Frequency domain reduced order model of aligned-spin effective-one-body waveforms with generic mass-ratios and spins

I provide a frequency domain reduced order model (ROM) for the aligned-spin effective-one-body (EOB) model "SEOBNRv2" for data analysis with second and third generation ground based gravitational wave (GW) detectors. SEOBNRv2 models the dominant mode of the GWs emitted by the coalescence of black hole (BH) binaries. The large physical parameter space (dimensionless spins $-1 \leq \chi_i \leq 0.99$ and symmetric mass-ratios $0.01 \leq \eta \leq 0.25$) requires sophisticated reduced order modeling techniques, including patching in the parameter space and in frequency. I find that the time window over which the inspiral-plunge and the merger-ringdown waveform in SEOBNRv2 are connected is discontinuous when the spin of the deformed Kerr BH $\chi=0.8$ or the symmetric mass-ratio $\eta \sim 0.083$. This discontinuity increases resolution requirements for the ROM. The ROM can be used for compact binary systems with total masses of $2 M_\odot$ or higher for the advanced LIGO (aLIGO) design sensitivity and a $10$ Hz lower cutoff frequency. The ROM has a worst mismatch against SEOBNRv2 of $\sim 1\%$, but in general mismatches are better than $\sim 0.1\%$. The ROM is crucial for key data analysis applications for compact binaries, such as GW searches and parameter estimation carried out within the LIGO Scientific Collaboration (LSC).Comment: 14 pages, 14 figure

Measuring intermediate mass black hole binaries with advanced gravitational wave detectors

We perform a systematic study to explore the accuracy with which the parameters of intermediate-mass black-hole binary systems can be measured from their gravitational wave (GW) signatures using second-generation GW detectors. We make use of the most recent reduced-order models containing inspiral, merger and ringdown signals of aligned-spin effective-one-body waveforms (SEOBNR) to significantly speed up the calculations. We explore the phenomenology of the measurement accuracies for binaries with total masses between 50 and 500 $M_\odot$ and mass ratios between 0.1 and 1. We find that (i) at total masses below ~200 $M_\odot$, where the signal-to-noise-ratio is dominated by the inspiral portion of the signal, the chirp mass parameter can be accurately measured; (ii) at higher masses, the information content is dominated by the ringdown, and total mass is measured more accurately; (iii) the mass of the lower-mass companion is poorly estimated, especially at high total mass and more extreme mass ratios; (iv) spin cannot be accurately measured for our injection set with non-spinning components. Most importantly, we find that for binaries with non-spinning components at all values of the mass ratio in the considered range and at network signal-to-noise ratio of 15, analyzed with spin-aligned templates, the presence of an intermediate-mass black hole with mass >100 $M_\odot$ can be confirmed with 95% confidence in any binary that includes a component with a mass of 130 $M_\odot$ or greater.Comment: 6 pages, 8 figures; published versio

Measuring neutron star tidal deformability with Advanced LIGO: a Bayesian analysis of neutron star - black hole binary observations

The discovery of gravitational waves (GW) by Advanced LIGO has ushered us into an era of observational GW astrophysics. Compact binaries remain the primary target sources for LIGO, of which neutron star-black hole (NSBH) binaries form an important subset. GWs from NSBH sources carry signatures of (a) the tidal distortion of the neutron star by its companion black hole during inspiral, and (b) its potential tidal disruption near merger. In this paper, we present a Bayesian study of the measurability of neutron star tidal deformability $\Lambda_\mathrm{NS}\propto (R/M)^{5}$ using observation(s) of inspiral-merger GW signals from disruptive NSBH coalescences, taking into account the crucial effect of black hole spins. First, we find that if non-tidal templates are used to estimate source parameters for an NSBH signal, the bias introduced in the estimation of non-tidal physical parameters will only be significant for loud signals with signal-to-noise ratios $> 30$. For similarly loud signals, we also find that we can begin to put interesting constraints on $\Lambda_\mathrm{NS}$ (factor of 1-2) with individual observations. Next, we study how a population of realistic NSBH detections will improve our measurement of neutron star tidal deformability. For astrophysical populations of $disruptive$ NSBH mergers, we find 20-35 events to be sufficient to constrain $\Lambda_\mathrm{NS}$ within $\pm 25-50\%$, depending on the chosen equation of state. In this we also assume that LIGO will detect black holes with masses within the astrophysical $mass$-$gap$. If the mass-gap remains preserved in NSBHs detected by LIGO, we estimate that $25\%$ $additional$ detections will furnish comparable tidal measurement accuracy. In both cases, we find that the loudest 5-10 events to provide most of the tidal information, thereby facilitating targeted follow-ups of NSBHs in the upcoming LIGO-Virgo runs.Comment: 21 pages, 17 figure

Statistical Gravitational Waveform Models: What to Simulate Next?

Models of gravitational waveforms play a critical role in detecting and characterizing the gravitational waves (GWs) from compact binary coalescences. Waveforms from numerical relativity (NR), while highly accurate, are too computationally expensive to produce to be directly used with Bayesian parameter estimation tools like Markov-chain-Monte-Carlo and nested sampling. We propose a Gaussian process regression (GPR) method to generate accurate reduced-order-model waveforms based only on existing accurate (e.g. NR) simulations. Using a training set of simulated waveforms, our GPR approach produces interpolated waveforms along with uncertainties across the parameter space. As a proof of concept, we use a training set of IMRPhenomD waveforms to build a GPR model in the 2-d parameter space of mass ratio $q$ and equal-and-aligned spin $\chi_1=\chi_2$. Using a regular, equally-spaced grid of 120 IMRPhenomD training waveforms in $q\in[1,3]$ and $\chi_1 \in [-0.5,0.5]$, the GPR mean approximates IMRPhenomD in this space to mismatches below $4.3\times 10^{-5}$. Our approach can alternatively use training waveforms directly from numerical relativity. Beyond interpolation of waveforms, we also present a greedy algorithm that utilizes the errors provided by our GPR model to optimize the placement of future simulations. In a fiducial test case we find that using the greedy algorithm to iteratively add simulations achieves GPR errors that are $\sim 1$ order of magnitude lower than the errors from using Latin-hypercube or square training grids

Surrogate model for an aligned-spin effective one body waveform model of binary neutron star inspirals using Gaussian process regression

Fast and accurate waveform models are necessary for measuring the properties of inspiraling binary neutron star systems such as GW170817. We present a frequency-domain surrogate version of the aligned-spin binary neutron star waveform model using the effective one body formalism known as SEOBNRv4T. This model includes the quadrupolar and octopolar adiabatic and dynamical tides. The version presented here is improved by the inclusion of the spin-induced quadrupole moment effect, and completed by a prescription for tapering the end of the waveform to qualitatively reproduce numerical relativity simulations. The resulting model has 14 intrinsic parameters. We reduce its dimensionality by using universal relations that approximate all matter effects in terms of the leading quadrupolar tidal parameters. The implementation of the time-domain model can take up to an hour to evaluate using a starting frequency of 20Hz, and this is too slow for many parameter estimation codes that require $O(10^7)$ sequential waveform evaluations. We therefore construct a fast and faithful frequency-domain surrogate of this model using Gaussian process regression. The resulting surrogate has a maximum mismatch of $4.5\times 10^{-4}$ for the Advanced LIGO detector, and requires 0.13s to evaluate for a waveform with a starting frequency of 20Hz. Finally, we perform an end-to-end test of the surrogate with a set of parameter estimation runs, and find that the surrogate accurately recovers the parameters of injected waveforms.Comment: 19 pages, 10 figures, submitted to PR