Constraining the Nanohertz Gravitational Wave Background with an X-ray Pulsar Timing Array from NICER observations

TL;DR

This work investigates constraints on the nanohertz GWB using X-ray pulsar timing data from NICER, treating six MSPs over a six-year baseline with a Bayesian framework to model white/red noise and a common red process consistent with a GWB of SMBHBs. The analysis fixes the spectral index to $\gamma_{\rm gwb}=13/3$ and derives an upper limit on the GWB amplitude $\log_{10}(A_{\rm gwb}) < -13.4$, with Bayes factors indicating only weak evidence for a GWB and inconclusive Hellings-Downs correlations ( $S=2.5$ ). When $\gamma_{\rm gwb}$ is allowed to vary, the posterior fails to converge to the theoretical value, suggesting that the observed correlations are dominated by pulsar-intrinsic common red noise. NICER thus demonstrates the feasibility of X-ray timing PTA constraints, albeit currently less stringent than radio or $\gamma$-ray PTAs, and points toward substantial gains with future X-ray facilities and joint multi-band PTA analyses that can robustly distinguish a stochastic GW background from instrument or pulsar noise. The study reinforces the potential of high-energy timing to complement traditional PTAs and to contribute to a robust, multi-band detection strategy in the nanohertz regime.

Abstract

We present constraints on the nanohertz gravitational wave background (GWB) using X-ray pulsar timing data from the Neutron Star Interior Composition Explorer(\textit{NICER}). By analyzing six millisecond pulsars over a six-year observational baseline, we employed a Bayesian framework to model noise components and search for a common red signal consistent with a GWB from supermassive black hole binaries (assuming a spectral index $γ_{\rm gwb}=13/3$). Our results show no significant evidence for a GWB, yielding a 95\% upper limit of $\log_{10}(A_{\rm gwb})<-13.4$. Weak evidence for Hellings-Downs spatial correlations was found (S=2.5), though the signal remains statistically inconclusive. Compared to radio and $γ$-ray pulsar timing arrays, the \textit{NICER} constraint is currently less stringent but demonstrates the feasibility of X-ray timing with \textit{NICER} for GWB studies and highlights the potential for improved sensitivity with future X-ray missions.

Figures (5)

• Figure 1: Observation epochs of six NICER millisecond pulsars: Each horizontal line represents the observation span of one pulsar, with markers indicating the epochs of available ToA measurements.
• Figure 2: Log-posterior distribution of $A_{\rm gwb}$ derived from NICER data.
• Figure 3: Plot of the cross-correlation coefficients between different pulsar pairs as a function of their angular separation.
• Figure 4: Constraints on the GWB Amplitude from Different PTAs: All GWB amplitude limits are shown at the reference frequency $f_c = 1\, \rm yr^{-1}$, assuming a spectral index of $\gamma_{\rm gwb} = 13/3$. The data are taken from the Parkes Pulsar Timing Array (PPTA) jenet2006uppershannon2013gravitationalshannon2015gravitationalgoncharov2021evidencereardon2023search, the European Pulsar Timing Array (EPTA) van2011placinglentati2015europeanchen2021commonantoniadis2023second, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) demorest2012limitsarzoumanian2018nanogravarzoumanian2020nanogravagazie2023nanograv, the International Pulsar Timing Array (IPTA) verbiest2016internationalantoniadis2022international, the Chinese Pulsar Timing Array (CPTA) xu2023searching, and the Fermi-LAT Pulsar Timing Array fermi2022gammakerr2024upgrading. The time associated with each data point corresponds to the publication date of the respective paper. The cyan dashed line represents the projected improvement of GWB constraints from NICER data over time.
• Figure 5: 95% Confidence Upper Limits on GWB Amplitude for Different Spectral Indices: The cyan points represent the 95% confidence upper limits on the GWB amplitude obtained from MCMC fitting for different values of $\alpha$. The red pentagrams, green triangles, and blue circles correspond to GWBs from SMBHBs, scale-invariant inflation in the early Universe, and the decay of cosmic strings, respectively. The black curve shows the smoothed trend obtained using a cubic spline fit based on these data.