The astrophysics of nanohertz gravitational waves

Pulsar timing array (PTA) collaborations in North America, Australia, and Europe, have been exploiting the exquisite timing precision of millisecond pulsars over decades of observations to search for correlated timing deviations induced by gravitational waves (GWs). PTAs are sensitive to the frequency band ranging just below 1 nanohertz to a few tens of microhertz. The discovery space of this band is potentially rich with populations of inspiraling supermassive black hole binaries, decaying cosmic string networks, relic post-inflation GWs, and even non-GW imprints of axionic dark matter. This article aims to provide an understanding of the exciting open science questions in cosmology, galaxy evolution, and fundamental physics that will be addressed by the detection and study of GWs through PTAs. The focus of the article is on providing an understanding of the mechanisms by which PTAs can address specific questions in these fields, and to outline some of the subtleties and difficulties in each case. The material included is weighted most heavily toward the questions which we expect will be answered in the near-term with PTAs; however, we have made efforts to include most currently anticipated applications of nanohertz GWs

The NANOGrav 15 yr Data Set: Search for Transverse Polarization Modes in the Gravitational-wave Background

\ua9 2024. The Author(s). Published by the American Astronomical Society.Recently we found compelling evidence for a gravitational-wave background with Hellings and Downs (HD) correlations in our 15 yr data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes, which produce different interpulsar correlations. In this work, we search the NANOGrav 15 yr data set for evidence of a gravitational-wave background with quadrupolar HD and scalar-transverse (ST) correlations. We find that HD correlations are the best fit to the data and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors ∼2 when comparing HD to ST correlations, and ∼1 for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis

How to Detect an Astrophysical Nanohertz Gravitational Wave Background

\ua9 2023. The Author(s). Published by the American Astronomical Society.Analyses of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nanohertz frequency band. The most plausible source of this background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for this background and assess its significance make several simplifying assumptions, namely (i) Gaussianity, (ii) isotropy, and most often, (iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated data sets. The data-set length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15 yr data set. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated data sets, even though their fundamental assumptions are not strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them

The high energy Universe at ultra-high resolution: the power and promise of X-ray interferometry

We propose the development of X-ray interferometry (XRI), to reveal the Universe at high energies with ultra-high spatial resolution. With baselines which can be accommodated on a single spacecraft, XRI can reach 100 μ as resolution at 10 Å (1.2 keV) and 20 μ as at 2 Å (6 keV), enabling imaging and imaging-spectroscopy of (for example) X-ray coronae of nearby accreting supermassive black holes (SMBH) and the SMBH ‘shadow’; SMBH accretion flows and outflows; X-ray binary winds and orbits; stellar coronae within ∼ 100 pc and many exoplanets which transit across them. For sufficiently luminous sources XRI will resolve sub-pc scales across the entire observable Universe, revealing accreting binary SMBHs and enabling trigonometric measurements of the Hubble constant with X-ray light echoes from quasars or explosive transients. A multi-spacecraft ‘constellation’ interferometer would resolve well below 1 μ as, enabling SMBH event horizons to be resolved in many active galaxies and the detailed study of the effects of strong field gravity on the dynamics and emission from accreting gas close to the black hole

On the amplitude and Stokes parameters of a stochastic gravitational-wave background

The direct detection of gravitational waves has provided new opportunities for studying the Universe, but also new challenges, such as the detection and characterization of stochastic gravitational-wave backgrounds at different gravitational-wave frequencies. In this paper, we examine two different methods for their description, one based on the amplitude of a gravitational-wave signal and one on its Stokes parameters. We find that the Stokes parameters are able to describe anisotropic and correlated backgrounds, whereas the usual power spectra of the amplitudes cannot – i.e. the Stokes spectra are sensitive to properties such as the spatial distribution of the gravitational-wave sources in a realistic backgrounds

A pulsar-based time-scale from the international pulsar timing array

We have constructed a new time-scale, TT(IPTA16), based on observations of radio pulsars presented in the first data release from the International Pulsar Timing Array (IPTA). We used two analysis techniques with independent estimates of the noise models for the pulsar observations and different algorithms for obtaining the pulsar time-scale. The two analyses agree within the estimated uncertainties and both agree with TT(BIPM17), a post-corrected time-scale produced by the Bureau International des Poids et Mesures (BIPM). We show that both methods could detect significant errors in TT(BIPM17) if they were present. We estimate the stability of the atomic clocks from which TT(BIPM17) is derived using observations of four rubidium fountain clocks at the US Naval Observatory. Comparing the power spectrum of TT(IPTA16) with that of these fountain clocks suggests that pulsar-based time-scales are unlikely to contribute to the stability of the best time-scales over the next decade, but they will remain a valuable independent check on atomic time-scales. We also find that the stability of the pulsar-based time-scale is likely to be limited by our knowledge of solar-system dynamics, and that errors in TT(BIPM17) will not be a limiting factor for the primary goal of the IPTA, which is to search for the signatures of nano-Hertz gravitational waves

From spin noise to systematics: Stochastic processes in the first International Pulsar Timing Array data release

We analyse the stochastic properties of the 49 pulsars that comprise the first International Pulsar Timing Array (IPTA) data release. We use Bayesian methodology, performing model selection to determine the optimal description of the stochastic signals present in each pulsar. In addition to spin-noise and dispersion-measure (DM) variations, these models can include timing noise unique to a single observing system, or frequency band. We show the improved radio-frequency coverage and presence of overlapping data from different observing systems in the IPTA data set enables us to separate both system and band-dependent effects with much greater efficacy than in the individual pulsar timing array (PTA) data sets. For example, we show that PSR J1643-1224 has, in addition to DM variations, significant band-dependent noise that is coherent between PTAs which we interpret as coming from time-variable scattering or refraction in the ionized interstellar medium. Failing to model these different contributions appropriately can dramatically alter the astrophysical interpretation of the stochastic signals observed in the residuals. In some cases, the spectral exponent of the spin-noise signal can vary from 1.6 to 4 depending upon the model, which has direct implications for the long-term sensitivity of the pulsar to a stochastic gravitational-wave (GW) background. By using a more appropriate model, however, we can greatly improve a pulsar's sensitivity to GWs. For example, including system and band-dependent signals in the PSR J0437-4715 data set improves the upper limit on a fiducial GW background by ~60 per cent compared to a model that includes DM variations and spin-noise only