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

The complete orbital and spin period evolutions of the double neutron star(NS) system PSR J0737-3039 are simulated from birth to coalescence,which include the two observed radio pulsars classified as primary NS PSR J0737-3039 A and companion NS PSR J0737-3039 B.By employing the characteristic age of PSR J0737-3039 B to constrain the true age of the double pulsar system,the initial orbital period and initial binary separation are obtained as 2.89 h and 1.44 x 106 km,respectively,and the coalescence age or the lifetime from the birth to merger of PSR J0737-3039 is obtained to be 1.38 x 108 yr.At the last minute of coalescence,corresponding to the gravitational wave frequency changing from 20 Hz to1180 Hz,we present the binary separation of PSR J0737-3039 to be from 442 km to 30 km,while the spin periods of PSR J0737-3039 A and PSR J0737-3039 B are 27.10 ms and 4.63 s,respectively.From the standard radio pulsar emission model,before the system merged,the primary NS could still be observed by a radio telescope,but the companion NS had crossed the death line in the pulsar magnetic-field versus period(B-P) diagram at which point it is usually considered to cease life as a pulsar.This is the first time that the whole life evolutionary simulation of the orbit and spin periods for a double NS system is presented,which provides useful information for observing a primary NS at the coalescence stage.