PSR J2222--0137. I. Improved physical parameters for the system

The PSR J2222-0137 binary system is a unique laboratory for testing gravity theories. To fully exploit its potential for the tests, we aim to improve the measurements of its physical parameters: spin, orbital orientation, and post-Keplerian parameters which quantify the observed relativistic effects. We present improved analysis of archival VLBI data, using a coordinate convention in full agreement with that used in timing. We also obtain much improved polarimetry with FAST. We provide an analysis of significantly extended timing data taken with Effelsberg, Nancay, Lovell and Green Bank telescopes. From VLBI analysis we obtain a new estimate of the position angle of ascending node, Omega=189(19) deg, and a new position of the pulsar with more conservative uncertainty. The FAST polarimetry and in particular the detection of an interpulse, yield much improved estimate for the spin geometry of the pulsar, in particular an inclination of the spin axis of 84 deg. From the timing we obtain a new 1% test of general relativity (GR) from the agreement of the Shapiro delay and the advance rate of periastron. Assuming GR in a self-consistent analysis of all effects, we obtain much improved mass: 1.831(10) M_sun for the pulsar and 1.319(4) M_sun for the companion; the total mass, 3.150(14) M_sun confirms it as the most massive double degenerate binary known in the Galaxy. This analysis also yields the orbital orientation: the orbital inclination is 85.27(4) deg, indicating a close alignment between the spin of the pulsar and the orbital angular momentum; Omega = 188(6) deg, matching our VLBI result. We also obtain precise value of the orbital period derivative, 0.251(8)e-12 s s^-1, consistent with the expected variation of Doppler factor plus the orbital decay caused by emission of gravitational wave (GW) predicted by GR. This agreement introduces stringent constraint on the emission of dipolar GW.