Gravitational-wave-driven tidal secular instability in neutron star binaries

We report the existence of a gravitational-wave-driven secular instability in neutron star binaries, acting on the equilibrium tide. The instability is similar to the classic Chandrasekhar-Friedman-Schutz instability of normal modes and is active when the spin of the primary star exceeds the orbital frequency of the companion. Modeling the neutron star as a Newtonian $n=1$ polytrope, we calculate the instability timescale, which can be as low as a few seconds at small orbital separations but still larger than the inspiral timescale. The implications for orbital and spin evolution are also briefly explored, where it is found that the instability slows down the inspiral and decreases the stellar spin.

Figure 1

Instability growth time ${\tau }_{\mathrm{GW}}$ (in sec) as a function of the angular velocity $\mathrm{\Omega }$ of the primary (normalized to the Kepler limit ${\mathrm{\Omega }}_K$; $x$ axis) and the orbital distance $D$ (normalized to the primary’s radius $R$; $y$ axis). The primary is a neutron star described by an $n=1$ polytropic equation of state, with $M=1.4M_{\odot }$ and $R=10\mathrm{km}$, orbited by an equal mass companion $(M^{\prime }=M)$. The inspiral timescale ${\tau }_{\mathrm{ins}}$ is also shown, as a function of the orbital distance, for comparison.

Figure 2

Change in the primary’s spin $\mathrm{\Omega }$, relative to its initial value ${\mathrm{\Omega }}_{\mathrm{in}}$ (left), and second-order contribution to the number of orbital cycles $\mathrm{\Delta }{N}_{\mathrm{orb}}^{(2)}$ (right), plotted against the orbital separation $D$ (normalized to the primary’s radius $R$). The primary is a neutron star described by an $n=1$ polytropic equation of state, with $M=1.4M_{\odot }$ and $R=10\mathrm{km}$, orbited by an equal mass companion $(M^{\prime }=M)$. The evolution is started at an orbital separation $D_{\mathrm{in}}=100R$ and the angular velocity of the primary is set to ${\mathrm{\Omega }}_{\mathrm{in}}=0.3{\mathrm{\Omega }}_K$, where ${\mathrm{\Omega }}_K$ is the Kepler limit (for spherical stars). The binary merger is taken to occur at $3R$.