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

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 $\times {10}^{-22}$, across frequencies between 0.66 and 5.87 $\times {10}^{-4}$ 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 $\mu$s/yr for the binary pulsar population. We derive common envelope efficiency parameters (${\alpha }_{CE}$) for representative progenitor scenarios within our sample, finding values between 0.63 and 1.16, with notable sensitivity to the binding energy parameter $\lambda$. 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