Searching for Anisotropy in the Gravitational Wave Background Using the Parkes Pulsar Timing Array

Abstract

In recent years, several pulsar timing array collaborations have reported evidence for a nanohertz gravitational wave background (GWB). Such a background signal could be produced by supermassive binary black holes, early-Universe processes such as inflation and phase transitions, or a mixture of both. One way to disentangle different contributions to the GWB is to search for anisotropic signatures. In this work, we search for anisotropy in the GWB using the third data release of the Parkes Pulsar Timing Array. Our analysis employs both the radiometer method and the spherical harmonic basis to characterize the distribution of GWB power across the sky. We calculate the angular power in the lowest five frequency bins and compare it with detection thresholds determined under the null hypothesis of isotropy. In the 5.26 nHz frequency bin, we identify a hotspot in the reconstructed sky map with a $p$-value of $0.016$ (the lowest in our analysis), which we attribute to noise fluctuations. While our search reveals no statistically significant anisotropy, we expect that the precise measurement of angular power spectrum of the GWB will become instrumental in determining the origin of the nanohertz GWB signal.

Figures (5)

• Figure 1: The angular power spectra measured using the square-root spherical harmonics basis. The orange dashed line indicates the detection threshold, corresponding to a significance level of $p = 3\times 10^{-3}$ for rejecting the isotropy hypothesis. The colored solid line shows the measured angular power spectrum in the lowest five frequency bins.
• Figure 2: Sky maps of the anisotropy SNR of the GWB reconstructed in the lowest five frequency bins using the radiometer method. Each panel corresponds to a different frequency bin, and the white stars indicate the positions of PPTA pulsars. A potential hotspot appears in the 5.26 nHz frequency bin, with the maximum SNR corresponding to a $p$-value of 0.016.
• Figure S1: Sky map of the expected GW sensitivity for the PPTA DR3. The color map represents $\sqrt{\mathcal{M}(\hat{\Omega})}$, which quantifies the directional sensitivity to GWB anisotropies across the sky. The sensitivity distribution closely follows the spatial density of pulsars, with the highest sensitivity achieved in regions where the pulsar population is most concentrated.
• Figure S2: The results in both panels are obtained assuming a power-law strain spectrum. Left panel: The noise-marginalized anisotropic SNR distribution (solid green line) and the SNR distribution under the null hypothesis (assuming an isotropic background; dashed orange line). The green vertical line marks the mean SNR, and the corresponding $p$-value from the null distribution is 0.277. Right panel: The blue solid line represents the measured angular power spectrum, while the orange dashed line denotes the detection threshold.
• Figure S3: The sky maps are reconstructed assuming a power-law strain spectrum. The GWB sky map reconstructed based on the radiometer basis ($N_{\text{pix}}=192$). White stars mark the positions of the PPTA pulsars. The left panel shows the SNR in each pixel, while the right panel displays the corresponding $p$-value distribution. Although some directions exhibit relatively high SNR values, all $p$-values remain above the detection threshold of $3 \times 10^{-3}$, indicating consistency with an isotropic GWB.