The stochastic background: scaling laws and time to detection for pulsar timing arrays

By X. Siemens, J. Ellis, Fredrick A. Jenet, J. Romano. 2013

165 citations recorded by the source corpus.

We derive scaling laws for the signal-to-noise ratio of the optimal cross-correlation statistic, and show that the large power-law increase of the signal-to-noise ratio as a function of the observation time T that is usually assumed holds only at early times. After enough time has elapsed, pulsar timing arrays enter a new regime where the signal to noise only scales as T?>. In addition, in this regime the quality of the pulsar timing data and the cadence become relatively unimportant. This occurs because the lowest frequencies of the pulsar timing residuals become gravitational-wave dominated. Pulsar timing arrays enter this regime more quickly than one might naively suspect. For T = 10 yr observations and typical stochastic background amplitudes, pulsars with residual root-mean-squares of less than about 1 μs are already in that regime. The best strategy to increase the detectability of the background in this regime is to increase the number of pulsars in the array. We also perform realistic simulations of the NANOGrav pulsar timing array, which through an aggressive pulsar survey campaign adds new millisecond pulsars regularly to its array, and show that a detection is possible within a decade, and could occur as early as 2016.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/33d62e9d081617454d73c3ae960862039e967914

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Citations in the corpus

The NANOGrav 11 Year Data Set: Pulsar-timing Constraints on the Stochastic Gravitational-wave Background (2018, unknown): “…0.7(9) DE435 5.9×10−31 0.7(6) 8.5×10−32 0.5(5) 5.7×10−32 1(1) DE436 9.7×10−31 0.8(7) 2.0×10−31 0.9(7) 1.9×10−31 1(1) BAYESEPHEM 1.3×10−31 0.1(9) 2.7×10−32 0(1) −4.3×10−32 0(1) (Siemens et al. 2013), for which the additional two years of data should reduce the limit from 2.91×10−15 to…”
Sensitivity curves for searches for gravitational-wave backgrounds (2013, background): “[1] Xavier Siemens, Justin Ellis, Fredrick Jenet, and Joseph D.”
Expected properties of the first gravitational wave signal detected with pulsar timing arrays (2015, methodology): “Therefore, having an array formed by many pulsars with decent precision might be a better strategy to detect a GWB than having few ultra-precise pulsars (a point that has also been made by Siemens et al. 2013).”
The NANOGrav 15 yr Data Set: Observations and Timing of 68 Millisecond Pulsars (2023, background): “…push to evaluate many new MSPs discovered in large-area sky surveys and targeted gamma-ray-guided surveys; it is notable because a PTA’s sensitivity to a GWB increases linearly with the number of pulsars in the array and as the square root of the overall timing baseline (Siemens et al. 2013).”
European Pulsar Timing Array Limits On An Isotropic Stochastic Gravitational-Wave Background (2015, methodology): “As a consistency check of our Bayesian method, we also employ a weak-signal regime maximum-likelihood estimator of the GWB strain-spectrum amplitude, known as the optimal-statistic (Anholm et al. 2009; Siemens et al. 2013; Chamberlin et al. 2014).”
Dark, cold, and noisy: constraining secluded hidden sectors with gravitational waves (2018, unknown): “[92].”
The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background (2023, background): “…our data are dominated by the GWB, the optimal statistic S/N should grow with the square root of the time span of the data and linearly with the number of pulsars in the array (Siemens et al. 2013); in this regime increasing the number of pulsars is the best way to boost PTA sensitivity to the GWB.”
Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array (2023, methodology): “If the purported common-spectrum noise is a genuine signature of an isotropic, stochastic GWB, then we can expect the IPTA to make a detection using the current-generation data sets (Siemens et al. 2013).”
The International Pulsar Timing Array: First Data Release (2016, background): “In the low-S/N regime where the GWB contributes less power to the data than the other noise sources outlined in Section 1.1, Siemens et al. (2013) derived that the S/N of a PTA’s detection sensitivity scales as S/N ∝ NCA2T 13/3/σ 2, (3) where N is the number of pulsars in the array, C the cadence…”