Supernova neutrino burst detection with the Deep Underground Neutrino Experiment

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Supernova neutrino burst detection with the Deep Underground Neutrino Experiment © The Author(s) 2021 Published version DUNE Collaboration DUNE Collaboration. (2021). Supernova neutrino burst detection with the Deep Underground Neutrino Experiment. European Physical Journal C, 81(5), Article 423. https://doi.org/10.1140/epjc/s10052-021-09166-w 2021 Eur. Phys. J. C (2021) 81:423 https://doi.org/10.1140/epjc/s10052-021-09166-w Regular Article - Experimental Physics Supernova neutrino burst detection with the Deep Underground Neutrino Experiment DUNE Collaboration B. Abi140, R. Acciarri61, M. A. Acero8, G. Adamov65, D. Adams17, M. Adinolfi16, Z. Ahmad179, J. Ahmed182, T. Alion168, S. Alonso Monsalve21,C.Alt 53, J. Anderson4, C. Andreopoulos117,157, M. P. Andrews61, F. Andrianala2, S. Andringa113,A.Ankowski 158, M. Antonova77, S. Antusch10, A. Aranda-Fernandez39, A. Ariga11,L.O.Arnold 42, M. A. Arroyave52, J. Asaadi172, A. Aurisano37, V. Aushev112,D.Autiero 89, F. Azfar140, H. Back141, J. J. Back182, C. Backhouse177, P. Baesso16, L. Bagby61, R. Bajou143, S. Balasubramanian186, P. Baldi26, B. Bambah75, F. Barao91,113, G. Barenboim77, G. J. Barker182, W. Barkhouse134, C. Barnes124, G. Barr140, J. Barranco Monarca70, N. Barros55,113, J. L. Barrow61,170, A. Bashyal139, V. Basque122,F.Bay 133, J. L. Bazo Alba150, J. F. Beacom138, E. Bechetoille89, B. Behera41, L. Bellantoni61, G. Bellettini148, V. Bellini33,79, O. Beltramello21,D.Belver 22, N. Benekos21, F. Bento Neves113, J. Berger149, S. Berkman61, P. Bernardini81,160, R. M. Berner11, H. Berns25, S. Bertolucci14,78, M. Betancourt61, Y. Bezawada25, M. Bhattacharjee95, B. Bhuyan95, S. Biagi87,J.Bian 26, M. 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Zutshi135,R.Zwaska 61 1University of Amsterdam, 1098 XG Amsterdam, The Netherlands 2University of Antananarivo, 101 Antananarivo, Madagascar 3Universidad Antonio Nariño, Bogotá, Colombia 4Argonne National Laboratory, Argonne, IL 60439, USA 5University of Arizona, Tucson, AZ 85721, USA 6Universidad Nacional de Asunción, San Lorenzo, Paraguay 7University of Athens, 157 84 Zografou, Greece 8Universidad del Atlántico, Atlántico, Colombia 9Banaras Hindu University, Varanasi 221 005, India 10 University of Basel, 4056 Basel, Switzerland 11 University of Bern, 3012 Bern, Switzerland 12 Beykent University, Istanbul, Turkey 13 University of Birmingham, Birmingham B15 2TT, UK 14 Università del Bologna, 40127 Bologna, Italy 15 Boston University, Boston, MA 02215, USA 16 University of Bristol, Bristol BS8 1TL, UK 17 Brookhaven National Laboratory, Upton, NY 11973, USA 18 University of Bucharest, Bucharest, Romania 19 Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro, RJ 22290-180, Brazil 123 423 Page 4 of 26 Eur. Phys. J. C (2021) 81:423 20 CEA/Saclay, IRFU Institut de Recherche sur les Lois Fondamentales de l’Univers, 91191 Gif-sur-Yvette Cedex, France 21 CERN, The European Organization for Nuclear Research, 1211 Meyrin, Switzerland 22 CIEMAT, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, 28040 Madrid, Spain 23 Central University of South Bihar, Gaya 824236, India 24 University of California Berkeley, Berkeley, CA 94720, USA 25 University of California Davis, Davis, CA 95616, USA 26 University of California Irvine, Irvine, CA 92697, USA 27 University of California Los Angeles, Los Angeles, CA 90095, USA 28 University of California Riverside, Riverside, CA 92521, USA 29 University of California Santa Barbara,, Santa Barbara CA 93106, USA 30 California Institute of Technology, Pasadena, CA 91125, USA 31 University of Cambridge, Cambridge CB3 0HE, UK 32 Universidade Estadual de Campinas, Campinas, SP 13083-970, Brazil 33 Università di Catania, 2, 95131 Catania, Italy 34 Institute of Particle and Nuclear Physics of the Faculty of Mathematics and Physics of the Charles University, 180 00 Prague 8, Czech Republic 35 University of Chicago, Chicago, IL 60637, USA 36 Chung-Ang University, Seoul 06974, South Korea 37 University of Cincinnati, Cincinnati, OH 45221, USA 38 Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (Cinvestav), Mexico City, Mexico 39 Universidad de Colima, Colima, Mexico 40 University of Colorado Boulder, Boulder, CO 80309, USA 41 Colorado State University, Fort Collins, CO 80523, USA 42 Columbia University, New York, NY 10027, USA 43 Institute of Physics, Czech Academy of Sciences, 182 00 Prague 8, Czech Republic 44 Czech Technical University, 115 19 Prague 1, Czech Republic 45 Dakota State University, Madison, SD 57042, USA 46 University of Dallas, Irving, TX 75062-4736, USA 47 Laboratoire d’Annecy-le-Vieux de Physique des Particules, CNRS/IN2P3 and Université Savoie Mont Blanc, 74941 Annecy-le-Vieux, France 48 Daresbury Laboratory, Cheshire WA4 4AD, UK 49 Drexel University, Philadelphia, PA 19104, USA 50 Duke University, Duke University, Durham, NC 27708, USA 51 Durham University, Durham DH1 3LE, UK 52 Universidad EIA, Antioquia, Colombia 53 ETH Zurich, Zurich, Switzerland 54 University of Edinburgh, Edinburgh EH8 9YL, UK 55 Faculdade de Ciências da Universidade de Lisboa, FCUL, 1749-016 Lisbon, Portugal 56 Universidade Federal de Alfenas, Poços de Caldas, MG 37715-400, Brazil 57 Universidade Federal de Goias, Goiania, GO 74690-900, Brazil 58 Universidade Federal de São Carlos, Araras, SP 13604-900, Brazil 59 Universidade Federal do ABC, Santo André, SP 09210-580, Brazil 60 Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-901, Brazil 61 Fermi National Accelerator Laboratory, Batavia, IL 60510, USA 62 University of Florida, Gainesville, FL 32611-8440, USA 63 Fluminense Federal University, 9 Icaraí, Niterói, RJ 24220-900, Brazil 64 Università degli Studi di Genova, Genoa, Italy 65 Georgian Technical University, Tbilisi, Georgia 66 Gran Sasso Science Institute, L’Aquila, Italy 67 Laboratori Nazionali del Gran Sasso, L’Aquila, AQ, Italy 68 University of Granada and CAFPE, 18002 Granada, Spain 69 University Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France 70 Universidad de Guanajuato, CP 37000, Guanajuato, Mexico 71 Harish-Chandra Research Institute, Jhunsi, Allahabad 211 019, India 72 Harvard University, Cambridge, MA 02138, USA 73 University of Hawaii, Honolulu, HI 96822, USA 74 University of Houston, Houston, TX 77204, USA 75 University of Hyderabad, Gachibowli, Hyderabad 500 046, India 76 Institut de Fìsica d’Altes Energies, Barcelona, Spain 77 Instituto de Fisica Corpuscular, 46980 Paterna, Valencia, Spain 78 Istituto Nazionale di Fisica Nucleare Sezione di Bologna, 40127 Bologna, BO, Italy 79 Istituto Nazionale di Fisica Nucleare Sezione di Catania, 95123 Catania, Italy 80 Istituto Nazionale di Fisica Nucleare Sezione di Genova, 16146 Genoa, GE, Italy 81 Istituto Nazionale di Fisica Nucleare Sezione di Lecce, 73100 Lecce, Italy 82 Istituto Nazionale di Fisica Nucleare Sezione di Milano Bicocca, 3, 20126 Milan, Italy 83 Istituto Nazionale di Fisica Nucleare Sezione di Milano, 20133 Milan, Italy 84 Istituto Nazionale di Fisica Nucleare Sezione di Napoli, 80126 Naples, Italy 123 Eur. Phys. J. C (2021) 81:423 Page 5 of 26 423 85 Istituto Nazionale di Fisica Nucleare Sezione di Padova, 35131 Padua, Italy 86 Istituto Nazionale di Fisica Nucleare Sezione di Pavia, 27100 