Search

Supermassive black hole binary systems (SMBHBs) should be the most powerful sources of gravitational waves (GWs) in the universe. Once pulsar timing arrays (PTAs) detect the stochastic GW background from their cosmic merger history, searching for individually resolvable binaries will take on new importance. Since these individual SMBHBs are expected to be rare, here we explore how strong gravitational lensing can act as a tool for increasing their detection prospects by magnifying fainter sources and bringing them into view. Unlike for electromagnetic waves, when the geometric optics limit is nearly always valid, for GWs the wave-diffraction-interference effects can become important when the wavelength of the GWs is larger than the Schwarzchild radius of the lens, i.e., ${M}_{\mathrm{lens}}\sim {10}^{8}{\left(\tfrac{f}{\mathrm{mHz}}\right)}^{-1}\,{M}_{\odot }$ . For the GW frequency range explored in this work, the geometric optics limit holds. We investigate GW signals from SMBHBs that might be detectable with current and future PTAs under the assumption that quasars serve as bright beacons that signal a recent merger. Using the black hole mass function derived from quasars and a physically motivated magnification distribution, we expect to detect a few strongly lensed binary systems out to z ≈ 2. Additionally, for a range of fixed magnifications 2 ≤ μ ≤ 100, strong lensing adds up to ∼30 more detectable binaries for PTAs. Finally, we investigate the possibility of observing both time-delayed electromagnetic signals and GW signals from these strongly lensed binary systems—that will provide us with unprecedented multi-messenger insights into their orbital evolution.

Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15 yr pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese pulsar timing arrays. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational-wave background (GWB). To explore the internal consistency of this result, we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure the correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic GWB in the NANOGrav 15 yr data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data.

The cosmic merger history of supermassive black hole binaries (SMBHBs) is expected to produce a low-frequency gravitational wave background (GWB). Here we investigate how signs of the discrete nature of this GWB can manifest in pulsar timing arrays (PTAs) through excursions from, and breaks in, the expected ${f}_{\mathrm{GW}}^{-2/3}$ power law of the GWB strain spectrum. To do this, we create a semianalytic SMBHB population model, fit to North American Nanohertz Observatory for Gravitational Waves (NANOGrav’s) 15 yr GWB amplitude, and with 1000 realizations, we study the populations’ characteristic strain and residual spectra. Comparing our models to the NANOGrav 15 yr spectrum, we find two interesting excursions from the power law. The first, at 2 nHz, is below our GWB realizations with a p -value significance p = 0.05–0.06 (≈1.8 σ –1.9 σ ). The second, at 16 nHz, is above our GWB realizations with p = 0.04–0.15 (≈1.4 σ –2.1 σ ). We explore the properties of a loud SMBHB that could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by 3 orders of magnitude, from ∼10 ^6 to ∼10 ^3 , between 2 and 20 nHz. This causes a break in the strain spectrum as the stochasticity of the background breaks down at ${26}_{-19}^{+28}\,\mathrm{nHz}$ , consistent with predictions pre-dating GWB measurements. The diminished GWB signal from SMBHBs at frequencies above the 26 nHz break opens a window for PTAs to detect continuous GWs from individual SMBHBs or GWs from the early Universe.

We present the results of a Bayesian search for gravitational wave (GW) memory in the NANOGrav 12.5 yr data set. We find no convincing evidence for any gravitational wave memory signals in this data set. We find a Bayes factor of 2.8 in favor of a model that includes a memory signal and common spatially uncorrelated red noise (CURN) compared to a model including only a CURN. However, further investigation shows that a disproportionate amount of support for the memory signal comes from three dubious pulsars. Using a more flexible red-noise model in these pulsars reduces the Bayes factor to 1.3. Having found no compelling evidence, we go on to place upper limits on the strain amplitude of GW memory events as a function of sky location and event epoch. These upper limits are computed using a signal model that assumes the existence of a common, spatially uncorrelated red noise in addition to a GW memory signal. The median strain upper limit as a function of sky position is approximately 3.3 × 10 ^−14 . We also find that there are some differences in the upper limits as a function of sky position centered around PSR J0613−0200. This suggests that this pulsar has some excess noise that can be confounded with GW memory. Finally, the upper limits as a function of burst epoch continue to improve at later epochs. This improvement is attributable to the continued growth of the pulsar timing array.

