E-18 - O-1 × HC-12 — Shapiro-delay two-solar-mass measurement anchors the stiff EOS

O-1 - PSR J1614-2230 pulsar mass measured at 1.97 solar masses via Shapiro delay

Key system parameters (Table 1): spin period 3.15 ms; orbital period 8.6866194196(2) d; eccentricity 1.30(4)e-6; sin i = 0.999894(5); companion mass 0.500(6) Msun; 2,206 pulse times of arrival, rms residual 1.1 us; reduced chi^2 = 1.4 (2165 dof). MCMC error analysis; orbital dispersion-measure variation limited to < 2e-4 pc cm^-3 (delays < 0.4 us), and three conjunction epochs over 2 months give consistent results. Unlike X-ray or periastron-advance mass determinations, the Shapiro-delay measurement involves essentially no astrophysical model assumptions.

Methodology

Radio timing of PSR J1614-2230 with the GBT and the GUPPI backend: a dense orbital campaign in March 2010 (three superior-conjunction epochs over two months) plus long-term 2002-2010 timing; 2,206 pulse times of arrival, rms residual 1.1 us, reduced chi^2 = 1.4 (2165 dof). The nearly edge-on orbit (sin i = 0.999894(5)) produces a strong Shapiro delay whose shape yields companion mass and inclination — hence the pulsar mass — from general relativity alone, with essentially no astrophysical model assumptions; MCMC error analysis, orbital dispersion-measure variation bounded to < 2e-4 pc cm^-3 (delays < 0.4 us), and the three conjunction epochs give mutually consistent results.

Link to original

Link to original

Why this is evidence

H-1 (stiff EOS) predicts neutron stars up to and beyond this mass exist and will eventually be found; H-44 (softened by exotic degrees of freedom) predicts a lower maximum mass, so a precisely measured pulsar at this mass should not exist. The measurement rests only on general-relativistic orbital dynamics (the HC-13 dependency), not on neutron-star structure models, so within GR it directly separates the two members.

Likelihood

# E-18 (HC-12) — lone edge, one observation O-1 "PSR J1614-2230 = 1.97 Msun via Shapiro delay". Members in
# HC-12.hypotheses order: [H-1 stiff EOS, H-44 softened by exotic dof]. No residual
# (exhaustive_by_construction). The mass rests only on GR orbital dynamics, not on NS structure models, so
# within GR it separates the members cleanly (the HC-13 dependency is noted at cluster level, not repriced
# in t here). Anchored on H-1 = 1 (rule 7).
lik_o1_H1  = 1.0    # anchor: a stiff EOS expects neutron stars at and beyond 1.97 Msun, so this measurement
                    # is exactly what H-1 predicts
lik_o1_H44 = 0.27   # ratio to H-1: exotic softening pulls the maximum mass down. A-13 (approved) shows
                    # 1.97 Msun excludes every EOS with Mmax below it and rules out the soft
                    # hyperon/kaon-condensate models (GS1, GM3), so most softened EOSs cannot produce this
                    # star at all. Not zero: A-13 notes some strange-quark-matter models survive and
                    # repulsive-interaction hyperonic EOSs can still reach ~2 Msun (cf. the prior's
                    # p_stiff_if_exotic ~ 0.25)
t_o1 = 0.9          # cap = trust_score(S-66) = 0.9. Shapiro delay involves essentially no astrophysical
                    # model assumptions (high significance, dense-campaign timing, MCMC error analysis), so
                    # there is no data-to-observation weakness to dock for; t at the cap
evidence("HC-12", ["O-1"], [lik_o1_H1, lik_o1_H44], t=t_o1)