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Register a new userAre we there yet? Time to detection of nanohertz gravitational waves based on pulsar-timing array limits
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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 be detected in the near future. In this letter, we answer this question quantitatively using simple statistical estimates, deriving the range of true signal amplitudes that are compatible with current upper limits, and computing expected detection probabilities as a function of observation time. We conclude that small arrays consisting of the pulsars with the least timing noise, which yield the tightest upper limits, have discouraging prospects of making a detection in the next two decades. By contrast, we find large arrays are crucial to detection because the quadrupolar spatial correlations induced by gravitational waves can be well sampled by many pulsar pairs. Indeed, timing programs which monitor a large and expanding set of pulsars have an $sim 80%$ probability of detecting gravitational waves within the next ten years, under assumptions on merger rates and environmental influences ranging from optimistic to conservative. Even in the extreme case where $90%$ of binaries stall before merger and environmental coupling effects diminish low-frequency gravitational-wave power, detection is delayed by at most a few years.
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We have searched for continuous gravitational wave (CGW) signals produced by individually resolvable, circular supermassive black hole binaries (SMBHBs) in the latest EPTA dataset, which consists of ultra-precise timing data on 41 millisecond pulsars. We develop frequentist and Bayesian detection algorithms to search both for monochromatic and frequency-evolving systems. None of the adopted algorithms show evidence for the presence of such a CGW signal, indicating that the data are best described by pulsar and radiometer noise only. Depending on the adopted detection algorithm, the 95% upper limit on the sky-averaged strain amplitude lies in the range $6times 10^{-15}<A<1.5times10^{-14}$ at $5{rm nHz}<f<7{rm nHz}$. This limit varies by a factor of five, depending on the assumed source position, and the most constraining limit is achieved towards the positions of the most sensitive pulsars in the timing array. The most robust upper limit -- obtained via a full Bayesian analysis searching simultaneously over the signal and pulsar noise on the subset of ours six best pulsars -- is $Aapprox10^{-14}$. These limits, the most stringent to date at $f<10{rm nHz}$, exclude the presence of sub-centiparsec binaries with chirp mass $cal{M}_c>10^9$M$_odot$ out to a distance of about 25Mpc, and with $cal{M}_c>10^{10}$M$_odot$ out to a distance of about 1Gpc ($zapprox0.2$). We show that state-of-the-art SMBHB population models predict $<1%$ probability of detecting a CGW with the current EPTA dataset, consistent with the reported non-detection. We stress, however, that PTA limits on individual CGW have improved by almost an order of magnitude in the last five years. The continuing advances in pulsar timing data acquisition and analysis techniques will allow for strong astrophysical constraints on the population of nearby SMBHBs in the coming years.
Automated detection of software vulnerabilities is a fundamental problem in software security. Existing program analysis techniques either suffer from high false positives or false negatives. Recent progress in Deep Learning (DL) has resulted in a surge of interest in applying DL for automated vulnerability detection. Several recent studies have demonstrated promising results achieving an accuracy of up to 95% at detecting vulnerabilities. In this paper, we ask, how well do the state-of-the-art DL-based techniques perform in a real-world vulnerability prediction scenario?. To our surprise, we find that their performance drops by more than 50%. A systematic investigation of what causes such precipitous performance drop reveals that existing DL-based vulnerability prediction approaches suffer from challenges with the training data (e.g., data duplication, unrealistic distribution of vulnerable classes, etc.) and with the model choices (e.g., simple token-based models). As a result, these approaches often do not learn features related to the actual cause of the vulnerabilities. Instead, they learn unrelated artifacts from the dataset (e.g., specific variable/function names, etc.). Leveraging these empirical findings, we demonstrate how a more principled approach to data collection and model design, based on realistic settings of vulnerability prediction, can lead to better solutions. The resulting tools perform significantly better than the studied baseline: up to 33.57% boost in precision and 128.38% boost in recall compared to the best performing model in the literature. Overall, this paper elucidates existing DL-based vulnerability prediction systems potential issues and draws a roadmap for future DL-based vulnerability prediction research. In that spirit, we make available all the artifacts supporting our results: https://git.io/Jf6IA.
We present the sensitivity of the Parkes Pulsar Timing Array to gravitational waves emitted by individual super-massive black-hole binary systems in the early phases of coalescing at the cores of merged galaxies. Our analysis includes a detailed study of the effects of fitting a pulsar timing model to non-white timing residuals. Pulsar timing is sensitive at nanoHertz frequencies and hence complementary to LIGO and LISA. We place a sky-averaged constraint on the merger rate of nearby ($z < 0.6$) black-hole binaries in the early phases of coalescence with a chirp mass of $10^{10},rmn{M}_odot$ of less than one merger every seven years. The prospects for future gravitational-wave astronomy of this type with the proposed Square Kilometre Array telescope are discussed.
The NANOGrav Collaboration reported strong Bayesian evidence for a common-spectrum stochastic process in its 12.5-yr pulsar timing array dataset, with median characteristic strain amplitude at periods of a year of $A_{rm yr} = 1.92^{+0.75}_{-0.55} times 10^{-15}$. However, evidence for the quadrupolar Hellings & Downs interpulsar correlations, which are characteristic of gravitational wave signals, was not yet significant. We emulate and extend the NANOGrav dataset, injecting a wide range of stochastic gravitational wave background (GWB) signals that encompass a variety of amplitudes and spectral shapes, and quantify three key milestones: (I) Given the amplitude measured in the 12.5 yr analysis and assuming this signal is a GWB, we expect to accumulate robust evidence of an interpulsar-correlated GWB signal with 15--17 yrs of data, i.e., an additional 2--5 yrs from the 12.5 yr dataset; (II) At the initial detection, we expect a fractional uncertainty of $40%$ on the power-law strain spectrum slope, which is sufficient to distinguish a GWB of supermassive black-hole binary origin from some models predicting more exotic origins;(III) Similarly, the measured GWB amplitude will have an uncertainty of $44%$ upon initial detection, allowing us to arbitrate between some population models of supermassive black-hole binaries. In addition, power-law models are distinguishable from those having low-frequency spectral turnovers once 20~yrs of data are reached. Even though our study is based on the NANOGrav data, we also derive relations that allow for a generalization to other pulsar-timing array datasets. Most notably, by combining the data of individual arrays into the International Pulsar Timing Array, all of these milestones can be reached significantly earlier.
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 feasibility of the proposed method with simulated timing data. Using a selected dataset from the Parkes Pulsar Timing Array data release 1 and the North American Nanohertz Observatory for Gravitational Waves publicly available datasets, we try to detect the signals from single SNFGW sources. The result is consistent with no GW detection with 65.5% probability. An all-sky map of the sensitivity of the selected pulsar timing array to single SNFGW sources is generated, and the position of the GW source where the selected pulsar timing array is most sensitive to is $lambda_{rm{s}}=-0.82$, $beta_{rm{s}}=-1.03$ (rad); the corresponding minimum GW strain is $h=6.31times10^{-11}$ at $f=1times10^{-5}$ Hz.
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