Toward robust detections of nanohertz gravitational waves
Monash University（莫纳什大学）；OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery（ARC引力波发现卓越中心）；CSIRO, Space and Astronomy（CSIRO空间与天文部）；Swinburne University of Technology（斯威本科技大学）
Valentina Di Marco, Andrew Zic, Matthew T. Miles, Daniel J. Reardon, Eric Thrane, Ryan M. Shannon
备注：
Paper accepted for publication on ApJ on the 7th of August 2023
The recent observation of a common red-noise process in pulsar timing arrays (PTAs) suggests that the detection of nanohertz gravitational waves might be around the corner. However, in order to confidently attribute this red process to gravitational waves, one must observe the Hellings-Downs curve -- the telltale angular correlation function associated with a gravitational-wave background. This effort is complicated by the complex modelling of pulsar noise. Without proper care, mis-specified noise models can lead to false-positive detections. Background estimation using bootstrap methods such as sky scrambles and phase shifts, which use the data to characterize the noise, are therefore important tools for assessing significance. We investigate the ability of current PTA experiments to estimate their background with "quasi-independent" scrambles -- characterized by a statistical "match" below the fiducial value: $|M|<0.1$. We show that sky scrambling is affected by "saturation" after $O(10)$ quasi-independent realizations; subsequent scrambles are no longer quasi-independent. We show phase scrambling saturates after $O(100)$ quasi-independent realizations. With so few independent scrambles, it is difficult to make reliable statements about the $\gtrsim 5 σ$ tail of the null distribution of the detection statistic. We discuss various methods by which one may increase the number of independent scrambles. We also consider an alternative approach wherein one re-frames the background estimation problem so that the significance is calculated using statistically dependent scrambles. The resulting $p$-value is in principle well-defined but may be susceptible to failure if assumptions about the data are incorrect.
Complementary to ground-based laser interferometers, pulsar timing array experiments are being carried out to search for nanohertz gravitational waves. Using the world's most powerful radio telescopes, three major international collaborations have collected $\sim$10-year high precision timing data for tens of millisecond pulsars. In this paper we give an overview on pulsar timing experiments, gravitational wave detection in the nanohertz regime, and recent results obtained by various timing array projects.
Pulsar timing array experiments have recently reported strong evidence for a common-spectrum stochastic process with a strain spectral index consistent with that expected of a nanohertz-frequency gravitational-wave background, but with negligible yet non-zero evidence for spatial correlations required for a definitive detection. However, it was pointed out by the Parkes Pulsar Timing Array (PPTA) collaboration that the same models used in recent analyses resulted in strong evidence for a common-spectrum process in simulations where none is present. In this work, we introduce a methodology to d…
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) is a collaboration of researchers who are actively engaged in using North American radio telescopes to detect and study gravitational waves via pulsar timing. To achieve this goal, we regularly observe millisecond pulsars (MSPs) with the Arecibo and Green Bank Telescopes and develop and implement new instrumentation and algorithms for searching for and observing pulsars, calculating arrival times, understanding and correcting for propagation delays and sources of noise in our data, and detecting and characterizing a va…
Decade-long timing observations of arrays of millisecond pulsars have placed highly constraining upper limits on the amplitude of the nanohertz gravitational-wave stochastic signal from the mergers of supermassive black-hole binaries ($\sim 10^{-15}$ strain at $f = 1/\mathrm{yr}$). These limits suggest that binary merger rates have been overestimated, or that environmental influences from nuclear gas or stars accelerate orbital decay, reducing the gravitational-wave signal at the lowest, most sensitive frequencies. This prompts the question whether nanohertz gravitational waves are likely to b…
Decades long monitoring of millisecond pulsars, which exhibit highly stable rotational periods, in pulsar timing array experiments is on the threshold of discovering nanohertz stochastic gravitational wave background. This paper describes the Indian Pulsar timing array (InPTA) experiment, which employs the upgraded Giant Metrewave Radio Telescope (uGMRT) for timing an ensemble of millisecond pulsars for this purpose. We highlight InPTA's observation strategies and analysis methods, which are relevant for a future PTA experiment with the more sensitive Square Kilometer Array (SKA) telescope. We…
