Black-hole production from ultrarelativistic collisions

Determining the conditions under which a black hole can be produced is a long-standing and fundamental problem in general relativity. We use numerical simulations of colliding selfgravitating fluid objects to study the conditions of black-hole formation when the objects are boosted to ultrarelativistic speeds. Expanding on previous work, we show that the collision is characterized by a type-I critical behaviour, with a black hole being produced for masses above a critical value, M_c, and a partially bound object for masses below the critical one. More importantly, we show for the first time that the critical mass varies with the initial effective Lorentz factor following a simple scaling of the type M_c ~ K ^{-1.0}, thus indicating that a black hole of infinitesimal mass is produced in the limit of a diverging Lorentz factor. Furthermore, because a scaling is present also in terms of the initial stellar compactness, we provide a condition for black-hole formation in the spirit of the hoop conjecture.Comment: Accepted as FTC on CQG; no discussion of LHC (seen as too speculative but available in v1); expanded considerations on hoop conjectur

A Unified Model of the Prompt Optical Emission of Gamma-Ray Bursts

The observational diversity of optical emission, which coincides with prompt gamma-ray bursts (GRBs), has been discovered in the recent Swift era. We show that on the assumption of the synchrotron radiation for the observed energy range below the X-ray band, the observed diversity can be explained using the internal shock model by taking into account a high-latitude emission and the spectral change due to the synchrotron self-absorption. It may even be possible in our model to include bright optical flashes found, e.g., in GRB~990123. The prediction of our model is that the spectral index in the optical band is dependent on whether the optical light curve correlates with those in the X-rays and/or gamma-rays or not, which will be tested in the near future.Comment: 9 pages, 1 figur

Probing the Structure of Gamma-Ray Burst Jets with Steep Decay Phase of their Early X-ray Afterglows

We show that the jet structure of gamma-ray bursts (GRBs) can be investigated with the tail emission of the prompt GRB. The tail emission which we consider is identified as a steep-decay component of the early X-ray afterglow observed by the X-ray Telescope onboard Swift. Using a Monte Carlo method, we derive, for the first time, the distribution of the decay index of the GRB tail emission for various jet models. The new definitions of the zero of time and the time interval of a fitting region are proposed. These definitions for fitting the light curve lead us an unique definition of the decay index, which is useful to investigate the structure of the GRB jet. We find that if the GRB jet has a core-envelope structure, the predicted distribution of the decay index of the tail has a wide scatter and has multiple peaks, which cannot be seen for the case of the uniform and the Gaussian jet. Therefore, the decay index distribution tells us the information on the jet structure. Especially, if we observe events whose decay index is less than about 2, both the uniform and the Gaussian jet models will be disfavored according to our simulation study.Comment: 21 pages, 10 figures, the paper with full resolution images is http://theo.phys.sci.hiroshima-u.ac.jp/~takami/research/achievements/papers/003_full.pd

Neutron-star Radius from a Population of Binary Neutron Star Mergers

We show how gravitational-wave observations with advanced detectors of tens to several tens of neutron-star binaries can measure the neutron-star radius with an accuracy of several to a few percent, for mass and spatial distributions that are realistic, and with none of the sources located within 100 Mpc. We achieve such an accuracy by combining measurements of the total mass from the inspiral phase with those of the compactness from the postmerger oscillation frequencies. For estimating the measurement errors of these frequencies we utilize analytical fits to postmerger numerical-relativity waveforms in the time domain, obtained here for the first time, for four nuclear-physics equations of state and a couple of values for the mass. We further exploit quasi-universal relations to derive errors in compactness from those frequencies. Measuring the average radius to well within 10% is possible for a sample of 100 binaries distributed uniformly in volume between 100 and 300 Mpc, so long as the equation of state is not too soft or the binaries are not too heavy.Comment: 9 pages and 7 figure

Host redshifts from gravitational-wave observations of binary neutron star mergers