Pavia, Italy 87 Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, 95123 Catania, Italy 88 Institute for Nuclear Research of the Russian Academy of Sciences, Moscow 117312, Russia 89 Institut de Physique des 2 Infinis de Lyon, 69622 Villeurbanne, France 90 Institute for Research in Fundamental Sciences, Tehran, Iran 91 Instituto Superior Técnico, IST, Universidade de Lisboa, Lisbon, Portugal 92 Idaho State University, Pocatello, ID 83209, USA 93 Illinois Institute of Technology, Chicago, IL 60616, USA 94 Imperial College of Science Technology and Medicine, London SW7 2BZ, UK 95 Indian Institute of Technology Guwahati, Guwahati 781 039, India 96 Indian Institute of Technology Hyderabad, Hyderabad 502285, India 97 Indiana University, Bloomington, IN 47405, USA 98 Universidad Nacional de Ingeniería, Lima 25, Peru 99 University of Iowa, Iowa City, IA 52242, USA 100 Iowa State University, Ames, IA 50011, USA 101 Iwate University, Morioka, Iwate 020-8551, Japan 102 University of Jammu, Jammu 180006, India 103 Jawaharlal Nehru University, New Delhi 110067, India 104 Jeonbuk National University, Jeonju, Jeonrabuk 54896, South Korea 105 University of Jyvaskyla, 40014 Jyvaskyla, Finland 106 High Energy Accelerator Research Organization (KEK), Ibaraki 305-0801, Japan 107 Korea Institute of Science and Technology Information, Daejeon 34141, South Korea 108 K L University, Vaddeswaram, Andhra Pradesh 522502, India 109 Kansas State University, Manhattan, KS 66506, USA 110 Kavli Institute for the Physics and Mathematics of the Universe, Kashiwa, Chiba 277-8583, Japan 111 National Institute of Technology, Kure College, Hiroshima 737-8506, Japan 112 Kyiv National University, Kyiv 01601, Ukraine 113 Laboratório de Instrumentação e Física Experimental de Partículas, 1649-003 Lisbon and 3004-516 Coimbra, Portugal 114 Laboratoire de l’Accélérateur Linéaire, 91440 Orsay, France 115 Lancaster University, Lancaster LA1 4YB, UK 116 Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 117 University of Liverpool, Liverpool L69 7ZE, UK 118 Los Alamos National Laboratory, Los Alamos, NM 87545, USA 119 Louisiana State University, Baton Rouge, LA 70803, USA 120 University of Lucknow, Lucknow, Uttar Pradesh 226007, India 121 Madrid Autonoma University and IFT UAM/CSIC, 28049 Madrid, Spain 122 University of Manchester, Manchester M13 9PL, UK 123 Massachusetts Institute of Technology, Cambridge, MA 02139, USA 124 University of Michigan, Ann Arbor, MI 48109, USA 125 Michigan State University, East Lansing, MI 48824, USA 126 Università del Milano-Bicocca, 20126 Milan, Italy 127 Università degli Studi di Milano, 20133 Milan, Italy 128 University of Minnesota Duluth, Duluth, MN 55812, USA 129 University of Minnesota Twin Cities, Minneapolis, MN 55455, USA 130 University of Mississippi, Oxford, MS 38677, USA 131 University of New Mexico, Albuquerque, NM 87131, USA 132 H. Niewodnicza´nski Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland 133 Nikhef National Institute of Subatomic Physics, 1098 XG Amsterdam, The Netherlands 134 University of North Dakota, Grand Forks, ND 58202-8357, USA 135 Northern Illinois University, DeKalb, IL 60115, USA 136 Northwestern University, Evanston, Il 60208, USA 137 University of Notre Dame, Notre Dame, IN 46556, USA 138 Ohio State University, Columbus, OH 43210, USA 139 Oregon State University, Corvallis, OR 97331, USA 140 University of Oxford, Oxford OX1 3RH, UK 141 Pacific Northwest National Laboratory, Richland, WA 99352, USA 142 Universtà degli Studi di Padova, 35131 Padua, Italy 143 Université de Paris, CNRS, Astroparticule et Cosmologie, 75006 Paris, France 144 Università degli Studi di Pavia, 27100 Pavia, PV, Italy 145 University of Pennsylvania, Philadelphia, PA 19104, USA 146 Pennsylvania State University, University Park, PA 16802, USA 147 Physical Research Laboratory, Ahmedabad 380 009, India 148 Università di Pisa, 56127 Pisa, Italy 149 University of Pittsburgh, Pittsburgh, PA 15260, USA 150 Pontificia Universidad Católica del Perú, Lima, Peru 123 423 Page 6 of 26 Eur. Phys. J. C (2021) 81:423 151 University of Puerto Rico, Mayaguez, PR 00681, USA 152 Punjab Agricultural University, Ludhiana 141004, India 153 Radboud University, 6525 AJ Nijmegen, The Netherlands 154 University of Rochester, Rochester, NY 14627, USA 155 Royal Holloway College, London TW20 0EX, UK 156 Rutgers University, Piscataway, NJ 08854, USA 157 STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, UK 158 SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA 159 Sanford Underground Research Facility, Lead, SD 57754, USA 160 Università del Salento, 73100 Lecce, Italy 161 Universidad Sergio Arboleda, Bogotá 11022, Colombia 162 University of Sheffield, Sheffield S3 7RH, UK 163 South Dakota School of Mines and Technology, Rapid City, SD 57701, USA 164 South Dakota State University, Brookings, SD 57007, USA 165 University of South Carolina, Columbia, SC 29208, USA 166 Southern Methodist University, Dallas, TX 75275, USA 167 Stony Brook University, SUNY, Stony Brook, NY 11794, USA 168 University of Sussex, Brighton BN1 9RH, UK 169 Syracuse University, Syracuse, NY 13244, USA 170 University of Tennessee, Knoxville, TN 37996, USA 171 Texas A&M University , Corpus Christi, TX 78412, USA 172 University of Texas at Arlington, Arlington, TX 76019, USA 173 University of Texas at Austin, Austin, TX 78712, USA 174 University of Toronto, Toronto, ON M5S 1A1, Canada 175 Tufts University, Medford, MA 02155, USA 176 Universidade Federal de São Paulo, 09913-030 São Paulo, Brazil 177 University College London, London WC1E 6BT, UK 178 Valley City State University, Valley City, ND 58072, USA 179 Variable Energy Cyclotron Centre, Kolkata, West Bengal 700 064, India 180 Virginia Tech, Blacksburg, VA 24060, USA 181 University of Warsaw, 00-927 Warsaw, Poland 182 University of Warwick, Coventry CV4 7AL, UK 183 Wichita State University, Wichita, KS 67260, USA 184 William and Mary, Williamsburg, VA 23187, USA 185 University of Wisconsin Madison, Madison, WI 53706, USA 186 Yale University, New Haven, CT 06520, USA 187 Yerevan Institute for Theoretical Physics and Modeling, Yerevan 0036, Armenia 188 York University, Toronto M3J 1P3, Canada Received: 15 August 2020 / Accepted: 21 April 2021 © The Author(s) 2021 Abstract The Deep Underground Neutrino Experiment (DUNE), a 40-kton underground liquid argon time projection chamber experiment, will be sensitive to the electronneutrino flavor component of the burst of neutrinos expected from the next Galactic core-collapse supernova. Such an observation will bring unique insight into the astrophysics of core collapse as well as into the properties of neutrinos. The general capabilities of DUNE for neutrino detection in the relevant few- to few-tens-of-MeV neutrino energy range will be described. As an example, DUNE’s ability to constrain the νespectral parameters of the neutrino burst will be considered. ae-mail: [email protected] (corresponding author) 1 Introduction The Deep Underground Neutrino Experiment (DUNE) will be made up of four 10-kton liquid argon time projection chambers underground in South Dakota as part of the DUNE/Long-Baseline Neutrino Facility (LNBF) program. DUNE will record and reconstruct neutrino interactions in the ∼GeV and higher range for studies of neutrino oscillation parameters and searches