arXiv subjects

Scott A. Hughes

Publications and source records attributed to Scott A. Hughes.

At least 91 records · Page 5Linked to original sources

arXiv2008

Localizing coalescing massive black hole binaries with gravitational waves

Massive black hole binary coalescences are prime targets for space-based gravitational wave (GW) observatories such as {\it LISA}. GW measurements can localize the position of a coalescing binary on the sky to an ellipse with a major axis of a few tens of arcminutes to a few degrees, depending on source redshift, and a minor axis which is $2 - 4$ times smaller. Neglecting weak gravitational lensing, the GWs would also determine the source's luminosity distance to better than percent accuracy for close sources, degrading to several percent for more distant sources. Weak lensing cannot, in fact, be neglected and is expected to limit the accuracy with which distances can be fixed to errors no less than a few percent. Assuming a well-measured cosmology, the source's redshift could be inferred with similar accuracy. GWs alone can thus pinpoint a binary to a three-dimensional ``pixel'' which can help guide searches for the hosts of these events. We examine the time evolution of this pixel, studying it at merger and at several intervals before merger. One day before merger, the major axis of the error ellipse is typically larger than its final value by a factor of $\sim 1.5-6$. The minor axis is larger by a factor of $\sim 2-9$, and, neglecting lensing, the error in the luminosity distance is larger by a factor of $\sim 1.5-7$. This large change over a short period of time is due to spin-induced precession, which is strongest in the final days before merger. The evolution is slower as we go back further in time. For $z = 1$, we find that GWs will localize a coalescing binary to within $\sim 10\ \mathrm{deg}^2$ as early as a month prior to merger and determine distance (and hence redshift) to several percent.

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arXiv2008

Measuring coalescing massive binary black holes with gravitational waves: The impact of spin-induced precession

The coalescence of massive black holes generates gravitational waves (GWs) that will be measurable by space-based detectors such as LISA to large redshifts. The spins of a binary's black holes have an important impact on its waveform. Specifically, geodetic and gravitomagnetic effects cause the spins to precess; this precession then modulates the waveform, adding periodic structure which encodes useful information about the binary's members. Following pioneering work by Vecchio, we examine the impact upon GW measurements of including these precession-induced modulations in the waveform model. We find that the additional periodicity due to spin precession breaks degeneracies among certain parameters, greatly improving the accuracy with which they may be measured. In particular, mass measurements are improved tremendously, by one to several orders of magnitude. Localization of the source on the sky is also improved, though not as much -- low redshift systems can be localized to an ellipse which is roughly ${a few} \times 10$ arcminutes in the long direction and a factor of 2-4 smaller in the short direction. Though not a drastic improvement relative to analyses which neglect spin precession, even modest gains in source localization will greatly facilitate searches for electromagnetic counterparts to GW events. Determination of distance to the source is likewise improved: We find that relative error in measured luminosity distance is commonly $\sim 0.2%-0.7%$ at $z \sim 1$. Finally, with the inclusion of precession, we find that the magnitude of the spins themselves can typically be determined for low redshift systems with an accuracy of about $0.1%-10 %$, depending on the spin value, allowing accurate surveys of mass and spin evolution over cosmic time.

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arXiv2008

"Kludge" gravitational waveforms for a test-body orbiting a Kerr black hole

One of the most exciting potential sources of gravitational waves for low-frequency, space-based gravitational wave (GW) detectors such as the proposed Laser Interferometer Space Antenna (LISA) is the inspiral of compact objects into massive black holes in the centers of galaxies. The detection of waves from such "extreme mass ratio inspiral" systems (EMRIs) and extraction of information from those waves require template waveforms. The systems' extreme mass ratio means that their waveforms can be determined accurately using black hole perturbation theory. Such calculations are computationally very expensive. There is a pressing need for families of approximate waveforms that may be generated cheaply and quickly but which still capture the main features of true waveforms. In this paper, we introduce a family of such "kludge" waveforms and describe ways to generate them. We assess performance of the introduced approximations by comparing "kludge" waveforms to accurate waveforms obtained by solving the Teukolsky equation in the adiabatic limit (neglecting GW backreaction). We find that the kludge waveforms do extremely well at approximating the true gravitational waveform, having overlaps with the Teukolsky waveforms of 95% or higher over most of the parameter space for which comparisons can currently be made. Indeed, we find these kludges to be of such high quality (despite their ease of calculation) that it is possible they may play some role in the final search of LISA data for EMRIs.

