Astrophysics from data analysis of spherical gravitational wave detectors

The direct detection of gravitational waves will provide valuable astrophysical information about many celestial objects. Also, it will be an important test to general relativity and other theories of gravitation. The gravitational wave detector SCHENBERG has recently undergone its first test run. It is expected to have its first scientific run soon. In this work the data analysis system of this spherical, resonant mass detector is tested through the simulation of the detection of gravitational waves generated during the inspiralling phase of a binary system. It is shown from the simulated data that it is not necessary to have all six transducers operational in order to determine the source's direction and the wave's amplitudes.Comment: 8 pages and 3 figure

Local dynamics and gravitational collapse of a self-gravitating magnetized Fermi gas

We use the Bianchi-I spacetime to study the local dynamics of a magnetized self-gravitating Fermi gas. The set of Einstein-Maxwell field equations for this gas becomes a dynamical system in a 4-dimensional phase space. We consider a qualitative study and examine numeric solutions for the degenerate zero temperature case. All dynamic quantities exhibit similar qualitative behavior in the 3-dimensional sections of the phase space, with all trajectories reaching a stable attractor whenever the initial expansion scalar H_{0} is negative. If H_{0} is positive, and depending on initial conditions, the trajectories end up in a curvature singularity that could be isotropic(singular "point") or anisotropic (singular "line"). In particular, for a sufficiently large initial value of the magnetic field it is always possible to obtain an anisotropic type of singularity in which the "line" points in the same direction of the field.Comment: 6 pages, 3 figures (accepted in General Relativity and Gravitation

Relativistic Models for Binary Neutron Stars with Arbitrary Spins

We introduce a new numerical scheme for solving the initial value problem for quasiequilibrium binary neutron stars allowing for arbitrary spins. The coupled Einstein field equations and equations of relativistic hydrodynamics are solved in the Wilson-Mathews conformal thin sandwich formalism. We construct sequences of circular-orbit binaries of varying separation, keeping the rest mass and circulation constant along each sequence. Solutions are presented for configurations obeying an n=1 polytropic equation of state and spinning parallel and antiparallel to the orbital angular momentum. We treat stars with moderate compaction ((m/R) = 0.14) and high compaction ((m/R) = 0.19). For all but the highest circulation sequences, the spins of the neutron stars increase as the binary separation decreases. Our zero-circulation cases approximate irrotational sequences, for which the spin angular frequencies of the stars increases by 13% (11%) of the orbital frequency for (m/R) = 0.14 ((m/R) = 0.19) by the time the innermost circular orbit is reached. In addition to leaving an imprint on the inspiral gravitational waveform, this spin effect is measurable in the electromagnetic signal if one of the stars is a pulsar visible from Earth.Comment: 21 pages, 14 figures. A few explanatory sentences added and some typos corrected. Accepted for publication in Phys. Rev.

On the Circular Orbit Approximation for Binary Compact Objects In General Relativity

One often-used approximation in the study of binary compact objects (i.e., black holes and neutron stars) in general relativity is the instantaneously circular orbit assumption. This approximation has been used extensively, from the calculation of innermost circular orbits to the construction of initial data for numerical relativity calculations. While this assumption is inconsistent with generic general relativistic astrophysical inspiral phenomena where the dissipative effects of gravitational radiation cause the separation of the compact objects to decrease in time, it is usually argued that the timescale of this dissipation is much longer than the orbital timescale so that the approximation of circular orbits is valid. Here, we quantitatively analyze this approximation using a post-Newtonian approach that includes terms up to order ({Gm/(rc^2)})^{9/2} for non-spinning particles. By calculating the evolution of equal mass black hole / black hole binary systems starting with circular orbit configurations and comparing them to the more astrophysically relevant quasicircular solutions, we show that a minimum initial separation corresponding to at least 6 (3.5) orbits before plunge is required in order to bound the detection event loss rate in gravitational wave detectors to < 5% (20%). In addition, we show that the detection event loss rate is > 95% for a range of initial separations that include all modern calculations of the innermost circular orbit (ICO).Comment: 10 pages, 12 figures, revtex

Aligned-spin neutron-star-black-hole waveform model based on the effective-one-body approach and numerical-relativity simulations