for new physics using neutrinos from a beam sent from Fermilab and using neutrinos from the atmosphere. DUNE’s dynamic range is such that it is also sensitive to neutrinos with energies down to about 5 MeV. Charged-current (CC) interactions of neutrinos from around 5 MeV to several tens of MeV create short electron tracks in liquid argon, potentially accompanied by gamma-ray and other secondary particle signatures. This regime is of particular interest for detection of the burst of neutrinos from a 123 Eur. Phys. J. C (2021) 81:423 Page 7 of 26 423 galactic core-collapse supernova. Such a detection would be ofgreatinterestinthecontext of multi-messenger astronomy. The sensitivity of DUNE is primarily to electron-flavor neutrinos from supernovae, and this capability is unique among existing and proposed supernova neutrino detectors for the next decades. Neutrinos and antineutrinos from other astrophysical sources, such as solar and diffuse supernova background neutrinos, are also potentially detectable. This lowenergy (few to few tens of MeV) event regime has particular reconstruction, background and triggering challenges. One of the primary physics goals of DUNE as stated in the technical design report (TDR) [1–3] is to “Detect and measure the νeflux from a core-collapse supernova within ourgalaxy,shouldoneoccur during the lifetime of the DUNE experiment. Such a measurement would provide a wealth of unique information about the early stages of core collapse, and could even signal the birth of a black hole.” [4]. This paper will document selected studies from the DUNE TDR aimed at understanding DUNE’s sensitivity to lowenergy neutrino physics, with an emphasis on supernova burst signals. Section 2describes basic supernova neutrino physics, as well as prospects for astrophysics and particle physics from observation of a burst. Section 3gives an overview of the landscape of supernova neutrino burst detection. Section 4gives a brief description of the DUNE far detector. Section 5describes the general properties of low-energy events in DUNE, including interaction channels, simulation and reconstruction tools, and backgrounds. The tools include MARLEY, a neutrino event generator specifically developed for this energy regime [5], and the SNOw- GLoBES fast event-rate calculation tool [6]. These are both open-source community tools, rather than DUNE-specific software. The studies described here make use of MARLEY and SNOwGLoBES with input from the full DUNE simulation-reconstruction chain. Section 5.3 describes the expected supernova signal in DUNE, and Sect. 5.4 describes burst triggering studies (as distinct from offline reconstruction studies.) Section 6describes an example of a study of supernova flux parameter sensitivity in DUNE. Details on supernova pointing capabilities and solar neutrino capabilities will be described in separate publications. 2 Supernova neutrino bursts The burst of neutrinos from the celebrated core-collapse supernova 1987A in the Large Magellanic Cloud, about 50 kpc from Earth, heralded the era of extragalactic neutrino astronomy. This single neutrino-based observation of a core collapse confirmed our basic understanding of its physical mechanism. Theoretical understanding of the process and of the potential to gain far deeper knowledge from a future observation has advanced considerably in the past decades. 2.1 Neutrinos from collapsed stellar cores: basics A core-collapse supernova1occurs when a massive star reaches the end of its life. As a result of nuclear burning throughout the star’s life, the central region of such a star gains an “onion” structure, with an iron core at the center surrounded by concentric shells of lighter elements (silicon, oxygen, neon, magnesium, carbon, etc). At temperatures of T∼1010 K and densities of ρ∼1010 g/cm3, the Fe core continuouslyloses energybyneutrinoemission(throughpair annihilationandplasmondecay[7]).Sinceironcannotbefurther burned, the lost energy cannot be replenished throughout the volume and the core continues to contract and heat up, while also growing in mass thanks to the shell burning. Eventually, the critical mass of about 1.4Mof Fe is reached, at which point a stable configuration is no longer possible. As electrons are absorbed by the protons in nuclei and some iron is disintegrated by thermal photons, the degeneracy pressure support is suddenly removed and the core collapses essentially in free fall, reaching speeds of about a quarter of the speed of light.2 The collapse of the central region is suddenly halted after ∼10−2s, as the density reaches nuclear (or super-nuclear) values. The central core rebounds and an outward-moving shock wave is formed. The extreme physical conditions of this core, in particular the densities of order 1012−1014 g/cm3, create a medium that is opaque even for neutrinos. As a consequence, the core initially has a trapped lepton number. The gravitational energy of the collapse at this stage is stored mostly in the degenerate Fermi sea of electrons (EF∼200 MeV) and electron neutrinos, which are in equilibrium with the former. The temperature of this core is not more than 30 MeV, which means the core is relatively cold. At the next stage, the trapped energy and lepton number both escape from the core, carried by the least interacting particles, which in the standard model are neutrinos. Neutrinos and antineutrinos of all flavors are emitted in a time span of a few seconds (their diffusion time). The resulting central object then settles to a neutron star, or a black hole. A tremendous amount of energy, some 1053 ergs, is released in 1058 neutrinos with energies ∼10 MeV. A fraction of this energy is absorbed by beta reactions into the material behind the shock wave that then blasts away the rest of the star, creating, in many cases, a spectacular explosion. Yet, from the energetics point of view, this visible explosion is but a tiny perturbation on the total event. Over 99% of all gravitational 1“Supernova” always refers to a “core-collapse supernova” in this paper, although we are aware that not all core collapses produce electromagnetically visible supernovae, and not all supernovae result from stellar core collapse. 2Other collapse mechanisms are possible: an “electron-capture” supernova does not reach the final burning phase before highly degenerate electrons break apart nuclei and trigger a collapse. 123 423 Page 8 of 26 Eur. Phys. J. C (2021) 81:423 binding energy of the 1.4Mcollapsed core – some 10% of its rest mass – is emitted in neutrinos. 