Probing the properties of the pulsar wind via studying the dispersive effects in the pulses from the pulsar companion in a double neutron-star binary system

Abstract

The velocity and density distribution of $e^\pm$ in the pulsar wind are crucial distinction among magnetosphere models, and contains key parameters determining the high energy emission of pulsar binaries. In this work, a direct method is proposed, which might probe the properties of the wind from one pulsar in a double-pulsar binary. When the radio signals from the first-formed pulsar travel through the relativistic $e^\pm$ flow in the pulsar wind from the younger companion, the components of different radio frequencies will be dispersed. It will introduce an additional frequency-dependent time-of-arrival delay of pulses, which is function of the orbital phase. In this paper, we formulate the above-mentioned dispersive delay with the properties of the pulsar wind. As examples, we apply the formula to the double pulsar system PSR J0737-3039A/B and the pulsar-neutron star binary PSR B1913+16. For PSR J0737-3039A/B, the time delay in 300\,MHz is $\lesssim10\mu$s near the superior-conjunction, under the optimal pulsar wind parameters, which is $\sim$ half of the current timing accuracy. For PSR B1913+16, with the assumption that the neutron star companion has a typical spin down luminosity of $10^{33}$\,ergs/s, the time delay is as large as $10\sim20\mu$s in 300\,MHz. The best timing precision of this pulsar is $\sim5\mu$s in 1400\,MHz. Therefore, it is possible that we can find this signal in archival data. Otherwise, we can set an upper-limit on the spin down luminosity. Similar analysis can be apply to other eleven known pulsar-neutron star binaries