DRAFT VERSION JANUARY 8, 2020Typeset using LATEX twocolumn style in AASTeX62

A search for IceCube events in the direction of ANITA neutrino candidates

M. G. AARTSEN,16 M. ACKERMANN,55 J. ADAMS,16 J. A. AGUILAR,12 M. AHLERS,20 M. AHRENS,46 C. ALISPACH,26 K. ANDEEN,37

T. ANDERSON,52 I. ANSSEAU,12 G. ANTON,24 C. ARGÜELLES,14 J. AUFFENBERG,1 S. AXANI,14 P. BACKES,1 H. BAGHERPOUR,16

X. BAI,43 A. BALAGOPAL V.,29 A. BARBANO,26 S. W. BARWICK,28 B. BASTIAN,55 V. BAUM,36 S. BAUR,12 R. BAY,8 J. J. BEATTY,18, 19

K.-H. BECKER,54 J. BECKER TJUS,11 S. BENZVI,45 D. BERLEY,17 E. BERNARDINI,55 D. Z. BESSON,30 G. BINDER,8, 9 D. BINDIG,54

E. BLAUFUSS,17 S. BLOT,55 C. BOHM,46 S. BÖSER,36 O. BOTNER,53 J. BÖTTCHER,1 E. BOURBEAU,20 J. BOURBEAU,35

F. BRADASCIO,55 J. BRAUN,35 S. BRON,26 J. BROSTEAN-KAISER,55 A. BURGMAN,53 J. BUSCHER,1 R. S. BUSSE,38 T. CARVER,26

C. CHEN,6 E. CHEUNG,17 D. CHIRKIN,35 S. CHOI,48 K. CLARK,31 L. CLASSEN,38 A. COLEMAN,39 G. H. COLLIN,14 J. M. CONRAD,14

P. COPPIN,13 P. CORREA,13 D. F. COWEN,51, 52 R. CROSS,45 P. DAVE,6 C. DE CLERCQ,13 J. J. DELAUNAY,52 H. DEMBINSKI,39

K. DEOSKAR,46 S. DE RIDDER,27 P. DESIATI,35 K. D. DE VRIES,13 G. DE WASSEIGE,13 M. DE WITH,10 T. DEYOUNG,22 A. DIAZ,14

J. C. DÍAZ-VÉLEZ,35 H. DUJMOVIC,29 M. DUNKMAN,52 E. DVORAK,43 B. EBERHARDT,35 T. EHRHARDT,36 P. ELLER,52 R. ENGEL,29

P. A. EVENSON,39 S. FAHEY,35 A. R. FAZELY,7 J. FELDE,17 K. FILIMONOV,8 C. FINLEY,46 D. FOX,51 A. FRANCKOWIAK,55

E. FRIEDMAN,17 A. FRITZ,36 T. K. GAISSER,39 J. GALLAGHER,34 E. GANSTER,1 S. GARRAPPA,55 L. GERHARDT,9 K. GHORBANI,35

T. GLAUCH,25 T. GLÜSENKAMP,24 A. GOLDSCHMIDT,9 J. G. GONZALEZ,39 D. GRANT,22 Z. GRIFFITH,35 S. GRISWOLD,45

M. GÜNDER,1 M. GÜNDÜZ,11 C. HAACK,1 A. HALLGREN,53 R. HALLIDAY,22 L. HALVE,1 F. HALZEN,35 K. HANSON,35 A. HAUNGS,29

D. HEBECKER,10 D. HEEREMAN,12 P. HEIX,1 K. HELBING,54 R. HELLAUER,17 F. HENNINGSEN,25 S. HICKFORD,54 J. HIGNIGHT,23

G. C. HILL,2 K. D. HOFFMAN,17 R. HOFFMANN,54 T. HOINKA,21 B. HOKANSON-FASIG,35 K. HOSHINA,35 F. HUANG,52 M. HUBER,25

T. HUBER,29, 55 K. HULTQVIST,46 M. HÜNNEFELD,21 R. HUSSAIN,35 S. IN,48 N. IOVINE,12 A. ISHIHARA,15 G. S. JAPARIDZE,5

M. JEONG,48 K. JERO,35 B. J. P. JONES,4 F. JONSKE,1 R. JOPPE,1 D. KANG,29 W. KANG,48 A. KAPPES,38 D. KAPPESSER,36 T. KARG,55

