IceCube's response to supernovae and periodic features in the count rates

The IceCube Neutrino Observatory is highly sensitive to neutrino bursts of $\mathcal{O}$(10) MeV energy that are would be generated by core collapse supernovae in our Galaxy. It will resolve temporal structures in supernova light curves particularly well. In the light of an improved understanding of the ice properties and the detector response, the effective area and the corresponding uncertainties were newly determined with a Geant4-based Monte Carlo. Uncertainties due to cross sections and oscillation effects in the Earth were also investigated. This analysis has been extended by simulating a very large sample to determine the small coincidence probability between optical modules that bears information on the average neutrino energy. These simulation results were then used to interpret the data in time and frequency space. While the availability to record data for low energy neutrinos from supernovae is close to perfect (99.2$\%$ between 2013-2020), the analysis requires that the detector works faultlessly and artifacts do not mimic the signal in the 13 years of data taken so far. An effort has been made to keep the uptime after all analysis steps similarly high. The frequency space can be studied in a range between 1 Hz and 1/year to test the detector stability with high accuracy, to study the influence of cosmic rays, and to search for periodic phenomena that lead to sub-threshold increases in the count rates. Here we discuss the results of the simulations and the corresponding systematic limitations, the method to reconstruct the mean neutrino energy for a recorded supernova, as well as aspects of the analyses of continuously taken optical module rate data in the time and frequency domain.