After the discovery of gravitational waves from binary black holes (BBHs) and binary neutron stars (BNSs) with the LIGO and Virgo detectors, neutron-star--black-holes (NSBHs) are the natural next class of binary systems to be observed. In this work, we develop a waveform model for aligned-spin neutron-star--black-holes (NSBHs) combining a binary black-hole baseline waveform (available in the effective-one-body approach) with a phenomenological description of tidal effects (extracted from numerical-relativity simulations), and correcting the amplitude during the late inspiral, merger and ringdown to account for the NS's tidal disruption. In particular, we calibrate the amplitude corrections using NSBH waveforms obtained with the numerical-relativity spectral Einstein code (SpEC) and the SACRA code. Based on the simulations used, and on checking that sensible waveforms are produced, we recommend our model to be employed with NS's mass in the range $1-3 M_\odot$, tidal deformability 0\mbox{-}5000, and (dimensionless) BH's spin magnitude up to $0.9$. We also validate our model against two new, highly accurate NSBH waveforms with BH's spin 0.9 and mass ratios 3 and 4, characterized by tidal disruption, produced with SpEC, and find very good agreement. Furthermore, we compute the unfaithfulness between waveforms from NSBH, BBH, and BNS systems, finding that it will be challenging for the advanced LIGO-Virgo--detector network at design sensitivity to distinguish different source classes. We perform a Bayesian parameter-estimation analysis on a synthetic numerical-relativity signal in zero noise to study parameter biases. Finally, we reanalyze GW170817, with the hypothesis that it is a NSBH. We do not find evidence to distinguish the BNS and NSBH hypotheses, however the posterior for the mass ratio is shifted to less equal masses under the NSBH hypothesis

Conformal-thin-sandwich initial data for a single boosted or spinning black hole puncture

Sequences of initial-data sets representing binary black holes in quasi-circular orbits have been used to calculate what may be interpreted as the innermost stable circular orbit. These sequences have been computed with two approaches. One method is based on the traditional conformal-transverse-traceless decomposition and locates quasi-circular orbits from the turning points in an effective potential. The second method uses a conformal-thin-sandwich decomposition and determines quasi-circular orbits by requiring the existence of an approximate helical Killing vector. Although the parameters defining the innermost stable circular orbit obtained from these two methods differ significantly, both approaches yield approximately the same initial data, as the separation of the binary system increases. To help understanding this agreement between data sets, we consider the case of initial data representing a single boosted or spinning black hole puncture of the Bowen-York type and show that the conformal-transverse-traceless and conformal-thin-sandwich methods yield identical data, both satisfying the conditions for the existence of an approximate Killing vector.Comment: 13 pages, 2 figure

Towards a Realistic Neutron Star Binary Inspiral: Initial Data and Multiple Orbit Evolution in Full General Relativity

This paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity. We analyze under what conditions the conformally flat quasiequilibrium (CFQE) approach can generate ``astrophysically relevant'' initial data, by developing an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. We show that the CFQE assumptions significantly violate the Einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit (ISCO) separation, thus calling into question the astrophysical relevance of the ISCO determined in the CFQE approach. With the need to start numerical simulations at large orbital separation in mind, we push for stable and long term integrations of the full Einstein equations for the binary neutron star system. We demonstrate the stability of our numerical treatment and analyze the stringent requirements on resolution and size of the computational domain for an accurate simulation of the system.Comment: 22 pages, 18 figures, accepted to Phys. Rev.

Various features of quasiequilibrium sequences of binary neutron stars in general relativity

Quasiequilibrium sequences of binary neutron stars are numerically calculated in the framework of the Isenberg-Wilson-Mathews (IWM) approximation of general relativity. The results are presented for both rotation states of synchronized spins and irrotational motion, the latter being considered as the realistic one for binary neutron stars just prior to the merger. We assume a polytropic equation of state and compute several evolutionary sequences of binary systems composed of different-mass stars as well as identical-mass stars with adiabatic indices gamma=2.5, 2.25, 2, and 1.8. From our results, we propose as a conjecture that if the turning point of binding energy (and total angular momentum) locating the innermost stable circular orbit (ISCO) is found in Newtonian gravity for some value of the adiabatic index gamma_0, that of the ADM mass (and total angular momentum) should exist in the IWM approximation of general relativity for the same value of the adiabatic index.Comment: Text improved, some figures changed or deleted, new table, 38 pages, 31 figures, accepted for publication in Phys. Rev.

Innermost circular orbit of binary black holes at the third post-Newtonian approximation

The equations of motion of two point masses have recently been derived at the 3PN approximation of general relativity. From that work we determine the location of the innermost circular orbit or ICO, defined by the minimum of the binary's 3PN energy as a function of the orbital frequency for circular orbits. We find that the post-Newtonian series converges well for equal masses. Spin effects appropriate to corotational black-hole binaries are included. We compare the result with a recent numerical calculation of the ICO in the case of two black holes moving on exactly circular orbits (helical symmetry). The agreement is remarkably good, indicating that the 3PN approximation is adequate to locate the ICO of two black holes with comparable masses. This conclusion is reached with the post-Newtonian expansion expressed in the standard Taylor form, without using resummation techniques such as Pad\'e approximants and/or effective-one-body methods.Comment: 21 pages, to appear in Phys. Rev. D (spin effects appropriate to corotational black-hole binaries are included; discussion on the validity of the approximation is added