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Geant4 illustration of the energy deposition for examples of two event types: (a) $\nu_e$CC: A 25\,MeV electron neutrino is absorbed by an argon nucleus resulting in the excitation of the nucleus and the emission of an electron. (b) eES: An incoming electron neutrino of 12\,MeV scatters elastically in the LAr. Charged particles are emitted in the forward direction of the primary electron. The $\nu_e$CC primary electron tracks are on average longer than eES tracks due to the lower energies of the eES recoils; in contrast, $\nu_e$CC electrons tend to retain most of the energy of the incoming neutrino. Gamma tracks are not shown in the display, but red blips (representing electrons) from gamma interactions with the argon (primarily Compton scatters) can be seen.

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: : Comparison of the cross-section-weighted energy and angular distributions of electrons for the $\nu_e + \prescript{40}{}{} \text{Ar}$ $\nu_e$CC events in red and the eES events in blue. The angular plots are shown as a function of the cosine of the angle between the neutrino direction and the final-state electron direction. For both types of interactions, the supernova energy spectrum is assumed for the incoming neutrinos. Top left: distribution of the energy of incoming neutrinos (continuous line) and outgoing electrons (dashed line). Top right: distribution of the cosine of the scattering angle. Bottom: two-dimensional distributions showing the relative number of events as a function of both the neutrino energy and the cosine of the scattering angle, for the two types of interactions.

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The contribution of Fermi and Gamow-Teller transitions to the angular distribution for $\nu_e$CC events, generated from MARLEY for the GVKM flux model. For this model's neutrino spectrum, the angular correlation cancels out to a good approximation.

Example standard DUNE event display of an eES event. The colors show a heat map of the charge deposited on each wire segment per time tick. From top to bottom, the three plots show the view of the three wire planes, U, V, and X respectively, for one APA of the LArTPC. The trajectories with numerical labels are reconstructed tracks, where ``0'' corresponds to the primary electron track, while "1" and "2" refer to the brems particles.

Illustration of brems flipping: The angles between the brems particles (blue) and the primary track marked in black correspond to the actual direction of the primary electron, while the ones marked in red belong to the incorrect opposite direction. The average of the cosine of these angles is larger in the case of the correct set of angles.

Effectiveness of the brems-flipping algorithm: The top plot shows the bimodal distribution of the angular difference between true and reconstructed electron directions using the supernova eES electron energy spectrum, centering around the parallel ($\cos{\theta} = 1$) and anti-parallel ($\cos{\theta} = -1$) directions. Brems flipping significantly decreases the magnitude of the anti-parallel peak. The bottom plot shows the relationship between the covered sky fraction and mono-energetic electron energy. The black curve corresponds to a perfect directional disambiguation always resulting the true direction. Brems flipping performs better at higher energies, as there are more secondary tracks to reference. The electron energy spectrum from eES in gray illustrates the energies relevant to supernova pointing.

Effectiveness of the brems-flipping algorithm: The top plot shows the bimodal distribution of the angular difference between true and reconstructed electron directions using the supernova eES electron energy spectrum, centering around the parallel ($\cos{\theta} = 1$) and anti-parallel ($\cos{\theta} = -1$) directions. Brems flipping significantly decreases the magnitude of the anti-parallel peak. The bottom plot shows the relationship between the covered sky fraction and mono-energetic electron energy. The black curve corresponds to a perfect directional disambiguation always resulting the true direction. Brems flipping performs better at higher energies, as there are more secondary tracks to reference. The electron energy spectrum from eES in gray illustrates the energies relevant to supernova pointing.

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: : Pointing resolution, defined in terms of ``sky fraction" as described in the text, of individual electron events as a function of the electron's true direction in the detector coordinate system to study anisotropies in the performance. The coordinate system is defined with $\pm\hat{x}$ being the drift directions, and $+\hat{z}$ being approximately the beam direction. $\theta$ (shown vertically) and $\phi$ (shown horizontally) are spherical coordinates in a coordinate system for which $\theta = 90^\circ$ correspond to the $+\hat{z}$ direction and $\theta = 0^\circ, \phi=0^\circ$ corresponds to the $+\hat{x}$ direction. The supernova eES electron energy distribution is used. (a) shows the pointing resolution given perfect track head-tail disambiguation (b) depicts the pointing resolution for the actual performance of the reconstruction algorithm including the brems-flipping algorithm.

PDFs of eES and $\nu_e$CC events. The eES PDF demonstrates a high correlation between the supernova and primary electrons' direction increasing towards higher electron energies. The $\nu_e$CC PDF is mostly flat, as the correlation between primary electron and neutrino directions is weak.

PDFs of eES and $\nu_e$CC events. The eES PDF demonstrates a high correlation between the supernova and primary electrons' direction increasing towards higher electron energies. The $\nu_e$CC PDF is mostly flat, as the correlation between primary electron and neutrino directions is weak.

