Optimal strategies for continuous wave detection in pulsar timing arrays: Realistic pulsar noise and a gravitational wave background

Abstract

Pulsar timing arrays are sensitive to low-frequency gravitational waves (GWs), such as those produced by supermassive binary black holes at subparsec separations. The incoherent superposition of GWs emitted by a cosmological population of these sources produces a gravitational wave background (GWB), while some individual sources may be resolvable as deterministic signals with slowly varying GW frequencies, which are often referred to as "continuous waves" (CWs). The Fp-statistic is a frequentist method of detecting these CWs. In this paper, we study how the presence of pulsar red noise and a GWB affect the Fp-statistic. We compare results when marginalizing over the red noise and using the maximum-likelihood values of the red noise, and find little difference between the two. We also present results of using the Fp-statistic to analyze the NANOGrav 12.5-year data set, where we find no evidence for CWs in agreement with the previously published Bayesian results.

Figures (11)

• Figure 1: The blue histogram shows the $2 \mathcal{F}_p$ values for 10 simulations of the 15yr dataset with only white noise injected, marginalized across 150 frequency bins. The orange curve is the expected chi squared distribution with zero non-centrality and the black dashed line is the expected degrees of freedom.
• Figure 2: (Left) The 2$\mathcal{F}_p$ value for simulations with white noise and intrinsic red noise for the NMFP values. Both the Bayesian and the frequentist analysis were performed for 50 red noise frequency components (black dashed line), beyond which the $\mathcal{F}_p$ value becomes large and unreliable. (Right) The histograms showing the $\mathcal{F}_p$ values below 100 nHz ($50 \mathrm{yr}^{-1}$) $\mathcal{F}_p$ in light blue, and the $\mathcal{F}_p$ values above 100 nHz in dark blue.
• Figure 3: TOP: (Left) The violin plot and histograms for $\mathcal{F}_p$ values when we do not include the CURN model. We see that at all frequencies the $\mathcal{F}_p$ values are greatly overestimated. (Right) The histograms for the $2\mathcal{F}_p$ values as compared to the expected central chi-squared distribution with 134 degrees of freedom. MIDDLE: The violin plots for the mean NMFP values of 50 simulations with white noise, intrinsic red noise, and a common process as a function of frequency. BOTTOM: The figure shows the violin plots for the NMFP values when the common process is kept fixed to the maximum likelihood values and only intrinsic red noise parameters are marginalized over. At low values, the $\mathcal{F}_p$ values recover a slightly higher mean and variance due to the common process not being modeled correctly.
• Figure 4: TOP: The violin plots of the NMFP values for simulations with white noise, intrinsic red noise, and a common correlated background (left) and a plot of the histograms of $\mathcal{F}_p$ values for each frequency (right). We see that this figure is nearly identical to Fig. \ref{['fig:curn fp']}. BOTTOM: The S/N of the optimal statistic testing the strength of correlations injected in the simulations.
• Figure 5: (Left) The violin plots for both the NMFP values of simulations with white noise, intrinsic red noise, a common process, and a continuous wave signal with a medium S/N. (Right) Histograms of all frequencies compared to the null distribution (black curve). The darker colored histograms indicate the fourth frequency component. Bottom figure: Histogram for the NMFP (blue) and MLFP (orange) values at the injected frequency of 8nHz compared to the expected non-central chi-squared distribution