Multimessenger observations of double neutron stars in the Galactic disk with gravitational and radio waves

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 $\mathrm{TQ}+\mathrm{LISA}$ are 217, 368, and 429, respectively. For the joint GW detection of $\mathrm{TQ}+\mathrm{LISA}$, the forecasted parameter estimation accuracies, based on the Fisher information matrix, for the detectable sources can reach the levels of $\mathrm{\Delta }{P}_{\mathrm{b}}/P_{\mathrm{b}}\lesssim {10}^{-6}$, $\mathrm{\Delta }\mathrm{\Omega }\lesssim 100{\mathrm{deg}}^2$, $\mathrm{\Delta }e/e\lesssim 0.3$, and $\mathrm{\Delta }{\dot{P}}_{\mathrm{b}}/{\dot{P}}_{\mathrm{b}}\lesssim 0.02$. 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 $\mathrm{TQ}+\mathrm{LISA}$, 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 ns while the most probable value is about $100\mathrm{\mu }\mathrm{s}$.

Figure 1

The histograms for the number of detectable DNSs by TQ, LISA, and $\mathrm{TQ}+\mathrm{LISA}$ network from 100 independent Monte Carlo simulations. Black curves are the best-fit Gaussian distributions.

Figure 2

The characteristic strain of the simulated DNSs from one of the Monte Carlo simulations. The bottom abscissa is the GW frequency of the 2nd harmonics $f_{n=2}$, and the top abscissa is the evolution of the orbital eccentricity of the DNSs and the corresponding time before its merger based on the parameters of the benchmark source PSR $\mathrm{B}1913+16$. The red solid, blue solid and green dashed curves represent the characteristic sensitivity of TQ, LISA, and $\mathrm{TQ}+\mathrm{LISA}$, respectively. The red, blue, and green dots represent the detectable DNSs by TQ, LISA, and $\mathrm{TQ}+\mathrm{LISA}$. The blue vertical dotted line is the chirp frequency limit for a circular orbit, above which the evolution of the frequency is detectable.

Figure 3

The rms errors of the parameters for the DNSs from one of the Monte-Carlo simulations. All sources have an SNR of the $\mathrm{TQ}+\mathrm{LISA}$ network larger than the threshold (vertical dashed lines near the left edges). The green dots correspond to relatively low-frequency systems with ${\dot{P}}_{\mathrm{b}}$ set to zero and excluded from the parameter estimation space. Overall, the parameter estimation accuracies improve as the SNR increases. There is a strong anticorrelation between the amplitude and the inclination as well as the polarization angle and the periastron phase, hence their distributions show larger scattering.

Figure 4

Same as Fig. 3, but remove the inclination $\iota$ and polarization angle $\psi$ in the two pairs of strongly correlated parameters.

Figure 5

Histograms of the numbers of the pulsar binaries jointly detectable by TQ and the radio telescopes (Parkes, FAST, SKA1-Mid, and SKA-Mid). $\mathrm{MSP}+\mathrm{NS}$ represents the DNSs that contain an MSP and a NS with no visible radio pulses.

Figure 6

Histograms as in Fig. 5, but for LISA.

Figure 7

Histograms as in Fig. 5, but for $\mathrm{TQ}+\mathrm{LISA}$.

Figure 8

Histograms of the distances for the pulsars in Sec. 4c that are simultaneously detectable by the GW detectors and the radio telescopes.

Figure 9

Histograms of the total rms errors of the TOA measurements for the pulsars in Sec. 4c that are simultaneously detectable by the GW detectors and the radio telescopes. In each panel, the pulsars from 100 Monte-Carlo simulations are combined. The red and blue histograms represent the results for the MSPs and NPs, respectively.