Detection prospects of core-collapse supernovae with supernova-optimized third-generation gravitational-wave detectors

We discuss how to optimize the third-generation gravitational-wave detector to maximize the range to detect core-collapse supernovae. Based on three-dimensional simulations for core-collapse and the corresponding gravitational-wave waveform emitted, the corresponding detection range for these waveforms is limited to within our Galaxy even in the era of third-generation detectors. The corresponding event rate is two per century. We find from the waveforms that to detect core-collapse supernovae with an event rate of one per year, the gravitational-wave detectors need a strain sensitivity of $3\times {10}^{-27}{\mathrm{Hz}}^{-1/2}$ in a frequency range from 100 to 1500 Hz. We also explore detector configurations technologically beyond the scope of third-generation detectors. We find with these improvements, the event rate for gravitational-wave observations from core-collapse supernovae is still low, but is improved to one in twenty years.

Figure 1

Spectrograms of gravitational-wave waveforms from 3D (left column) and 2D (right column) simulations of $19M_{\odot }$ progenitor. The number on the top left corner of each plot with a white background is the distance for which these GW signals have an optimal SNR of 8. For the 2D simulations, we recalculate this distance (shown on red background) by truncating the waveform at the end time of the corresponding 3D simulation. The red vertical dashed line shows the truncation time.

Figure 2

The figure shows the phenomenological waveform used as a representative for gravitational-wave emission from CCSNe. The waveform is constructed by using five sine-Gaussian bursts with different central frequencies $f_o=95$, 175, 525, 950, and 1500 Hz. The quality factor and the amplitude at each central frequency are then derived by minimizing the normalized power emitted in four different bins of frequency from 10 to 250 Hz, 250 to 500 Hz, 500 to 1000 Hz, and 1000 to 2000 Hz. The overall amplitude of the phenomenological waveform is not calculated by the fit and can be rescaled. We are interested in the broad features in frequency in different waveforms that are effectively captured in the phenomenological waveform.

Figure 3

The figure summarizes the noise budget of the supernovae-optimized detector for a gravitational-wave signal with a 45 degrees tilt with respect to the arm cavities [61]. Over the broad range of frequencies of interest, 500 to 1500 Hz, the sensitivity is limited by quantum noise. The dip in sensitivity at 4 kHz corresponds to the pole of the signal recycling cavity.

Figure 4

The figure summarizes the sky-averaged and orientation-averaged power spectral density of Cosmic Explorer and supernovae-tuned detector [67]. We see that the Cosmic Explorer has a better noise floor from 10 to 450 Hz. The supernovae-tuned detector has improved sensitivity over the range from 450 to 1600 Hz. The numerical waveforms of CCSNe suggest that a significant amount of power is emitted in this range. The optimization for CCSNe improves the range from 70 to 95 kpc for CCSNe. However, this range improvement does not add any new galaxies. Therefore, the event rate does not change with the improved sensitivity and we are limited to sources within our Galaxy.

Figure 5

The figure summarizes the distance of the 3D waveforms for different second- and third-generation gravitational-wave detectors. We see for the second-generation advanced LIGO detector that the optimal distances for the 3D numerical waveforms are limited to 10 kpc. The optimal distance is small enough such that we are not sensitive to all the galactic supernovae. All the third-generation detectors have optimal distance such that each detector is sensitive enough to detect gravitational waves from galactic CCSNe. However, as evident from the plot above, for a source at a fixed distance, the ET will have the lower SNR as compared to Cosmic Explorer. The supernovae-optimized detector provides approximately a 25% improvement in the SNR as compared to Cosmic Explorer.

Figure 6

We explore the possibility of detuning the signal recycling cavity to improve the sensitivity towards CCSNe. We find that detuning can be used to improve sensitivity in narrow bins of frequency below 400 Hz. This could, therefore, be used to study the ringdown modes of binary black-hole systems in collaboration with eLISA [62]. However, for improvements to the range of CCSNe, this technique is not useful.

Figure 7

The figure summarizes the optimal distance of the different 3D waveforms for narrow-band detectors at frequencies 500, 750, and 1000 Hz. The hollow circles denote the narrow-band detectors with a bandwidth of 250 Hz while the filled circles denote the bandwidth of 1600 Hz. The optimal distances from the broadband supernovae-optimized detector are represented as stars. We see tighter narrow banding with a bandwidth of 250 Hz degrades the performance of the detector. The wider bandwidth of 1600 Hz around the 750 Hz narrow-band detector improves the optimal distances for most of the numerical waveforms.

Figure 8

Considering a toy detector with a flat PSD of $3\times {10}^{-27}{\mathrm{Hz}}^{-1/2}$ in range 10 Hz to $f_{\mathrm{High}}$ (above) and $f_{\mathrm{low}}$ to 2 kHz (below), the figure summarizes the range with the corresponding sensitivity and numerical waveform CCSNe corresponding to their ZAMS mass. We see a broadband detector with a strain sensitivity of $3\times {10}^{-27}{\mathrm{Hz}}^{-1/2}$ from 200 Hz to 1.5 kHz is desired to achieve the ranges that would correspond to an observed event rate of one per year for gravitational waves from CCSNe.

Figure 9

The figure above summarizes the noise budgets for the hypothetical detector configurations. We see from the figure on the top that the detector’s sensitivity is limited by residual gas noise. Therefore, we reduce the residual gas pressure by a factor of 10 from CE design. The plot in the middle and bottom plots shows optimization results without changing the transmittance of the power recycling cavity and with active changes in the transmittance of the power recycling cavity, thereby changing the gain of the power recycling cavity and the finesse of the detector. We refer to the two detector configurations as hypothetical 1 and hypothetical 2, respectively.

Figure 10

The plot shows that with extreme technological upgrades to the third-generation detectors discussed in Sec. 5 the optimal distances for the CCSNe is limited to 1 Mpc. The event rate for the observation of gravitational waves from CCSNe is still low but improves to one in twenty years.