M. KARL,25 A. KARLE,35 U. KATZ,24 M. KAUER,35 J. L. KELLEY,35 A. KHEIRANDISH,35 J. KIM,48 T. KINTSCHER,55 J. KIRYLUK,47

T. KITTLER,24 S. R. KLEIN,8, 9 R. KOIRALA,39 H. KOLANOSKI,10 L. KÖPKE,36 C. KOPPER,22 S. KOPPER,50 D. J. KOSKINEN,20

M. KOWALSKI,10, 55 K. KRINGS,25 G. KRÜCKL,36 N. KULACZ,23 N. KURAHASHI,42 A. KYRIACOU,2 J. L. LANFRANCHI,52

M. J. LARSON,17 F. LAUBER,54 J. P. LAZAR,35 K. LEONARD,35 A. LESZCZYNSKA,29 M. LEUERMANN,1 Q. R. LIU,35 E. LOHFINK,36

C. J. LOZANO MARISCAL,38 L. LU,15 F. LUCARELLI,26 J. LÜNEMANN,13 W. LUSZCZAK,35 Y. LYU,8, 9 W. Y. MA,55 J. MADSEN,44

G. MAGGI,13 K. B. M. MAHN,22 Y. MAKINO,15 P. MALLIK,1 K. MALLOT,35 S. MANCINA,35 I. C. MARIS,12 R. MARUYAMA,40

K. MASE,15 R. MAUNU,17 F. MCNALLY,33 K. MEAGHER,35 M. MEDICI,20 A. MEDINA,19 M. MEIER,21 S. MEIGHEN-BERGER,25

G. MERINO,35 T. MEURES,12 J. MICALLEF,22 D. MOCKLER,12 G. MOMENTÉ,36 T. MONTARULI,26 R. W. MOORE,23 R. MORSE,35

M. MOULAI,14 P. MUTH,1 R. NAGAI,15 U. NAUMANN,54 G. NEER,22 H. NIEDERHAUSEN,25 M. U. NISA,22 S. C. NOWICKI,22

D. R. NYGREN,9 A. OBERTACKE POLLMANN,54 M. OEHLER,29 A. OLIVAS,17 A. O’MURCHADHA,12 E. O’SULLIVAN,46

T. PALCZEWSKI,8, 9 H. PANDYA,39 D. V. PANKOVA,52 N. PARK,35 P. PEIFFER,36 C. PÉREZ DE LOS HEROS,53 S. PHILIPPEN,1

D. PIELOTH,21 E. PINAT,12 A. PIZZUTO,35 M. PLUM,37 A. PORCELLI,27 P. B. PRICE,8 G. T. PRZYBYLSKI,9 C. RAAB,12 A. RAISSI,16

M. RAMEEZ,20 L. RAUCH,55 K. RAWLINS,3 I. C. REA,25 R. REIMANN,1 B. RELETHFORD,42 M. RENSCHLER,29 G. RENZI,12

E. RESCONI,25 W. RHODE,21 M. RICHMAN,42 S. ROBERTSON,9 M. RONGEN,1 C. ROTT,48 T. RUHE,21 D. RYCKBOSCH,27

D. RYSEWYK,22 I. SAFA,35 S. E. SANCHEZ HERRERA,22 A. SANDROCK,21 J. SANDROOS,36 M. SANTANDER,50 S. SARKAR,41

S. SARKAR,23 K. SATALECKA,55 M. SCHAUFEL,1 H. SCHIELER,29 P. SCHLUNDER,21 T. SCHMIDT,17 A. SCHNEIDER,35

J. SCHNEIDER,24 F. G. SCHRÖDER,29, 39 L. SCHUMACHER,1 S. SCLAFANI,42 S. SEUNARINE,44 S. SHEFALI,1 M. SILVA,35 R. SNIHUR,35