Inspiralling compact binaries as standard sirens will soon become an invaluable tool for cosmology when advanced interferometric gravitational-wave detectors begin their observations in the coming years. However, a degeneracy in the information carried by gravitational waves between the total rest-frame mass $M$ and the redshift $z$ of the source implies that neither can be directly extracted from the signal, but only the combination $M(1+z)$, the redshifted mass. Recent work has shown that for binary neutron star systems, a tidal correction to the gravitational-wave phase in the late-inspiral signal that depends on the rest-frame source mass could be used to break the mass-redshift degeneracy. We propose here to use the signature encoded in the post-merger signal to deduce the redshift to the source. This will allow an accurate extraction of the intrinsic rest-frame mass of the source, in turn permitting the determination of source redshift and luminosity distance solely from gravitational-wave observations. This will herald a new era in precision cosmography and astrophysics. Using numerical simulations of binary neutron star mergers of very slightly different mass, we model gravitational-wave signals at different redshifts and use Bayesian parameter estimation to determine the accuracy with which the redshift can be extracted for a source of known mass. We find that the Einstein Telescope can determine the source redshift to $sim 10$--$20$ at redshifts of $z<0.04$.Comment: 10 pages, 4 figures; same as the version before except for acknowledgment

Computing Fast and Reliable Gravitational Waveforms of Binary Neutron Star Merger Remnants

Gravitational waves have been detected from the inspiral of a binary neutron-star, GW170817, which allowed constraints to be placed on the neutron star equation of state. The equation of state can be further constrained if gravitational waves from a post-merger remnant are detected. Post-merger waveforms are currently generated by numerical-relativity simulations, which are computationally expensive. Here we introduce a hierarchical model trained on numerical-relativity simulations, which can generate reliable post-merger spectra in a fraction of a second. Our spectra have mean fitting factors of 0.95, which compares to fitting factors of 0.76 and 0.85 between different numerical-relativity codes that simulate the same physical system. This method is the first step towards generating large template banks of spectra for use in post-merger detection and parameter estimation.Comment: Submitted to PRL. 6 pages, 4 figure

Tidal effects on magnetic gyration of a charged particle in Fermi coordinates

We examine the gyration motion of a charged particle, viewed from a reference observer falling along the Z axis into a Schwarzschild black hole. It is assumed that the magnetic field is constant and uniform along the Z axis, and that the particle has a circular orbit in the X-Y plane far from the gravitational source. When the particle as well as the reference observer approaches the black hole, its orbit is disrupted by the tidal force. The final plunging velocity increases in the non-relativistic case, but decreases if the initial circular velocity exceeds a critical value, which is approximately 0.7c. This toy model suggests that disruption of a rapidly rotating star due to a velocity-dependent tidal force may be quite different from that of a non-relativistic star. The model also suggested that collapse of the orbit after the disruption is slow in general, so that the particle subsequently escapes outside the valid Fermi coordinates.Comment: 10 pages, 12 figure

The Impact of Nutritional Status and Body Mass Index on Rehabilitation Outcomes in Patients Receiving Home-Based Medical Care

Background: Home-based medical care is expanding rapidly in Japan.Objectives: We aimed to identify the factors associated with outcomes of therapy in patients receiving home-visit rehabilitation.Methods: One hundred twenty-one patients receiving home-based rehabilitation were investigated. Nutritional status was assessed by the Mini Nutritional Assessment Short Form (MNA-SF). The Functional Independence Measure (FIM) was employed to assess the activities of daily living (ADL). The body mass index (BMI), medical history, and orthopedic disease-related pain were also recorded. The primary outcome was the improvement in FIM scores in one year.Results: A total of 19 (17%) patients were malnourished and 58 (48%) were at risk of malnutrition. Malnourished patients had a lower FIM score at initiation than those at risk of malnutrition or with normal nutritional status. Only changes in patients’ BMI and MNA-SF scores over one year were significantly associated with improved FIM scores (p = 0.0079 and p = 0.0049, respectively). No association was noted with the other factors.Conclusions: This is the first report to demonstrate that changes in MNA-SF scores and BMI are significantly associated with rehabilitation outcomes in home-based care. Nutritional management is essential along with rehabilitation to improve ADL in the long-term home care setting