Modeling the Uncertainties of Solar System Ephemerides for Robust Gravitational-wave Searches with Pulsar-timing Arrays

The regularity of pulsar emissions becomes apparent once we reference the pulses' times of arrivals to the inertial rest frame of the solar system. It follows that errors in the determination of Earth's position with respect to the solar system barycenter can appear as a time-correlated bias in pulsar-timing residual time series, affecting the searches for low-frequency gravitational waves performed with pulsar-timing arrays. Indeed, recent array data sets yield different gravitational-wave background upper limits and detection statistics when analyzed with different solar system ephemerides. Crucially, the ephemerides do not generally provide usable error representations. In this article, we describe the motivation, construction, and application of a physical model of solar system ephemeris uncertainties, which focuses on the degrees of freedom (Jupiter's orbital elements) most relevant to gravitational-wave searches with pulsar-timing arrays. This model, BayesEphem, was used to derive ephemeris-robust results in NANOGrav's 11 yr stochastic-background search, and it provides a foundation for future searches by NANOGrav and other consortia. The analysis and simulations reported here suggest that ephemeris modeling reduces the gravitational-wave sensitivity of the 11 yr data set and that this degeneracy will vanish with improved ephemerides and with pulsar-timing data sets that extend well beyond a single Jovian orbital period.