J. SOEDINGREKSO,21 D. SOLDIN,39 M. SONG,17 G. M. SPICZAK,44 C. SPIERING,55 J. STACHURSKA,55 M. STAMATIKOS,19

T. STANEV,39 R. STEIN,55 J. STETTNER,1 A. STEUER,36 T. STEZELBERGER,9 R. G. STOKSTAD,9 A. STÖSSL,15 N. L. STROTJOHANN,55

T. STÜRWALD,1 T. STUTTARD,20 G. W. SULLIVAN,17 I. TABOADA,6 F. TENHOLT,11 S. TER-ANTONYAN,7 A. TERLIUK,55 S. TILAV,39

K. TOLLEFSON,22 L. TOMANKOVA,11 C. TÖNNIS,49 S. TOSCANO,12 D. TOSI,35 A. TRETTIN,55 M. TSELENGIDOU,24 C. F. TUNG,6

A. TURCATI,25 R. TURCOTTE,29 C. F. TURLEY,52 B. TY,35 E. UNGER,53 M. A. UNLAND ELORRIETA,38 M. USNER,55

J. VANDENBROUCKE,35 W. VAN DRIESSCHE,27 D. VAN EIJK,35 N. VAN EIJNDHOVEN,13 J. VAN SANTEN,55 S. VERPOEST,27

M. VRAEGHE,27 C. WALCK,46 A. WALLACE,2 M. WALLRAFF,1 N. WANDKOWSKY,35 T. B. WATSON,4 C. WEAVER,23 A. WEINDL,29

M. J. WEISS,52 J. WELDERT,36 C. WENDT,35 J. WERTHEBACH,35 B. J. WHELAN,2 N. WHITEHORN,32 K. WIEBE,36 C. H. WIEBUSCH,1

L. WILLE,35 D. R. WILLIAMS,50 L. WILLS,42 M. WOLF,25 J. WOOD,35 T. R. WOOD,23 K. WOSCHNAGG,8 G. WREDE,24 D. L. XU,35

X. W. XU,7 Y. XU,47 J. P. YANEZ,23 G. YODH,28 S. YOSHIDA,15 T. YUAN,35 AND M. ZÖCKLEIN1

ICECUBE COLLABORATION

1III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany2Department of Physics, University of Adelaide, Adelaide, 5005, Australia

3Dept. of Physics and Astronomy, University of Alaska Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA4Dept. of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA

5CTSPS, Clark-Atlanta University, Atlanta, GA 30314, USA6School of Physics and Center for Relativistic Astrophysics, Georgia Institute of Technology, Atlanta, GA 30332, USA

7Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA

analysis@icecube.wisc.edu

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2 M. AARTSEN ET AL.

8Dept. of Physics, University of California, Berkeley, CA 94720, USA9Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

10Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany11Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany

12Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium13Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium

14Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA15Dept. of Physics and Institute for Global Prominent Research, Chiba University, Chiba 263-8522, Japan

16Dept. of Physics and Astronomy, University of Canterbury, Private Bag 4800, Christchurch, New Zealand17Dept. of Physics, University of Maryland, College Park, MD 20742, USA

18Dept. of Astronomy, Ohio State University, Columbus, OH 43210, USA19Dept. of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH 43210, USA

20Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark21Dept. of Physics, TU Dortmund University, D-44221 Dortmund, Germany

22Dept. of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA23Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1

24Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany25Physik-department, Technische Universität München, D-85748 Garching, Germany

26Département de physique nucléaire et corpusculaire, Université de Genève, CH-1211 Genève, Switzerland27Dept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium

28Dept. of Physics and Astronomy, University of California, Irvine, CA 92697, USA29Karlsruhe Institute of Technology, Institut für Kernphysik, D-76021 Karlsruhe, Germany

30Dept. of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA31SNOLAB, 1039 Regional Road 24, Creighton Mine 9, Lively, ON, Canada P3Y 1N2

32Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095, USA33Department of Physics, Mercer University, Macon, GA 31207-0001, USA