Studies have shown that the use of pulsar timing arrays (PTAs) is among the approaches with the highest potential to detect very low-frequency gravitational waves in the near future. Although the capture of gravitational waves (GWs) by PTAs has not been reported yet, many related theoretical studies and some meaningful detection limits have been reported. In this study, we focused on the nanohertz GWs from individual supermassive binary black holes. Given specific pulsars (PSR J1909$-$3744, PSR J1713$+$0747, PSR J0437$-$4715), the corresponding GW$-$induced timing residuals in PTAs with Gaussi…
We present an analysis of high-precision pulsar timing data taken as part of the North American Nanohertz Observatory for Gravitational waves (NANOGrav) project. We have observed 17 pulsars for a span of roughly five years using the Green Bank and Arecibo radio telescopes. We analyze these data using standard pulsar timing models, with the addition of time-variable dispersion measure and frequency-variable pulse shape terms. Sub-microsecond timing residuals are obtained in nearly all cases, and the best root-mean-square timing residuals in this set are ~30-50 ns. We present methods for analyzi…
Within the next several years pulsar timing arrays (PTAs) are positioned to detect the stochastic gravitational-wave background (GWB) likely produced by the collection of inspiralling super-massive black holes binaries, and potentially constrain some exotic physics. So far most of the pulsar timing data analysis has focused on the monopole of the GWB, assuming it is perfectly isotropic. The natural next step is to search for anisotropies in the GWB. In this paper, we use the recently developed PTA Fisher matrix to gain insights into optimal search strategies for GWB anisotropies. For concreten…
We describe the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) and its efforts to directly detect and study gravitational waves and other synergistic physics and astrophysics using radio timing observations of millisecond pulsars.
The dynamical evolution of supermassive black-hole binary systems is tethered on large scales to the merger rate of massive galaxies, and on small scales to the stellar and gaseous environments of galactic cores. The population of these systems will create an ensemble gravitational-wave signal at nanohertz frequencies that is detectable by Pulsar Timing Arrays (PTA), such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). By measuring nanohertz gravitational waves, we will be able to definitively demonstrate that supermassive black-hole binaries reach milliparsec s…
Modeling the nanohertz gravitational wave background with the t-process: Improved frequentist analysis of gravitational-wave power
Università degli Studi di Milano-Bicocca（米兰比可卡大学）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）；INAF – Osservatorio Astronomico di Cagliari（意大利国家天体物理研究所卡利亚里天文台）；INAF – Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Vanderbilt University（范德堡大学）
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) is a consortium of astronomers whose goal is the creation of a galactic scale gravitational wave observatory sensitive to gravitational waves in the nHz-microHz band. It is just one component of an international collaboration involving similar organizations of European and Australian astronomers who share the same goal. Gravitational waves, a prediction of Einstein's general theory of relativity, are a phenomenon of dynamical space-time generated by the bulk motion of matter, and the dynamics of space-time itself. They…
Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: II. Posterior predictive distributions and pseudo Bayes factors
Not just a phase: detecting nanohertz gravitational waves from phase alone
Max-Planck-Institut für Radioastronomie（马克斯·普朗克射电天文研究所）；Monash University（莫纳什大学）；OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery（引力波发现ARC卓越中心）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Jodrell Bank Centre for Astrophysics, University of Manchester（曼彻斯特大学乔德雷尔银行天体物理学中心）
Gravitational waves (GWs) are fluctuations in the fabric of spacetime predicted by Einstein's theory of general relativity. Using a collection of millisecond pulsars as high-precision clocks, the nanohertz band of this radiation is likely to be directly detected within the next decade. Nanohertz-frequency GWs are expected to be emitted by mergers of massive black hole binary systems, and potentially also by cosmic strings or superstrings formed in the early Universe. Direct detection of GWs will open a new window to the Universe, and provide astrophysical information inaccessible via electroma…
