Probing Crust Meltdown in Inspiraling Binary Neutron Stars

Thanks to recent measurements of tidal deformability and radius, the nuclear equation of state and structure of neutron stars are now better understood. Here, we show that through resonant tidal excitations in a binary inspiral, the neutron crust generically undergoes elastic-to-plastic transition, which leads to crust heating and eventually meltdown. This process could induce $\sim \mathcal{O}(0.1)$ phase shift in the gravitational waveform. Detecting the timing and induced phase shift of this crust meltdown will shed light on the crust structure, such as the core-crust transition density, which previous measurements are insensitive to. A direct search using GW170817 data has not found this signal, possibly due to limited signal-to-noise ratio. We predict that such a signal may be observable with Advanced LIGO Plus and more likely with third-generation gravitational-wave detectors such as the Einstein Telescope and Cosmic Explorer.

Figure 1

Left three panels are the heat maps $e_i/e_{\mathrm{melt}}$ of the neutron star crust (within a $1.3M_{\odot }+1.3M_{\odot }$ binary) at binary separations $D=12.0/11.6/11.4R_{\star }$, respectively. In the rightmost panel, dashed lines denote the evolution of the $i$-mode frequency $f_0$ and the gravitational wave (GW) frequency $f_{\mathrm{GW}}$, and solid lines denote the evolution of mode amplitude $a_m$ with $m=\pm 2$, 0.

Figure 2

The crust melting induced phase change $\delta {\varphi }_a$ in GWs of a BNS merger with each star of $M_{\star }=1.3M_{\odot }$ and $R_{\star }=12.5/11.3/11.7/12.7\mathrm{km}$ for the EOS SkI6/APR4/SLy4/MPA1, respectively, which are not ruled out by the LIGO tidal measurement with GW170817. Note that the core-crust transition density $n_{b,\mathrm{cc}}$ is subject to a large uncertainty in each EOS instead of being an accurately predicted value, so we take the transition density as a free parameter.

Figure 3

Posterior distribution of chirp mass $\mathcal{M}$, phase shift $\delta {\varphi }_a$ and melting frequency $f_a$ obtained with PyCBC, where the prior for $f_a$ is set to be [30, 300] Hz and [0, 2] for $\delta {\varphi }_a$. Left plot: the search using data from GW170817. Right plot: a search obtained assuming LIGO $\mathrm{A}+$ sensitivity and an mode resonance injection at $f_a=60\mathrm{Hz}$ and $\delta {\varphi }_a=0.3$.