2.2 Stages of the explosion The core-collapse neutrino signal starts with a short, sharp “neutronization” (or “break-out”) burst primarily composed of νefrom e−+p→νe+n. These neutrinos are messengers of the shock front breaking through the neutrinosphere (the surface of neutrino trapping): when this happens, iron is disintegrated, the neutrino scattering rate drops and the lepton numbertrapped just belowtheoriginalneutrinosphereissuddenly released. This quick and intense burst is followed by an “accretion” phase lasting some hundreds of milliseconds, depending on the progenitor star mass, as matter falls onto the collapsed core and the shock is stalled at the distance of ∼200 km. The gravitational binding energy of the accreting material is powering the neutrino luminosity during this stage. The later “cooling” phase over ∼10 s represents the main part of the signal, over which the proto-neutron star sheds its trapped energy. The flavor content and spectra of the neutrinos emitted from the neutrinosphere change throughout these phases, and the supernova’s evolution can be followed with the neutrino signal. The physics of neutrino decoupling and spectra formation isfarfromtrivial,owingtotheenergydependenceofthecross sections and the roles played by both CC and neutral-current (NC) reactions. Detailed transport calculations using methods such as MC or Boltzmann solvers have been employed. It has been observed that flux spectra coming out of such simulations can typically be parameterized at a given moment in time by the following ansatz (e.g., [10,11]): φ(Eν)=NEν Eνα exp −(α+1)Eν Eν,(0) where Eνis the neutrino energy, Eνis the mean neutrino energy, αis a “pinching parameter”, and Nis a normalization constant related to the total luminosity. Large αcorresponds to a more “pinched” spectrum (suppressed tails at high and low energy). This parameterization is referred to as a “pinched-thermal” form. The different νe,νeand νx(x=μ, τ, ¯μ, ¯τ) flavors are expected to have different average energy and αparameters and to evolve differently in time. The initial spectra get further processed by flavor transitions, and understanding these oscillations is very important for extracting physics from the detected signal (see Sect. 2.4.1). In general, one can describe the neutrino flux as a function of time by specifying the three pinching parameters in successive time slices. Figure 1gives an example of pinching ergs/s) 52 L (10 e ν e ν x ν Infall Neutronization Accretion Cooling 0.1 1 10 <E> (MeV) 6 8 10 12 14 Time (seconds) 2− 10 1− 10 1 Alpha 2.5 3 3.5 4 4.5 Fig. 1 Expected time-dependent flux parameters for a specific model foran electron-capture supernova[8]. Noflavor transitionsare assumed. The top plot shows the luminosity as a function of time, the second plot shows average neutrinoenergy, andthe thirdplot showsthe α(pinching) parameter. The vertical dashed line at 0.02 s indicates the time of core bounce, and the vertical lines indicate different eras in the supernova evolution. The leftmost time interval indicates the infall period. The next interval, from core bounce to 50 ms, is the neutronization burst era, in which the flux is composed primarily of νe. The next period, from 50 to 200 ms, is the accretion period. The final era, from 0.2 to 9 s, is the proto-neutron-star cooling period. The general features are qualitatively similar for most core-collapse supernova models parameters as a function of time for a specific model, and Fig. 2shows the spectra for the three flavors as a function of time corresponding to this parameterized description. We have verified that the time-integrated spectrum for each flavor is expected to be reasonably well approximated by the pinched-thermal form as well. 2.3 Astrophysical observables Anumberofastrophysicalphenomenaassociatedwithsupernovae are expected to be observable in the supernova neutrinosignal,providingaremarkablewindow intothe event.In particular, the supernova explosion mechanism, which in the current paradigm involves energy deposition into the stellar envelope via neutrino interactions, is still not well understood, and the neutrinos themselves will bring the insight needed to confirm or refute the paradigm. There are many other examples of astrophysical observables: – The initial burst, primarily composed of νeand called the “neutronization” or “breakout” burst, represents only a small component of the total signal. However, flavor transition effects can manifest themselves in an observable manner in this burst, and flavor transformations can 123 Eur. Phys. J. C (2021) 81:423 Page 15 of 26 423 Fig. 5 Visualization of an example MARLEY νeCC event simulated in LArSoft, showing the trajectories and energy deposition points of the interaction products respectively. B(F)and B(GT)are the Fermi and Gamow- Teller matrix elements. MARLEY computes this cross section using a table of Fermi and Gamow-Teller nuclear matrix elements. Their values are taken from experimental measurements at low excitation energies and a quasiparticle random phase approximation (QRPA) calculation at high excitation energies. After simulating the initial two-body 40Ar(νe,e−)40K∗ reaction for an event, MARLEY also handles the subsequent nuclear de-excitation. For bound nuclear states, the de-excitation gamma rays are sampled using tables of experimental branching ratios [88–90]. These tables are supplemented with theoretical estimates when experimental data are unavailable. For particle-unbound nuclear states, MARLEY simulates the competition between gamma-ray and nuclear fragment4emission using the Hauser-Feshbach statistical model. Figure 5shows an example visualization of a simulated MARLEY event. Figure 6shows the mean fraction of energy apportioned to the different possible interaction products by MARLEY as a function of neutrino energy. 5.2.2 Low-energy event reconstruction performance The LArSoft [86] Geant4-based software package is used to simulate the final-state products from MARLEY in the DUNE LArTPC. Both TPC ionization-based signals and scintillation photon signals are simulated. For the studies described here, the DUNE LArSoft 1 × 2×6 m far detector geometry was used [3], along with standard DUNE reconstruction tools included in the LArSoft package. To determine event-by-event reconstruction infor- 4Nucleons and light nuclei up to 4He are considered. 010 20 30 40 50 60 70 80 90 100 Truth Neutrino Energy (MeV) 0 0.2 0.4 0.6 0.8 1 Average Fractional Truth Particle Energy Proton Gamma Electron Neutron Binding Fig. 6 Fraction of incident neutrino energy going to each final-state particle type in the MARLEY simulation as a function of neutrino energy.“Binding energy”represents the difference in mass of theinitial- and final-state nuclei, representing the kinematic threshold for the CC interaction mation, 2D hits are formed using the HitFinder algorithm. HitFinder scans through wires and defines hits in regions between two signal minima where the maximum signal is above threshold. The algorithm then performs nGaussian fits for nconsecutive regions. The hit center is defined as the fitted Gaussian center, while the beginning and end are defined using the fitted Gaussian width. We used the Traj- Cluster algorithm to form reconstructed clusters. The TrajCluster algorithm creates clusters using local information from 2D trajectories, taking advantage of minimal ionization energy loss compared to the kinetic energy of the particle. A 2D trajectory is formed from trajectory points defined by the cryostat, plane, and TPC in which the trajectory resides. The trajectorypoints are made up of charge-weightedpositions of all hits used to form the point. The algorithm steps through the 2D space of hits sorted by wire ID number, region of interest in time, and then by “multiplet” (i.e., a collection of hits found using a multi-Gaussian fit). Clusters are formed in the algorithm by stitching together nearby 2D hits. 3D track information is produced using the Projection Matching Algorithm (PMA). PMA takes in 2D clusters formed through TrajCluster, and the algorithm matches clusters in the three 2D projection wire planes to build the tracks. PMA measures thedistancebetweenprojections,andtracksareformedbased on stitching together nearby projections. The photon (scintillation) simulation implemented ARAPUCA light collection devices with realistic light yields that differ between particle types. Reconstructed photon flashes are used to correct ionization charge loss during drift, which provides substantial improvement to energy reconstruction. Even in the absence of efficient TPC-flash matching, resolution smearing due to drift losses may end up being a small effect, particularly given the high electron lifetimes recently achieved in the DUNE prototype detector [91]. Photons may also be used for calorimetry, although that method has not been implemented for these studies. 