This paper presents an in-depth study of how to estimate the sensitivity of searches for gravitational-wave pulsars -- rapidly-rotating neutron stars which emit quasi-sinusoidal gravitational waves. It is particularly concerned with searches over a wide range of possible source parameters, such as searches over the entire sky and broad frequency bands. Traditional approaches to estimating the sensitivity of such searches use either computationally-expensive Monte Carlo simulations, or analytic methods which sacrifice accuracy by making an unphysical assumption about the population of sources being searched for. This paper develops a new, analytic method of estimating search sensitivity which does not rely upon this unphysical assumption. Unlike previous analytic methods, the new method accurately predicts the sensitivity obtained using Monte Carlo simulations, while avoiding their computational expense. The change in estimated sensitivity due to properties of the search template bank, and the geographic configuration of the gravitational wave detector network, are also investigated.
All-sky searches for gravitational-wave pulsars are generally limited in sensitivity by the finite availability of computing resources. Semicoherent searches are a common method of maximizing search sensitivity given a fixed computing budget. The work of Wette and Prix [Phys. Rev. D 88, 123005 (2013)] and Wette [Phys. Rev. D 92, 082003 (2015)] developed a semicoherent search method which uses metrics to construct the banks of pulsar signal templates needed to search the parameter space of interest. In this work we extend the range of validity of the parameter-space metrics using an empirically…
Resolvable Supermassive Black Hole Binaries are promising sources for Pulsar Timing Array based gravitational wave searches. Search algorithms for such targets must contend with the large number of so-called pulsar phase parameters in the joint log-likelihood function of the data. We compare the localization accuracy for two approaches: Maximization over the pulsar phase parameters (MaxPhase) against marginalization over them (AvPhase). Using simulated data from a pulsar timing array with 17 pulsars, we find that for weak and moderately strong signals, AvPhase outperforms MaxPhase significantl…
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong statistical evidence for a common-spectrum red-noise process for all pulsars, as seen in their 12.5-yr analysis for an isotropic stochastic gravitational-wave background. However, there is currently very little evidence for quadrupolar spatial correlations across the pulsars in the array, which is needed to make a confident claim of detection of a stochastic background. Here we give a frequentist analysis of a very simple signal+noise model showing that the current lack of evidence for spat…
Lattice template placement for coherent all-sky searches for gravitational-wave pulsars
对引力波星的全天空、宽带、相干搜索受到有限计算资源的限制。最小化覆盖天空位置和频率演变的搜索参数空间所需的模板的数量是减少搜索的计算成本的一个重要方式。我们展示了一种实用的算法，该算法首次使用Wette和Prix [Phys. Rev. D 88，123005（2013）]的简化超天空参数空间度量，以最小数量的模板进行全天空搜索来实现模板放置。该度量在信号参数中规定了恒定的模板密度，这允许将模板放置在网格的顶点处。我们演示了如何确保参数空间的完全覆盖，特别是在其边界。由算法生成的模板的数量与理论估计值以及Brady等人[Phys. Rev. D 57，2101（1998）]的先前预测值进行比较。该算法可以应用于具有恒定模板密度的任何搜索参数空间，其包括半相干搜索和针对已知低质量X射线二进制的搜索。
We propose a data processing technique to cancel monopole and dipole noise sources (such as clock and ephemeris noises respectively) in pulsar timing array searches for gravitational radiation. These noises are the dominant sources of correlated timing fluctuations in the lower-part ($ \approx 10^{-9} - 10^{-8}$ Hz) of the gravitational wave band accessible by pulsar timing experiments. After deriving the expressions that reconstruct these noises from the timing data, we estimate the gravitational wave sensitivity of our proposed processing technique to single-source signals to be at least one…
We present the first searches for gravitational waves from r-modes of the Crab pulsar, coherently and separately integrating data from three stretches of the first two observing runs of Advanced LIGO using the F-statistic. The second run was divided in two by a glitch of the pulsar roughly halfway through. The frequencies and derivatives searched were based on radio measurements of the pulsar's spin-down parameters as described in Caride et al., Phys. Rev. D 100, 064013 (2019). We did not find any evidence of gravitational waves. Our best 90% confidence upper limits on gravitational wave intri…
Searches for continuous gravitational waves from known pulsars so far have been targeted at or near the spin frequency or double the spin frequency of each pulsar, appropriate for mass quadrupole emission. But some neutron stars might radiate strongly through current quadrupoles via $r$-modes, which oscillate at about four thirds the spin frequency. We show for the first time how to construct searches over appropriate ranges of frequencies and spin-down parameters to target $r$-modes from known pulsars. We estimate computational costs and sensitivities of realistic $r$-mode searches using the …
Parameter-space metric for all-sky semicoherent searches for gravitational-wave pulsars
全天空搜索引力波星的灵敏度主要受到计算资源有限的限制。半相干搜索是一种以固定计算成本最大化对引力波探测器灵敏度的广泛使用的方法：将来自引力波探测器的数据划分为多个段，对每个段进行相干分析，并将每个段的分析结果相加在一起。生成模板银行的相干分析的每一个部分，并为求和，需要的知识的度量相关的相干和半相干的参数空间分别。我们提出了一个有用的近似半相干参数空间度量，类似于Wette和Prix [Phys. Rev. D 88，123005（2013）]中提出的相干度量。新的半相干度量与Pletsch [Phys. Rev. D 82，042002（2010）]和Brady和Creighton [Phys. Rev. D 61，082001（2000）]中的先前工作进行了比较。我们发现，半相干全天空搜索需要的数量级比以前预测的模板。
We conduct searches for continuous gravitational waves from seven pulsars, that have not been targeted in continuous wave searches of Advanced LIGO data before. We target emission at exactly twice the rotation frequency of the pulsars and in a small band around such frequency. The former search assumes that the gravitational wave quadrupole is changing phase-locked with the rotation of the pulsar. The search over a range of frequencies allows for differential rotation between the component emitting the radio signal and the component emitting the gravitational waves, for example the crust or ma…
This document describes a code to perform parameter estimation and model selection in targeted searches for continuous gravitational waves from known pulsars using data from ground-based gravitational wave detectors. We describe the general workings of the code and characterise it on simulated data containing both noise and simulated signals. We also show how it performs compared to a previous MCMC and grid-based approach to signal parameter estimation. Details how to run the code in a variety of cases are provided in Appendix A.
