Shapiro Delay Measurements from Fifteen Years of PSR J1231$-$1411 Radio Observations

Abstract

We present 15 years of Nan\c{c}ay and Green Bank radio telescope timing observations for PSR J1231$-$1411. This millisecond pulsar is a primary science target for the Neutron Star Interior Composition Explorer telescope (NICER, which discovered its X-ray pulsations), has accumulated near-continuous $\gamma$-ray data since the Fermi-Large Area Telescope's launch, and has been studied extensively with the Green Bank and Nan\c{c}ay radio telescopes. We have undertaken a campaign with the Green Bank Telescope targeting specific orbital phases designed to improve our constraint on the pulsar's mass through the detection of a relativistic Shapiro delay. Both frequentist and Bayesian techniques -- the latter incorporating priors from white dwarf binary evolution models -- are applied to fifteen years of radio observations, yielding relatively weak constraints on the companion and pulsar masses of $0.23^{+0.09}_{-0.06}$ M$_{\odot}$ and $1.87^{+1.11}_{-0.67}$ M$_{\odot}$, respectively (68.3% CI from Bayesian fits); however, the orbital inclination is measured to better relative precision ($79.80^{+3.47}_{-4.70}$ degrees). Restricting the maximum allowed pulsar mass to 3 M$_{\odot}$ improves the constraint and lowers the measured mass to $1.71^{+0.70}_{-0.56}$ M$_{\odot}$. A fully-generalized Bayesian fit that simultaneously samples the noise and timing models yields a pulsar mass in close agreement with this value. While our radio-derived inclination result has informed recent NICER X-ray studies of PSR J1231$-$1411, the lessons learned from this troublesome pulsar will also bolster future high-precision mass measurement campaigns and resulting constraints on the neutron star interior equation of state.