Astrometric Effects of Secular Aberration

Abstract

One of the main endeavors of fundamental astrometry is to establish a practical realization of a nonrotating, inertial reference frame anchored to celestial objects whose positions are defined in the barycentric coordinates of the solar system matching the current level of astrometric observational accuracy. The development of astrometric facilities operating from space at a microarcsecond level of precision makes the nonuniformity of the Galactic motion of the barycenter an observable and nonnegligible effect that violates the desired inertiality of the barycentric frame of the solar system. Most of the observable effect is caused by the nearly constant (secular) acceleration of the barycenter with respect to the center of the Galaxy. The acceleration results in a pattern of secular aberration that is observable astrometrically as a systematic vector field of the apparent proper motions of distant quasars. We employ the classic approximations of planar epicycle and vertical harmonic oscillation for the Sun's Galactic motion to estimate the magnitude of secular acceleration components in the Galactic coordinates and to show that the peculiar accelerations are smaller than the main galactocentric component. We employ the vector spherical harmonic formalism to describe the predicted field of proper motions and evaluate the amplitude of this field at each point on the celestial sphere. We show that the pattern of secular aberration is fully represented by three low-order electric-type vector harmonics; hence, it is easily distinguishable from the residual rotations of the reference frame and other possible effects, such as the hypothetical long-period gravitational waves, which are described by other types of vector or tensor harmonics. Comprehensive numerical simulations of the grid astrometry with Space Interferometry Mission (SIM) PlanetQuest are conducted assuming that 110 optically bright quasars are included as grid objects and observed on the same schedule, but to lower precision due to their faintness, as regular grid stars. The full covariance matrix of the simulated grid solution is used to evaluate the covariances of the three electric harmonic coefficients, representing the secular aberration pattern of proper motions. This is the only reliable method to estimate such sample-based statistics in view of the considerable star-to-star correlations in SIM global astrometry. We conclude that the grid astrometry with SIM PlanetQuest will be sensitive to the main galactocentric component of secular acceleration, arising from the circular motion of the local standard of rest (LSR) around the Galactic center, while the peculiar acceleration of the Sun with respect to the LSR is expected to be too small to be detected with this astrometric space interferometer.