34Dept. of Astronomy, University of Wisconsin, Madison, WI 53706, USA35Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA

36Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany37Department of Physics, Marquette University, Milwaukee, WI, 53201, USA

38Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany39Bartol Research Institute and Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA

40Dept. of Physics, Yale University, New Haven, CT 06520, USA41Dept. of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK

42Dept. of Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA43Physics Department, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA

44Dept. of Physics, University of Wisconsin, River Falls, WI 54022, USA45Dept. of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA

46Oskar Klein Centre and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden47Dept. of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA

48Dept. of Physics, Sungkyunkwan University, Suwon 16419, Korea49Institute of Basic Science, Sungkyunkwan University, Suwon 16419, Korea

50Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA51Dept. of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, USA

52Dept. of Physics, Pennsylvania State University, University Park, PA 16802, USA53Dept. of Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden

54Dept. of Physics, University of Wuppertal, D-42119 Wuppertal, Germany55DESY, D-15738 Zeuthen, Germany

(Dated: January 8, 2020)

ABSTRACT

During the first three flights of the Antarctic Impulsive Transient Antenna (ANITA) experiment, the collabo-ration detected several neutrino candidates. Two of these candidate events were consistent with an ultra-high-energy up-going air shower and compatible with a tau neutrino interpretation. A third neutrino candidate eventwas detected in a search for Askaryan radiation in the Antarctic ice, although it is also consistent with the back-

ICECUBE-ANITA POINT SOURCE SEARCH 3

ground expectation. The inferred emergence angle of the first two events is in tension with IceCube and ANITAlimits on isotropic cosmogenic neutrino fluxes. Here, we test the hypothesis that these events are astrophysicalin origin, possibly caused by a point source in the reconstructed direction. Given that any ultra-high-energy tauneutrino flux traversing the Earth should be accompanied by a secondary flux in the TeV-PeV range, we searchfor these secondary counterparts in seven years of IceCube data using three complementary approaches. In theabsence of any significant detection, we set upper limits on the neutrino flux from potential point sources. Wecompare these limits to ANITA’s sensitivity in the same direction and show that an astrophysical explanation ofthese anomalous events under standard model assumptions is severely constrained regardless of source spectrumor time profile.

1. INTRODUCTION

Ever since the detection of high-energy neutrinos of cos-mic origin by IceCube in 2013 (Aartsen et al. 2013a), exper-iments and theoreticians alike have continued to probe thenon-thermal processes in the Universe to understand theirorigins. The bulk of these astrophysical neutrinos are be-lieved to be created in hadronic interactions between cosmicrays and ambient matter or radiation fields in the vicinity ofcosmic accelerators (Gaisser et al. 1995) and their detectionscan be used to point back to the acceleration sites. Althoughthe first evidence of a neutrino point source, the blazar TXS0506+056, was reported in 2018 (Aartsen et al. 2018c,b),the overwhelming majority of the measured neutrino flux re-mains unexplained.

Additionally, another population of neutrinos could existat extremely high energies. Cosmogenic neutrinos are be-lieved to be the result of interactions between ultra-high en-ergy (UHE) cosmic rays with the cosmic microwave back-ground (CMB) (Greisen 1966; Zatsepin & Kuzmin 1966).This population is expected to manifest as an isotropic flux atEarth, as cosmic ray primaries can travel outside of the vicin-ity of their accelerators before interacting with the CMB.

The Antarctic Impulsive Transient Antenna (ANITA) ex-periment is a balloon experiment, designed with the pri-mary purpose of detecting the UHE cosmogenic neutrinoflux (Gorham et al. 2009; Hoover et al. 2010; Gorham et al.2018a). Although this is the experiment’s primary scientificgoal, it is sensitive to a wide array of impulsive radio sig-nals, and the experiment’s first three flights have resultedin a few interesting detections. In this work we focus onthree events observed by ANITA in their searches, all ofwhich have potential neutrino interpretations. Throughoutthis work we refer to and explore them as “neutrino candi-dates”. In the third flight, one Askaryan neutrino candidate(AAC) event was simultaneously identified in one analysissearching for Askaryan emission (Askar’yan 1962) and wasfound to be subthreshold in another. This Earth-skimmingevent has a signal shape consistent with impulsive broad-band emission characteristic of a neutrino origin and it alsocame from a location on the continent consistent with simu-lated distribution of neutrinos of all flavors (Gorham et al.2018a). However, the detection of one candidate event isconsistent with the background level estimates of 0.7+0.5

