Geodetic precession and timing of the relativistic binary pulsars PSR B1534+12 and PSR B1913+16

The pulsars B1534+12 and B1913+16 are two unique neutron star binaries exhibiting a wide range of relativistic phenomena that are impossible to detect in other systems. They constitute an exquisite observational ground on which theories can be tested. To date, the timing observations of B1534+12 and B1913+16 have been successfully used to test the strong field regime of relativistic gravity by measuring and then comparing with theory the evolution of the orbital elements of the pulsars. In this paper we develop a method that allows us to detect the timing signature of yet another relativistic phenomenon, the geodetic spin precession, and derive the misalignment angle between the orbital angular momentum and the spin vector of the pulsar, an important quantity that can be used to assess the degree of asymmetry of the supernova explosion that created the pulsar. Although we demonstrate that observations of PSR B1534+12 - using the Penn State Pulsar Machine and the Mark III system - do not yet have a sufficient time span to detect precessional effects in the timing, we show that in about 10-25 years we will be able to get a good grasp on the misalignment angle of this pulsar. This may seem a long time to wait but in fact is typical for timing relativistic binary pulsars and, as in the case of PSR B1913+16, patient observing will eventually turn out to be very rewarding.