On combining information from multiple gravitational wave sources

In the coming years, advanced gravitational wave detectors will observe signals from a large number of compact binary coalescences. The majority of these signals will be relatively weak, making the precision measurement of subtle effects, such as deviations from general relativity, challenging in the individual events. However, many weak observations can be combined into precise inferences, if information from the individual signals is combined in an appropriate way. In this study we revisit common methods for combining multiple gravitational wave observations to test general relativity, namely (i) multiplying the individual likelihoods of beyond-general-relativity parameters and (ii) multiplying the Bayes Factor in favor of general relativity from each event. We discuss both methods and show that they make stringent assumptions about the modified theory of gravity they test. In particular, the former assumes that all events share the same beyond-general-relativity parameter, while the latter assumes that the theory of gravity has a new unrelated parameter for each detection. We show that each method can fail to detect deviations from general relativity when the modified theory being tested violates these assumptions. We argue that these two methods are the extreme limits of a more generic framework of hierarchical inference on hyperparameters that characterize the underlying distribution of single-event parameters. We illustrate our conclusions first using a simple model of Gaussian likelihoods, and also by applying parameter estimation techniques to a simulated dataset of gravitational waveforms in a model where the graviton is massive. We argue that combining information from multiple sources requires explicit assumptions that make the results inherently model-dependent.Comment: 9 pages, 3 figure

Distinguishing types of compact-object binaries using the gravitational-wave signatures of their mergers

We analyze the distinguishability of populations of coalescing binary neutron stars, neutron-star black-hole binaries, and binary black holes, whose gravitational-wave signatures are expected to be observed by the advanced network of ground-based interferometers LIGO and Virgo. We consider population-synthesis predictions for plausible merging binary distributions in mass space, along with measurement accuracy estimates from the main gravitational-wave parameter-estimation pipeline. We find that for our model compact-object binary mass distribution, we can always distinguish binary neutron stars and black-hole--neutron-star binaries, but not necessarily black-hole--neutron-star binaries and binary black holes; however, with a few tens of detections, we can accurately identify the three subpopulations and measure their respective rates.Comment: Revised unabridged version (contains material omitted from published version

Efficient method for measuring the parameters encoded in a gravitational-wave signal

Once upon a time, predictions for the accuracy of inference on gravitational-wave signals relied on computationally inexpensive but often inaccurate techniques. Recently, the approach has shifted to actual inference on noisy signals with complex stochastic Bayesian methods, at the expense of significant computational cost. Here, we argue that it is often possible to have the best of both worlds: a Bayesian approach that incorporates prior information and correctly marginalizes over uninteresting parameters, providing accurate posterior probability distribution functions, but carried out on a simple grid at a low computational cost, comparable to the inexpensive predictive techniques.Comment: 17 pages, 5 figure

Reanalysis of LIGO black-hole coalescences with alternative prior assumptions

We present a critical reanalysis of the black-hole binary coalescences detected during LIGO's first observing run under different Bayesian prior assumptions. We summarize the main findings of Vitale et al. (2017) and show additional marginalized posterior distributions for some of the binaries' intrinsic parameters.Comment: Proceedings of IAU Symposium 338: Gravitational Wave Astrophysics (Baton Rouge, LA, October 2017

Impact of Bayesian prior on the characterization of binary black hole coalescences

In a regime where data are only mildly informative, prior choices can play a significant role in Bayesian statistical inference, potentially affecting the inferred physics. We show this is indeed the case for some of the parameters inferred from current gravitational-wave measurements of binary black hole coalescences. We reanalyze the first detections performed by the twin LIGO interferometers using alternative (and astrophysically motivated) prior assumptions. We find different prior distributions can introduce deviations in the resulting posteriors that impact the physical interpretation of these systems. For instance, (i) limits on the $90\%$ credible interval on the effective black hole spin $\chi_{\rm eff}$ are subject to variations of $\sim 10\%$ if a prior with black hole spins mostly aligned to the binary's angular momentum is considered instead of the standard choice of isotropic spin directions, and (ii) under priors motivated by the initial stellar mass function, we infer tighter constraints on the black hole masses, and in particular, we find no support for any of the inferred masses within the putative mass gap $M \lesssim 5 M_\odot$.Comment: 6 Pages, 2 Figures; see also 1712.06635 Data release at https://github.com/vitale82/GWprior

Eccentric Black Hole Mergers in Dense Star Clusters: The Role of Binary-Binary Encounters