The radio galaxy 3C 66B has been hypothesized to host a supermassive black hole binary (SMBHB) at its center based on electromagnetic observations. Its apparent 1.05 yr period and low redshift (∼0.02) make it an interesting testbed to search for low-frequency gravitational waves (GWs) using pulsar timing array (PTA) experiments. This source has been subjected to multiple searches for continuous GWs from a circular SMBHB, resulting in progressively more stringent constraints on its GW amplitude and chirp mass. In this paper, we develop a pipeline for performing Bayesian targeted searches for eccentric SMBHBs in PTA data sets, and test its efficacy by applying it to simulated data sets with varying injected signal strengths. We also search for a realistic eccentric SMBHB source in 3C 66B using the NANOGrav 12.5 yr data set employing PTA signal models containing Earth term-only as well as Earth+pulsar term contributions using this pipeline. Due to limitations in our PTA signal model, we get meaningful results only when the initial eccentricity e _0 < 0.5 and the symmetric mass ratio η > 0.1. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of 88.1 ± 3.7 ns for the Earth term-only and 81.74 ± 0.86 ns for the Earth+pulsar term searches for e _0 < 0.5 and η > 0.1. Similar 95% upper limits on the chirp mass are (1.98 ± 0.05) × 10 ^9 and (1.81 ± 0.01) × 10 ^9 M _☉ . These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5 yr data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations.

The millisecond pulsar J1713+0747 underwent a sudden and significant pulse shape change between 2021 April 16 and 17 (MJDs 59320 and 59321). Subsequently, the pulse shape gradually recovered over the course of several months. We report the results of continued multifrequency radio observations of the pulsar made using the Canadian Hydrogen Intensity Mapping Experiment and the 100 m Green Bank Telescope in a 3 yr period encompassing the shape change event, between 2020 February and 2023 February. As of 2023 February, the pulse shape had returned to a state similar to that seen before the event, but with measurable changes remaining. The amplitude of the shape change and the accompanying time-of-arrival residuals display a strong nonmonotonic dependence on radio frequency, demonstrating that the event is neither a glitch (the effects of which should be independent of radio frequency, ν ) nor a change in dispersion measure alone (which would produce a delay proportional to ν ^−2 ). However, it does bear some resemblance to the two previous “chromatic timing events” observed in J1713+0747, as well as to a similar event observed in PSR J1643−1224 in 2015.

Pulsar timing arrays (PTAs) are designed to detect low-frequency gravitational waves (GWs). GWs induce achromatic signals in PTA data, meaning that the timing delays do not depend on radio frequency. However, pulse arrival times are also affected by radio-frequency-dependent “chromatic” noise from sources such as dispersion measure (DM) and scattering delay variations. Furthermore, the characterization of GW signals may be influenced by the choice of chromatic noise model for each pulsar. To better understand this effect, we assess if and how different chromatic noise models affect the achromatic noise properties in each pulsar. The models we compare include existing DM models used by the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and noise models used for the European PTA Data Release 2 (EPTA DR2). We perform this comparison using a subsample of six pulsars from the NANOGrav 15 yr data set, selecting the same six pulsars as from the EPTA DR2 six-pulsar data set. We find that the choice of chromatic noise model noticeably affects the achromatic noise properties of several pulsars. This is most dramatic for PSR J1713+0747, where the amplitude of its achromatic red noise lowers from ${\mathrm{log}}_{10}{A}_{\mathrm{RN}}=-{14.1}_{-0.1}^{+0.1}$ to $-{14.7}_{-0.5}^{+0.3}$ , and the spectral index broadens from ${\gamma }_{\mathrm{RN}}={2.6}_{-0.4}^{+0.5}$ to ${\gamma }_{\mathrm{RN}}={3.5}_{-0.9}^{+1.2}$ . We also compare each pulsar's noise properties with those inferred from the EPTA DR2, using the same models. From the discrepancies, we identify potential areas where the noise models could be improved. These results highlight the potential for custom chromatic noise models to improve PTA sensitivity to GWs.

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.