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arXiv2007

LISA sources and science

LISA is a planned space-based gravitational-wave (GW) detector that would be sensitive to waves from low-frequency sources, in the band of roughly (0.03 - 0.1) mHz < f < 0.1 Hz. This is expected to be an extremely rich chunk of the GW spectrum -- observing these waves will provide a unique view of dynamical processes in astrophysics. Here we give a quick survey of some key LISA sources and what GWs can uniquely teach us about these sources. Particularly noteworthy science which is highlighted here is the potential for LISA to track the moderate to high redshift evolution of black hole masses and spins through the measurement of GWs generated from massive black hole binaries (which in turn form by the merger of galaxies and protogalaxies). Measurement of these binary black hole waves has the potential to determine the masses and spins of the constituent black holes with percent-level accuracy or better, providing a unique high-precision probe of an aspect of early structure growth. This article is based on the "Astrophysics and Relativity using LISA" talk given by the author at the Seventh Edoardo Amaldi Conference on Gravitational Waves; it is largely an updating of the author's writeup of a talk given at the Sixth International LISA Symposium.

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arXiv2007

Towards adiabatic waveforms for inspiral into Kerr black holes: I. A new model of the source for the time domain perturbation equation

We revisit the problem of the emission of gravitational waves from a test mass orbiting and thus perturbing a Kerr black hole. The source term of the Teukolsky perturbation equation contains a Dirac delta function which represents a point particle. We present a technique to effectively model the delta function and its derivatives using as few as four points on a numerical grid. The source term is then incorporated into a code that evolves the Teukolsky equation in the time domain as a (2+1) dimensional PDE. The waveforms and energy fluxes are extracted far from the black hole. Our comparisons with earlier work show an order of magnitude gain in performance (speed) and numerical errors less than 1% for a large fraction of parameter space. As a first application of this code, we analyze the effect of finite extraction radius on the energy fluxes. This paper is the first in a series whose goal is to develop adiabatic waveforms describing the inspiral of a small compact body into a massive Kerr black hole.

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arXiv2007

Circular and non-circular nearly horizon-skimming orbits in Kerr spacetimes

We have performed a detailed analysis of orbital motion in the vicinity of a nearly extremal Kerr black hole. For very rapidly rotating black holes (spin a=J/M>0.9524M) we have found a class of very strong field eccentric orbits whose angular momentum L_z increases with the orbit's inclination with respect to the equatorial plane, while keeping latus rectum and eccentricity fixed. This behavior is in contrast with Newtonian intuition, and is in fact opposite to the "normal" behavior of black hole orbits. Such behavior was noted previously for circular orbits; since it only applies to orbits very close to the black hole, they were named "nearly horizon-skimming orbits". Our analysis generalizes this result, mapping out the full generic (inclined and eccentric) family of nearly horizon-skimming orbits. The earlier work on circular orbits reported that, under gravitational radiation emission, nearly horizon-skimming orbits tend to evolve to smaller orbit inclination, toward prograde equatorial configuration. Normal orbits, by contrast, always demonstrate slowly growing orbit inclination (orbits evolve toward the retrograde equatorial configuration). Using up-to-date Teukolsky-fluxes, we have concluded that the earlier result was incorrect: all circular orbits, including nearly horizon-skimming ones, exhibit growing orbit inclination. Using kludge fluxes based on a Post-Newtonian expansion corrected with fits to circular and to equatorial Teukolsky-fluxes, we argue that the inclination grows also for eccentric nearly horizon-skimming orbits. We also find that the inclination change is, in any case, very small. As such, we conclude that these orbits are not likely to have a clear and peculiar imprint on the gravitational waveforms expected to be measured by the space-based detector LISA.

