Characterizing a supernova’s standing accretion shock instability with neutrinos and gravitational waves

We perform a novel multimessenger analysis for the identification and parameter estimation of the standing accretion shock instability (SASI) in a core-collapse supernova with neutrino and gravitational-wave (GW) signals. In the neutrino channel, this method performs a likelihood ratio test for the presence of SASI in the frequency domain. For gravitational-wave signals we process an event with a modified constrained likelihood method. Using simulated supernova signals, the properties of the Hyper-Kamiokande neutrino detector, and O3 LIGO interferometric data, we produce the two-dimensional probability density function (PDF) of the SASI activity indicator and calculate the probability of detection $P_{\mathrm{D}}$ as well as the false identification probability $P_{\mathrm{FI}}$. We discuss the probability to establish the presence of the SASI as a function of the source distance in each observational channel, as well as jointly. Compared to a single-messenger approach, the joint analysis results in a $P_{\mathrm{D}}$ (at $P_{\mathrm{FI}}=0.1$) of SASI activities that is larger by up to $\approx 40\%$ for a distance to the supernova of 5 kpc. We also discuss how accurately the frequency and duration of the SASI activity can be estimated in each channel separately. Our methodology is suitable for implementation in a realistic data analysis and a multimessenger setting.

Figure 1

Neutrino event rates with and without SASI-induced imprints predicted by KKHT [33] at Hyper-K for a supernova at distance $D=10\mathrm{kpc}$. The curve without SASI is obtained by applying a low-pass filter on the original signal. In the left (right) panel the rates are shown without (with) the realistic Poisson fluctuations—i.e., the neutrino shot noise—which are driven by the signal itself.

Figure 2

The cross and plus gravitational-wave polarizations of the KKHT model [33] are plotted versus time (black solid). We also plot the same quantities where a time-frequency filter is applied to remove the GW SASI component according to the discussion in Sec. 2b (blue dashed).

Figure 3

S15 model spectrogram for the plus polarization, with SASI (top) and without SASI (bottom). In the top spectrogram, the blue line indicates where the $g$-mode is located (with the red dot indicating the time that the $g$-mode is around 200 Hz). In green is the allowed time-frequency SASI region (to start after 50 ms of the $g$-mode initial time) and below the 200 Hz line. In yellow we indicate the temporal interval where the actual SASI oscillations (see the location of the SASI in the left plot of Fig. 1 and bottom plot of Fig. 2) are removed, after the yellow vertical line at 156.25 ms.

Figure 4

Flowchart of the multimessenger SASI meter developed in this work. Due to the absence of current detections, we characterize the pipeline with random realizations of reconstructed $\nu$ and GW signals for the test example. For the $\nu$, this means adding Poissonian fluctuations on signals that have a SASI as well as signals where the SASI was removed. In the case of future detections, we can achieve the same result by taking a smoothed-out version of the detected neutrino luminosities as the no-SASI $\nu$ signature, and randomize it with Poissonian fluctuations to identify the threshold for the desired $P_{\mathrm{FI}}$ used as a reference in this work for the single-channel or multiple-channel identification mode ($P_{\mathrm{FI}}=0.1$). For the GW channel, in the test example used in this paper, we inject the GWs with and without SASI in real interferometric noise. In a realistic scenario, the no-SASI injections can be used to tune the threshold on the identification metric for the desired single or multimessenger $P_{\mathrm{FI}}$ ($P_{\mathrm{FI}}=0.1$). The signals in the $\nu$ and GW channels with SASI are used in this paper to characterize the performance of the GW-$\nu$ SASI meter.

Figure 5

Top row: examples of distributions of the test statistics $\ln (\widehat{\mathcal{L}})$ obtained from Monte Carlo–generated neutrino data at Hyper-K with the starting time $t_0=150\mathrm{ms}$ and duration $\tau =50\mathrm{ms}$. The blue histograms correspond to the one from a simulation where the SASI component has been previously filtered out and the red histograms correspond to the one from a simulation where the SASI component has been kept. Here, $\ln (\widehat{\mathcal{L}})$ is the rescaled logarithmic likelihood ratio with its maximum in the SASI case being 1. The three columns correspond to distances $D=1$, 5, 10 kpc to the supernova. Bottom row: corresponding receiver operating curves describing the identification probability versus the false identification probability.

Figure 6

Histograms of the estimated SASI frequency from neutrino signatures. As expected, the variance decreases for closer distances since the amplitude of the Poissonian fluctuations decreases with closer distances, while the amplitude of the SASI fluctuations with respect to the DC component is distance independent.