We describe several new techniques which accelerate Bayesian searches for continuous gravitational-wave emission from supermassive black-hole binaries using pulsar timing arrays. These techniques mitigate the problematic increase of search-dimensionality with the size of the pulsar array which arises from having to include an extra parameter per pulsar as the array is expanded. This extra parameter corresponds to searching over the phase of the gravitational-wave as it propagates past each pulsar so that we can coherently include the pulsar-term in our search strategies. Our techniques make th…
Pulsar timing arrays (PTAs) detect low-frequency gravitational waves (GWs) by looking for correlated deviations in pulse arrival times. Current Bayesian searches use Markov Chain Monte Carlo (MCMC) methods, which struggle to sample the large number of parameters needed to model the PTA and GW signals. As the data span and number of pulsars increase, this problem will only worsen. An alternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC), utilizes Hamiltonian dynamics to produce sample proposals informed by first-order gradients of the model likelihood. This in turn allows it to…
Pulsar timing arrays (PTAs) are currently the only experiments directly sensitive to gravitational waves with decade-long periods. Within the next five to ten years, PTAs are expected to detect the stochastic gravitational-wave background (SGWB) collectively sourced by inspiralling supermassive black hole binaries. It is expected that this background is mostly isotropic, and current searches focus on the monopole part of the SGWB. Looking ahead, anisotropies in the SGWB may provide a trove of additional information both on known and unknown astrophysical and cosmological sources. In this paper…
It is difficult to discover pulsars via their gamma-ray emission because current instruments typically detect fewer than one photon per million rotations. This creates a significant computing challenge for isolated pulsars, where the typical parameter search space spans wide ranges in four dimensions. It is even more demanding when the pulsar is in a binary system, where the orbital motion introduces several additional unknown parameters. Building on earlier work by Pletsch & Clark (arXiv:1408.6962), we present optimal methods for such searches. These can also incorporate external constraints …
Continuous gravitational waves from neutron stars could provide an invaluable resource to learn about their interior physics. A common search method involves matched filtering a modeled template against the noisy gravitational-wave data to find signals. This method suffers a mismatch (i.e., relative loss of the signal-to-noise ratio) if the signal deviates from the template. One possible instance in which this may occur is if the neutron star undergoes a glitch, a sudden rapid increase in the rotation frequency seen in the timing of many radio pulsars. In this work, we use a statistical charac…
Gravitational-wave data analysis demands sophisticated statistical noise models in a bid to extract highly obscured signals from data. In Bayesian model comparison, we choose among a landscape of models by comparing their marginal likelihoods. However, this computation is numerically fraught and can be sensitive to arbitrary choices in the specification of parameter priors. In Bayesian cross validation, we characterize the fit and predictive power of a model by computing the Bayesian posterior of its parameters in a training dataset, and then use that posterior to compute the averaged likeliho…
The regularity of pulsar emissions becomes apparent once we reference the pulses' times of arrivals to the inertial rest frame of the solar system. It follows that errors in the determination of Earth's position with respect to the solar-system barycenter can appear as a time-correlated bias in pulsar-timing residual time series, affecting the searches for low-frequency gravitational waves performed with pulsar timing arrays. Indeed, recent array datasets yield different gravitational-wave background upper limits and detection statistics when analyzed with different solar-system ephemerides. C…
Time-domain datasets of many varieties can be prone to statistical outliers that result from instrumental or astrophysical anomalies. These can impair searches for signals within the time series and lead to biased parameter estimation. Versatile outlier mitigation methods tuned toward multimessenger time-domain searches for supermassive binary black holes have yet to be fully explored. In an effort to perform robust outlier isolation with low computational costs, we propose a Gibbs sampling scheme. This provides structural simplicity to outlier modeling and isolation, as it requires minimal mo…
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）
The Targeted Standard Siren Cosmology with Pulsar Timing Arrays
Indian Institute of Science Education and Research Bhopal（印度科学教育研究所博帕尔分校）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（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）
Red noise and evolving signals: a complete frequentist approach to supermassive black hole binary searches with pulsar timing arrays
Huazhong University of Science and Technology（华中科技大学）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（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）；University of Texas Rio Grande Valley（德克萨斯里奥格兰德河谷大学）；IIT Hyderabad（印度理工学院海德拉巴分校）
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…
