  The Deep Underground Neutrino Experiment (DUNE) could be revolutionary for
MeV neutrino astrophysics, because of its huge detector volume, unique event
reconstruction capabilities, and excellent sensitivity to the $\nu_e$ flavor.
However, its backgrounds are not yet known. A major background is expected due
to muon spallation of argon, which produces unstable isotopes that later beta
decay. We present the first comprehensive study of MeV spallation backgrounds
in argon, detailing isotope production mechanisms and decay properties,
analyzing beta energy and time distributions, and proposing experimental cuts.
We show that above a nominal detection threshold of 5-MeV electron energy, the
most important backgrounds are --- surprisingly --- due to low-A isotopes, such
as Li, Be, and B, even though high-A isotopes near argon are abundantly
produced. We show that spallation backgrounds can be powerfully rejected by
simple cuts, with clear paths for improvements. We compare these background
rates to rates of possible MeV astrophysical neutrino signals in DUNE,
including solar neutrinos (detailed in a companion paper [Capozzi et al.
arXiv:1808.08232 [hep-ph]]), supernova burst neutrinos, and the diffuse
supernova neutrino background. Further, to aid trigger strategies, in the
Appendixes we quantify the rates of single and multiple MeV events due to
spallation, radiogenic neutron capture, and other backgrounds, including
through pileup. Our overall conclusion is that DUNE has high potential for MeV
neutrino astrophysics, but reaching this potential requires new experimental
initiatives.
