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

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.

💡 Research Summary

This paper presents the first systematic search for a nanohertz stochastic gravitational‑wave background (GWB) using X‑ray pulsar timing data from the Neutron Star Interior Composition Explorer (NICER). The authors selected six bright millisecond pulsars—J1939+2134, J1824‑2452A, J0437‑4715, J0030+0451, J0218+4232, and J2124‑3358—each with high X‑ray flux, short spin period, and low period derivative, making them suitable for high‑precision timing. NICER observed these sources over a six‑year span (June 2017–September 2023), accumulating several megaseconds of exposure per pulsar.

Data reduction followed a standard NICER pipeline: photon events were filtered, barycentered using the IPTA Data Release 2 ephemerides, and grouped into 30‑day segments containing 5×10⁴–2×10⁵ photons. For each segment a high‑signal‑to‑noise template profile was built, and times of arrival (TOAs) were obtained by cross‑correlating segment profiles with the template. TOA uncertainties were derived from Gaussian sampling of the pulse profile. The timing model was refined with TEMPO2 and PINT, fixing deterministic parameters while allowing stochastic noise components to vary.

The noise model comprises two parts. White noise is described by EFAC and EQUAD parameters that rescale the measured TOA uncertainties and capture any excess instrumental noise. Red noise for each pulsar is modeled as a power‑law spectrum (P_I(f)=A_I^2/(12\pi^2)(f/f_c)^{-\gamma_I}) yr⁻³, with a reference frequency (f_c=1) yr⁻¹. Priors on the red‑noise amplitudes and spectral indices are taken from previous radio and γ‑ray studies, typically spanning (\gamma_I\in