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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.

 

Pulsar timing arrays (PTAs) are searching for gravitational waves from supermassive black hole binaries (SMBHBs). Here we show how future PTAs could use a detection of gravitational waves from individually resolved SMBHB sources to produce a purely gravitational wave-based measurement of the Hubble constant. This is achieved by measuring two separate distances to the same source from the gravitational wave signal in the timing residual: the luminosity distance DL through frequency evolution effects, and the parallax distance Dpar through wavefront curvature (Fresnel) effects. We present a generalized timing residual model including these effects in an expanding universe. Of these two distances, Dpar is challenging to measure due to the pulsar distance wrapping problem, a degeneracy in the Earth-pulsar distance and gravitational wave source parameters that requires highly precise, sub-parsec level, pulsar distance measurements to overcome. However, in this paper we demonstrate that combining the knowledge of two SMBHB sources in the timing residual largely removes the wrapping cycle degeneracy. Two sources simultaneously calibrate the PTA by identifying the distances to the pulsars, which is useful in its own right, and allow recovery of the source luminosity and parallax distances which results in a measurement of the Hubble constant. We find that, with optimistic PTAs in the era of the Square Kilometre Array, two fortuitous SMBHB sources within a few hundred Mpc could be used to measure the Hubble constant with a relative uncertainty on the order of 10 per cent.

 

ABSTRACT Merging supermassive black hole binaries produce low-frequency gravitational waves, which pulsar timing experiments are searching for. Much of the current theory is developed within the plane-wave formalism, and here we develop the more general Fresnel formalism. We show that Fresnel corrections to gravitational wave timing residual models allow novel measurements to be made, such as direct measurements of the source distance from the timing residual phase and frequency, as well as direct measurements of chirp mass from a monochromatic source. Probing the Fresnel corrections in these models will require future pulsar timing arrays with more distant pulsars across our Galaxy (ideally at the distance of the Magellanic Clouds), timed with precisions less than 100 ns, with distance uncertainties reduced to the order of the gravitational wavelength. We find that sources with chirp mass of order 109 M⊙ and orbital frequency ω0 > 10 nHz are good candidates for probing Fresnel corrections. With these conditions met, the measured source distance uncertainty can be made less than 10 per cent of the distance to the source for sources out to ∼100 Mpc, source sky localization can be reduced to sub-arcminute precision, and source volume localization can be made to less than 1 Mpc3 for sources out to 1-Gpc distances.