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Register a new userParameter Estimation of Gravitational Waves from Nonprecessing BH-NS Inspirals with higher harmonics: Comparing MCMC posteriors to an Effective Fisher Matrix
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Added by
Richard O'Shaughnessy
Publication date
2013
fields
Physics
and research's language is
English
Authors
R. OShaughnessy
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Using the texttt{lalinference} Markov-chain Monte Carlo parameter estimation code, we examine two distinct nonprecessing black hole-neutron star (BH-NS) binaries with and without higher-order harmonics. Our simulations suggest that higher harmonics provide a minimal amount of additional information, principally about source geometry. Higher harmonics do provide disproportionately more information than expected from the signal power. Our results compare favorably to the effective Fisher matrix approach. Extrapolating using analytic scalings, we expect higher harmonics will provide little new information about nonprecessing BH-NS binaries at the signal amplitudes expected for the first few detections. Any study of subdominant degrees of freedom in gravitational wave astronomy can adopt the tools presented here ($V/V_{rm prior}$ and $D_{KL}$) to assess whether new physics is accessible (e.g., modifications of gravity; spin-orbit misalignment) and if so precisely what information those new parameters provide. For astrophysicists, we provide a concrete illustration of how well parameters of a BH-NS binary can be measured, relevant to the astrophysical interpretation of coincident EM and GW events (e.g., short GRBs). For our fiducial initial-detector example, the individual masses can be determined to lie between $7.11-11.48 M_odot$ and $1.77-1.276M_odot$ at greater than 99% confidence, accounting for unknown BH spin. Assuming comparable control over waveform systematics, future measurements of BH-NS binaries can constrain the BH and perhaps NS mass distributions.
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Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binarys nature and inspiral kinematics. Using the lalinference_mcmc Markov-chain Monte Carlo parameter estimation code, we use two fiducial examples to illustrate how the geometry and kinematics are encoded into the modulated gravitational wave signal, using coordinates well-adapted to precession. Even for precessing binaries, we show the performance of detailed parameter estimation can be estimated by effective estimates: comparisons of a prototype signal with its nearest neighbors, adopting a fixed sky location and idealized two-detector network. We use detailed and effective approaches to show higher harmonics provide nonzero but small local improvement when estimating the parameters of precessing BH-NS binaries. That said, we show higher harmonics can improve parameter estimation accuracy for precessing binaries ruling out approximately-degenerate source orientations. Our work illustrates quantities gravitational wave measurements can provide, such as reliable component masses and the precise orientation of a precessing short gamma ray burst progenitor relative to the line of sight. Effective estimates may provide a simple way to estimate trends in the performance of parameter estimation for generic precessing BH-NS binaries in next-generation detectors. For example, our results suggest that the orbital chirp rate, precession rate, and precession geometry are roughly-independent observables, defining natural variables to organize correlations in the high-dimensional BH-NS binary parameter space.
Previous analytic and numerical calculations suggest that, at each instant, the emission from a precessing black hole binary closely resembles the emission from a nonprecessing analog. In this paper we quantitatively explore the validity and limitations of that correspondence, extracting the radiation from a large collection of roughly two hundred generic black hole binary merger simulations both in the simulation frame and in a corotating frame that tracks precession. To a first approximation, the corotating-frame waveforms resemble nonprecessing analogs, based on similarity over a band-limited frequency interval defined using a fiducial detector (here, advanced LIGO) and the sources total mass $M$. By restricting attention to masses $Min 100, 1000 M_odot$, we insure our comparisons are sensitive only to our simulated late-time inspiral, merger, and ringdown signals. In this mass region, every one of our precessing simulations can be fit by some physically similar member of the texttt{IMRPhenomB} phenomenological waveform family to better than 95%; most fit significantly better. The best-fit parameters at low and high mass correspond to natural physical limits: the pre-merger orbit and post-merger perturbed black hole. Our results suggest that physically-motivated synthetic signals can be derived by viewing radiation from suitable nonprecessing binaries in a suitable nonintertial reference frame. While a good first approximation, precessing systems have degrees of freedom (i.e., the transverse spins) which a nonprecessing simulation cannot reproduce. We quantify the extent to which these missing degrees of freedom limit the utility of synthetic precessing signals for detection and parameter estimation.
The recent direct observation of gravitational waves (GW) from merging black holes opens up the possibility of exploring the theory of gravity in the strong regime at an unprecedented level. It is therefore interesting to explore which extensions to General Relativity (GR) could be detected. We construct an Effective Field Theory (EFT) satisfying the following requirements. It is testable with GW observations; it is consistent with other experiments, including short distance tests of GR; it agrees with widely accepted principles of physics, such as locality, causality and unitarity; and it does not involve new light degrees of freedom. The most general theory satisfying these requirements corresponds to adding to the GR Lagrangian operators constructed out of powers of the Riemann tensor, suppressed by a scale comparable to the curvature of the observed merging binaries. The presence of these operators modifies the gravitational potential between the compact objects, as well as their effective mass and current quadrupoles, ultimately correcting the waveform of the emitted GW.
During the fifth science run of the Laser Interferometer Gravitational-wave Observatory (LIGO), signals modelling the gravitational waves emitted by coalescing non-spinning compact-object binaries were injected into the LIGO data stream. We analysed the data segments into which such injections were made using a Bayesian approach, implemented as a Markov-chain Monte-Carlo technique in our code SPINspiral. This technique enables us to determine the physical parameters of such a binary inspiral, including masses and spin, following a possible detection trigger. For the first time, we publish the results of a realistic parameter-estimation analysis of waveforms embedded in real detector noise. We used both spinning and non-spinning waveform templates for the data analysis and demonstrate that the intrinsic source parameters can be estimated with an accuracy of better than 1-3% in the chirp mass and 0.02-0.05 (8-20%) in the symmetric mass ratio if non-spinning waveforms are used. We also find a bias between the injected and recovered parameters, and attribute it to the difference in the post-Newtonian orders of the waveforms used for injection and analysis.
Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally characterize this picture, the physical parameters of the system can be extracted more efficiently from the gravitational wave data, and interpreted more easily. We assess the performance of MCMC parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binarys spins and orbital angular momentum and (b) a time at which the detectors are most sensitive to the binarys gravitational wave emission. Using anticipated noise curves for the advanced-generation LIGO and Virgo gravitational wave detectors, we find that this careful choice of reference frame and reference time significantly improves parameter estimation efficiency for BNS, NS-BH, and BBH signals.
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