−0.3 for

these analyses. ANITA also reported two additional events,each consistent with an astrophysical ντ emerging from theEarth (Gorham et al. 2016, 2018b). In this scenario, a ντ un-dergoes a charged-current interaction (CC) with a nucleus inthe Earth. The τ -lepton produced in this interaction subse-quently decays in the atmosphere, producing an extensive airshower (EAS). The polarity of the radio signal makes it pos-sible to identify and reject downward moving cosmic-ray in-duced EAS, as the radio signals of these EAS acquire a phasereversal (opposite polarity) from reflection off the Antarcticice, while an upgoing τ induced EAS does not acquire thisphase reversal. For a complete list of details of these events,see Table 1.

The interpretation of these events as extremely high en-ergy upgoing neutrinos poses many challenges under Stan-dard Model assumptions. First, from the observation an-gles and reconstructed energies of the ANITA events, neutri-nos are extremely unlikely to traverse the long chord lengths(Gorham et al. 2016), even after accounting for the probabil-ity increase due to ντ regeneration. Second, if these eventsare of cosmogenic origin, they would imply fluxes that are insevere tension with limits set by multiple experiments (Aabet al. 2015; Zas 2018; Aartsen et al. 2016a) as well as aself-inconsistency from ANITA data alone. For an isotropicflux of cosmogenic neutrinos ANITA should have detectedmany more events at other elevation angles than those of theanomalous ANITA events (AAE) as the detector differen-tial acceptance changes with the observation-angle (Romero-Wolf et al. 2018).

On the other hand, if the origin of ANITA events is con-sidered to be from individual cosmic accelerators there is noinconsistency with diffuse extremely-high-energy flux lim-its. This is especially true for accelerators with short char-acteristic timescales of emission, as many current limits onneutrino point-sources are for integrated emission over var-ious experiments’ livetimes (Aartsen et al. 2019a) and alsoas the acceptance of ANITA to a specific location on the skychanges throughout the detector’s flight. If we assume thatANITA detected single events of 1 EeV from a comic ac-celerator with a E−γ emission power-law spectrum, then oneshould expect also a larger flux of neutrinos at TeV - PeVenergies, where IceCube will be sensitive. Significant cor-relation between IceCube and ANITA data would not only

4 M. AARTSEN ET AL.

Table 1. Properties of the neutrino candidate events from the first three flights of ANITA, from (Gorham et al. 2018a,2016, 2018b). The two Anomalous ANITA Events (AAE) are those consistent with a steeply upgoing ντ interpretation.

AAE-061228 AAE-141220 AAC-150108

Event, Flight 3985267, ANITA-I 15717147, ANITA-III 83139414, ANITA-IIIDetection Channel Geomagnetic Geomagnetic AskaryanDate, Time (UTC) 2006-12-28, 00:33:20 2014-12-20, 08:33:22.5 2015-01-08, 19:04:24.237RA, Dec (J2000)

1282◦.14, +20◦.33 50◦.78, +38◦.65 171◦.45, +16◦.30

Localization Uncertainty2

1◦.5 × 1◦.5, 0◦.0 1◦.5 × 1◦.5, 0◦.0 5◦.0 × 1◦.0, +73◦.7Reconstructed Energy (EeV) 0.6 ± 0.4 0.56+0.30

−0.20 ≥ 10Earth Chord Length (km) 5740 ± 60 7210 ± 55 -

1Sky coordinates are projections from event arrival angles at ANITA

2Expressed as major and minor axis standard deviations, position angle. This angle describes the rotation of the major axis relative tothe North Celestial Pole turning positive into right ascension.

provide evidence for a neutrino point source, it would alsoeliminate non-astrophysical explanations of the AAE, suchas background and systematics or non-astrophysical modelswhich invoke physics beyond the Standard Model.

