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($\mathit{\text{NICER}}$). 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 ${\gamma }_{\mathrm{g}\mathrm{w}\mathrm{b}}=13\mathrm{/}3$). Our results show no significant evidence for a GWB, yielding a 95% upper limit of ${\log }_{10}(A_{\mathrm{g}\mathrm{w}\mathrm{b}})<-13.4$. Weak evidence for Hellings-Downs spatial correlations was found (S=2.5), though the signal remains statistically inconclusive. Compared to radio and $\gamma$-ray pulsar timing arrays, the $\mathit{\text{NICER}}$ constraint is currently less stringent but demonstrates the feasibility of X-ray timing with $\mathit{\text{NICER}}$ for GWB studies and highlights the potential for improved sensitivity with future X-ray missions.