123 423 Page 16 of 26 Eur. Phys. J. C (2021) 81:423 0 5 10 15 20 25 30 True Neutrino Energy (MeV) 0 0.1 0.2 0.3 0.4 Resolution TPC resolution PDS resolution Physics limited resolution Fig. 7 Left: reconstruction efficiency as a function of neutrino energy for MARLEY νeCC events, for different minimum required reconstructed energy. Right: fractional energy resolution (RMS of the distribution of the fractional difference between reconstructed and true energy with respect to true energy) as a function of neutrino energy for TPC tracks corrected for drift attenuation (black) and photon detector calorimetry (blue). The red “physics-limited resolution” is the ratio of the RMS to the mean of the deposited energy distribution, and assumes all energy deposited by final-state particles is reconstructed; the finite resolution represents loss of energy from escaping particles (primarily neutrons). Below 10 MeV the RMS of this distribution is zero Figure 7shows summarized fractional energy resolution and efficiency performance for MARLEY events. Angular resolution performance will be addressed in a separate publication. 5.2.3 Backgrounds Understanding of cosmogenic [92] and radiological backgrounds is also necessary for determination of low-energy event reconstruction quality and for setting detector requirements. The dominant radiological is expected to be 39Ar, which βdecays at a rate of ∼1 Bq/liter, with an endpoint of <1 MeV. Small single-hit blips from these decays or other radiologicals may fake de-excitation gammas. However preliminary studies show that these background blips will have a very minor effect on reconstruction of triggered supernova burst events. The effects of backgrounds on a data acquisition (DAQ) and triggering system that satisfies supernova burst triggering requirements need separate consideration. These will be the topics of future study. For studies presented here, theimpactofbackgroundsoneventreconstructionisignored. 5.3 Expected Supernova burst signal 5.3.1 SNOwGLoBES Many supernova neutrino studies done for DUNE so far have employedSNOwGLoBES [6],a fastevent-ratecomputation tool. This uses GLoBES front-end software [93] to convolve fluxes with cross sections and detector parameters. The output is in the form of both mean interaction rates for each channelas a function of neutrinoenergyand mean “smeared” rates as a function of detected energy for each channel (i.e., the spectrum that actually would be observed in a detector). The smearing (transfer) matrices incorporate both interaction product spectra for a given neutrino energy and detector response. Figure 8shows examples of such transfer matrices created using MARLEY and LArSoft. They were made by determining the distribution of reconstructed charge using a full simulation of the detector response (including the generation, transport, and detection of ionization signals and the electronics, followed by high-level reconstruction algorithms) as a function of neutrino energy in 0.5-MeV steps. Each column of a transfer matrix for a given interaction channel represents the detector response to interactions of monoenergetic neutrinos in the detector. An electron drift attenuation correction, which can be computed using the reconstructed photon signal (which determines the time of the interaction and hence the drift distance), improves resolution significantly; see Fig. 9. TimedependenceofasupernovafluxinSNOwGLoBES can be straightforwardly handled by providing multiple fluxes divided into different time bins (see Fig. 11), although studies here assume a time-integrated flux. While SNOwGLoBES is, and will continue to be, a fast, useful tool, it has limitations with respect to a full simulation. One loses correlated event-by-event angular and energy information, for example; studies of directionality require such complete event-by-event information [94]. Nevertheless, transfer matrices generated with full simulations can be used for fast computation of observed event rates and energy distributions from which useful conclusions can be drawn. 5.3.2 Expected event rates Table 1shows rates calculated for the dominant interactions in argon for the “Livermore” model [95] (included for comparison with literature), the “GKVM” model [96], and the 123 Eur. Phys. J. C (2021) 81:423 Page 17 of 26 423 Fig. 8 Left:transfer matrix for SNOwGLoBES created withmonoenergetic νeCC MARLEY samples run though LArSoft, with the color scale indicating the relative detected charge distribution as a function of neutrino energy. The effects of interaction product distributions and detectorsmearing are both incorporated in this transfer matrix. The right hand plot incorporates an assumed correction for charge attenuation due to electron drift in the TPC, based on Monte Carlo truth position of the interaction. This correction can be made using PDS information. The drift correction improves energy resolution 0 5 10 15 20 25 30 35 40 45 50 Reconstructed Energy (MeV) 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 Normalized units Blue: reco drift correction Black: no drift correction 10 MeV 20 MeV 30 MeV Fig. 9 Observed reconstructed energy distributions for specific interacting neutrino energies (corresponding to columns of the transfer matrices in Fig. 8), with and without reconstructed photon drift correction “Garching” electron-capture supernova model [8].5For the first and last, no flavor transitions are assumed in the supernova or Earth; the GKVM model assumes collective effects in the supernova. In general, there is a rather wide variation – up to an order of magnitude – in event rate for different models due to different numerical treatment (e.g., neutrino transport,dimensionality), physics input (nuclear equation of state, nuclear correlation and impact on neutrino opacities, neutrino-nucleus interactions) and flavor transition effects. In addition, there is intrinsic variation in the nature of the 5We are aware that, unlike the model in [8], the Livermore and GKVM fluxes are not based on full state-of-the-art simulations. However, they produceresultswithin rangeof more sophisticatedmodels. Furthermore the fluxes are available in SNOwGLoBESand appear frequently in past literature, so we include them as examples. Table 1 Event counts computed with SNOwGLoBES for different supernovamodelsin40 kton ofliquidargonfor a corecollapseat 10kpc, for νeCC and ¯νeCC channels and ES (Xrepresents all flavors) on electrons. Event rates will simply scale by active detector mass and inverse square of supernova distance. No flavor