The focus of this work is to use IceCube to investigate thehypothesis that the ANITA events were from neutrino point-sources, considering several neutrino emission time profiles.In section 2 we discuss the IceCube Neutrino Observatoryand the event samples used for these analyses. In section 3we describe the analysis techniques and summarize the re-sults in section 4. In section 5 and 6 we investigate neutrinopropagation through large Earth chord lengths to discuss theimplications of our results.

2. DATA SAMPLE

IceCube is a cubic-kilometer neutrino detector with 5160digital optical modules (DOMs) instrumented on 86 cablestrings in the clear glacial ice at the geographic South Pole,between depths of 1450 m and 2450 m (Achterberg et al.2006; Aartsen et al. 2017b). Neutrinos are detected throughthe Cherenkov radiation emitted by secondary particles pro-duced by neutrino interactions in the surrounding ice orbedrock. Each DOM consists of a 10 inch photomulti-plier tube, on-board read-out electronics, and a high-voltageboard, all contained in a pressurized spherical glass container(Abbasi et al. 2009, 2010). Parameterization of the scatter-ing and absorption of the glacial ice allows for accurate en-ergy and directional reconstruction of neutrino events (Aart-sen et al. 2013b).

The improved reconstruction techniques adopted to createthe event selection (Carver 2019; Aartsen et al. 2019b) in-clude updates in the direction reconstruction (Ahrens et al.2004; Aartsen et al. 2014a) to use information on the de-posited event energy in the detector. The median angularresolution benefits from a 10% improvement above 10 TeV(where it is smaller than 0.60◦) compared to previous selec-tions (Aartsen et al. 2017a).

While in the southern sky the trigger rate is dominatedby atmospheric muons from cosmic-ray air showers, all ofthe ANITA candidates have best-fit directions in the north-ern sky. Here, the Earth attenuates the majority of the atmo-spheric muon signal, and the background at final selectionlevel in the northern sky is dominated by atmospheric muonneutrinos from cosmic-ray air showers (Haack & Wiebusch2018). Poorly reconstructed atmospheric muons from thesouthern sky as well as neutrino induced cascades are alsonon-negligibile backgrounds in this region of the sky, and areremoved using a multivariate boosted decision tree trainedto distinguish between neutrino induced muon tracks, atmo-spheric muons, and cascades, which is described in (Carver2019; Aartsen et al. 2019b).

For the analyses presented here, we focus on the full de-tector configuration of 86 strings, spanning a time windowfrom 2011 to 2018. Approximately 900,000 events from2532 days are analyzed.

3. LIKELIHOOD ANALYSES

Many previous IceCube analyses searching for neutrinopoint sources relied on significant spatial clustering of Ice-Cube data alone or of significant association with knownpopulations of astrophysical objects (Aartsen et al. 2019a,2016b, 2017a, 2013c; Abbasi et al. 2011; Aartsen et al.2014b). Here, we adopt the procedure described in (Schu-macher 2019) to search for counterparts to ANITA events.Namely, we perform three separate analyses to test differenttemporal hypotheses in the neutrino emission. Each of theseanalyses incorporates the information from the localizationof the ANITA events through a joint likelihood. The sky isdivided into grid positions, xs, and at each point we maxi-mize the likelihood, L, with respect to the expected numberof signal events, ns, and other signal parameters contained inthe variable α depending on the different signal hypothesistested as described in sections 3.2 and 3.3. This likelihood isgiven by

ICECUBE-ANITA POINT SOURCE SEARCH 5

L = λN∏

i=1

(ns

ns + nbS(xi,xs,α) +

nb

ns + nbB(xi,xs)

