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The complete orbital and sin period evolutions of the double neutron star(NS) system PSR J0737-3039 are simulated from the birth to coalescence, whichinclude the two observed radio pulsars classified as primary NS PSR J0737-3039Aand companion NS PSR J0737-3039B. By employing the characteristic age of PSRJ0737-3039B to constrain the true age of the double pulsar system, the initialorbital period and initial binary separation are obtained as 2.89 hrs and $1.44\times 10^{6}$ km, respectively, and the coalescence age or the lifetime fromthe birth to merger of PSR J0737-3039 is obtained to be $1.38 \times 10^{8}$yr. At the last minute of coalescence, corresponding to that the gravitationalwave frequency changes from 20 Hz to 1180 Hz, we present the binary separationof PSR J0737-3039 to be from 442 km to 30 km, while the spin periods of PSRJ0737-3039A and PSR J0737-3039B are 27.10 ms and 4.63 s, respectively. From thestandard radio pulsar emission model, before the system merged, the primary NScould still be observed by the radio telescope, while the companion NS hascrossed the death line in the pulsar magnetic-field versus period ($B-P$)diagram which is usually considered to cease the life as a pulsar. It is forthe first time that the whole life evolutionary simulation of the orbit andspin periods for double NS system is presented, which provides the usefulinformation for observing the primary NS at the coalescence stage.

research in astronomy and astrophysics/research in astronomy and astrophysics

Simulation of the orbit and spin period evolution of the double pulsars  PSR J0737-3039 from their birth to coalescence induced by the gravitational  wave radiation