Several bins for the PDF of the eES interaction in Figure \ref{fig:2dpdfs}, re-binned to 10\,MeV / bin. The relative magnitude of the peak near $\cos{\theta_{SN}} = 1$ (the parallel direction) increases as energy increases because brems flipping improves at high energies. The width of the true direction peaks also decreases, indicating a decrease in directional variance.

An example directional map filled with the reconstructed electron directions for a simulated supernova burst, eES events carrying the directional information are marked in blue. Event statistics are shown for a core collapse at a distance of 10\,kpc, and 40\,kton of fiducial mass in the detector.

An example directional map filled with the negative log-likelihood values and confidence contours. This map is computed from the same burst shown as in Fig.~\ref{fig:burst_events}. Reconstruction is done assuming the classification parameters of $c_{eES\rightarrow eES} = 0.86$ and $c_{\nu_eCC\rightarrow eES} = 0.04$ and a successful direction reconstruction is achieved with the actual supernova direction marked with a star in the figure.

Distribution of the angular difference between the reconstructed and true supernova direction, for 10,000 simulated supernova bursts. The distribution is shown for both perfect event classification and for an assumed 4\% misclassification of $\nu_e$CC events as eES as described in \cite{erin_conley_2020_4122909}. The ranges to the right of the respective colored dashed lines correspond to the 68\% confidence intervals. The few bursts with a flipped reconstructed direction are excluded from the figure. The top figure corresponds to 10\,kton fiducial mass, while it is 40\,kton for the bottom figure.

Distribution of the angular difference between the reconstructed and true supernova direction, for 10,000 simulated supernova bursts. The distribution is shown for both perfect event classification and for an assumed 4\% misclassification of $\nu_e$CC events as eES as described in \cite{erin_conley_2020_4122909}. The ranges to the right of the respective colored dashed lines correspond to the 68\% confidence intervals. The few bursts with a flipped reconstructed direction are excluded from the figure. The top figure corresponds to 10\,kton fiducial mass, while it is 40\,kton for the bottom figure.

Burst pointing resolution as a function of eES true positives ($c_{eES\rightarrow eES}$) and $\nu_e$CC false negatives ($c_{\nu_eCC\rightarrow eES}$). Results assuming the fiducial mass of a single far detector module (10\,kton) and all four planned modules (40\,kton) are shown. For each pair of values, 1000 supernova bursts are simulated to determine the pointing resolution. Contour lines for various pointing resolution angles are also shown.

Burst pointing resolution as a function of eES true positives ($c_{eES\rightarrow eES}$) and $\nu_e$CC false negatives ($c_{\nu_eCC\rightarrow eES}$). Results assuming the fiducial mass of a single far detector module (10\,kton) and all four planned modules (40\,kton) are shown. For each pair of values, 1000 supernova bursts are simulated to determine the pointing resolution. Contour lines for various pointing resolution angles are also shown.

Burst pointing resolution as a function of the number of detected eES events ($N_{eES}$), as well as the corresponding supernova distance. The event rates are calculated assuming the GKVM model at a given distance and are for a fiducial volume of 40\,kton.

Burst pointing resolution as a function of the direction of the supernova, given in the detector coordinate system ($\pm\hat{x}$ is the drift direction, $+\hat{z}$ is approximately the beam direction). $\theta$ (shown vertically) and $\phi$ (shown horizontally) are spherical coordinates in a coordinate system for which $\theta = 90^\circ$ corresponds to the $+\hat{z}$ direction and $\theta = 0^\circ, \phi=0^\circ$ correspond to the $+\hat{x}$ direction. Pointing resolution is given for the fiducial volumes of 10\,kton and 40\,kton. Perfect classification between eES and $\nu_e$CC events is assumed in these plots. Note that the local pointing resolution is smeared by the event selection radius of 10\,degrees.

Burst pointing resolution as a function of the direction of the supernova, given in the detector coordinate system ($\pm\hat{x}$ is the drift direction, $+\hat{z}$ is approximately the beam direction). $\theta$ (shown vertically) and $\phi$ (shown horizontally) are spherical coordinates in a coordinate system for which $\theta = 90^\circ$ corresponds to the $+\hat{z}$ direction and $\theta = 0^\circ, \phi=0^\circ$ correspond to the $+\hat{x}$ direction. Pointing resolution is given for the fiducial volumes of 10\,kton and 40\,kton. Perfect classification between eES and $\nu_e$CC events is assumed in these plots. Note that the local pointing resolution is smeared by the event selection radius of 10\,degrees.

Burst pointing resolution as a function of the supernova direction, shown as a function of declination. The pointing resolution is averaged over right ascension. Shown on a separate axis is the expected declination distribution for galactic supernovae~\cite{mirizzi2006earth}.