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arXiv2006

A brief survey of LISA sources and science

LISA is a planned space-based gravitational-wave (GW) detector that would be sensitive to waves from low-frequency sources, in the band of roughly $(0.03 - 0.1) {\rm mHz} \lesssim f \lesssim 0.1 {\rm Hz}$. This is expected to be an extremely rich chunk of the GW spectrum -- observing these waves will provide a unique view of dynamical processes in astrophysics. Here we give a quick survey of some key LISA sources and what GWs can uniquely teach us about these sources. Particularly noteworthy science which is highlighted here is the potential for LISA to track the moderate to high redshift evolution of black hole masses and spins through the measurement of GWs generated from massive black hole binaries (which in turn form by the merger of galaxies and protogalaxies). Measurement of these binary black hole waves has the potential to determine the masses and spins of the constituent black holes with percent-level accuracy or better, providing a unique high-precision probe of an aspect of early structure growth. This article is based on the ``Astrophysics Tutorial'' talk given by the author at the Sixth International LISA Symposium.

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arXiv2006

(Sort of) Testing relativity with extreme mass ratio inspirals

The inspirals of ``small'' ($1 - 100 M_\odot$) compact bodies through highly relativistic orbits of massive (several $\times 10^5 M_\odot -$ several $\times 10^6 M_\odot$) black holes are among the most anticipated sources for the LISA gravitational-wave antenna. The measurement of these waves is expected to map the spacetime of the larger body with high precision, allowing us to test in detail the hypothesis that black hole candidates are described by the Kerr metric of general relativity. In this article, we will briefly describe how these sources can be used to perform such a test. These proposed measurements are often described as ``testing relativity''. This description is at best somewhat glib: Because -- at least to date -- all work related to these measurements assumes general relativity as the theoretical framework in which these tests are performed, the measurements cannot be said to ``test relativity'' in a fundamental way. More accurately, they test the {\it nature of massive compact bodies within general relativity}. A surprising result for such a test could point to deviations from general relativity, and would provide an experimentally motivated direction in which to pursue tests of gravity theories beyond GR.

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arXiv2006

Gravitational wave snapshots of generic extreme mass ratio inspirals

Using black hole perturbation theory, we calculate the gravitational waves produced by test particles moving on bound geodesic orbits about rotating black holes. The orbits we consider are generic - simultaneously eccentric and inclined. The waves can be described as having radial, polar, and azimuthal "voices", each of which can be made to dominate by varying eccentricity and inclination. Although each voice is generally apparent in the waveform, the radial voice is prone to overpowering the others. We also compute the radiative fluxes of energy and axial angular momentum at infinity and through the event horizon. These fluxes, coupled to a prescription for the radiative evolution of the Carter constant, will be used in future work to adiabatically evolve through a sequence of generic orbits. This will enable the calculation of inspiral waveforms that, while lacking certain important features, will approximate those expected from astrophysical extreme mass ratio captures sufficiently well to aid development of measurement algorithms on a relatively short timescale.

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arXiv2006

Short GRB and binary black hole standard sirens as a probe of dark energy

Observations of the gravitational radiation from well-localized, inspiraling compact object binaries can measure absolute source distances with high accuracy. When coupled with an independent determination of redshift through an electromagnetic counterpart, these standard sirens can provide an excellent probe of the expansion history of the Universe and the dark energy. Short gamma-ray bursts, if produced by merging neutron star binaries, would be standard sirens with known redshifts detectable by ground-based GW networks such as LIGO-II, Virgo, and AIGO. Depending upon the collimation of these GRBs, a single year of observation of their gravitational waves can measure the Hubble constant to about 2%. When combined with measurement of the absolute distance to the last scattering surface of the cosmic microwave background, this determines the dark energy equation of state parameter w to 9%. Similarly, supermassive binary black hole inspirals will be standard sirens detectable by LISA. Depending upon the precise redshift distribution, 100 sources could measure w at the 4% level.

