Observing the post-merger signal of GW170817-like events with improved gravitational-wave detectors

The recent detection of a neutron star binary through gravitational waves, GW170817, has offered another source of information about the properties of cold supranuclear matter. Information from the signal emitted before the neutron stars merged has been used to study the equation of state of these bodies, however, any complementary information included in the signal emitted after the merger has been lost in the detector noise. In this paper we investigate the prospects of studying GW170817-like post-merger signals with future gravitational-wave detectors. We first compute the expected properties of the possible GW170817 post-merger signal using information from pre-merger analyses. We then quantify the required improvement in detector sensitivity in order to extract key features of the post-merger signal. We find that if we observe a signal of similar strength to GW170817 when the aLIGO detectors have been improved by $\sim 2–3$ times over their design sensitivity in the kHz regime, we will be able to extract the dominant frequency component of the post-merger. With further improvements and next-generation detectors we will also be able to extract subdominant frequencies. We conclude that post-merger signals could be brought within our reach in the coming years given planned detector upgrades, such as $\mathrm{A}+$, Voyager, and the next-generation detectors.

Figure 1

Probability density for $f_{\mathrm{peak}}$, inferred from the premerger data from GW170817. The top panel uses the first three samples sets from [64] described in Sec. 2 and the $f_{\mathrm{peak}}-{\kappa }_2^T$ EoS-insensitive relation. The bottom panel uses the parametrized EoS analysis with a maximum mass samples from [64] (third set in Sec. 2) and three EoS-insensitive relations. The bimodal structure of the posterior distributions is an outcome of the bimodality of the radius and tidal parameter posterior already observed in [64].

Figure 2

Probability density for the contact frequency, the merger frequency, and the dominant post-merger frequency of GW170817, computed from the premerger results of [64].

Figure 3

Pressure–rest-mass density (top panel) and mass-radius (bottom panel) for the 8 EoS models that we study. In the top panel we include for illustration purposes the pressure–rest-mass posterior (50% and 90% credible intervals) computed in [64]. The dashed vertical lines denote the transition points for EoS6, EoS7, and EoS8. The horizontal lines in the bottom panel denote the NS masses in our simulations.

Figure 4

Main frequency content of the simulated signals. We show $f_{\mathrm{peak}}$ as a function of the radius of a nonrotating $1.6M_{\odot }$ star for each EoS with points. The grey band shows the 90% credible interval of the expected EoS-insensitive relation between $f_{\mathrm{peak}}$ and $R_{1.6}$ as computed in [70].

Figure 5

Sensitivity curves for the detectors we include in our networks. To illustrate the high-frequency region better, the $x$ axis uses by a logarithmic scale below 1000 Hz and linear above that. Dotted lines represent the aLIGO design sensitivity improved by various constant factors.

Figure 6

Reconstruction of the post-merger signal emitted during the coalescence of an equal-mass binary with EoS5 at various network sensitivities. In each panel the top plot shows the 50% and 90% credible interval for the signal spectrum with dark and light shaded regions respectively. The bottom plot shows the posterior density for $f_{\mathrm{peak}}$ and $f_{\mathrm{sub}}$ (where applicable). The merger phase is reconstructed at $\sim 1.5\mathrm{xDS}$, the main post-merger peak is extracted at $\sim 3\mathrm{xDS}$, while hints of a subdominant peak appear at $\sim 4\mathrm{xDS}$.

Figure 7

Posterior for the number of wavelets used in the reconstruction of selected signals from Fig. 6. As the detector sensitivity improves, the reconstruction employs an increasing number of wavelets. This results in a more faithful reconstruction of the injected signal.

Figure 8

Reconstruction of the post-merger signal and posterior density for $f_{\mathrm{peak}}$ for various EoSs consistent with GW170817 that lead to a NSR and an equal-mass binary. The signals are injected in a network of two LIGO detectors at 4.0xDS and Virgo at is design sensitivity. In each panel the top plot shows the 50% and 90% credible interval for the signal spectrum with dark and light shaded regions respectively. The bottom plot shows the posterior density for $f_{\mathrm{peak}}$.

Figure 9

Reconstruction of the post-merger signal and posterior density for $f_{\mathrm{peak}}$ for various EoSs consistent with GW170817 that lead to a SNR and an unequal-mass binary. The signals are injected in a network of two LIGO detectors at 4xDS and Virgo at is design sensitivity. In each panel the top plot shows the 50% and 90% credible interval for the signal spectrum with dark and light shaded regions respectively. The bottom plot shows the posterior density for $f_{\mathrm{peak}}$.

Figure 10

Width of the 90% credible interval of the $f_{\mathrm{peak}}$ posterior for different network sensitivities for equal mass (top) and unequal mass (bottom) systems for the EoSs that result in a NS merger remnant. At low sensitivities the posterior width is equal to the prior width since the signal is not reconstructed. With increasing detector sensitivity we reconstruct the dominant post-merger spectral peak and obtain a measurement of $f_{\mathrm{peak}}$ to within dozens of Hz. The unequal mass reconstruction and $f_{\mathrm{peak}}$ measurement is worse than the equal mass one due to the substructure of the spectral peaks, as shown in Fig. 9. Next generation detectors with sensitivity above 7.0xDS will result in further improvements in the measurement of $f_{\mathrm{peak}}$, to within tens of Hz for all EoSs, see Sec. 4b.

Figure 11

Reconstruction of the post-merger signal emitted during the coalescence of an equal-mass binary with EoS5 at various network sensitivities characteristic of third-generation detectors. In each panel the top plot shows the 50% and 90% credible interval for the signal spectrum with dark and light shaded regions respectively. The bottom plot shows the posterior density for $f_{\mathrm{peak}}$ and $f_{\mathrm{sub}}$.

Figure 12

Reconstruction of the post-merger spectrum for a case where the remnant collapses into a BH. We show EoS1 and a binary with equal masses injected in two different network sensitivities. The shape of the reconstructed spectrum allows us to determine whether the remnant collapsed promptly into a BH, placing constrains on the high-density EoS.

Figure 13

Reconstruction of the post-merger signal emitted during the coalescence of an equal-mass binary with EoS2 at various network sensitivities. In each panel the top plot shows the 50% and 90% credible interval for the signal spectrum with dark and light shaded regions respectively. The bottom plot shows the posterior density for $f_{\mathrm{peak}}$, defined as the frequency of the highest peak of the post-merger spectrum. Due to the shape of the spectrum, a subdominant peak is reconstructed at lower sensitivity than the main peak.