arXiv subjects

Eanna E. Flanagan

Publications and source records attributed to Eanna E. Flanagan.

63 records · Page 4Linked to original sources

arXiv1998

Possible explanation for star-crushing effect in binary neutron star simulations

A possible explanation is suggested for the controversial star-crushing effect seen in numerical simulations of inspiraling neutron star binaries by Wilson, Mathews and Marronetti (WMM). An apparently incorrect definition of momentum density in the momentum constraint equation used by WMM gives rise to a post-1-Newtonian error in the approximation scheme. We show by means of an analytic, post-1-Newtonian calculation that this error causes an increase of the stars' central densities which is of the order of several percent when the stars are separated by a few stellar radii, in agreement with what is seen in the simulations.

astro-ph↗

arXiv1998

How unique is the expected stress-energy tensor of a massive scalar field?

We show that the set of ambiguities in the renormalized expected stress-energy tensor allowed by the Wald axioms is much larger for a massive scalar field (an infinite number of free parameters) than for a massless scalar field (two free parameters). We also use the closed-time-path effective action formalism of Schwinger to calculate the expected value of the stress-energy tensor in the incoming vacuum state, for a massive scalar field, on any spacetime which is a linear perturbation off Minkowski spacetime. This result generalizes an earlier result of Horowitz and also Jordan in the massless case, and can be used as a testbed for comparing different calculational methods.

gr-qc↗

arXiv1998

General-relativistic coupling between orbital motion and internal degrees of freedom for inspiraling binary neutron stars

We analyze the coupling between the internal degrees of freedom of neutron stars in a close binary, and the stars' orbital motion. Our analysis is based on the method of matched asymptotic expansions and is valid to all orders in the strength of internal gravity in each star, but is perturbative in the ``tidal expansion parameter'' (stellar radius)/(orbital separation). At first order in the tidal expansion parameter, we show that the internal structure of each star is unaffected by its companion, in agreement with post-1-Newtonian results of Wiseman (gr-qc/9704018). We also show that relativistic interactions that scale as higher powers of the tidal expansion parameter produce qualitatively similar effects to their Newtonian counterparts: there are corrections to the Newtonian tidal distortion of each star, both of which occur at third order in the tidal expansion parameter, and there are corrections to the Newtonian decrease in central density of each star (Newtonian ``tidal stabilization''), both of which are sixth order in the tidal expansion parameter. There are additional interactions with no Newtonian analogs, but these do not change the central density of each star up to sixth order in the tidal expansion parameter. These results, in combination with previous analyses of Newtonian tidal interactions, indicate that (i) there are no large general-relativistic crushing forces that could cause the stars to collapse to black holes prior to the dynamical orbital instability, and (ii) the conventional wisdom with respect to coalescing binary neutron stars as sources of gravitational-wave bursts is correct: namely, the finite-stellar-size corrections to the gravitational waveform will be unimportant for the purpose of detecting the coalescences.

gr-qc↗

arXiv1997

Quantum mechanical instabilities of Cauchy horizons in two dimensions - a modified form of the blueshift instability mechanism

There are several examples known of two dimensional spacetimes which are linearly stable when perturbed by test scalar classical fields, but which are unstable when perturbed by test scalar quantum fields. We elucidate the mechanism behind such instabilities by considering minimally coupled, massless, scalar, test quantum fields on general two dimensional spacetimes with Cauchy horizons which are classically stable. We identify a geometric feature of such spacetimes which is a necessary condition for obtaining a quantum mechanical divergence of the renormalized expected stress tensor on the Cauchy horizon for regular initial states. This feature is the divergence of the affine parameter length of a one parameter family of null geodesics which lie parallel to the Cauchy horizon, where the affine parameter normalization is determined by parallel transport along a fixed, transverse null geodesic which intersects the Cauchy horizon. (By contrast, the geometric feature of such spacetimes which underlies classical blueshift instabilities is the divergence of a holonomy operator). We show that the instability can be understood as a ``delayed blueshift'' instability, which arises from the infinite blueshifting of an energy flux which is created locally and quantum mechanically. The instability mechanism applies both to chronology horizons in spacetimes with closed timelike curves, and to the inner horizon in black hole spacetimes like two dimensional Reissner-Nordstrom-de Sitter.

gr-qc↗

arXiv1997

Measuring gravitational waves from binary black hole coalescences: I. Signal to noise for inspiral, merger, and ringdown

