Reconciling optical and radio observations of the binary millisecond pulsar PSR J1640+2224

Previous optical and radio observations of the binary millisecond pulsar PSR J1640+2224 have come to inconsistent conclusions about the identity of its companion, with some observations suggesting the companion is a low-mass helium-core (He-core) white dwarf (WD), while others indicate it is most likely a high-mass carbon-oxygen (CO) WD. Binary evolution models predict PSR J1640+2224 most likely formed in a low-mass X-ray binary (LMXB) based on the pulsar's short spin period and long-period, low-eccentricity orbit, in which case its companion should be a He-core WD with mass about $0.35 - 0.39 \, M_\odot$, depending on metallicity. If it is instead a CO WD, that would suggest the system has an unusual formation history. In this paper we present the first astrometric parallax measurement for this system from observations made with the Very Long Baseline Array (VLBA), from which we determine the distance to be $1520^{+170}_{-150}\,\mathrm{pc}$. We use this distance and a reanalysis of archival optical observations originally taken in 1995 with the Wide Field Planetary Camera 2 (WFPC2) on the Hubble Space Telescope (HST) in order to measure the WD's mass. We also incorporate improvements in calibration, extinction model, and WD cooling models. We find that the existing observations are not sufficient to tightly constrain the companion mass, but we conclude the WD mass is $>0.4\,M_\odot$ with $>90\%$ confidence. The limiting factor in our analysis is the low signal-to-noise ratio of the original HST observations.