Multi-messenger observations of double neutron stars in Galactic disk with gravitational and radio waves

Abstract

We evaluate the prospects for radio follow-up of the double neutron stars (DNSs) in the Galactic disk that could be detected through future space-borne gravitational wave (GW) detectors. We first simulate the DNS population in the Galactic disk that is accessible to space-borne GW detectors according to the merger rate from recent LIGO results. Using the inspiraling waveform for the eccentric binary, the average number of the DNSs detectable by TianQin (TQ), LISA, and TQ+LISA are 217, 368, and 429, respectively. For the joint GW detection of TQ+LISA, the forecasted parameter estimation accuracies, based on the Fisher information matrix, for the detectable sources can reach the levels of $\Delta P_{\mathrm b}/P_{\mathrm b} \lesssim 10^{-6}$, $\Delta \Omega \lesssim 100~{\mathrm {deg}}^2$, $\Delta e/e \lesssim 0.3$, and $\Delta \dot{P}_{\mathrm b} / \dot{P}_{\mathrm b} \lesssim 0.02$. These estimation accuracies are fitted in the form of power-law function of signal-to-noise ratio. Next, we simulate the radio pulse emission from the possible pulsars in these DNSs according to pulsar beam geometry and the empirical distributions of spin period and luminosity. For the DNSs detectable by TQ+LISA, the average number of DNSs detectable by the follow-up pulsar searches using the Parkes, FAST, SKA1, and SKA are 8, 10, 43, and 87, respectively. Depending on the radio telescope, the average distances of these GW-detectable pulsar binaries vary from 1 to 7 kpc. Considering the dominant radiometer noise and phase jitter noise, the timing accuracy of these GW-detectable pulsars can be as low as 70 ${\rm ns}$ while the most probable value is about 100 $\mu {\rm s}$.