Spectral analysis of gravitational waves from binary neutron star merger remnants

In this work we analyze the gravitational wave signal from hypermassive neutron stars formed after the merger of binary neutron star systems, focusing on its spectral features. The gravitational wave signals are extracted from numerical relativity simulations of models already considered by De Pietri et al. [Phys. Rev. D 93, 064047 (2016)], Maione et al. [Classical Quantum Gravity 33, 175009 (2016)], and Feo et al. [Classical Quantum Gravity 34, 034001 (2017)], and allow us to study the effect of the total baryonic mass of such systems (from $2.4M_{\odot }$ to $3M_{\odot }$), the mass ratio (up to $q=0.77$), and the neutron star equation of state, in both equal and highly unequal mass binaries. We use the peaks we find in the gravitational spectrum as an independent test of already published hypotheses of their physical origin and empirical relations linking them with the characteristics of the merging neutron stars. In particular, we highlight the effects of the mass ratio, which in the past was often neglected. We also analyze the temporal evolution of the emission frequencies. Finally, we introduce a modern variant of Prony’s method to analyze the gravitational wave postmerger emission as a sum of complex exponentials, trying to overcome some drawbacks of both Fourier spectra and least-squares fitting. Overall, the spectral properties of the postmerger signal observed in our simulation are in agreement with those proposed by other groups. More specifically, we find that the analysis of Bauswein and Stergioulas [Phys. Rev. D 91, 124056 (2015)] is particularly effective for binaries with very low masses or with a small mass ratio and that the mechanical toy model of Takami et al. [Phys. Rev. D 91, 064001 (2015)] provides a comprehensive and accurate description of the early stages of the postmerger.

Figure 1

Amplitude of the spectral density of the GW signal $|\tilde{h}(f)|f^{1/2}$, computed with Eq. (10) for an optimally aligned source at 100 Mpc. The Fourier transform is taken from 8 ms before to 15 ms after the merger. Filled circles mark the instantaneous frequency at merger. The top-left panel shows equal mass models with the SLy EOS and different total masses. On the top-left, unequal mass models are shown with the same EOS and a fixed total baryonic mass of $M_T=2.8M_{\odot }$. The bottom panels show models with different EOSs, reproducing the observed PSR $\mathrm{J}0453+1559$ system (left), or with baryonic mass $M=1.4M_{\odot }$ for each star (right). The filled circles mark the instantaneous frequency at merger. The dashed black line shows the Advanced Ligo design sensitivity curve in the “zero detuning–high power” configuration [83].

Figure 2

Fourier spectrograms of all the not promptly collapsing models represented in Fig. 1. The red lines show the combination of the dominant peak frequency $f_{2i}$ reported in Table 2 (dashed blue lines) with the oscillation frequency $f_0$ reported in Table 3, namely $f_{2i}\pm f_0$.

Figure 3

Amplitude of the spectral densities for all models also presented in Fig. 1, except the promptly collapsing one. The red vertical lines correspond to $f_{2i}-f_0$ and $f_{2i}+f_0$. The vertical green solid lines correspond to the empirical relationship $f_1^T$ of Eq. (a5) and the associated frequency $f_3^T=2f_{2i}-f_1^T$. The cyan line shows the application of empirical relationship $f_{\text{spiral}}^T$ of Eq. (a6). It should be noted that although this relationship does not always match the $f_1$ peak, it seems to correspond to others (even more) subdominant peaks in the spectrum.

Figure 4

Evolution of the maximum density in the merger remnant.

Figure 5

Fourier spectra of the maximum density and minimum lapse oscillations, computed between the merger and 10 ms after it. The black vertical lines mark, in models for which the subdominant GW spectral peaks are not well explained by $m=2$ and $m=0$ mode combination, the frequency $f_{2i}-f_1$, at which a modulation in the quasiradial oscillations. In these cases $f_1$ corresponds to $f_{\text{spiral}}$, as hypothesized in [31].

Figure 6

Spectrograms constructed applying an ESPRIT Prony algorithm in an interval 2 ms wide around each point. The color code refers to the signal component amplitude (darker colors refer to higher amplitudes), normalized to the maximum amplitude for a component in all the postmerger signals for each model. The horizontal lines correspond to the $f_1$ (green lines), $f_{2i}$ (dashed-black lines), and $f_{2i}-f_0$ and $f_{2i}+f_0$ (dotted-red lines) frequencies reported in Tables 2 and 3.