Dense, continuous pulsar timing observations over a 24-hr period provide a method for probing intermediate gravitational wave (GW) frequencies from 10 microhertz to 20 millihertz. The European Pulsar Timing Array (EPTA), the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the Parkes Pulsar Timing Array (PPTA), and the combined International Pulsar Timing Array (IPTA) all use millisecond pulsar observations to detect or constrain GWs typically at nanohertz frequencies. In the case of the IPTA's nine-telescope 24-Hour Global Campaign on millisecond pulsar J1713+0747, GW …
Pulsar timing arrays (PTAs) can be used to detect and study gravitational waves in the nanohertz band (i.e., wavelengths of order light-years). This requires high-precision, decades-long data sets from sensitive, instrumentally stable telescopes. NANOGrav and its collaborators in the International Pulsar Timing Array consortium are on the verge of the first detection of the stochastic background produced by supermassive binary black holes, which form via the mergers of massive galaxies. By providing Northern hemisphere sky coverage with exquisite sensitivity and higher frequency coverage compa…
The observation of gravitational-waves from merging supermassive black holes will be transformative: the detection of a low-frequency gravitational-wave background can tell us if and how supermassive black holes merge, inform our knowledge of galaxy merger rates and supermassive black hole masses, and enable the possibility of detecting new physics at nanohertz frequencies. All we have to do is time pulsars.
Pulsar Timing Arrays (PTAs) are a collection of precisely timed millisecond pulsars (MSPs) that can search for gravitational waves (GWs) in the nanohertz frequency range by observing characteristic signatures in the timing residuals. The sensitivity of a PTA depends on the direction of the propagating gravitational wave source, the timing accuracy of the pulsars, and the allocation of the available observing time. The goal of this paper is to determine the optimal time allocation strategy among the MSPs in the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) for a single…
Gravitational wave astronomy using a pulsar timing array requires high-quality millisecond pulsars, correctable interstellar propagation delays, and high-precision measurements of pulse times of arrival. Here we identify noise in timing residuals that exceeds that predicted for arrival time estimation for millisecond pulsars observed by the North American Nanohertz Observatory for Gravitational Waves. We characterize the excess noise using variance and structure function analyses. We find that 26 out of 37 pulsars show inconsistencies with a white-noise-only model based on the short timescale …
To successfully detect gravitational waves with pulsar timing arrays, we need to have a comprehensive understanding of the physical origins and statistical characteristics of the noise in pulse arrival times and identify mitigation methods to reduce the noise. In this paper we will review radiometer noise, phase jitter noise and timing noise in the noise budget of pulsar timing and show various efforts used to reduce them. We will briefly discuss the results of an overall assessment of the components and physical causes of the timing residuals for millisecond pulsars in the North American Nano…
We describe the design of a gravitational wave timing array, a novel scheme that can be used to search for low-frequency gravitational waves by monitoring continuous gravitational waves at higher frequencies. We show that observations of gravitational waves produced by Galactic binaries using a space-based detector like LISA provide sensitivity in the nanohertz to microhertz band. While the expected sensitivity of this proposal is not competitive with other methods, it fills a gap in frequency space around the microhertz regime, which is above the range probed by current pulsar timing arrays a…
Mitigating the Timing Impact of Anomalous Pulse Profile Shape Variability in PSR J1713+0747 with Gaussian Component Modeling
NANOGrav Physics Frontiers Center（NANOGrav物理前沿中心）；SETI Institute（SETI研究所）；Center for Gravitation, Cosmology and Astrophysics, Department of Physics and Astronomy, University of Wisconsin-Milwaukee（威斯康星大学密尔沃基分校物理与天文学系引力、宇宙学与天体物理中心）；Department of Physics, Oregon State University（俄勒冈州立大学物理系）；Department of Physics and Astronomy, Vanderbilt University（范德堡大学物理与天文学系）；Department of Physics and Astronomy, University of British Columbia（不列颠哥伦比亚大学物理与天文学系）；Department of Physics and Astronomy, George Mason University（乔治梅森大学物理与天文学系）；National Radio Astronomy Observatory（美国国家射电天文台）；Institute of Astrophysics, FORTH（希腊基础与研究基金会天体物理研究所）
