First measurement of the total gravitational quadrupole moment of a black widow companion

We present the first measurement of the gravitational quadrupole moment of the companion star of a spider pulsar, namely the black widow PSR J2051–0827. To this end, we have re-analysed radio timing data using a new model that is able to account for periastron precession caused by tidal and centrifugal deformations of the star as well as by general relativity. The model allows for a time-varying component of the quadrupole moment, thus self-consistently accounting for the ill-understood orbital period variations observed in these systems. Our analysis results in the first detection of orbital precession in a spider system at ω˙=−68∘.6+0∘.9−0∘.5 yr−1 and the most accurate determination of orbital eccentricity for PSR J2051–0827 with e = (4.2 ± 0.1) × 10−5. We show that the variable quadrupole component is about 100 times smaller than the average quadrupole moment Q¯=−2.2+0.6−1×1041 kgm2⁠. We discuss how accurate modelling of high-precision optical light curves of the companion star will allow its apsidal motion constant to be derived from our results.