulation results in Hirose et al. (2009b), such as the time delay, the relationship of power spectra, and the correlation between magnetic energy and radiation energy, can be well understood by our analytic results.Comment: 13 pages, 3 figure, accepted for publication in Ap

Event Rate of Fast Radio Burst from Binary Neutron-star Mergers

It is proposed that one-off fast radio burst (FRB) with periodic structures may be produced during the inspiral phase of a binary neutron-star (BNS) merger. In this paper, we study the event rate of such kind of FRB. We first investigate the properties of two one-off FRBs with periodic structures (i.e., FRB~20191221A and FRB~20210213A) in this scenario, by assuming the fast magnetosonic wave is responsible for their radio emission. For the luminosities and periods of these bursts, it is found that the pre-merger BNS with magnetic field strength $B\gtrsim 10^{12}\,{\rm Gs}$ is required. This is relatively high compared with that of the most of the BNSs observed in our Galaxy, of which the magnetic field is around $10^{9}\,{\rm Gs}$. Since the observed BNSs in our Galaxy are the binaries without suffering merger, a credited event rate of BNS-merger originated FRBs should be estimated by considering the evolution of both the BNS systems and their magnetic fields. Based on the population synthesis and adopting a decaying magnetic field of NSs, we estimate the event rate of BNS-mergers relative to their final magnetic fields. We find that the rapid merged BNSs tend to merge with high magnetization, and the event rate of BNS-merger originated FRBs, i.e., the BNS-mergers with both NSs' magnetic field being higher than $10^{12}\,{\rm Gs}$ is $\sim8\times10^{4}\,\rm{yr}^{-1}$ ($19 \%$ of the total BNS-mergers) in redshift $z<1$.Comment: 11 pages, 2 figures, accepted for publication in Astrophysical Journa

Gamma-Ray Burst Jet Breaks Revisited

Gamma-ray Burst (GRB) collimation has been inferred with the observations of achromatic steepening in GRB light curves, known as jet breaks. Identifying a jet break from a GRB afterglow light curve allows a measurement of the jet opening angle and true energetics of GRBs. In this paper, we re-investigate this problem using a large sample of GRBs that have an optical jet break that is consistent with being achromatic in the X-ray band. Our sample includes 99 GRBs from 1997 February to 2015 March that have optical and, for Swift GRBs, X-ray light curves that are consistent with the jet break interpretation. Out of the 99 GRBs we have studied, 55 GRBs are found to have temporal and spectral behaviors both before and after the break, consistent with the theoretical predictions of the jet break models, respectively. These include 53 long/soft (Type II) and 2 short/hard (Type I) GRBs. Only 1 GRB is classified as the candidate of a jet break with energy injection. Another 41 and 3 GRBs are classified as the candidates with the lower and upper limits of the jet break time, respectively. Most jet breaks occur at 90 ks, with a typical opening angle θj = (2.5 ± 1.0)°. This gives a typical beaming correction factor ${f}_{b}^{-1}\sim 1000$ for Type II GRBs, suggesting an even higher total GRB event rate density in the universe. Both isotropic and jet-corrected energies have a wide span in their distributions: log(Eγ,iso/erg) = 53.11 with σ = 0.84; log(EK,iso/erg) = 54.82 with σ = 0.56; log(Eγ/erg) = 49.54 with σ = 1.29; and log(EK/erg) = 51.33 with σ = 0.58. We also investigate several empirical correlations (Amati, Frail, Ghirlanda, and Liang–Zhang) previously discussed in the literature. We find that in general most of these relations are less tight than before. The existence of early jet breaks and hence small opening angle jets, which were detected in the Swfit era, is most likely the source of scatter. If one limits the sample to jet breaks later than 104 s, the Liang–Zhang relation remains tight and the Ghirlanda relation still exists. These relations are derived from Type II GRBs, and Type I GRBs usually deviate from them