Gravitational Wave Strain and Orbital Dynamics of Binary Pulsars from LIGO-Virgo to LISA

TL;DR

This work addresses how binary pulsars emit gravitational waves detectable across multiple bands, from ground-based detectors to LISA. It combines post-Newtonian calculations, common envelope evolution, and simple DNS population estimates to derive GW strain, PN effects, merger times, and merger rates, and then assesses detectability with LISA. Key findings include characteristic GW strains from $3.0\times10^{-22}$ to $73\times10^{-22}$, periastron advances of $1.6$–$80.5$ degrees per year, orbital-decay rates of $-5$ to $-176$ microseconds per year, CE efficiencies $\alpha_{CE}$ between $0.63$ and $1.16$, and a Galactic DNS merger rate around $23\,\mathrm{Myr}^{-1}$ corresponding to a volumetric rate near $230\,\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$. The study demonstrates the potential of multi-band GW observations to constrain neutron star physics and common envelope evolution, inform merger time predictions, and guide future observational strategies. While individual known Galactic binaries may be challenging for LISA to detect as continuous sources, their collective contribution shapes the Galactic GW background and informs multi-messenger inferences about binary evolution.

Abstract

We summarize the current state of the art and calculate gravitational wave strain amplitudes for known binary pulsars, using data from current ground-based detectors (LIGO-Virgo-KAGRA) and the upcoming space-based missions (LISA). We present detailed calculations of the characteristic gravitational wave strain values, ranging from 3.0 to 73 $\times10^{-22}$, across frequencies between 0.66 and 5.87 $\times10^{-4}$ Hz. Our post-Newtonian approximation analysis yields predicted periastron advance rates from 1.6 to 80.5 deg/yr and orbital period decay rates between -5 and -176 $μ$s/yr for the binary pulsar population. We derive common envelope efficiency parameters ($α_{CE}$) for representative progenitor scenarios within our sample, finding values between 0.63 and 1.16, with notable sensitivity to the binding energy parameter $λ$. Binary neutron star merger rates are estimated at $22.77^{+6.83}_{-6.83}$ Myr$^{-1}$ for the Milky Way, corresponding to a volumetric rate of $227.71^{+68.31}_{-68.31}$ Gpc$^{-3}$ yr$^{-1}$, consistent with the latest LIGO-Virgo-KAGRA observational constraints. Our results illustrate how multi-band gravitational wave observations, from LIGO/Virgo to LISA, can contribute to precise measurements of binary pulsar strain and orbital evolution histories, improving merger time predictions and constraining neutron star physics and common envelope processes

Figures (5)

• Figure 1: Flow-Chart illustrating the main evolutionary channels and processes considered in binary pulsar formation and their connection to gravitational wave observations. The chart outlines pathways involving common envelope evolution, stable mass transfer, and no interaction, leading to different types of binary systems detectable by LISA or LVK, or resulting in mergers.
• Figure 2: Gravitational wave characteristic strain amplitude as a function of frequency for binary pulsar systems (colored circles) in relation to representative sensitivity curves of Advanced LIGO (LVK, O4 sensitivity) and LISA (4-year observation, SNR=7 threshold). The plot shows that while these systems are prime targets for pulsar timing arrays (not shown), their continuous GW signals fall mostly within the LISA band but below current LVK sensitivity and generally below the nominal LISA sensitivity for individual detection.
• Figure 3: Orbital eccentricity (e) versus merger time ($T_{merge}$) for the selected binary pulsar systems. The plot highlights the inverse relationship, where higher eccentricity generally leads to shorter merger times due to enhanced GW emission, J1946+2052 is the fastest merging DNS in this sample.
• Figure 4: Periastron advance rate as a function of total mass, for the selected binary pulsar systems. The plot shows the expected relativistic precession rate, which is a key test of General Relativity measurable through pulsar timing.
• Figure 5: Calculated Signal-to-Noise Ratios (SNRs) for selected binary pulsar systems observable by LISA (assuming 4 years observation). The plot compares the expected SNRs (colored circles) against the LISA sensitivity threshold (dashed line, typically SNR= 7-8).