Theocharis A. Apostolatos

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 ≪10^-3 and relativistic effects are large, the wave forms will be far more complex and carry more information than has been expected. Improved wave form modeling is needed as a foundation for extracting the waves’ information, but is not necessary for wave detection.

The inverse problem for pulsating neutron stars: a 'fingerprint analysis' for the supranuclear equation of state

We study the problem of detecting, and inferring astrophysical information from, gravitational waves from a pulsating neutron star. We show that the fluid f and p modes, as well as the gravitational-wave w modes, may be detectable from sources in our own Galaxy, and investigate how accurately the frequencies and damping rates of these modes can be inferred from a noisy gravitational-wave data stream. Based on the conclusions of this discussion we propose a strategy for revealing the supranuclear equation of state using the neutron star fingerprints: the observed frequencies of an f and a p mode. We also discuss how well the source can be located in the sky using observations with several detectors.

Revising the multipole moments of numerical spacetimes and its consequences.

Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one in order to yield a reliable representation. In this Letter, we show that there has been a widespread delusion in the way the multipole moments of a numerical metric are read from the asymptotic expansion of the metric functions. We show how one should read correctly the first few multipole moments (starting from the quadrupole mass moment) and how these corrected moments improve the efficiency of describing the metric functions with analytic metrics that have already been used in the literature, as well as other consequences of using the correct moments.

Non-linear pulsations in differentially rotating neutron stars: mass-shedding-induced damping and splitting of the fundamental mode

We study small-amplitude, non-linear pulsations of uniformly and differentially rotating neutron stars employing a two-dimensional evolution code for general-relativistic hydrodynamics. Using Fourier transforms at several points inside the star, both the eigenfrequencies and two-dimensional eigenfunctions of pulsations are extracted. The centrifugal forces and the degree of differential rotation have significant effects on the mode eigenfunction. We find that near the mass-shedding limit, the pulsations are damped due to shocks forming at the surface of the star. This new damping mechanism may set a small saturation amplitude for modes that are unstable to the emission of gravitational waves. After correcting for the assumption of the Cowling approximation (used in our numerical code), we construct empirical relations that predict the range of gravitational-wave frequencies from quasi-periodic post-bounce oscillations in the core collapse of massive stars. We also find that the fundamental quasi-radial mode is split, at least in the Cowling approximation and mainly in differentially rotating stars, into two different sequences.

How to Observe a Non-Kerr Spacetime Using Gravitational Waves

We present a generic criterion which can be used in gravitational-wave data analysis to distinguish an extreme-mass-ratio inspiral into a Kerr background spacetime from one into a non-Kerr spacetime. We exploit the fact that when an integrable system, such as the system that describes geodesic orbits in a Kerr spacetime, is perturbed, the tori in phase space which initially corresponded to resonances disintegrate so as to form Birkhoff chains on a surface of section. The KAM curves of the islands in such a chain share the same ratio of frequencies, even though the frequencies themselves vary from one KAM curve to another inside an island. However the KAM curves, which do not lie in a Birkhoff chain, do not share this characteristic property. Such a temporal constancy of the ratio of frequencies during the evolution of the gravitational-wave signal will signal a non-Kerr spacetime.

Observable signature of a background deviating from the Kerr metric

By detecting gravitational wave signals from extreme mass ratio inspiraling sources (EMRIs) we will be given the opportunity to check our theoretical expectations regarding the nature of supermassive bodies that inhabit the central regions of galaxies. We have explored some qualitatively new features that a perturbed Kerr metric induces in its geodesic orbits. Since a generic perturbed Kerr metric does not possess all the special symmetries of a Kerr metric, the geodesic equations in the former case are described by a slightly nonintegrable Hamiltonian system. According to the

Effective No-Hair Relations for Neutron Stars and Quark Stars: Relativistic Results

Astrophysical charge-free black holes are known to satisfy no-hair relations through which all multipole moments can be specified in terms of just their mass and spin angular momentum. We here investigate the possible existence of no-hair-like relations among multipole moments for neutron stars and quark stars that are independent of their equation of state. We calculate the multipole moments of these stars up to hexadecapole order by constructing uniformly-rotating and unmagnetized stellar solutions to the Einstein equations. For slowly-rotating stars, we construct stellar solutions to quartic order in spin in a slow-rotation expansion, while for rapidly-rotating stars, we solve the Einstein equations numerically with the LORENE and RNS codes. We find that the multipole moments extracted from these numerical solutions are consistent with each other. We confirm that the current-dipole is related to the mass-quadrupole in an approximately equation of state independent fashion, which does not break for rapidly rotating neutron stars or quark stars. We further find that the current-octupole and the mass-hexadecapole moments are related to the mass-quadrupole in an approximately equation of state independent way to

An all-purpose metric for the exterior of any kind of rotating neutron star

\sim 10%

ORBITS IN A NON-KERR DYNAMICAL SYSTEM

, worsening in the hexadecapole case. All of our findings are in good agreement with previous work that considered stellar solutions to leading-order in a weak-field expansion. The quartic in spin, slowly-rotating solutions found here allow us to estimate the systematic errors in the measurement of the neutron stars mass and radius with future X-ray observations, such as NICER and LOFT. We find that the effect of these quartic-in-spin terms on the quadrupole and hexadecapole moments and stellar eccentricity may dominate the error budget for very rapidly-rotating neutron stars. The new universal relations found here should help to reduce such systematic errors.

Corrections and comments on the multipole moments of axisymmetric electrovacuum spacetimes

We have tested the appropriateness of two-soliton analytic metric to describe the exterior of all types of neutron stars, no matter what their equation of state or rotation rate is. The particular analytic solution of the vacuum Einstein equations proved quite adjustable to mimic the metric functions of all numerically constructed neutron star models that we used as a testbed. The neutron star models covered a wide range of stiffness, with regard to the equation of state of their interior, and all rotation rates up to the maximum possible rotation rate allowed for each such star. Apart from the metric functions themselves, we have compared the radius of the innermost stable circular orbit RISCO, the orbital frequency � ≡ dφ dt of circular geodesics, and their epicyclic frequencies � ρ, � z, as well as the change of the energy of circular orbits per logarithmic change of orbital frequency � ˜ E. All these quantities, calculated by means of the two-soliton analytic metric, fitted with good accuracy the corresponding numerical ones as in previous analogous comparisons (although previous attempts were restricted to neutron star models with either high or low rotation rates). We believe that this particular analytic solution could be considered as an analytic faithful representation of the gravitation field of any rotating neutron star with such accuracy, that one could explore the interior structure of a neutron star by using this space–time to interpret observations of astrophysical processes that take place around it.