We present the first systematic study of strong binary-single and binary-binary black hole interactions with the inclusion of general relativity. When including general relativistic effects in strong encounters, dissipation of orbital energy from gravitational waves (GWs) can lead to captures and subsequent inspirals with appreciable eccentricities when entering the sensitive frequency ranges of the LIGO and Virgo GW detectors. In this study, we perform binary-binary and binary-single scattering experiments with general relativistic dynamics up through the 2.5 post-Newtonian order included, both in a controlled setting to gauge the importance of non-dissipative post-Newtonian terms and derive scaling relations for the cross-section of GW captures, as well as experiments tuned to the strong interactions from state-of-the art globular cluster models to assess the relative importance of the binary-binary channel at facilitating GW captures and the resultant eccentricity distributions of inspiral from channel. Although binary-binary interactions are 10-100 times less frequent in globular clusters than binary-single interactions, their longer lifetime and more complex dynamics leads to a higher probability for GW captures to occur during the encounter. We find that binary-binary interactions contribute 25-45% of the eccentric mergers which occur during strong black hole encounters in globular clusters, regardless of the properties of the cluster environment. The inclusion of higher multiplicity encounters in dense star clusters therefore have major implications on the predicted rates of highly eccentric binaries potentially detectable by the LIGO/Virgo network. As gravitational waveforms of eccentric inspirals are distinct from those generated by merging binaries which have circularized, measurements of eccentricity in such systems would highly constrain their formation scenario.Comment: 18 pages, 6 figures. Published in The Astrophysical Journa

Ready for what lies ahead? -- Gravitational waveform accuracy requirements for future ground based detectors

Future third generation (3G) ground-based GW detectors, such as the Einstein Telescope and Cosmic Explorer, will have unprecedented sensitivities enabling studies of the entire population of stellar mass binary black hole coalescences in the Universe. To infer binary parameters from a GW signal we require accurate models of the gravitational waveform as a function of black hole masses, spins, etc. Such waveform models are built from numerical relativity (NR) simulations and/or semi-analytical expressions in the inspiral. We investigate the limits of the current waveform models and study at what detector sensitivity these models will yield unbiased parameter inference for loud ''golden'' binary black hole systems, what biases we can expect beyond these limits, and what implications such biases will have for GW astrophysics. For 3G detectors we find that the mismatch error for semi-analytical models needs to be reduced by at least \emph{three orders of magnitude} and for NR waveforms by \emph{one order of magnitude}. In addition, we show that for a population of one hundred high mass precessing binary black holes, measurement errors sum up to a sizable population bias, about 10 -- 30 times larger than the sum of 90\% credible intervals for key astrophysical parameters. Furthermore we demonstrate that the residual signal between the GW data recorded by a detector and the best fit template waveform obtained by parameter inference analyses can have significant SNR ratio. This coherent power left in the residual could lead to the observation of erroneous deviations from general relativity. To address these issues and be ready to reap the scientific benefits of 3G GW detectors in the 2030s, waveform models that are significantly more physically complete and accurate need to be developed in the next decade along with major advances in efficiency and accuracy of NR codes

Gravitational-wave astrophysics with effective-spin measurements: asymmetries and selection biases

Gravitational waves emitted by coalescing compact objects carry information about the spin of the individual bodies. However, with present detectors only the mass-weighted combination of the components of the spin along the orbital angular momentum can be measured accurately. This quantity, the effective spin $\chi_{\mathrm{eff}}$, is conserved up to at least the second post-Newtonian order. The measured distribution of $\chi_{\mathrm{eff}}$ values from a population of detected binaries, and in particular whether this distribution is symmetric about zero, encodes valuable information about the underlying compact-binary formation channels. In this paper we focus on two important complications of using the effective spin to study astrophysical population properties: (i) an astrophysical distribution for $\chi_{\mathrm{eff}}$ values which is symmetric does not necessarily lead to a symmetric distribution for the detected effective spin values, leading to a \emph{selection bias}; and (ii) the posterior distribution of $\chi_{\mathrm{eff}}$ for individual events is \emph{asymmetric} and it cannot usually be treated as a Gaussian. We find that the posterior distributions for $\chi_{\mathrm{eff}}$ systematically show fatter tails toward larger positive values, unless the total mass is large or the mass ratio $m_2/m_1$ is smaller than $\sim 1/2$. Finally we show that uncertainties in the measurement of $\chi_{\mathrm{eff}}$ are systematically larger when the true value is negative than when it is positive. All these factors can bias astrophysical inference about the population when we have more than $\sim 100$ events and should be taken into account when using gravitational-wave measurements to characterize astrophysical populations.Comment: An online generator for synthetic $\chi_{\mathrm{eff}}$ posteriors can be found at: http://superstring.mit.edu/welcome.html Comments are welcom