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

TL;DR

This study analyzes 15 years of radio timing data for PSR J1231-1411 to measure the Shapiro delay, aiming to constrain neutron star and companion masses and improve understanding of neutron star interiors.

Contribution

It applies both frequentist and Bayesian methods to long-term radio observations to measure the Shapiro delay and constrain system parameters, incorporating priors from binary evolution models.

Findings

Measured pulsar mass: approximately 1.71 M$_{\ m\odot}$ with uncertainties.

Orbital inclination constrained to about 80 degrees.

Radio timing results inform X-ray studies and future neutron star mass measurements.

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.