An updated constraint for the Gravitational Wave Background from the Gamma-ray Pulsar Timing Array

TL;DR

The paper tackles constraining the nanohertz gravitational-wave background using a gamma-ray pulsar timing array by directly analyzing Fermi-LAT photons. It introduces a two-step regularized Fourier likelihood that infers cross-pulsar Hellings-Downs correlations from photon data while marginalizing over pulse-profile and per-pulsar noise parameters. Through simulations, the method shows comparable sensitivity to folding-based TOA analyses but with improved robustness and reduced bias; applying it to 35 pulsars yields an updated 95% upper limit of $A_{\rm gw} < 1.18\times10^{-14}$ at $f=1\,\mathrm{yr}^{-1}$ (with an optimal weight threshold giving $1.09\times10^{-14}$), consistent with IPTA DR2. These results demonstrate that gamma-ray PTAs provide a complementary, dispersion-measure-free channel for GWB searches and can cross-validate radio PTA findings, with potential gains from further DM-independent timing in the future.

Abstract

Fermi LAT observations of gamma-ray pulsars can be used to build a pulsar timing array (PTA) experiment to search for gravitational wave (GW) signals at nanohertz frequencies. At those frequencies, the dominant signal is expected to be a stochastic gravitational wave background (GWB) produced by the incoherent superposition of the quasi-monochromatic GW emissions from a population of supermassive black hole binaries. While the radio PTAs have recently announced compelling evidence for a GWB signal with a power law spectrum of strain amplitude $\approx2-3\times10^{-15}$ (at the frequency of $1 {\rm yr}^{-1}$), in 2022 an analysis of $12.5$ years of Fermi data for 35 pulsars led to an upper limit of $1\times10^{-14}$ for the GWB amplitude. The analysis was carried out on times-of-arrival (TOAs) obtained by folding from six months up to one year of photon observations. A photon-by-photon approach was also tested to infer constraints on the GWB amplitude from individual pulsars, but without accounting for the cross-pulsar correlations that a GWB would induce. Here, we reanalyse the same dataset using a regularized likelihood method that correctly models cross-pulsar correlations directly from the photons, while additionally marginalising over the uncertain pulse profile shape. While the two methods are not expected to have significant differences in sensitivity, we prove through simulations of gamma-ray PTA datasets that the photon-by-photon method for GWB recoveries is, statistically, more robust. The resulting upper limit obtained for the GWB strain amplitude is $1.2\times10^{-14}$, indicating that the improved method yields a consistent result with the previous analyses.

Figures (5)

• Figure 1: Summary of the posterior distributions obtained for the 200 simulated GPTA datasets. The x-axis shows the prior interval of the GWB log-amplitude. Each line corresponds to a different simulation and the red crosses indicate the injected GWB amplitude. Brighter color corresponds to a higher value of the posterior distribution. It is evident from this plot that recovery gets more and more accurate for stronger simulated GWBs. Left panel: recovery directly from single photon data with the regularized likelihood method. Right panel: recovery from TOAs computed by folding the photon observations.
• Figure 2: Probability-Probability plot for the recovery of the GWB amplitude for the set of 200 simulated GPTA datasets. The x-axis shows the cumulative distribution function, while the y-axis shows the empirical cumulative distribution function. The solid red line corresponds to the recoveries obtained directly from the photon data with the regularized likelihood method, while the dashed red line corresponds to the recovery obtained from the TOAs computed after folding the photon data. The gray areas show the 1$\sigma$ and 3$\sigma$ confidence interval from the expected distribution for an unbiased recovery model (solid black thin line).
• Figure 3: GWB log-amplitude and slope posterior distribution obtained from the GPTA dataset of 35 pulsars directly from the photons with the regularized Fourier likelihood method. For each pulsar, the optimal photon weight threshold was considered (details in the text). The vertical line shows the nominal value $\gamma_{\rm gwb} = 13/3$ expected for a GWB produced by a population of SMBHBs. For comparison, the GWB posterior published in the latest IPTA data release ipta_dr2 is also shown. (Note that the 1D posteriors are re-normalized for visualization purposes.)
• Figure 4: GWB amplitude posteriors for $\gamma_{\rm gwb} = 13/3$ obtained for the GPTA dataset from the TOAs and from the photon-by-photon analysis using two different photon weight thresholds (the vertical lines mark the corresponding $95\%$ confidence upper limits). The posterior published in the latest IPTA data release ipta_dr2 is also shown for reference.
• Figure 5: Constraints on the GWB from radio and gamma-ray PTAs (updated version of Figure 1 of gammaPTA1). The inferred constraints on the GWB amplitude at $1 {\rm yr}^{-1}$ (see Table \ref{['tab:upperlim']} for the references of the results shown in this figure) are plotted as a function of dataset publication date and assume $\gamma_{\rm gwb} = 13/3$, as predicted for a GWB produced by a population of supermassive black hole binaries. Upper limits at $95\%$ confidence are shown with arrows while amplitude ranges indicate detections of a common noise process. [Note: for clarity, the CPTA result is shown as an upper limit; see Table \ref{['tab:upperlim']} for the complete confidence interval.] Recently, an additional upper limit on the GWB amplitude of $A_{\rm gwb} < 10^{-13.4}$ was obtained from X-ray pulsar observations collected by the Neutron Start Interior Composition Explorer (NICER) xpta.