Very High Lorentz Factor Fireballs and Gamma-Ray Burst Spectra

Collisionless entrainment of the surrounding matter imports the relativistic baryon component in the Gamma-Ray Burst (GRB) fireball frame. We show that half the fireball energy can be transferred from radiation to the comoving hot motions of baryons under the photosphere. The yet baryon-poor fireball can reexpand to a very high Lorentz factor (VHLF) \Gamma ~ 10^3-10^6 by its own relativistic collisionless pressure beyond the photosphere (so-called collisionless bulk acceleration), leading to internal and external shocks. A simple synchrotron emission from the VHLF internal shocks produces (i) the extra power-law spectral component with variability observed in the Fermi GeV bursts, up to the TeV range for the future Cherenkov Telescope Array (CTA), (ii) the GeV onset delay with a weak luminosity dependence t_{delay} ~ L^{-1/5}, and (iii) the spectral break of GRB 090926 by the synchrotron cooling break or the maximum synchrotron cutoff limited by the dynamical time, not by the e+- creation cutoff. The relativistic baryon component could also heat the photospheric thermal photons into the main GRB Band spectrum via pp, p\gamma (Bethe-Heitler and photomeson), and Coulomb thermalization processes. In this hot photosphere-internal-external shock model, we can predict the anticorrelation of ~TeV neutrinos and GeV gamma-rays, which may be detectable using IceCube. The spectral peak and luminosity (Yonetoku) relation is also reproduced if the progenitor stars are nearly identical. We also discuss the steep/shallow decay of early X-ray afterglows and short GRBs.Comment: 21 pages, 6 figures, final version to be published in Progress of Theoretical Physic

Second and higher-order quasi-normal modes in binary black hole mergers

Black hole (BH) oscillations known as quasi-normal modes (QNMs) are one of the most important gravitational wave (GW) sources. We propose that higher perturbative order of QNMs, generated by nonlinear gravitational interaction near the BHs, are detectable and worth searching for in observations and simulations of binary BH mergers. We calculate the metric perturbations to second-order and explicitly regularize the master equation at the horizon and spatial infinity. We find that the second-order QNMs have frequencies twice the first-order ones and the GW amplitude is up to ~10% that of the first-order one. The QNM frequency would also shift blueward up to ~1%. This provides a new test of general relativity as well as a possible distance indicator.Comment: 5 pages, 1 figure, accepted for publication in PRD Rapid Communication

Efficiency Crisis of Swift Gamma-Ray Bursts with Shallow X-ray Afterglows: Prior Activity or Time-Dependent Microphysics?

Most X-ray afterglows of gamma-ray bursts (GRBs) observed by the Swift satellite have a shallow decay phase t^{-1/2} in the first few hours. This is not predicted by the standard afterglow model and needs an explanation. We discuss that the shallow decay requires an unreasonably high gamma-ray efficiency, >75-90%, within current models, which is difficult to produce by internal shocks. Such a crisis may be avoided if a weak relativistic explosion occurs ~10^3-10^6 s prior to the main burst or if the microphysical parameter of the electron energy increases during the shallow decay, \epsilon_e ~ t^{1/2}. The former explanation predicts a very long precursor, while both prefer dim optical flashes from the reverse shock, as was recently reported. We also calculate the multi-wavelength afterglows and compare them with observations. No optical break at the end of the shallow X-ray decay indicates a preference for the time-dependent microphysics model with additionally decaying magnetic fields, \epsilon_B ~ t^{-0.6}.Comment: 7 pages, 1 figure, accepted for publication in A&

Second Order Quasi-Normal Mode of the Schwarzschild Black Hole

We formulate and calculate the second order quasi-normal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational wave (GW) from a distorted BH, so called ringdown, is well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numerically solve the second order Zerilli equation by implementing the modified Leaver's continued fraction method. The second order QNM frequencies are found to be twice the first order ones, and the GW amplitude is up to $\sim 10$ that of the first order for the binary BH mergers. Since the second order QNMs always exist, we can use their detections (i) to test the nonlinearity of general relativity, in particular the no-hair theorem, (ii) to remove fake events in the data analysis of QNM GWs and (iii) to measure the distance to the BH.Comment: 23 pages, no figur

Gravitational Wave Memory of Gamma-Ray Burst Jets

Gamma-Ray Bursts (GRBs) are now considered as relativistic jets. We analyze the gravitational waves from the acceleration stage of the GRB jets. We show that (i) the point mass approximation is not appropriate if the opening half-angle of the jet is larger than the inverse of the Lorentz factor of the jet, (ii) the gravitational waveform has many step function like jumps, and (iii) the practical DECIGO and BBO may detect such an event if the GRBs occur in Local group of galaxy. We found that the light curve of GRBs and the gravitational waveform are anti-correlated so that the detection of the gravitational wave is indispensable to determine the structure of GRB jets.Comment: Revtex4, 10 pages, 6 figures, Fig.2 and Fig.3 replaced, minor changes to text in Sec.I and Sec.V, typos corrected, some reference added, Version to be published in PR