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

Abstract We present 15 yr of Nançay 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 γ -ray data since the Fermi-Large Area Telescope’s launch, and has been studied extensively with the Green Bank and Nançay 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 15 yr of radio observations, yielding relatively weak constraints on the companion and pulsar masses of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.2</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.06</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> M ⊙ and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1.8</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.67</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.11</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> M ⊙ , respectively (68.3% CI from Bayesian fits); however, the orbital inclination is measured to better relative precision ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>79.8</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4.70</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>3.47</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> °). Restricting the maximum allowed pulsar mass to 3 M ⊙ improves the constraint and lowers the measured mass to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1.7</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.56</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.70</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> M ⊙ . 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 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.