The maximum frequency of gravitational waves (GWs) detectable with traditional pulsar timing methods is set by the Nyquist frequency ($f_{\rm{Ny}}$) of the observation. Beyond this frequency, GWs leave no temporal-correlated signals; instead, they appear as white noise in the timing residuals. The variance of the GW-induced white noise is a function of the position of the pulsars relative to the GW source. By observing this unique functional form in the timing data, we propose that we can detect GWs of frequency $>$ $f_{\rm{Ny}}$ (super-Nyquist frequency GWs; SNFGWs). We demonstrate the feasib…
We construct realistic sensitivity curves for pulsar timing array searches for gravitational waves, incorporating both red and white noise contributions to individual pulsar noise spectra, as well as the effect of fitting to a pulsar timing model. We demonstrate the method on both simulated pulsars and a realistic array consisting of a subset of NANOGrav pulsars used in recent analyses. A comparison between the results presented here and exact sensitivity curves shows agreement to tens of percent. The resulting sensitivity curves can be used to assess the detectability of predicted gravitation…
The new field of gravitational wave astrophysics requires a growing pool of students and researchers with unique, interdisciplinary skill sets. It also offers an opportunity to build a diverse, inclusive astronomy community from the ground up. We describe the efforts used by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) NSF Physics Frontiers Center to foster such growth by involving students at all levels in low-frequency gravitational wave astrophysics with pulsar timing arrays (PTAs) and establishing collaboration policies that ensure broad participation by dive…
The characterization of nanohertz-frequency gravitational waves (GWs) with pulsar-timing arrays requires a continual expansion of datasets and monitored pulsars. Whereas detection of the stochastic GW background is predicated on measuring a distinctive pattern of inter-pulsar correlations, characterizing the background's spectrum is driven by information encoded in the power spectra of the individual pulsars' time series. We propose a new technique for rapid Bayesian characterization of the stochastic GW background that is fully parallelized over pulsar datasets. This Factorized Likelihood (FL…
Pulsar Timing Arrays use a set of millisecond pulsars in an attempt to directly detect nanohertz gravitational waves. For this purpose, high precision timing of the pulsars is essential and ultimately a precision of the order of ~100 ns is required. Propagation effects in the interstellar medium cause the radio emission from a pulsar to be dispersed and scattered, introducing time variable delays of the pulses on their way to Earth. If these delays are not properly corrected for, they may cause significant errors in the timing analysis of a pulsar. These proceedings will review the effects of …
Observations of low-frequency gravitational waves will require the highest possible timing precision from an array of the most spin-stable pulsars. We can improve the sensitivity of a pulsar timing array (PTA) to different gravitational-wave sources by observing pulsars with low timing noise over years to decades and distributed across the sky. We discuss observing strategies for a PTA focused on a stochastic gravitational-wave background such as from unresolved supermassive black hole binaries as well as focused on single continuous-wave sources. First we describe the method to calculate a PT…
Searching for a waveform-agnostic gravitational wave signal in pulsar timing arrays
Columbia University（哥伦比亚大学）；University of Birmingham（伯明翰大学）；Monash University（蒙纳士大学）；Montana State University（蒙大拿州立大学）；Oregon State University（俄勒冈州立大学）
From new physics to a running power law and back again: Minimal refitting techniques for the reconstruction of the gravitational-wave background signal in pulsar timing array data
Sensitivity of Weak Lensing Surveys to Gravitational Waves from Inspiraling Supermassive Black Hole Binaries
University of Southern California（南加州大学）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；California Institute of Technology（加州理工学院）
At nanohertz frequencies gravitational waves (GWs) cause variations in time-of-arrival of pulsar signals potentially measurable via precision timing observations. Here we compute very-low-frequency GW sensitivity constrained by instrumental, propagation, and other noises fundamentally limiting pulsar timing observations. Reaching expected GW signal strengths will require estimation and removal of $\simeq$99% of time-of-arrival fluctuations caused by typical interstellar plasma turbulence and a reduction of white rms timing noise to $\sim$100 nsec or less. If these were achieved, single-pulsar …
