We perform Bayesian model selection with parameter estimation to identify potentially lensed gravitational-wave images from the second observing run (O2) of Advanced LIGO and Advanced Virgo. ...Specifically, we compute the Bayesian evidence for a pair of events being lensed or not lensed (unlensed) using nested sampling. We consider in the model selection the discrete coalescence phase shifts that can be induced if the gravitational-wave signal intersects with the lens caustics. We find that the pair of events, GW170104 and GW170814 with a π/2 coalescence phase shift, has a significant Bayes factor ( ) favoring the lensing hypothesis. However, after taking into account the long time delay of approximately 7 months between events, the timing Bayes factor is significantly small (Bt ∼ 8.7 × 10−2). The prior probability for detecting strongly lensed pairs at O2 sensitivity is exceedingly small for both galaxy and galaxy cluster lensing. Combining the lensing and timing Bayes factors with the prior odds on lensing gives an odds ratio of . With the value of the odds ratio after including model dependence of the timing and prior odds factors, we do not have strong evidence to demonstrate that the aforementioned pair is strongly lensed.
The observation of binary neutron star merger GW170817, along with its optical counterpart, provided the first constraint on the Hubble constant H0 using gravitational wave standard sirens. When no ...counterpart is identified, a galaxy catalog can be used to provide the necessary redshift information. However, the true host might not be contained in a catalog which is not complete out to the limit of gravitational-wave detectability. These electromagnetic and gravitational-wave selection effects must be accounted for. We describe and implement a method to estimate H0 using both the counterpart and the galaxy catalog standard siren methods. We perform a series of mock data analyses using binary neutron star mergers to confirm our ability to recover an unbiased estimate of H0. Our simulations used a simplified universe with no redshift uncertainties or galaxy clustering, but with different magnitude-limited catalogs and assumed host galaxy properties, to test our treatment of both selection effects. We explore how the incompleteness of catalogs affects the final measurement of H0 , as well as the effect of weighting each galaxy's likelihood of being a host by its luminosity. In our most realistic simulation, where the simulated catalog is about three times denser than the density of galaxies in the local universe, we find that a 4.4% measurement precision can be reached using galaxy catalogs with 50% completeness and ∼ 250 binary neutron star detections with sensitivity similar to that of Advanced LIGO's second observing run.
Abstract
The observation of gravitational waves from multiple compact binary coalescences by the LIGO–Virgo–KAGRA detector networks has enabled us to infer the underlying distribution of compact ...binaries across a wide range of masses, spins, and redshifts. In light of the new features found in the mass spectrum of binary black holes and the uncertainty regarding binary formation models, nonparametric population inference has become increasingly popular. In this work, we develop a data-driven clustering framework that can identify features in the component mass distribution of compact binaries simultaneously with those in the corresponding redshift distribution, from gravitational-wave data in the presence of significant measurement uncertainties, while making very few assumptions about the functional form of these distributions. Our generalized model is capable of inferring correlations among various population properties, such as the redshift evolution of the shape of the mass distribution itself, in contrast to most existing nonparametric inference schemes. We test our model on simulated data and demonstrate the accuracy with which it can reconstruct the underlying distributions of component masses and redshifts. We also reanalyze public LIGO–Virgo–KAGRA data from events in GWTC-3 using our model and compare our results with those from some alternative parametric and nonparametric population inference approaches. Finally, we investigate the potential presence of correlations between mass and redshift in the population of binary black holes in GWTC-3 (those observed by the LIGO–Virgo–KAGRA detector network in their first three observing runs), without making any assumptions about the specific nature of these correlations.
The discovery of the coalescence of binary neutron star GW170817 was a watershed moment in the field of gravitational wave astronomy. Among the rich variety of information that we were able to ...uncover from this discovery was the first non-electromagnetic measurement of the neutron star radius, and the cold nuclear equation of state. It also led to a large equation of state model selection study from gravitational-wave data. In those studies Bayesian nested sampling runs were conducted for each candidate equation of state model to compute their evidence in the gravitational-wave data. Such studies, though invaluable, are computationally expensive and require repeated, redundant, computation for any new models. We present a novel technique to conduct model selection of equation of state in an extremely rapid fashion (~ minutes) on any arbitrary model. We test this technique against the results of a nested-sampling model selection technique published earlier by the LIGO/Virgo collaboration, and show that the results are in good agreement with a median fractional error in Bayes factor of about 10%, where we assume that the true Bayes factor is calculated in the aforementioned nested sampling runs. We found that the highest fractional error occurs for equation of state models that have very little support in the posterior distribution, thus resulting in large statistical uncertainty. We then used this method to combine multiple binary neutron star mergers to compute a joint-Bayes factor between equation of state models. This is achieved by stacking the evidence of the individual events and computing the Bayes factor from these stacked evidences for each pairs of equation of state.
Abstract
We outline the “dark siren” galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of ...this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz, one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Huterer recently claimed that this approach results in a biased estimate of the Hubble constant,
H
0
, when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias.
Alternative theories of gravity predict up to six distinct polarization modes for gravitational waves. Strong gravitational lensing of gravitational waves allows us to probe the polarization content ...of these signals by effectively increasing the number of observations from the same astrophysical source. The lensing time delays due to the multiple observed lensed images combined with the rotation of the Earth allows for effective non-collocated interferometers to be defined with respect to the source location and hence probe the alternative polarization amplitudes with more observations. To measure these amplitudes, we jointly fit the image observations to a single gravitational wave signal model that takes into account the image magnifications, time delays, and polarization mode amplitudes. We show that for certain systems, we can make a measurement of the relative mode amplitudes for lensed events with two detectable images.
PDF
