Modeling gravitational waves from exotic compact objects

Exotic compact objects can be difficult to distinguish from black holes in the inspiral phase of the binaries observed by gravitational-wave detectors, but significant differences may be present in the merger and post-merger signal. We introduce a toy model capturing the salient features of binaries of exotic compact objects with compactness below 0.2, which do not collapse promptly following the merger. We use it to assess their detectability with current and future detectors, and whether they can be distinguished from black hole binaries. We find that the Einstein Telescope (LISA) could observe exotic binaries with total mass $\mathcal{O}({10}^2)M_{\odot }$ (${10}^4–{10}^6{M}_{\odot }$), and potentially distinguish them from black hole binaries, throughout the observable Universe, as compared to $z\lesssim 1$ for Advanced LIGO. Moreover, we show that using standard black hole templates for detection could lead to a loss of up to 60% in the signal-to-noise ratio, greatly reducing our chances of observing these signals. Finally, we estimate that if the loudest events in the $\mathrm{O}1/\mathrm{O}2$ catalog released by the LIGO/Virgo collaboration were ECO binaries as the ones considered in this paper, they would have left a post-merger signal detectable with model-agnostic searches, making this hypothesis unlikely.

Figure 1

Schematic representation of our knowledge of the GW signal emitted by an ECO binary: within GR we have a good idea of the qualitative features of the inspiral and post-merger, but the connection between these two regimes is still largely unknown. We expect that the merger leads to the formation of either a BH or an (excited) object of the same nature as the initial ECOs, possibly rotating. The remnant relaxes through emission of GWs, which are related to its fundamental properties and/or the dynamics of the merger.

Figure 2

Numerical simulations of BNS waveforms for different EoSs. For the 2B EoS, the system promptly collapses to a BH after contact. For the ALF2 and the DD2 EoS, a hypermassive NS is formed following contact. In the former case the hypermassive NS ends up collapsing to a BH after $\simeq 7\mathrm{ms}$, whereas in the latter case it does not collapse for the duration of the simulation, seemingly relaxing to a stable NS.

Figure 3

Amplitude-frequency decomposition of the GW signal emitted by a BNS following the ALF2 EoS. The signal is characterized by the oscillations in amplitude (blue) and frequency (red) in the post-contact stage.

Figure 4

Illustration of the setup we use to model the dynamics of the post-contact stage, adapted from [87]. The hypermassive ECO is treated as a disk containing two point particles that interact gravitationally, but also through an effective spring. The latter mimics the effect of the restoring forces, making the cores bounce.

Figure 5

Evolution of the effective potential and the energy for an $RS$ system. As the evolution proceeds, the energy reaches the minimum of the potential, leading to a “circularization” of the orbit.

Figure 6

Waveform for an $RS$ system with $m_0=30M_{\odot }$ and $C_0=0.17$. We show the real part of the 22-mode and its decomposition into amplitude and frequency. The black dashed lines indicate the start of the post-contact stage.

Figure 7

The same as Fig. 6, but for an $RBH$ system with $m_0=30M_{\odot }$ and $C_0=0.17$ ($C_0=0.2$) in blue (red). After contact, the collapse to a BH happens faster for more compact systems.

Figure 8

Real part of the 22-mode for an $NRS$ system with $m_0=30M_{\odot }$ and $C_0=0.17$.

Figure 9

Amplitude of the frequency-domain signal of the three types of ECO binaries, for different values of the initial compactness. The vertical dashed lines indicate the corresponding value of $2f_c$ for each $C_0$.

Figure 10

Lower panel: total and post-contact SNR in LISA as a function of the detector-frame mass, for the three types of ECO binaries. Lower panel: ratio of post-contact to total SNR. We take $C_0=0.17$ and place the sources at $z=10$. As the total mass increases, LISA becomes more sensitive to the post-contact stage and less sensitive to the inspiral, and thence $r_{\mathrm{pc}}$ approaches unity.

Figure 11

Maximum redshift up to which we could observe and potentially distinguish different types of ECO binaries from BBHs, as a function of the total mass in the source frame. The threshold for observation and distinguishability is set at a total SNR of 8 and at a post-contact SNR of 4, respectively. The maximum redshift typically increases with $C_0$ and, among ECO binaries, is largest for $NRS$ systems.

Figure 12

FF as a function of the total mass in the detector frame, for the different types of ECO binaries (one on each panel) and different values of $C_0$ (distinguished by the color) in aLIGO (full lines) and ET (dashed lines). Up to 60% of the SNR could be lost if ECO binaries are detected with BBH templates, potentially jeopardizing detection of weaker signals.

Figure 13

Evolution of the distance of the cores to the center of mass (half the distance between the cores) and the orbital angular velocity for an $RBH$ (upper panel) and an $RS$ (lower panel) system.