Possible tidal dissipation in millisecond pulsar binaries

The post-Keplerian(PK) parameters inferred from pulsar timing provide a convenient way to test Einstein's general theory of relativity. However, before obtaining a pure orbital decay $\dot{P}_b$ induced by gravitational wave radiation, which is one of the PK parameters, a number of factors need to be accounted for carefully. The effect of tidal dissipation on $\dot{P}_b$ has been thought of as negligible. Here, we investigate the data for possible effects of tidal dissipation on $\dot{P}_b$. The possibility of the tidal dissipation as a contributor to $\dot{P}_b$ in a large sample of millisecond pulsar binaries is investigated in detail. We collected a large sample of pulsar binaries with measured $\dot{P}_b$. All of the systems are millisecond pulsars. The residual $\dot{P}^{Res}_b$ of these systems was obtained by subtracting the three normal effects, that is to say the effect of Shklovskii, line-of-sight acceleration, and gravitational radiation. Assuming that tidal dissipation is responsible for such a residual $\dot{P}^{Res}_b$, the tidal parameters of these systems can be calculated and compared with the tidal models. The residual $\dot{P}^{Res}_b$ is distributed over the half positive and half negative. The dynamical tidal model can explain the residual $\dot{P}_b$ of millisecond pulsar-white dwarf binaries. And the Love number of the main-sequence companion of \object{PSR J1227-4853} can be derived as a reasonable value $k_2=0.177^{+0.098}_{-0.058}$ with the equilibrium tidal model. Those results are compatible with the scenario of tidal dissipation. Additionally, a weak correlation between the tidal parameter and orbital period is revealed, likely originating in the tidal process of the recycled stage which is worthy of further investigation.