The parallax, mass and age of the PSR J2145-0750 binary system

We present results of high-precision timing measurements of the binary millisecond pulsar PSR J2145-0750. Combining 10 yrs of radio timing data obtained with the Effelsberg 100-m radio telescope and the Lovell 76-m radio telescope we measure a significant timing parallax of 2.0(6) mas placing the system at 500 pc distance to the solar system. The detected secular change of the projected semi-major axis of the orbit dot x=1.8(6)× 10^-14 lt-s s^-1, where x=(a_p sin i)/c, is caused by the proper motion of the system. With this measurement we can constrain the orbital inclination angle to i<61°, with a median likelihood value of 46° which is consistent with results from polarimetric studies of the pulsar magnetosphere. This constraint together with the non-detection of Shapiro delay rules out certain combinations of the companion mass, m₂, and the inclination, i. For typical neutron star masses and using optical observations of the carbon/oxygen-core white dwarf we derive a mass range for the companion of 0.7 M_⊙≤ m₂≤ 1.0 M_⊙. We apply evolutionary white dwarf cooling models to revisit the cooling age of the companion. Our analysis reveals that the companion has an effective temperature of T_eff= 5750±600 K and a cooling age of τ_cool=3.6(2) Gyr, which is roughly a factor of three lower than the pulsar's characteristic age of 10.4 Gyr. The cooling age implies an initial spin period of P₀= 13.0(5) ms, which is very close to the current period.