Within the next several years, pulsar-timing array programs will likely usher in the next era of gravitational-wave astronomy through the detection of a stochastic background of nanohertz-frequency gravitational waves, originating from a cosmological population of inspiraling supermassive binary black holes. While the source positions will likely be isotropic to a good approximation, the gravitational-wave angular power distribution will be anisotropic, with the most massive and/or nearby binaries producing signals that may resound above the background. We study such a realistic angular power …
A background of nanohertz gravitational waves from supermassive black hole binaries could soon be detected by pulsar timing arrays, which measure the times-of-arrival of radio pulses from millisecond pulsars with very high precision. The European Pulsar Timing Array uses five large European radio telescopes to monitor high-precision millisecond pulsars, imposing in this way strong constraints on a gravitational wave background. To achieve the necessary precision needed to detect gravitational waves, the Large European Array for Pulsars (LEAP) performs simultaneous observations of pulsars with …
A pulsar timing array is a Galactic-scale detector of nanohertz gravitational waves (GWs). Its target signals contain two components: the `Earth term' and the `pulsar term' corresponding to GWs incident on the Earth and pulsar respectively. In this work we present a Frequentist method for the detection and localization of continuous waves that takes into account the pulsar term and is significantly faster than existing methods. We investigate the role of pulsar terms by comparing a full-signal search with an Earth-term-only search for non-evolving black hole binaries. By applying the method to…
In-spiraling supermassive black holes should emit gravitational waves, which would produce characteristic distortions in the time of arrival residuals from millisecond pulsars. Multiple national and regional consortia have constructed pulsar timing arrays by precise timing of different sets of millisecond pulsars. An essential aspect of precision timing is the transfer of the times of arrival to a (quasi-)inertial frame, conventionally the solar system barycenter. The barycenter is determined from the knowledge of the planetary masses and orbits, which has been refined over the past 50 years b…
Precision pulsar timing at the level of tens to hundreds of nanoseconds allows detection of nanohertz gravitational waves (GWs) from supermassive binary black holes (SMBBHs) at the cores of merging galaxies and, potentially, from exotic sources such as cosmic strings. The same timing data used for GW astronomy also yield precision masses of neutron stars orbiting other compact objects, constraints on the equation of state of nuclear matter, and precision tests of General Relativity, the Strong Equivalence Principle, and alternative theories of gravity. Timing can also lead to stringent constra…
We present high-precision timing observations spanning up to nine years for 37 millisecond pulsars monitored with the Green Bank and Arecibo radio telescopes as part of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) project. We describe the observational and instrumental setups used to collect the data, and methodology applied for calculating pulse times of arrival; these include novel methods for measuring instrumental offsets and characterizing low signal-to-noise ratio timing results. The time of arrival data are fit to a physical timing model for each source, i…
In pulsar timing, timing residuals are the differences between the observed times of arrival and the predictions from the timing model. A comprehensive timing model will produce featureless residuals, which are presumably composed of dominating noise and weak physical effects excluded from the timing model (e.g. gravitational waves). In order to apply the optimal statistical methods for detecting the weak gravitational wave signals, we need to know the statistical properties of the noise components in the residuals. In this paper we utilize a variety of non-parametric statistical tests to anal…
Noise is ubiquitous in pulsar signals where red noise has been attributed to effects arising from the interstellar medium, spin noise, and pulsar mode changes, among others. The red noise, however, has not been detected in all pulsars. Using the dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), we investigate twenty-three pulsars and show that an evaluation of the mean square deviation and probability distribution of timing residuals can provide a straightforward way of determining the presence of red noise. The results agree with those reported in the l…
