A spider timing model: accounting for quadrupole deformations and
  relativity in close pulsar binaries
  Spider millisecond pulsars are, along with some eclipsing post-common
envelope systems and cataclysmic variables, part of an expanding category of
compact binaries with low-mass companions for which puzzling timing anomalies
have been observed. The most prominent type of irregularities seen in them are
orbital period variations, a phenomenon which has been proposed to originate
from changes in the gravitational quadrupole moment of the companion star. A
physically sound modelling of the timing of these systems is key to
understanding their structure and evolution. In this paper we argue that a
complete timing model must account for relativistic corrections as well as
rotationally and tidally induced quadrupole distortions. We solve for the
resulting orbital dynamics using perturbation theory and derive the
corresponding timing model in the low eccentricity limit. We find that the
expected strong quadrupole deformation of the companion star results in an
effective minimum orbital eccentricity. It is accompanied by a fast periastron
precession which, if not taken into account, averages out any measurement of
the said eccentricity. We show that, with our model, detection of both
eccentricity and precession is likely to be made in many if not all spider
pulsar systems. Combined with optical light curves, this will allow us to
measure the apsidal motion constant, connecting the quadrupole deformation to
the internal structure, and thus opening a new window into probing the nature
of their exotic stellar interiors. Moreover, more accurate timing may
eventually lead spider pulsars to be used for high-precision timing experiments
such as pulsar timing arrays.