transitions are assumed for the “Livermore”and “Garching”models; the“GKVM” modelincludes collective effects. Note that flavor transitions (both standard and collective) will potentially have a large, model-dependent effect, as discussed in Sect. 2.4.1 Channel Liver-more GKVM Garching νe+40 Ar →e−+40 K∗2648 3295 882 νe+40 Ar →e++40 Cl∗224 155 23 νX+e−→νX+e−341 206 142 Total 3213 3656 1047 progenitor and collapse mechanism. Neutrino emission from the supernova may furthermore have an emitted lepton-flavor asymmetry [97], so that observed rates may be dependent on the supernova direction. Figure10showstheexpectedeventspectrumandtheinter- action channel breakdown for the “Garching” model before and after detector response smearing with SNOwGLoBES. Clearly, the νeflavor dominates. Although water and scintillatordetectors will record νeevents[98,99], theνeflavor may not be cleanly separable in these detectors. Liquid argon is the only future prospect for a large, cleanly tagged supernova νesample [50]. Figure 11 shows computed event rates showing the effect of different mass orderings, using the assumptions in Sect. 2.4.1. MSW-dominated transitions affect the subsequent rise of the signal over a fraction of a second; the time profile will depend on the turn-on of the non-νeflavors. 123 423 Page 18 of 26 Eur. Phys. J. C (2021) 81:423 510 15 20 25 30 35 40 45 50 Neutrino energy (MeV) 0 5 10 15 20 25 30 35 40 45 Events per 0.5 MeV ES Ar 40 e ν Ar 40 e ν 510 15 20 25 30 35 40 45 50 Observed energy (MeV) 0 5 10 15 20 25 30 35 40 Events per 0.5 MeV ES Ar 40 e ν Ar 40 e ν Fig. 10 Top:Spectrumasafunctionofinteractedneutrinoenergycomputed with SNOwGLoBES in 40 kton of liquid argon for the electroncapture supernova [8] (“Garching” model) at 10 kpc, integrated over time, and indicating the contributions from different interaction channels.Nooscillations are assumed.Bottom: expectedmeasured spectrum as a function of observed energy, after detector response smearing For this model at 10 kpc there are statistically-significant differences in the time profile of the signal for the different orderings. For a given supernova, the number of signal events scales with detector mass and inverse square of distance as shown in Fig. 12. The standard supernova distance is 10 kpc, which is just beyond the center of the Milky Way. At this distance, DUNEwill observefrom severalhundredtoseveralthousand events. For a collapse in the Andromeda galaxy, 780 kpc away, a 40-kton detector would observe a few events at most. 5.4 Burst triggering Given the rarity of a supernova neutrino burst in our galactic neighbourhood and the importance of its detection, it is essential to develop a redundant and highly efficient triggering scheme in DUNE. In DUNE, the trigger on a supernova neutrino burst can be done using either TPC or photon detection system information. In both cases, the trig- 40 kton argon, 10 kpc Time (seconds) 0.05 0.1 0.15 0.2 0.25 Events per bin 10 20 30 40 50 60 70 80 Infall Neutronization Accretion Cooling No oscillations Normal ordering Inverted ordering 40 kton argon, 10 kpc Fig. 11 Expected event rates as a function of time for the electroncapture model in [8] for 40 kton of argon during early stages of the event – the neutronization burst and early accretion phases, for which self-induced effects are unlikely to be important. Shown are: the event rate for the unrealistic case of no flavor transitions (blue) and the event rates including the effect of matter transitions for the normal (red) and inverted (green) orderings. Error bars are statistical, in unequal time bins 110 2 10 3 10 Distance to supernova (kpc) 2 − 10 1− 10 1 10 2 10 3 10 4 10 5 10 Number of interactions AndromedaGalaxy Edge LMC 40 kton 10 kton Fig. 12 Estimated numbers of supernova neutrino interactions in DUNE as a function of distance to the supernova, for different detector masses (νeevents dominate). The red dashed lines represent expected events for a 40-kton detector and the green dotted lines represent expectedeventsfora10-ktondetector.Thelineslimitafairlywiderange of possibilities for pinched-thermal-parameterized supernova flux spectra (Eq. 2.2) with luminosity 0.5×1052 ergs over 10 s. The optimistic upper line of a pair gives the number of events for average νeenergy of Eνe=12 MeV, and pinching parameter α=2; the pessimistic lower line of a pair gives the number of events for Eνe=8 MeV and α=6. (Note that the luminosity, average energy and pinching parameters will vary over the time frame of the burst, and these estimates assume a constant spectrum in time. Flavor transitions will also affect the spectra and event rates.) The solid lines represent the integrated number of events for the specific time-dependent neutrino flux model in [8] (see Figs. 1 and 2; this model has relatively cool spectra and low event rates). Core collapses are expected to occur a few times per century, at a most-likely distance of around 10–15 kpc ger scheme exploits the time coincidence of multiple signals over a timescale matching the supernova luminosity evolution. Development of such a data acquisition and triggering scheme is a major activity within DUNE and will be the topic of future dedicated publications. Both TPC and PD information can be used for triggering, for both SP and DP. Here 123 Eur. Phys. J. C (2021) 81:423 Page 19 of 26 423 Number of events in SNB 110 2 10 Triggering efficiency 0 0.2 0.4 0.6 0.8 1 Fig. 13 Supernova neutrino burst triggering efficiency for the DP photon detectors as a function of the number of interactions in one module of the dual phase active volume for the wavelength-shifting reflective half-foil configuration of the baseline design are described two concrete examples of preliminary trigger design studies. Note that the general strategy will be to record data from all channels over a 30-100 second period around every trigger [3], so that the individual event reconstruction efficiency as described in Sect. 5.2.2 will apply for physics performance. Thefirst exampleisa triggerbasedon thephoton detection system of the DP module. A real-time algorithm should provide trigger primitives by searching for photomultiplier hits and optical clusters, where the latter combines several hits together based on their time/spatial information. According to simulations, the optimal cluster reconstruction parameters yield a 0.05 Hz radiological background cluster rate for a supernova νeCC signal cluster efficiency of 11.8%. Once the optimal cluster parameters are found, the computation of the supernova neutrino burst trigger efficiency is performed using the minimum cluster multiplicity. This value, set by the radiological background cluster rate and the maximum fake trigger rate (one per month), is ≥3 in a 2-second window (time in which about half of the events are expected). Approximately 3/0.118≃25 interactions must occur in the activevolumetoobtain approximately 45% trigger efficiency while maintaining a fake trigger rate of one per month. The triggering efficiency as a function of the number of supernova neutrino interactions is shown in Fig. 13.At 20 kpc, the edge of the Galaxy, about 80 supernova neutrino interactions in the 12.1-kton active mass (assumed supernova-burst-sensitive mass for a single DP module) are expected (see Fig. 12). Therefore, the DP photon detection