Impact of the tidal $p\text{−}g$ instability on the gravitational wave signal from coalescing binary neutron stars

Recent studies suggest that coalescing neutron stars are subject to a fluid instability involving the nonlinear coupling of the tide to $p$ modes and $g$ modes. Its influence on the inspiral dynamics and thus the gravitational wave signal is, however, uncertain because we do not know precisely how the instability saturates. Here we construct a simple, physically motivated model of the saturation that allows us to explore the instability’s impact as a function of the model parameters. We find that for plausible assumptions about the saturation, current gravitational wave detectors might miss $>70\%$ of events if only point particle waveforms are used. Parameters such as the chirp mass, component masses, and luminosity distance might also be significantly biased. On the other hand, we find that relatively simple modifications to the point particle waveform can alleviate these problems and enhance the science that emerges from the detection of binary neutron stars.

Figure 1

Time domain GW strain $h(t)$ for a $1.4M_{\odot }-1.4M_{\odot }$ nonspinning binary NS system at three different stages of the inspiral. The blue dotted curves are the PP waveforms, and the green solid curves are the waveforms with nonlinear tidal effects assuming $A=4\times {10}^{-8}$, $f_0=50\mathrm{Hz}$, and $n=0$.

Figure 2

Cumulative phase shift $\mathrm{\Delta }\varphi$ as a function of GW frequency $f$ and its dependence on the model parameters $A$, $f_0$, and $n$ (top, middle, and bottom panels, respectively).

Figure 3

Odds ratio ${\mathcal{O}}_N^{PP}$ for injected signals that include nonlinear tidal effects but are recovered using PP waveforms. The signals are injected at ${\rho }_{\mathrm{net}}\simeq 25$. The right axis shows the recovered signal-to-noise ratio ${\rho }_{\mathrm{rec}}$, computed from ${\mathcal{O}}_N^{PP}$ in the Laplace approximation as ${\mathcal{O}}_N^{PP}={{\rho }_{\mathrm{rec}}}^2/2$.

Figure 4

Surface plots of ${\mathcal{O}}_N^{PP}$ as a function of $n$ and $f_0$ at $A=6.3\times {10}^{-8}$ (top panel) and $A=4.0\times {10}^{-7}$ (bottom panel). The signals are injected at ${\rho }_{\mathrm{net}}\simeq 25$.

Figure 5

(top) Joint and marginal posterior distributions of $\mathcal{M}$ and $q$ for injected signals that include nonlinear tidal effects but are recovered using PP waveforms. (bottom) Marginal distributions for the individual component masses, which are restricted to $M_1\ge M_2$. The different curves show results for different values of $A$. We take $f_0=50\mathrm{Hz}$ and $n=0$, and inject the signals at ${\rho }_{\mathrm{net}}\simeq 25$.

Figure 6

Posterior distributions for luminosity distance $D_L$ and inclination ${\theta }_{jn}$ for injected signals that include nonlinear tidal effects but are recovered using PP waveforms. We take $f_0=50\mathrm{Hz}$, and $n=0$, and inject the signals at ${\rho }_{\mathrm{net}}\simeq 25$, corresponding to $D_L\simeq 100\mathrm{Mpc}$.

Figure 7

Odds ratio ${\mathcal{O}}_{PP}^{NL}$ for the same parameters as Fig. 3.

Figure 8

Surface plots of ${\mathcal{O}}_{PP}^{NL}$ as a function of $n$ and $f_0$ at (top panel) $A=6.3\times {10}^{-8}$ and (bottom panel) $A=4.0\times {10}^{-7}$. The signals are injected at ${\rho }_{\mathrm{net}}\simeq 25$.

Figure 9

Posterior distributions for $A$ when the injected signal does not include nonlinear tide effects.

Figure 10

Measurability of (top) $A$, (middle) $f_0$, and (bottom) $n$ as a function of $A$. Vertical dashed lines show injected values. We take $f_0=50\mathrm{Hz}$ and $n=0$, and inject the signals at ${\rho }_{\mathrm{net}}\simeq 25$.

Figure 11

Joint and marginal posterior distributions of $\mathcal{M}$ and $A$ for various values of $A$. We take $f_0=50\mathrm{Hz}$ and $n=0$, and inject the signals at ${\rho }_{\mathrm{net}}\simeq 25$.

Figure 12

Joint and marginal posterior distributions of $\mathcal{M}$, $q$, and $A$ for various values of $A$. We take $f_0=50\mathrm{Hz}$ and $n=2$, and inject the signals at ${\rho }_{\mathrm{net}}\simeq 50$.