Figure 7

Left: example of a standard cWB scalogram for a GW event. Each wavelet component involved in the reconstructed event is represented with a rectangle of sides equal to the frequency and temporal resolution. The darker blue regions highlight the reconstructed SASI and $g$-mode features. The duration resolution of tens of milliseconds of some of the wavelets below 200 Hz indicates that some impact on the duration reconstruction is to be expected. Right: the same event is displayed with a single dot for each wavelet, with the coordinates representing the central time and frequency of the wavelets. While the color bar to the right corresponds to the single-pixel likelihood, the color bar to the left (not used in the calculations of this paper) corresponds to the likelihood for a fixed-size time-frequency region. For each wavelet, we use/define different parameters for the ${\chi }^2$ localization of the $g$-mode frequency evolution (red) with slope ($s=\frac{\mathrm{\Delta }f}{\mathrm{\Delta }t}$): the wavelet central time ($t_c$), wavelet central frequency ($f_c$), wavelet likelihood ($\rho$), and density of wavelets ($\mathrm{\Xi }$) in a given time-frequency box. For details on these parameters and their usage, see Appendix pp2.

Figure 8

Top row: examples of distributions of the test-statistics $\widehat{\rho }$ obtained from simulated GW data, for distances $D=1$, 5, 10 kpc to the supernova. Here, $\widehat{\rho }$ is the rescaled logarithmic likelihood ratio of GW signals with its maximum in the SASI case being 1. Bottom row: corresponding receiver operating curves.

Figure 9

Probability density distribution of the SASI central frequency (upper) and SASI duration (lower) estimations based on GW signals.

Figure 10

Two-dimensional probability density distribution of $\{\ln ({\widehat{\mathcal{L}}}_{\nu }),{\widehat{\rho }}_{\mathrm{GW}}\}$ at 1 kpc (upper panels), 5 kpc (middle panels), and 10 kpc (lower panels), where the distributions in the left (right) panels are based on neutrino and GW signals without (with) SASI activities. Here, $\ln (\widehat{\mathcal{L}})$ is the rescaled logarithmic likelihood ratio with its maximum in the SASI case being 1, and $\widehat{\rho }$ is the rescaled logarithmic likelihood ratio of GW signals with its maximum in the SASI case being 1. In the upper left panel, the colored curves illustrate the different integration thresholds that can be used to identify the presence of the SASI, as discussed in Sec. 4a. Specifically, the region inside the green dashed rectangle is for “Logical and” case, and the region outside the blue solid rectangle is for “Logical or” case. The region outside the red solid triangle corresponds to the “$x+y=\text{const}$” case, and the region to the upper right of the orange dashed curve represents the “$x\times y=\text{const}$” case.

Figure 11

Combined receiver operating curve at 1 kpc (upper left), 5 kpc (upper right), and 10 kpc (lower) based on Fig. 10, using different selection thresholds.

Figure 12

Probability of detection $P_{\mathrm{D}}$ of SASI at a false alarm rate $P_{\mathrm{FI}}=10\%$. The $P_{\mathrm{D}}$’s are evaluated in neutrino time series with different durations and starting times. The upper left, upper right, and lower panels are for $P_{\mathrm{D}}$’s with CCSNe distances of 10, 5, and 1 kpc.

Figure 13

Averaged optimal frequency (left) and amplitude (right) evaluated in neutrino time series with different durations and starting times. The corresponding distance to the CCSNe is 1 kpc.

Figure 14

Optimal choices of bpp (left) and the $CC$ threshold (right) at 5 Kpc in terms of maximizing the number of triggers produced by the cWB algorithm, while other cWB parameters remain unchanged. The cWB algorithm arranges a number of triggers into job files that are executed individually. Here, the analysis is carried out for ten such jobs for each bpp value and 50 jobs for each $CC$ value shown in the graph.

Figure 15

$g$-mode slope histograms for $D=1$, 5, 10 Kpc. The center solid vertical line identifies the slope of the $g$-mode evolution estimated from the spectrogram in Fig. 3, which is $3000{\mathrm{s}}^{-2}$ (which is the $g$-mode slope of our illustrative example, estimated visually from Fig. 3). The left and right dashed vertical lines represent the range of slopes for slowly rotating progenitors observed in the literature (derived from Refs. [35, 51]), which are 1100 and $4000{\mathrm{s}}^{-2}$, respectively. The variance of the distribution shrinks with closer distances.