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arXiv2005

The basics of gravitational wave theory

Einstein's special theory of relativity revolutionized physics by teaching us that space and time are not separate entities, but join as ``spacetime''. His general theory of relativity further taught us that spacetime is not just a stage on which dynamics takes place, but is a participant: The field equation of general relativity connects matter dynamics to the curvature of spacetime. Curvature is responsible for gravity, carrying us beyond the Newtonian conception of gravity that had been in place for the previous two and a half centuries. Much research in gravitation since then has explored and clarified the consequences of this revolution; the notion of dynamical spacetime is now firmly established in the toolkit of modern physics. Indeed, this notion is so well established that we may now contemplate using spacetime as a tool for other science. One aspect of dynamical spacetime -- its radiative character, ``gravitational radiation'' -- will inaugurate entirely new techniques for observing violent astrophysical processes. Over the next one hundred years, much of this subject's excitement will come from learning how to exploit spacetime as a tool for astronomy. This article is intended as a tutorial in the basics of gravitational radiation physics.

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arXiv2005

Rotating black hole orbit functionals in the frequency domain

In many astrophysical problems, it is important to understand the behavior of functions that come from rotating (Kerr) black hole orbits. It can be particularly useful to work with the frequency domain representation of those functions, in order to bring out their harmonic dependence upon the fundamental orbital frequencies of Kerr black holes. Although, as has recently been shown by W. Schmidt, such a frequency domain representation must exist, the coupled nature of a black hole orbit's $r$ and $θ$ motions makes it difficult to construct such a representation in practice. Combining Schmidt's description with a clever choice of timelike coordinate suggested by Y. Mino, we have developed a simple procedure that sidesteps this difficulty. One first Fourier expands all quantities using Mino's time coordinate $λ$. In particular, the observer's time $t$ is decomposed with $λ$. The frequency domain description is then built from the $λ$-Fourier expansion and the expansion of $t$. We have found this procedure to be quite simple to implement, and to be applicable to a wide class of functionals. We test the procedure using a simple test function, and then apply it in a particularly interesting case, the Weyl curvature scalar $ψ_4$ used in black hole perturbation theory.

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arXiv2005

Computing inspirals in Kerr in the adiabatic regime. I. The scalar case

A key source for LISA will be the inspiral of compact objects into supermassive black holes. Recently Mino has shown that in the adiabatic limit, gravitational waveforms for these sources can be computed using for the radiation reaction force the gradient of one half the difference between the retarded and advanced metric perturbations. Using post-Newtonian expansions, we argue that the resulting waveforms should be sufficiently accurate for signal detection with LISA. Data-analysis templates will require higher accuracy, going beyond adiabaticity; this remains a significant challenge. We describe an explicit computational procedure for obtaining waveforms based on Mino's result, for the case of a point particle coupled to a scalar field. We derive an expression for the time-averaged time derivative of the Carter constant, and verify that the expression correctly predicts that circular orbits remain circular while evolving via radiation reaction. The derivation uses detailed properties of mode expansions, Green's functions and bound geodesic orbits in the Kerr spacetime, which we review in detail. This paper is about three quarters review and one quarter new material. The intent is to give a complete and self-contained treatment of scalar radiation reaction in the Kerr spacetime, in a single unified notation, starting with the Kerr metric and ending with formulae for the time evolution of all three constants of the motion that are sufficiently explicit to be used immediately in a numerical code.

