Extending the high-energy cosmic ray electron spectrum with deep learning

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The cosmic ray electron (CRe) spectrum is a unique tool to improve our understanding of the sources of high-energy particles (cosmic rays, CRs) in the vicinity of Earth. In this project, we will study properties of local sources of CR electrons and constrain the properties of the propagation of these particles in our vicinity by extending the energy spectrum to 20 TeV. CR protons (CRp) probe large distances, while, due to cooling, CRe with energies above 1 TeV should come from sources within about 1 kpc from Earth. Current measurements of the CRe spectrum by space-based and ground-based instruments extend to about 5 TeV. Measurements at energies higher than 5 TeV by space-based telescopes are problematic due to small effective area of these instruments. As a result, the measurement of the spectrum to larger energies is only feasible with ground-based telescopes, most prominently with imaging atmospheric Cherenkov telescopes (IACTs), such as H.E.S.S. and the future CTA. We propose to use 18 years of available H.E.S.S. data with the goal of extending the measurement of the CRe spectrum up to ∼ 20 TeV (the exact value depends on assumptions about the shape of the spectrum beyond 5 TeV). The previously published (unpublished) measurements of CRe spectrum with H.E.S.S. include 3 years (6 years) of data collection. We will also determine the sensitivity of the future CTA to measurements of CRe using deep learning methods. In order to realize the full potential of IACTs, we will use telescopes of different types (medium and large telescopes in H.E.S.S. or small, medium and large telescopes in CTA) – such hybrid analysis of the CRe spectrum (compared to stereo analysis where telescopes of the same type are used) have not been performed up to date. Given that the flux of hadronic CRs above 1 TeV is more than a factor of 1000 larger than the CRe flux, a high rejection factor on the order of 1000 or better for hadronic CRs is needed, while the majority of CRe should be kept. We propose to use modern deep learning methods (specifically, graph neural networks) for the separation of hadronic and leptonic showers using full camera shower images. We will test the main sources of systematic uncertainties related to (1) the hadronic interaction models (which impact the performance of the rejection of hadronic showers based on MC simulations), (2) the atmospheric fluctuations and changes in the telescope performance during the 18 years of observations, and (3) the choice of reconstruction method (by comparing with the standard background rejection methods based on boosted decision trees and semi-analytic modelling of air showers). The measured CRe spectrum will allow us to infer the supernova rate in the vicinity of Earth, constrain the efficiency of CRe acceleration, put a lower limit on the highest energies of CRe escaping from supernova remnants and derive properties of their propagation to Earth.