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The Supernova Neutrino Early Warning Pointing Directed Acyclic Graph.

The calculation engine for SNEWS2 pointing and possibly other burst-related ephemera.

The contents of this page were drawn from discussions before and around the SNEWS workshop of 19-20 June 2020, the workshop itself, and subsequent SNEWS calls. It is meant for discussion, in particular on the Slack channel.

Output

(Decided at SNEWS call of 14 July 2020)

1. The output of SNEWS pointing will be an all-sky map in which the value of each pixel is a probability.
   1. LIGO/Virgo use a HEALPix projection in FITS format, which is widely used. Visualizers are readily available.
   2. Python has an official library, healpy, which reads and writes FITS files.
2. The probabilities in the pixels will incorporate systematic uncertainties.
3. The skymap resolution (or, alternatively, N_side, the number of divisions along the side of a base-resolution pixel) will be determined by the resolution of the output, rather than in advance.
4. Following LIGO/Virgo convention, the HEALPix projection will use the celestial (equatorial) frame with nested ordering.

Combination of pointing information

1. An input or internal pointing result can take one of two forms:
   1. An all-sky map of probabilities reflecting statistical uncertainties
   2. A direction in equatorial coordinates, with a likelihood profile, covariance matrix, or other parameterization reflecting statistical uncertainties
2. Different methods of calculating skymap probabilities can be implemented as separate plugins.
   1. Taking measured time delays as true values (or best estimates) is quickest, but is most optimistic.
   2. Toy MC evaluation takes longer, is usually more accurate, but can return artificially reduced values in situations with fake solutions.
3. Experiments and methods may have common systematic uncertainties, such as variations due to different supernova models. SNEWS should identify different classes which can be combined under different circumstances.
4. Systematic uncertainties may be represented by intervals in coordinates (assuming they can be combined as if Gaussian), or as a skymap of shifts.

Pointing from individual experiments

1. Individual experiments will provide pointing and uncertainties as in the previous section.
2. Examples of possible correlated systematic uncertainties:
   1. common supernova models
   2. common detector response models, such as the pointing resolution of IBD events in a Gd-loaded water Cherenkov detector
3. Pointing based on aggregate quantities from individual experiments
   1. The main aggregate quantities are expected to be times of agreed-upon features in the time series observed at each experiment.
   2. Individual experiments will provide relevant uncertainties.
   3. As in the previous section, possible correlated systematic uncertainties include the use of common models for the the supernova or detector response.

Pointing based on combination of time series

1. Each time series will consist of “physics” events (i.e., removing those due to known instrumental effects) for a given channel, and a background model for that channel.
   1. Example background models include a uniform distribution over the time window, a proportion of observed events, or a combination of models.
   2. Another possibility is to assign a weight to each event, reflecting the background and cross-talk contribution.
2. Alternatively, the time series may be binned with some agreed bin width, in which case each experiment can correct it for background and response. However, do bins need to be aligned?
   1. A time series from IceCube, for instance, will take this form, with time bin widths on the order of ms.
3. Detector response and acceptance can sculpt the shape of each channel. Examples include energy and detector thresholds, rate limitations (multiple neutrino events in the same trigger window!), and flavor composition (via cross-talk between channels).
4. Some methods may exhibit biases when combining large and small samples.

Other checks

1. We assume everyone will use UTC to represent time. At least several experiments (possibly all) use GPS for synchronization. It is expected that the synchronization (assuming no fixed offset) is better than within 1 µsec, in which case it can be neglected as a systematic uncertainty.
   1. For instance, radio astronomy traditionally use maser clocks and GPS synchronization. SKA requirements appear to be much more stringent than for SNEWS.
2. What is the effect of saturation in case a supernova is too close? This situation may need a separate "fire drill", as it is expected that only a small number of candidates could cause such a situation.

Internal structure

1. Inputs, each with uncertainties and quality indicators such as goodness-of-fit:
   1. a direction p
   2. an aggregate t
   3. a time series T
2. Output: alerts A(p) which contains a direction p with its uncertainties and quality indicators
3. Six types of plug-ins:
   1. T₁, T₂ → Δt
   2. t₁, t₂ → Δt
   3. { Δt } → p
   4. { t_i } → p
   5. { p_i } → p
   6. p → A(p)
4. Plug-ins can be arranged in a directed acyclic graph.
5. It has been pointed out that for near supernovae, it may be useful to compare a pointing to a catalog of near progenitors. Yield could be used to as an indication for distance. However, this would require a detector-specific comparison with an expected yield at a nominal distance - and therefore carrying around such information (detector and yield) among the quality indicators.