Core collapse supernova gravitational wave emission for progenitors of 9.6, 15, and $25{\mathrm{M}}_{\odot }$

We present gravitational wave emission predictions based on three core collapse supernova simulations corresponding to three different progenitor masses. The masses span a large range, between 9.6 and $25M_{\odot }$, are all initially nonrotating, and are of two metallicities: zero and solar. We compute both the temporal evolution of the gravitational wave strains for both the plus and the cross polarizations, as well as their spectral decomposition and characteristic strains. The temporal evolution of our zero metallicity $9.6M_{\odot }$ progenitor model is distinct from the temporal evolution of our solar metallicity $15M_{\odot }$ progenitor model and our zero metallicity $25M_{\odot }$ progenitor model. In the former case, the high-frequency gravitational wave emission is largely confined to a brief time period $\sim 75\mathrm{ms}$ after bounce, whereas in the latter two cases high-frequency emission does not commence until $\sim 125\mathrm{ms}$ after bounce or later. The excitation mechanisms of the high-frequency emission in all three cases correspond to proto-neutron star convection and accretion onto the proto-neutron star from the convective gain layer above it, with the former playing the dominant role for most of the evolution. The low-frequency emission in all three models exhibits very similar behavior. At frequencies below $\sim 250\mathrm{Hz}$, gravitational waves are emitted by neutrino-driven convection and the standing accretion shock instability (SASI). This emission extends throughout the simulations when a gain region is present. In all three models, explosion is observed at $\sim 125$, $\sim 500$, and $\sim 250\mathrm{ms}$ after bounce in the 9.6, 15, and $25M_{\odot }$ progenitor models, respectively. At these times, the low-frequency gravitational wave emission is joined by very low-frequency emission, below $\sim 10\mathrm{Hz}$. These very low-frequency episodes are the result of explosion and begin at the above designated explosion times in each of our models. Our characteristic strains tell us that, in principle, all three gravitational wave signals would be detectable by current-generation detectors for a supernova at a distance of 10 kpc. However, our $9.6M_{\odot }$ progenitor model is a significantly weaker source of gravitational waves, with strain amplitudes approximately 5–10 times less than in our other two models. The characteristic strain for this model tells us that such a supernova would be detectable only within a much more narrow frequency range around the maximum sensitivity of today’s detectors. Finally, in our $9.6M_{\odot }$ progenitor model, we see very high-frequency gravitational radiation, extending up to $\sim 2000\mathrm{Hz}$. This feature results from the interaction of shock- and deleptonization-induced convection with perturbations introduced in the progenitor by nuclear burning during core collapse. While unique to the $9.6M_{\odot }$ progenitor model analyzed here, this very high-frequency emission may, in fact, be a generic feature of the predictions for the gravitational wave emission from all core collapse supernova models when simulations are performed with three-dimensional progenitors.

Figure 1

Boundaries of regions 1 (R1) through 5 (R5) for D9.6, D15, and D25, respectively, together with a color map of the proto-neutron star Brunt–Väisälä frequency (in Hz).

Figure 2

Gravitational wave strains for D9.6, D15, and D25, respectively.

Figure 3

Gravitational wave strains, $D{h}_{+}$ (cm), by region for D9.6, during the first 75 ms postbounce.

Figure 4

Entropy per baryon cross sections in the $xy$-plane at select times postbounce in D9.6.

Figure 5

Electron fraction cross section in the $xy$-plane at 150 ms postbounce in D9.6.

Figure 6

Gravitational wave strains, $D{h}_{+}$ (cm), by region for D9.6, D15, and D25, respectively.

Figure 7

The angle-averaged, minimum, and maximum shock trajectories as a function of postbounce time for each of our three models.

Figure 8

Slices of electron fraction at 125, 200, and 700 ms after bounce, for D15.

Figure 9

Slices of electron fraction at 200 and 450 ms after bounce, for D25.

Figure 10

Slices of entropy at 700 ms after bounce, for two viewing angles and D15.

Figure 11

Slices of entropy at 450 ms after bounce, for two viewing angles and D25.

Figure 12

Heat maps for regions 1 through 5 for D9.6. The plots are of the quantity ${\tilde{h}}_{+}(\tau ,f)$ as a function of postbounce time window $\tau$ and frequency. The color map gives the value (in cm s) of $\mathrm{l}\mathrm{n}(|\mathrm{D}{\tilde{h}}_{+}(\tau ,f)|)$ for a particular window and frequency. Note, we do not normalize our results to the length of the array $N=\frac{\mathrm{Square\; Window\; Width}}{\mathrm{Sampling\; Frequency}}$, which for D9.6 is 66.

Figure 13

Heat maps for regions 1 through 5 for D15. As in Fig. 12, the color map gives the value (in cm s) of $\mathrm{l}\mathrm{n}(|\mathrm{D}{\tilde{h}}_{+}(\tau ,f)|)$ for a particular window and frequency. Note, we do not normalize our results to the length of the array $N=\frac{\mathrm{Square\; Window\; Width}}{\mathrm{Sampling\; Frequency}}$, which for D15 is 41.

Figure 14

Heat maps for regions 1 through 5 for D25. As in Fig. 12, the color map gives the value (in cm s) of $\mathrm{l}\mathrm{n}(|\mathrm{D}{\tilde{h}}_{+}(\tau ,f)|)$ for a particular window and frequency. Note, we do not normalize our results to the length of the array $N=\frac{\mathrm{Square\; Window\; Width}}{\mathrm{Sampling\; Frequency}}$, which for D25 is 66.

Figure 15

Peak frequency, determined by Eq. (27) along three density contours, as a function of postbounce time for D9.6, D15, and D25, respectively, superimposed on our heat maps for each of the three cases.

Figure 16

Gravitational wave luminosity and total energy emitted for all three models.

Figure 17

Characteristic strains for the D9.6, D15, and D25, respectively.

Figure 18

Time evolution of the center-of-mass of the gain region in each of our three models.

Figure 19

Region 5 gravitational wave spectra prior to explosion.

Figure 20

Region 5 gravitational wave spectra after explosion.

Figure 21

Comparisons of the gravitational wave strains by region for D15, computed using the three different methods for determining $A_{2m}$, outlined in the text.

Figure 22

Comparisons of the gravitational wave strains by region for D25, computed using the three different methods for determining $A_{2m}$, outlined in the text.

Figure 23

Comparisons of the gravitational wave strains by region for D9.6, computed using the three different methods for determining $A_{2m}$, outlined in the text.

Figure 24

Comparison of the gravitational wave strains from our C15-3D and D15-3D models.