system should yield a highly efficient trigger for a supernova neutrino burst occurring anywhere in the Milky Way. The second example considered is a TPC-based supernova neutrino burst trigger in a SP module (SP photon-based triggering will be considered in a future study). Such a trigger considering the time coincidence of multiple neutrino interactions over a period of up to 10 s yields roughly comparable efficiencies. Figure 14 shows efficiencies for supernova bursts obtained in this way for a DUNE SP module and for supernova bursts with an energy and time evolution as shown in Fig. 1. Triggering using TPC information is facilitated by a multi-level data selection chain whereby ionization charge deposits are first selected on a per wire basis, using a threshold-based hit finding scheme. This results in low-level trigger primitives (hit summaries) which can be correlated in time and channel space to construct higher-level trigger candidate objects. Low-energy trigger candidates, each consistent with the ionization deposition due to a single supernova neutrino interaction, subsequently serve as input to the supernova burst trigger. Simulations demonstrate that the trigger candidate efficiency for any individual supernova burst neutrino interaction is on the order of 20–30%; see Fig. 14.However, a multiplicity-based supernova burst trigger that integrates low-energy trigger candidates over ∼10 s integration window yields high trigger efficiency out to the galactic edge while keeping fake supernova burst trigger rates due to noise and radiological backgrounds to the required level of one per month or less. An energy-weighted multiplicity count scheme further increases efficiency and minimizes fake triggers due to noise and/or radiological backgrounds. This effect is illustrated in Fig. 14, where a nearly 100% efficiency is possible out to the edge of the galaxy, and 70% efficiency is possible for a burst at the Large Magellanic Cloud (or for any supernova burst creating ∼10 events). This performance is obtained by considering the summed-waveform digitized-charge distribution of trigger candidates over 10 s and comparing to a background-only vs. background-plus-burst hypothesis. The efficiency gain compared to a simpler, trigger candidate counting-based approach is significant; using only counting information, the efficiency for a supernova burst at the Large Magellanic Cloud is only 6.5%. These algorithms are being refined to further improve supernova burst trigger efficiency for more distant supernova bursts. Alternative data selection and triggering schemes are also being investigated, involving, e.g., deep neural networks implemented for real-time or online data processing in the DAQ [100]. 5.5 Event timing in DUNE Timing for supernova neutrino events is provided by both the TPC and the photon detector system. Basic timing requirements are set by event vertexing and fiducialization needs. Here we note a few supernova-specific design considerations. During the first 50 ms of a 10-kpc-distant supernova, the mean interval between successive neutrino interactions is 0.5−1.7 ms depending on the model. The TPC alone provides a time resolution of 0.6 ms (corresponding to the drift time at 500 V/cm), commensurate with the fundamental sta- 123 423 Page 20 of 26 Eur. Phys. J. C (2021) 81:423 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Visible Energy[Gev] 0 0.2 0.4 0.6 0.8 1 Efficiency - Trigger Candidate Efficiency for e 0 5 10 15 20 25 30 Number of SN event in 10 kT 0 0.2 0.4 0.6 0.8 1 1.2 Triggering efficiency (1 fake / month) Fig. 14 Top: Single-interaction efficiency for forming trigger candidates from trigger primitives generated online (in blue) and offline (in red), using SP TPC information, as a function of visible energy for electrons such as those from low-energy νeCC scattering on argon. Middle: Supernova burst trigger efficiency as a function of the number of supernova neutrino interactions expected in a 10-kton SP module, for a likelihood trigger approach that utilizes sum digitized-charge shape information of trigger candidates input into the trigger decision. Bottom: Supernova burst trigger efficiency as a function of total (signal and fake) trigger bursts per month, for a supernova burst at the Large Magellanic Cloud, where about 10 neutrino interactions are expected in a 10 kton module (see Fig. 12). The efficiency gain with an energyweighted scheme over a counting-only trigger is significantly improved tistical limitations at this distance. However nearly half of galactic supernova candidates lie closer to Earth than this, so the rate can be tens or (less likely) hundreds of times higher. A resolution of <1µs, as already provided by the photon detector system, ensures that DUNE’s measurement of the neutrino burst time profile is always limited by rate and not detector resolution. The hypothesized oscillations of the neutrino flux due to standing accretion shock instabilities would lead to features with a characteristic time of ∼10 ms, comfortably greater than the time resolution. The possible neutrino “trapping notch” (dip in luminosity due to trapping of neutrinos in the stellar core) right before the start of the neutronization burst has a width of 1 −2 ms. Identifying the trapping notch could be possible for the closest supernovae (few kpc). 6 Extraction of Supernova flux parameters This example of a complete study investigates how well it will be possible to fit to the supernova pinched-thermal flux parameters, to determine, for example, the εparameter related to the total binding energy release of the supernova (proportional to the normalization in Eq. 2.2). Similar studies in the literature for different detectors include e.g., [10,101– 103]. We examine generically the effect of energy resolution and statistics on the ability to reconstruct flux parameters. The SNOwGLoBES package models neutrino signals described by the pinched-thermal form. A forward-fitting algorithm requiring a SNOwGLoBES-generated energy spectrum for a supernova at a given distance and a chosen “true”set of pinched-thermal parameters (α0,Eν0,ε 0)was developed. As an example, the true parameter values are chosen (α0,Eν0,ε 0)=(2.5,9.5,5×1052), with Eν0in MeV and εin ergs, assumed integrated over a ten-second burst. The study focuses on the νeflux and νeCC interactions. The algorithm uses this spectrum as a “test spectrum” to compare against a grid of predicted energy spectra generated with many different combinations of (α, Eν,ε).To quantifythese comparisons, the algorithmemploysaχ2min- imization technique to find the best-fit spectrum. The χ2 function is defined as χ2(x)= Nb  i=1Ni(α, Eν,ε)−Ni(α0,Eν0,ε 0)2 σ2 i(x)(2) In this expression, Nbis the number of bins for the energy spectra, Niis the number of events in bin i,σiis the uncertainty of the contents in bin i(Poisson statistical uncertainty), (α, Eν,ε)are the set of model parameters used and (α0,Eν0,ε 0)are the model parameters used to generate the test spectrum. 