We estimate the expected signal-to-noise ratios (SNRs) from the three phases (inspiral,merger,ringdown) of coalescing binary black holes (BBHs) for initial and advanced ground-based interferometers (LIGO/VIRGO) and for space-based interferometers (LISA). LIGO/VIRGO can do moderate SNR (a few tens), moderate accuracy studies of BBH coalescences in the mass range of a few to about 2000 solar masses; LISA can do high SNR (of order 10^4) high accuracy studies in the mass range of about 10^5 to 10^8 solar masses. BBHs might well be the first sources detected by LIGO/VIRGO: they are visible to much larger distances (up to 500 Mpc by initial interferometers) than coalescing neutron star binaries (heretofore regarded as the "bread and butter" workhorse source for LIGO/VIRGO, visible to about 30 Mpc by initial interferometers). Low-mass BBHs (up to 50 solar masses for initial LIGO interferometers; 100 for advanced; 10^6 for LISA) are best searched for via their well-understood inspiral waves; higher mass BBHs must be searched for via their poorly understood merger waves and/or their well-understood ringdown waves. A matched filtering search for massive BBHs based on ringdown waves should be capable of finding BBHs in the mass range of about 100 to 700 solar masses out to 200 Mpc (initial LIGO interferometers), and 200 to 3000 solar masses out to about z=1 (advanced interferometers). The required number of templates is of order 6000 or less. Searches based on merger waves could increase the number of detected massive BBHs by a factor of order 10 or more over those found from inspiral and ringdown waves, without detailed knowledge of the waveform shapes, using a "noise monitoring" search algorithm. A full set of merger templates from numerical relativity could further increase the number of detected BBHs by an additional factor of up to 4.

gr-qc↗

arXiv1997

Measuring gravitational waves from binary black hole coalescences: II. the waves' information and its extraction, with and without templates

We discuss the extraction of information from detected binary black hole (BBH) coalescence gravitational waves, focusing on the merger phase that occurs after the gradual inspiral and before the ringdown. Our results are: (1) If numerical relativity simulations have not produced template merger waveforms before BBH detections by LIGO/VIRGO, one can band-pass filter the merger waves. For BBHs smaller than about 40 solar masses detected via their inspiral waves, the band pass filtering signal to noise ratio indicates that the merger waves should typically be just barely visible in the noise for initial and advanced LIGO interferometers. (2) We derive an optimized (maximum likelihood) method for extracting a best-fit merger waveform from the noisy detector output; one "perpendicularly projects" this output onto a function space (specified using wavelets) that incorporates our prior knowledge of the waveforms. An extension of the method allows one to extract the BBH's two independent waveforms from outputs of several interferometers. (3) If numerical relativists produce codes for generating merger templates but running the codes is too expensive to allow an extensive survey of the merger parameter space, then a coarse survey of this parameter space, to determine the ranges of the several key parameters and to explore several qualitative issues which we describe, would be useful for data analysis purposes. (4) A complete set of templates could be used to test the nonlinear dynamics of general relativity and to measure some of the binary parameters. We estimate the number of bits of information obtainable from the merger waves (about 10 to 60 for LIGO/VIRGO, up to 200 for LISA), estimate the information loss due to template numerical errors or sparseness in the template grid, and infer approximate requirements on template accuracy and spacing.

gr-qc↗

arXiv1997

Quantum inequalities in two dimensional Minkowski spacetime

We generalize some results of Ford and Roman constraining the possible behaviors of renormalized expected stress-energy tensors of a free massless scalar field in two dimensional Minkowski spacetime. Ford and Roman showed that the energy density measured by an inertial observer, when averaged with respect to that observers proper time by integrating against some weighting function, is bounded below by a negative lower bound proportional to the reciprocal of the square of the averaging timescale. However, the proof required a particular choice for the weighting function. We extend the Ford-Roman result in two ways: (i) We calculate the optimum (maximum possible) lower bound and characterize the state which achieves this lower bound; the optimum lower bound differs by a factor of three from the bound derived by Ford and Roman for their choice of smearing function. (ii) We calculate the lower bound for arbitrary, smooth positive weighting functions. We also derive similar lower bounds on the spatial average of energy density at a fixed moment of time.

gr-qc↗

arXiv1997

Bayesian Analysis of the Polarization of Distant Radio Sources: Limits on Cosmological Birefringence

A recent study of the rotation of the plane of polarization of light from 160 cosmological sources claims to find significant evidence for cosmological anisotropy. We point out methodological weaknesses of that study, and reanalyze the same data using Bayesian methods that overcome these problems. We find that the data always favor isotropic models for the distribution of observed polarizations over counterparts that have a cosmological anisotropy of the type advocated in the earlier study. Although anisotropic models are not completely ruled out, the data put strong lower limits on the length scale $λ$ (in units of the Hubble length) associated with the anisotropy; the lower limits of 95% credible regions for $λ$ lie between 0.43 and 0.62 in all anisotropic models we studied, values several times larger than the best-fit value of $λ\approx 0.1$ found in the earlier study. The length scale is not constrained from above. The vast majority of sources in the data are at distances closer than 0.4 Hubble lengths (corresponding to a redshift of $\approx$0.8); the results are thus consistent with there being no significant anisotropy on the length scale probed by these data.

astro-ph↗

arXiv1992

The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries

Gravitational-wave interferometers are expected to monitor the last three minutes of inspiral and final coalescence of neutron star and black hole binaries at distances approaching cosmological, where the event rate may be many per year. Because the binary's accumulated orbital phase can be measured to a fractional accuracy $\ll 10^{-3}$ and relativistic effects are large, the waveforms will be far more complex, carry more information, and be far harder to model theoretically than has been expected. Theorists must begin now to lay a foundation for extracting the waves' information.

astro-ph↗