Neutron star tidal disruption in mixed binaries: The imprint of the equation of state

We study the tidal disruption of neutron stars in black hole-neutron star coalescing binaries. We calculate the critical orbital separation at which the star is disrupted by the black hole tidal field for several equations of state describing the matter inside the neutron star, and for a large set of the binary parameters. When the disruption occurs before the star reaches the innermost stable circular orbit, the gravitational wave (GW) signal emitted by the system is expected to exhibit a cutoff frequency ${\nu }_{\mathrm{GW}\mathrm{tide}}$, which is a distinctive feature of the waveform. We evaluate ${\nu }_{\mathrm{GW}\mathrm{tide}}$ and show that, if this frequency will be found in a detected gravitational wave, it will allow one to determine the neutron star radius with an error of a few percent, providing valuable information on the behavior of matter in the stellar core.

Figure 1

The neutron star mass is plotted versus the stellar radius for the EOSs used in this paper.

Figure 2

The NS radius is plotted versus ${\nu }_{\mathrm{GW}\mathrm{tide}}$ for any possible combination of the following data: $M_{\mathrm{NS}}=1.4\pm 0.02M_{\odot }$, $a/M_{\mathrm{BH}}=0.5\pm 0.05$, $q=5\pm 0.15$, and for the EOS BPAL12. The horizontal and vertical spread of the data identify the error bars (red cross).

Figure 3

$R_{\mathrm{NS}}$ is plotted versus ${\nu }_{\mathrm{GW}\mathrm{tide}}$, for a black hole with angular momentum $a/M_{\mathrm{BH}}=0.9\pm 0.09$ and a neutron star with mass $M_{\mathrm{NS}}=1.4M_{\odot }\pm \Delta M_{\mathrm{NS}}$ (upper panel) and $M_{\mathrm{NS}}=1.2M_{\odot }\pm \Delta M_{\mathrm{NS}}$ (lower panel). The data are plotted for different values of the mass ratio $q\pm \Delta q$ and for the EOSs considered in Sec. 4. The values of $\Delta M_{\mathrm{NS}}$ and $\Delta q$ are given in Table . Black continuous lines are the parabolic fits of the data corresponding to each EOS at fixed $q$.

Figure 4

The tidal disruption radius, $r_{\mathrm{tide}}$, is plotted versus ${\nu }_{\mathrm{GW}\mathrm{tide}}$ for the EOSs BGN1H1 (top curve) and BPAL12 (middle curve), assuming $M_{\mathrm{NS}}=1.4M_{\odot }$ and $a/M_{\mathrm{BH}}=0.9$. The numbers label points corresponding to different values of $q$. For the same values of $q$ we also plot the value of $r_{\mathrm{ISCO}}$ (bottom curve) versus the corresponding frequency ${\nu }_{\mathrm{GW}\mathrm{ISCO}}$ (see text). The dashed part of the curve for BPAL12 refers to values of $q$ for which the star is not disrupted before the ISCO, i.e., for which $r_{\mathrm{tide}}<r_{\mathrm{ISCO}}$.

Figure 5

The same plot as in Fig. 3, but for $M_{\mathrm{NS}}=1.6M_{\odot }\pm \Delta M_{\mathrm{NS}}$.

Figure 6

The same plot as in Fig. 3 for a black hole with angular momentum $a/M_{\mathrm{BH}}=0.5\pm 0.05$. The data for $q=10$ and 15 are missing because no disruption occurs for the considered EOSs.

Figure 7

The plot of $R_{\mathrm{NS}}$ versus ${\nu }_{\mathrm{GW}\mathrm{tide}}$ is done for the same NS mass, $M_{\mathrm{NS}}=1.4M_{\odot }\pm \Delta M_{\mathrm{NS}}$, the same mass ratio $q=3\pm \Delta q$, and two different values of the angular momentum, $a=0.9\pm 10\%$ and $a=0.5\pm 10\%$.

Figure 8

The data of Fig. 3 are compared to the fit given in Eq. (40) [12].

Figure 9

$R_{\mathrm{NS}}$ versus ${\nu }_{\mathrm{GW}\mathrm{tide}}$ is plotted for $M_{\mathrm{NS}}=1.4M_{\odot }\pm M_{\mathrm{NS}}$, $q=5\pm \Delta q$, and $a/M_{\mathrm{BH}}=0.9\pm 0.09$. The black continuous lines are the parabolic fits of the extreme points of the horizontal error bar for each EOS. The vertical dashed line corresponds to the supposed detected value of ${\nu }_{\mathrm{GW}\mathrm{tide}}$. The two horizontal dashed lines identify the uncertainty on the evaluation of $R_{\mathrm{NS}}$.