123 Eur. Phys. J. C (2021) 81:423 Page 21 of 26 423 6 8 10 12 14 16 18 (MeV) 〉 ν E 〈 1 2 3 4 5 6 α 10kpc supernova, 90% C.L. xscn + 5 MeV detection thresh. MARLEY smearing + (p, n) Nakazato Huedepohl, Black Hole Huedepohl, Cooling erg 52 10× = 5 ε = 9.5 MeV,〉 ν E〈 = 2.5, αTruth: 6810 12 14 16 18 (MeV) 〉 ν E 〈 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10ε 123 456 α 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 erg) 53 (10ε Fig. 15 Sensitivity regions for the three pinched-thermal parameters (90% C.L.). The black star represents the assumed true parameters. SNOwGLoBES assumes a cross section model from MARLEY, realistic detector smearing from LArSoft, and a step efficiency function with a 5-MeV detected energy threshold, for a supernova at 10 kpc. Superimposed are parameters corresponding to the time-integrated flux for three different sets of models: Nakazato [104], Huedepohl black hole formation models, and Huedepohl cooling models [105]. For the Nakazato parameters (for which there is no pinching, corresponding to α=2.3), the parameters are given directly; for the Huedepohl models, they are fit to a time-integrated flux A test spectrum input into the forward-fitting algorithm produces a set of χ2values for every element in a grid. While the smallest χ2value determines the best fit to the test spectrum, there exist other grid elements that reasonably fit the test spectrum according to their χ2values. The collection of these grid elements help determine the expected parameter measurement uncertainty, represented using sensitivity regions in 2D flux parameter space. Three sets of 2D parameter spaces are shown: (Eν,α),(Eν,ε), and (α, ε). Onepointin2D parameterspaceencompassesseveralgrid elements, e.g., the (Eν,α)space contains different εvalues for a given values of Eνand α. To determine the χ2value, εis profiled over to select the grid element with the smallest χ2. Sensitivity regions are determined by placing a cut of χ2=4.61 corresponding to a 90% coverage probability for two free parameters. Figure 15 shows an example of a resulting fit, where for each set of two parameters, the other is profiled over. In this plot, the approximate parameters for three sets of specific models [104,105] are superimposed, to indicate the expected spread for different assumed progenitor masses, equations of state, and simulation codes. A spectral measurementbyDUNE wouldconstrainthe spaceof allowed models. Figures 16 and 17 show the precision with which DUNE can measure two of the spectral parameters, ε, related to the binding energy of the neutron star remnant, and Eνe,the average energy of the νecomponent, for the time-integrated spectrum (profiling over α). Figure 16 shows the statistical effect of different assumed supernova distances on determination of the parameters. In Fig. 17, the effect of detector energy resolution is examined. The assumed measured spectrum estimated with SNOwGLoBES takes into account degradation from the neutrino interaction process itself (e.g., energy lost to neutrons), via the MARLEY model. The colored contours in Fig. 17 show increasing levels of assumed detector smearing on the measurement of interaction product energy deposition. For 0% resolution, perfect measurement of the energies of interaction products in the detector is assumed. A 10% measured energy resolution is noticeable but insignificant, and the overall precision on the pinched-thermal flux parameters up to 30% resolution does not change dramatically. According to detector simulation, realisticenergyresolutionisclosesttothe20%level.According to Figs. 16 and 17, in general, the precision of the measurement of supernova spectral parameters (and the ability to constrain supernova models) is limited more strongly by statistics than by energy resolution. Given the dominance of νeCC events in the supernova neutrino sample, particle identification is not a requirement for the primary physics measurements. However, additional 123 423 Page 22 of 26 Eur. Phys. J. C (2021) 81:423 Fig. 16 Sensitivity regions generated in (Eν,ε) space (profiled over α) for three different supernova distances (90% C.L.). SNOw- GLoBES assumes a transfer matrix made using MARLEY with a 20% Gaussian resolution on detected energy, and a step efficiency function with a 5 MeV detected energy threshold Fig. 17 90% C.L. contours for the luminosity and average νeenergy spectral parameters for a supernova at 5 kpc. The contours are obtained using the time-integrated spectrum. As discussed in the text, the allowed regions change noticeably but not drastically as one moves from no detector smearing (pink) to various realistic resolutions (wider regions) capability may be possible by identifying separately NC and ES interactions. In these studies, we assume that the distance to the core collapse is known. The interpretation of the εparameter as a binding energy will be affected by uncertainty on the distance. We furthermore assume that mass ordering is known; assumption of incorrect mass ordering results in biases on parameter determination. 7 Conclusion This paper gives an overview of the DUNE experiment’s sensitivity to neutrinos with about 5 MeV up to several tens of MeV, the regime of relevance for core-collapse supernova burst neutrinos. This low-energy regime presents particular challenges for triggering and reconstruction. Preliminary DUNE studies show that expected low-energy background rates should not impede efficient detection of nearby supernovae. DUNE’s time projection chamber and photon detection systems will both provide information about these events, and DUNE’s software tools have enabled preliminary physics and astrophysics sensitivity studies. DUNE will have good sensitivity to the entire Milky Way and possibly beyond, depending on the neutrino luminosity of the corecollapse supernova. According to current understanding, the energy threshold turn-on is a few MeV deposited energy. The energy resolution will be between 10 and 20% in the few tens of MeV range. DUNE will be able to measure the supernova νespectral parameters. By exploiting aspects of a DUNE supernova burst signal, including the time dependence of its energy and flavor profile and non-thermal spectral features, DUNE has the capability to uncover a broad range of supernova and neutrino physics phenomena, including sensitivity to neutrino mass ordering, collective effects, and potentially many other topics. Acknowledgements This document was prepared by the DUNE collaboration using the resources of the Fermi National Accelerator Laboratory (Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility. Fermilab is managed by Fermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359. This work was supported by CNPq, FAPERJ, FAPEG and FAPESP, Brazil; CFI, IPP and NSERC, Canada; CERN; MŠMT, Czech Republic; ERDF, H2020-EU and MSCA, European Union; CNRS/IN2P3 and CEA, France; INFN, Italy; FCT, Portugal; NRF, South Korea; CAM, Fundación “La Caixa” and MICINN, Spain; SERI and SNSF, Switzerland; TÜB˙ ITAK, Turkey; The Royal Society and UKRI/STFC, United Kingdom; DOE and NSF, United States of America. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. Data Availability Statement This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This manuscript describes sensitivity studies for the DUNE experiment using simulation only, and as such there are no experimental data to report.] Open Access This article is licensed under a Creative Commons Attribution 4.0InternationalLicense,whichpermits use, sharing,adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. 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