Search for Continuous Gravitational Wave Signals in Pulsar Timing Residuals: A New Scalable Approach with Diffusive Nested Sampling

Abstract

Detecting continuous nanohertz gravitational waves (GWs) generated by individual close binaries of supermassive black holes (CB-SMBHs) is one of the primary objectives of pulsar timing arrays (PTAs). The detection sensitivity is slated to increase significantly as the number of well-timed millisecond pulsars will increase by more than an order of magnitude with the advent of next-generation radio telescopes. Currently, the Bayesian analysis pipeline using parallel tempering Markov chain Monte Carlo has been applied in multiple studies for CB-SMBH searches, but it may be challenged by the high dimensionality of the parameter space for future large-scale PTAs. One solution is to reduce the dimensionality by maximizing or marginalizing over uninformative parameters semi-analytically, but it is not clear whether this approach can be extended to more complex signal models without making overly simplified assumptions. Recently, the method of diffusive nested (DNest) sampling shown the capability of coping with high dimensionality and multimodality effectively in Bayesian analysis. In this paper, we apply DNest to search for continuous GWs in simulated pulsar timing residuals and find that it performs well in terms of accuracy, robustness, and efficiency for a PTA including O 10 2 pulsars. DNest also allows a simultaneous search of multiple sources elegantly, which demonstrates its scalability and general applicability. Our results show that it is convenient and also high beneficial to include DNest in current toolboxes of PTA analysis.

Iterative time-domain method for resolving multiple gravitational wave sources in Pulsar Timing Array data

“…7 with Fig. 4 of [46] shows that the errors in sky localization are similar in size. The sky distribution, in RA and Dec, of true, reported, and confirmed sources for data realizations Y1 to Y3 in order from top to bottom.…”

“…The parameter estimation performance of SAPTAR-ISHI for Y 6 (c.f., Table III) compares well with the global fit approach in [46]. Here, it should be emphasized that the notion of error is different in frequentist and Bayesian methods: while SAPTARISHI provides a point estimate of parameters, with the inference of errors requiring a separate analysis using multiple data realizations, the DNest method provides samples from the joint (or marginalized) posterior probability density function of the parameters for a single data realization.…”

“…The results for Y 6 allow a direct comparison between the ISE approach of SAPTARISHI and the global fit approach used in [46]. In the latter, the DNest method was able to resolve 8 to 9 sources with SNR 25.…”

“…Realizations Y 1 to Y 5 correspond to the large-scale PTA while Y 6 corresponds to the midscale one. The latter is identical to the data used in [46]. In all realizations, the GW source parameters α ∈ The user-defined parameters of SAPTARISHI are listed in Sec.…”

“…Secondly, while the GW signal in the timing residual for any one pulsar contains two contributions [45], called the Earth and pulsar terms, the latter is ignored in both approaches as it results in a simpler, albeit sub-optimal, fitness function. Some of these limitations are removed in [46], where it is shown that the method of diffusive nested sampling (DNest) allows the Bayesian global fit approach to extend to O(10 2 ) pulsars with both signal terms included.…”