A dynamical approach in exploring the unknown mass in the Solar system using pulsar timing arrays

TL;DR

This paper develops a Bayesian framework to detect and measure unknown masses in the Solar system using pulsar timing arrays, enabling constraints or measurements of such objects' properties.

Contribution

It introduces a novel Bayesian data-analysis method to identify and characterize unmodelled Solar system objects through pulsar timing residuals, including upper limits and parameter estimation.

Findings

Algorithm can detect unknown objects in simulated data

Future data could constrain masses lighter than 10^{-11} to 10^{-12} solar masses

Potential to measure Jovian system mass with high precision

Abstract

The error in the Solar system ephemeris will lead to dipolar correlations in the residuals of pulsar timing array for widely separated pulsars. In this paper, we utilize such correlated signals, and construct a Bayesian data-analysis framework to detect the unknown mass in the Solar system and to measure the orbital parameters. The algorithm is designed to calculate the waveform of the induced pulsar-timing residuals due to the unmodelled objects following the Keplerian orbits in the Solar system. The algorithm incorporates a Bayesian-analysis suit used to simultaneously analyse the pulsar-timing data of multiple pulsars to search for coherent waveforms, evaluate the detection significance of unknown objects, and to measure their parameters. When the object is not detectable, our algorithm can be used to place upper limits on the mass. The algorithm is verified using simulated data sets, and cross-checked with analytical calculations. We also investigate the capability of future pulsar-timing-array experiments in detecting the unknown objects. We expect that the future pulsar timing data can limit the unknown massive objects in the Solar system to be lighter than $10^{-11}$ to $10^{-12}$ $M_{\odot}$, or measure the mass of Jovian system to fractional precision of $10^{-8}$ to $10^{-9}$.