The PSR J0435+3233 Triple System

The detailed evolution of triple star systems is complicated and poorly known. Based on the optical/infrared and gamma-ray archived data, we identified that the pulsar, PSR J0435+3233, is a gamma-ray pulsar in a hierarchical triple system, with a helium white dwarf (WD) as a close inner binary companion and a Sun-like star as the distant tertiary. PSR J0435+3233 and the WD companion are in a circular orbit with a period of P orb1 = 8 days and an eccentricity of e=0.00016.The tertiary is a G-type subgiant with a mass of 0.98(12) M at a distance of 2.1(4) kpc from the Earth. By simultaneously fitting the observed spin-period variations of the gamma-ray emission (over 16.7 years) and radio emission (over 4.6 years) from PSR J0435+3233, the changes of the inner orbital parameters, the Shapiro delay, Gaia astrometry, and the outer companion mass, we determined the outer elliptical orbit for the tertiary, with a period P orb2 about 26900 days and an eccentricity e 2 = 0.5983. The outer orbit is either nearly perpendicular to the inner orbit (mutual inclination about 84), or exhibits a moderate mutual inclination of about 55. For the former geometry, the pulsar, the WD, and the tertiary star have masses of 1.15+0.06-0.04 M, 0.271+0.010-0.006 M, and 0.96(4) M, respectively; for the latter geometry, the corresponding masses are 1.29+0.14-0.11 M, 0.296+0.022-0.018 M, and 1.12+0.06-0.05 M. This is a unique triple system for detailed multi-band observations and for studying the evolutionary path and dynamic processes of a primordial triple star system. It will ultimately evolve into a system consisting of a neutron star and two white dwarfs.