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arXiv2005

Cosmology with coalescing massive black holes

The gravitational waves generated in the coalescence of massive binary black holes will be measurable by LISA to enormous distances. Redshifts z~10 or larger (depending somewhat on the mass of the binary) can potentially be probed by such measurements, suggesting that binary coalescences can be made into cosmological tools. We discuss two particularly interesting types of probes. First, by combining gravitational-wave measurements with information about the universe's cosmography, we can study the evolution of black hole masses and merger rates as a function of redshift, providing information about the growth of structures at high redshift and possibly constraining hierarchical merger scenarios. Second, if it is possible to associate an ``electromagnetic'' counterpart with a coalescence, it may be possible to measure both redshift and luminosity distance to an event with less than ~1% error. Such a measurement would constitute an amazingly precise cosmological standard candle. Unfortunately, gravitational lensing uncertainties will reduce the quality of this candle significantly. Though not as amazing as might have been hoped, such a candle would nonetheless very usefully complement other distance-redshift probes, in particular providing a valuable check on systematic effects in such measurements.

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arXiv2005

Using gravitational-wave standard sirens

Gravitational waves (GWs) from supermassive binary black hole (BBH) inspirals are potentially powerful standard sirens (the GW analog to standard candles) (Schutz 1986, 2002). Because these systems are well-modeled, the space-based GW observatory LISA will be able to measure the luminosity distance (but not the redshift) to some distant massive BBH systems with 1-10% accuracy. This accuracy is largely limited by pointing error: GW sources generally are poorly localized on the sky. Localizing the binary independently (e.g., through association with an electromagnetic counterpart) greatly reduces this positional error. An electromagnetic counterpart may also allow determination of the event's redshift. In this case, BBH coalescence would constitute an extremely precise (better than 1%) standard candle visible to high redshift. In practice, gravitational lensing degrades this precision, though the candle remains precise enough to provide useful information about the distance-redshift relation. Even if very rare, these GW standard sirens would complement, and increase confidence in, other standard candles.

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arXiv2005

Gravitational radiation reaction and inspiral waveforms in the adiabatic limit

We describe progress evolving an important limit of binary orbits in general relativity, that of a stellar mass compact object gradually spiraling into a much larger, massive black hole. These systems are of great interest for gravitational wave observations. We have developed tools to compute for the first time the radiated fluxes of energy and angular momentum, as well as instantaneous snapshot waveforms, for generic geodesic orbits. For special classes of orbits, we compute the orbital evolution and waveforms for the complete inspiral by imposing global conservation of energy and angular momentum. For fully generic orbits, inspirals and waveforms can be obtained by augmenting our approach with a prescription for the self force in the adiabatic limit derived by Mino. The resulting waveforms should be sufficiently accurate to be used in future gravitational-wave searches.

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arXiv2005

Golden Binary Gravitational-Wave Sources: Robust Probes of Strong-Field Gravity

Space-born gravitational-wave interferometers such as {\it LISA} will detect the gravitational wave (GW) signal from the inspiral, plunge and ringdown phases of massive black hole binary mergers at cosmological distances. From the inspiral waves, we will be able to measure the masses of the binaries' members; from the ringdown waves, we will be able to measure the mass of the final merged remnant. A subset of detected events allow the identification of both the inspiral and the ringdown waveforms in a given source, and thus allow a measurement of the total mass-energy lost to GWs over the coalescence, $M_{\rm GW}$. We define ``golden'' binary mergers to be those with measurement errors likely to be small enough for a physically useful determination of $M_{\rm GW}$. A detailed sensitivity study, combined with simple black hole population models, suggests that a few golden binary mergers may be detected during a 3-year {\it LISA} mission lifetime. Any such mass deficit measurement would constitute a robust and valuable observational test of strong-field relativistic gravity. An extension of this concept to include spin measurements may allow a direct empirical test of the black hole area theorem.

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arXiv2004

How black holes get their kicks: Radiation recoil in binary black hole mergers

Gravitational waves from the coalescence of binary black holes carry linear momentum, causing center of mass recoil. This ``radiation rocket'' has important implications for systems with escape speeds of order the recoil velocity. We describe new recoil calculations using high precision black hole perturbation theory to estimate the magnitude of the recoil for the slow ``inspiral'' coalescence phase; coupled with a cruder calculation for the final ``plunge'', we estimate the total recoil imparted to a merged black hole. We find that velocities of many tens to a few hundred km/sec can be achieved fairly easily. The recoil probably never exceeds about 500 km/sec.

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