Numerical study on the hydrodynamic instability of binary stars in the first post Newtonian approximation of general relativity

TL;DR

This study numerically investigates the hydrodynamic stability of binary stars in the first post-Newtonian approximation, revealing that relativistic effects influence the innermost stable orbit and gravitational wave frequency.

Contribution

It provides new numerical insights into the hydrodynamical stability of binary stars in 1PN gravity, identifying the stability limit and its relation to relativistic corrections.

Findings

Stability limit near energy and angular momentum minima in 1PN and Newtonian cases.

1PN effects increase the angular frequency at the innermost stable circular orbit.

Hydrodynamical instability onset correlates with minima in energy and angular momentum.

Abstract

We present numerical results on the hydrodynamic stability of coalescing binary stars in the first post Newtonian(1PN) approximation of general relativity. We pay particular attention to the hydrodynamical instability of corotating binary stars in equilibrium states assuming the stiff polytropic equation of state with the adiabatic constant $\Gamma=3$. In previous 1PN numerical studies on corotating binary stars in equilibrium states, it was found that along the sequence of binary stars as a function of the orbital separation, they have the energy and/or angular momentum minima where the secular instability sets in, and that with increase of the 1PN correction, the orbital separation at these minima decreases while the angular velocity there increases. In this paper, to know the location of the innermost stable circular orbit(ISCO), we perform numerical simulations and find where the hydrodynamical instability along the corotating sequences of binary sets in. From the numerical results, we found that the dynamical stability limit seems to exist near the energy and/or angular momentum minima not only in the Newtonian, but also in the 1PN cases. This means that the 1PN effect of general relativity increases the angular frequency of gravitational waves at the ISCO.