  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
datasets 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 dataset; and that this degeneracy will vanish with improved
ephemerides and with the longer pulsar timing datasets that will become
available in the near future.
