Relativistic modeling of atmospheric occultations with time transfer functions

Context. Occultation experiments represent unique opportunities to remotely probe the physical properties of atmospheres. The data processing involved in modeling the time and frequency transfers of an electromagnetic signal requires that refractivity be properly accounted for. On theoretical grounds, little work has been done concerning the elaboration of a covariant approach for modeling occultation data. Aims. We present an original method allowing fully analytical expressions to be derived up to the appropriate order for the covariant description of time and frequency transfers during an atmospheric occultation experiment. Methods. We make use of two independent powerful relativistic theoretical tools, namely the optical metric and the time transfer functions formalism. The former allows us to consider refractivity as spacetime curvature while the latter is used to determine the time and frequency transfers occurring in a curved spacetime. Results. We provide the integral form of the time transfer function up to any post-Minkowskian order. The discussion focuses on the stationary optical metric describing an occultation by a steadily rotating and spherically symmetric atmosphere. Explicit analytical expressions for the time and frequency transfers are provided at the first post-Minkowskian order and their accuracy is assessed by comparing them to results of a numerical integration of the equations for optical rays. Conclusions. The method accurately describes vertical temperature gradients and properly accounts for the light-dragging effect due to the motion of the optical medium. It can be pushed further in order to derive the explicit form of the time transfer function at higher order and beyond the spherical symmetry assumption.