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

Binary pulsars emit both radio waves and gravitational waves (GWs), serving as valuable tools for testing theories of gravity. The Double Pulsar, PSR J0737-3039A/B, is a prime example. Current radio surveys are limited in detecting systems with orbital periods shorter than an hour due to Doppler smearing effects. However, upcoming space-borne GW detectors like LISA, TianQin (TQ), and Taiji, are expected to detect systems with much shorter orbital periods. This motivates the investigation of radio follow-up observations of short-period DNSs detected via GWs. To date, radio surveys have discovered 20 DNS systems, the shortest having an orbital period of 1.88 hours. The challenges of directly detecting DNSs via radio surveys, especially those with orbital periods in the 3-60 minute range, are significant. These short-period systems emit GWs in the mHz band, detectable by space-borne GW detectors. The merger rate density inferred from LIGO and Virgo observations of DNS merger events suggests a substantial number of such systems in our Galaxy, estimated to be around 2100 with orbital periods less than an hour. Previous studies have focused on GW detection alone; this work explores a multi-messenger approach, combining GW and radio observations to overcome the limitations of each method and improve our understanding of DNS populations and neutron star properties.

Several works have explored the number of DNSs detectable by LISA, employing various merger rates and population synthesis models. These studies, however, primarily focus on GW detection. Kyutoku et al. proposed a multi-messenger strategy using LISA and the Square Kilometre Array (SKA) to detect Galactic pulsar-NS binaries with orbital periods less than 10 minutes. Their study highlighted the potential of using LISA's accurate sky position and orbital parameter measurements to significantly reduce the computational burden of radio searches. Thrane et al. further explored the potential of LISA+SKA multi-messenger observations to constrain the equation of state of neutron stars by using the Lense-Thirring precession effect. These previous studies laid the groundwork for this research, which aims to extend the analysis to include a broader range of GW detectors and radio telescopes, providing a more comprehensive assessment of the prospects for multi-messenger detection of DNSs.

This study employs a multi-stage simulation approach. First, the authors simulate a Galactic DNS population using a model that considers the merger rate from recent LIGO results and a Galactic disk model to determine the number and location of DNSs merging within 10 Myr. Component masses are assumed to be m1 = m2 = 1.4 M⊙. The evolution of orbital parameters (semi-major axis and eccentricity) is calculated using equations that account for gravitational wave emission. Second, the detectability of the simulated DNSs by the GW detectors (TQ, LISA, and TQ+LISA) is assessed based on their inspiraling waveforms and the noise characteristics of the detectors. The Fisher information matrix (FIM) is used to estimate parameter estimation accuracies (orbital period, sky location, eccentricity, and orbital period derivative). The waveforms incorporate effects of eccentricity, orbital frequency derivative, and Doppler modulation. The third step focuses on the radio follow-up. The authors simulate the radio pulse emission from possible pulsars in the detectable DNSs, accounting for pulsar beam geometry, spin period, and luminosity distributions. The number of detectable pulsars is estimated for four different radio telescopes based on SNR thresholds considering radiometer noise and phase jitter noise. The overall methodology combines astrophysical modeling with GW signal analysis and radio detection simulations to provide a comprehensive assessment of the prospects for multi-messenger observation of DNSs.

The simulation of the Galactic DNS population within 10 Myr yields approximately 2100 systems. The number of detectable DNSs by TQ, LISA, and TQ+LISA networks is estimated at 217, 368, and 429, respectively, using a SNR threshold of 7. For the TQ+LISA network, the parameter estimation accuracies for detectable sources are: ΔPb/Pb ≈ 10−6, ΔΩ ≈ 100 deg2, Δe/e ≈ 0.3, and ΔṖb/Ṗb ≈ 0.02. These accuracies are found to follow power-law functions of the signal-to-noise ratio (SNR). For radio follow-up, using the DNSs detectable by TQ+LISA, the average number of detectable DNSs with observable pulsars varies depending on the telescope: 8 for Parkes, 10 for FAST, 43 for SKA1, and 87 for SKA. The average distances of these GW-detectable pulsar binaries range from 1 to 7 kpc. Considering radiometer noise and phase jitter noise, the timing accuracy of detectable pulsars ranges from 70 ns to 100 µs (with the most probable values around 100 µs for MSPs and 130 µs for NPs). Strong correlations between parameters like amplitude and inclination angle, as well as polarization angle and periastron phase, are observed; removing one of the correlated parameters from the FIM substantially improves the estimation accuracy of the other. Power-law fits are provided for the parameter estimation accuracy in the case of excluding the frequency derivative. For sources where Ṗb is included in the FIM, the relative error of the eccentricity shows larger dispersion at higher SNRs.

The findings demonstrate the significant potential of multi-messenger observations to detect and characterize short-period DNSs. The high number of detectable sources using space-borne GW detectors coupled with the ability of sensitive radio telescopes to detect pulsars in these systems provides a promising avenue for studying DNS formation and evolution. The precise parameter estimation achievable through the combined observations holds the key to understanding neutron star equation of state with higher accuracy than GW or radio observations alone. The estimated timing accuracies suggest the feasibility of conducting high-precision timing measurements, which can further probe fundamental physics in the strongly relativistic regime. The detection of these systems bridges the observational gap between coalescing DNSs (observed by ground-based detectors) and long-period DNSs (observed by radio telescopes), providing crucial information about the entire DNS population. The ability to measure Ṗb significantly enhances the accuracy of chirp mass and distance estimations.

This work demonstrates the synergistic potential of combining space-borne GW detectors and radio telescopes for multi-messenger observations of Galactic DNSs. The high number of potentially detectable sources and the achievable precision in parameter estimation highlight the rich scientific opportunities available. Future studies should consider more detailed modeling of pulsar emission and incorporate other types of electromagnetic observations to further refine the predictions and unlock the full potential of this multi-messenger approach.

The simulations rely on several assumptions. The choice of orbital parameters for the benchmark source (PSR B1913+16) influences the eccentricity distribution of simulated DNSs. The assumed spin period distribution for MSPs in DNSs is based on limited data. The luminosity distribution is assumed to be similar for both NPs and MSPs, although the luminosity of pulsars in tight binaries might be dimmer over time. The analysis focuses primarily on SKA1-Mid and SKA-Mid, neglecting the potential contribution of SKA1-Low and SKA-Low which may improve sensitivity, particularly for steep spectrum pulsars. Solar wind effects on pulsars close to the ecliptic plane are not directly accounted for.