Overview of the Supernova DAQ

The baseline behavior of SNDAQ is to search for a significant deviation in the collective DOM hit rates from the expected rate of background-only hits. SNDAQ compares the instantaneous hit rate across the detector to the collective average DOM rate computed with a 10-minute sliding window.

IceCube Hit Rate

The individual hit rates of the DOMs,

\[R_i, \qquad i=1, \ldots, N_\mathrm{DOM},\]

are measured online with 2 ms resolution. The average hit rates are above 500 Hz per DOM, which is reduced to 280 Hz after the application of an artificial deadtime. The DOM rates exhibit season variations of 30 Hz due to muons interacting in the detector. The muon correlation can be measured and removed.

DOM hit rates showing seasonal effect (blue curve) and after the seasonal effect is removed using the in-ice muon rate (red curve). From Abbasi et al., 2023.

For neutrino energies below 1 GeV, the signal is dominated by backgrounds due to radioactive decays in the DOM glass and triboluminescence in the ice. The dominant neutrino interaction below 100 MeV is caused by inverse beta decay,

\[\bar{\nu}_e + p \to n + e^+.\]

The signal hit rate per DOM from this process is

\[\begin{split}\begin{align*} R(t) &= \epsilon_\mathrm{dead~time} \frac{n_\mathrm{target}\mathcal{L}^\nu_\mathrm{SN}(t)}{4\pi d^2\langle E_\nu(t)\rangle} \int_0^\infty dE_{e^+} \int_0^\infty dE_{\nu} \\ &\qquad \times \frac{d\sigma}{dE_{e^+}}(E_{e^+}, E_\nu)\ V_{e^+}^\mathrm{eff}\ f(E_\nu, \langle E_\nu\rangle, \alpha_\nu, t), \end{align*}\end{split}\]

where \(n_\mathrm{target}\) is the density of protons in ice, \(d\) is the distance to the supernova, \(\mathcal{L}^\nu_\mathrm{SN}(t)\) is the supernova neutrino luminosity, and \(f(E_\nu,\langle E_\nu\rangle,\alpha_\nu,t)\) is the normalized neutrino energy distribution depending on the average neutrino energy \(\langle E_\nu\rangle\) and spectrum shape parameter \(\alpha_\nu\). The quantity \(d\sigma/dE\) is the differential cross section for producing a positron of energy \(E_{e^+}\) from a neutrino of energy \(E_\nu\) interacting via inverse beta decay. The effective volume for a single positron is \(V_{e^+}^\mathrm{eff}\). Further details are provided in Abbasi et al., 2011 and Abbasi et al., 2023.

The SNDAQ Likelihood

The best-fit collective change in hit rates, \(\Delta\mu\), is computed by maximizing the likelihood

\[\mathcal{L}(\Delta\mu) = \prod_{i=1}^{N_\mathrm{DOM}} \frac{1}{\sqrt{2i\pi}\langle\sigma_i\rangle} \exp{ \left( -\frac{(R_i - (\langle R_i\rangle + \epsilon_i\Delta\mu))^2}{2\langle\sigma_i\rangle^2} \right) },\]

where \(\epsilon_i\) is the relative efficiency of DOM i and \(\langle\sigma_i\rangle\) is the variance of the hit rate estimated in DOM i in the sliding window.

The maximum likelihood estimator of \(\Delta\mu\) is

\[\Delta\mu = \sigma^2_{\Delta\mu} \sum_i^{N_\mathrm{DOM}} \frac{\epsilon_i(R_i - \langle R_i\rangle)}{\langle\sigma_i\rangle^2}\]

with estimated uncertainty

\[\sigma_{\Delta\mu}^2 = \left(\sum_i^{N_\mathrm{DOM}} \frac{\epsilon_i^2}{\langle\sigma_i\rangle^2} \right)^2.\]

The SNDAQ Test Statistic

The signficance of the collective rise \(\Delta\mu\) is expressed in terms of a test statistic

\[\mathrm{TS} = \xi = \frac{\Delta\mu}{\sigma_{\Delta\mu}},\]

which is the ratio of the estimated collective rate increase divided by the uncertainty in the estimator. The test statistic is estimated in time windows lasting 0.5 s, 1.5 s, 4.0 s, and 10.0 s, which are optimized for various core-collapse scenarios.

Correlation between muon rate and the TS \(\xi\) in SNDAQ data (blue, top) and distribution of \(\xi\) (blue, bottom). The red points and histogram show the TS \(\xi_\mathrm{corr}\) after the muon rate has been decorrelated. From Abbasi et al., 2023.

SNDAQ sends out a variety of public and private alerts when the TS exceeds a set of preprogrammed thresholds (see the escalation scheme on THIS PAGE). There is a strong seasonal effect observed that produces a tail of high TS values during the austral summer, when the atmosphere is less dense and the muon rate in IceCube increases. We zero out this effect by measuring the muon rate online and de-trending TS in real time to produce a corrected test statistic

\[\mathrm{TS_corr} = \xi_\mathrm{corr}.\]

A value of \(\xi_\mathrm{corr}>6\) occurs by chance less than once per year.

Distribution of the muon-rate corrected SNDAQ test statistic in data (gray) and four CCSN models distributed throughout the Milky Way (top) and the Magellanic Clouds (bottom). From Abbasi et al., 2023.

Bayesian Blocks Trigger

An additional calculation based on the Bayesian Blocks algorithm is run in real time on the SNDAQ hit stream. The Bayesian Blocks calculation constructs a piecewise-constant approximation of the hit rate and reports statistically significant changes in the rate. Unlike the SNDAQ likelihood, this calculation is independent of underlying assumptions about particular supernova models. It is not currently used to trigger SNDAQ alerts, but is saved in the SNDAQ output stream.