)PA(xs), (1)

where nb is the expected number of observed backgroundevents, and N is the total number of observed events in thetime window. The vector xi contains the event observablessuch as its reconstructed energy, direction, and reconstructionuncertainty. PA is the spatial probability distribution function(PDF) of ANITA events, which are included in Table 1. Bdescribes the energy and declination PDF of our background,which is parameterized from data and is the same among allanalyses. Temporal terms in B are described in sections 3.1and 3.2. While the signal PDF S describes the signal hypoth-esis, the parameter λ modifies the likelihood formalism inorder to take into account low-statistics problems in some ofthe analyses. In general, the signal PDF, S, is defined as

S = Sspace(xi,xs,σi) ·Senergy(Ei, δi,γ) ·Stime . (2)

These three terms reflect the spatial, energy, and time PDF,respectively, of our signal hypothesis. The spatial term,Sspace, expresses the probability for an event with best-fit re-constructed direction xi to originate from a source at the di-rection xs, according to a two-dimensional Gaussian functionwith angular resolution σi. The energy PDF Senergy describesthe probability of obtaining an event with reconstructed en-ergy Ei given a declination δi under the hypothesis of an E−γ

power-law energy spectrum, which helps differentiate signalfrom the known atmospheric backgrounds in our event selec-tion. The time term, Stime describes the time PDF of eventsobserved from the source. While the spatial term is sharedbetween all analyses, the energy and temporal term is uniqueto each individual analysis. This joint likelihood procedure iscarried out in three complementary search strategies: prompt,rolling, and steady.

3.1. Prompt

The first analysis searches for IceCube events in spatialcoincidence with the ANITA events in short time windows,∆t, centered on each ANITA event. We call this period theon-time window. This is equivalent to setting Stime equal to auniform PDF in this on-time window, and set to zero for alltimes outside of this window. To help distinguish potentialsignals for time windows in which the expected number ofbackground events is small, we set

λ =(ns + nb)N

N!· e−(ns+nb) (3)

as in (Aartsen et al. 2018a, 2015a). Due to the small statis-tics for short time windows, the likelihood is only maximizedwith respect to ns, and the energy dependence in Senergy is

fixed to an E−2 spectrum. To account for the temperature de-pendence of atmospheric muon rates (Aartsen et al. 2013d),we determine nb by calculating the rate of events from thesurrounding 5 days of data on either side of our on-time win-dow. Taking the logarithmic likelihood ratio between themaximum likelihood and that of the null hypothesis resultsin our test statistic (TS), defined as

TS = −2ns +

N∑i=1

2log[

1 +nsS(xi,xs)

nbB(xi)

]+ 2log

[PA(xs)PA(x0)

], (4)

where x0 is the reported best fit location of the ANITA event.TS is calculated for all xs, and the maximum value is re-ported. For this analysis, PA is a two-dimensional Gaussianassuming the localization uncertainties reported in Table 1.As we are not motivated by a specific astrophysical class ofobjects with characteristic timescales of emission, we con-sider constant emission over various time windows for eachof the ANITA events. This technique is similar to previousIceCube searches for gamma-ray bursts and fast radio bursts(Aartsen et al. 2018a, 2015a). AAE-061228 is excluded fromthis analysis because it occurred before IceCube had attaineda full detector configuration. For AAC-150109 we considerthree separate time windows, (10 s, 103 s, 105 s). Duringthe event time of AAE-141220, IceCube was temporarily notcollecting data, due to a run transition that had begun approx-imately 0.5 seconds before the event and lasting for aboutone minute. Because of this, we only investigate hypothesesof constant emission over two time windows (103 s and 105

s), where the period of time from the run transition is not anappreciable portion of our on-time window.

3.2. Rolling

The second analysis also searches for temporal and spatialclustering of IceCube events, but does not require the tempo-ral coincidence between IceCube and ANITA events. In thisuntriggered analysis (Braun et al. 2010; Aartsen et al. 2015b),we assume a Gaussian time dependence to parameterize alimited duration increase in the emission of the source:

Stime =1√2πσ

e−

(t0−ti)2

2σ2t , (5)

where t0 and σt are the Gaussian mean time and Gaussianwidth of the flare, respectively. In the limit of large N, we arefree to set λ to 1, and the increase in statistics allows us to fitfor γ in the range 1 ≤ γ ≤ 4 in addition to ns, as is donein many previous IceCube analyses (Aartsen et al. 2016b,2017a, 2013c; Abbasi et al. 2011; Aartsen et al. 2014b). Ad-ditionally, we set ns + nb to be equal to the number of events,N. The TS for this analysis is then

TS = −2log[

T√2πσt

× L(ns = 0)L(ns, γ, σt , t0)

], (6)

6 M. AARTSEN ET AL.

Figure 1. Skymaps (top) and TS distributions (bottom) for AAE-141220 for the prompt (left), rolling (middle), and steady (right) analyses.Observed TS values (shown in red) are compared to distributions from time-scrambled data realizations to quantify the significance. In theprompt analysis skymap, the best-fit location of each IceCube event is represented with an x, and the size of the circle represents the uncertainty(90% containment) on the event’s reconstruction, with color representing the IceCube event arrival time relative to the ANITA event. In therolling and steady analysis skymaps, color reflects the TS values defined in sections 3.2 and 3.3 respectively.

where ns, γ, σt , t0 are the best-fit values from the likelihoodmaximization and T is the total live time of the data-takingperiod. The multiplicative factor in front of the likelihoodratio in Eq. 6 is a marginalization term to avoid undesiredbiases toward finding short flares, as explained in (Braunet al. 2010). The TS is calculated at the positions of a coarsesky grid (1◦×1◦ bin widths), built at the central coordinatesof the ANITA events and covering 99.9% of the their two-dimensional spatial PDFs, but sets PA to be a uniform distri-bution covering this extended region. As the PDF is taken tobe uniform in this analysis, there is no term in the TS thatis dependent on PA. The location of the maximum TS fromthe coarse search is then used as a seed to perform a furtherlikelihood maximization, where the direction of the source,xs, is also reconstructed.

3.3. Steady

The third and final analysis tests for spatial clustering overseven years of IceCube data, assuming constant emission inthe signal hypothesis, by setting Stime to be a uniform PDFover the entire data collection period. As in the rolling anal-ysis, we take λ to be 1, and fit for γ in the likelihood max-imization process. At all xs we calculate the redefined TS

TS = 2 · log[ L (xs, ns, γ)L (xs,ns = 0)

]+ 2log

[PA(xs)PA(x0)

], (7)

with best-fit values ns and γ. The PDF of ANITA events inthis analysis is taken to be the same as in the prompt analysis,namely, a two-dimensional Gaussian.

4. RESULTS

No significant correlation is found in any of the analysesabove the expectation from background. In order to calculatep-values, results are compared against pseudo-experimentsfrom time-scrambled data (Aartsen et al. 2015b). The mostsignificant observation results from the steady search forAAE-141220, with a p-value of 0.08, which we find to beconsistent with background.

Figure 1 displays the skymaps for the prompt, rolling,and steady analyses from left to right in the top panels forAAE-141220. Bottom panels of Figure 1 show the com-parison of the observed TS values for each analysis, at theposition of the red lines, to their respective TS distributionsfrom pseudo-experiments using time-scrambled data. Simi-lar plots for AAE-061228 and AAC-150108 are displayed inFigure 6.

ICECUBE-ANITA POINT SOURCE SEARCH 7

101 102 103 104 105 106 107 108

∆t (seconds)

10−2

10−1

100

E2F

@1

TeV

(GeV

cm−

2)

E−2 Upper Limits (90% C.L.)

Prompt Sensitivity

Prompt Discovery Potential (3σ, 90% C.L.)

Steady Upper Limit

AAE-061228

AAE-141220

AAC-150108

Figure 2. Sensitivity (dotted) and upper limits (arrows) (90% confi-dence level) on the time-integrated νµ + νµ flux normalization for anE−2 source spectrum as a function of ∆t from the prompt analysis,compared to the upper limits (solid) from the steady analysis. Thecentral 90% intervals of the expected neutrino energies for thesespectra are 1TeV-1PeV.

In the absence of a significant signal, upper limits (90%confidence level) for the time-integrated νµ + νµ flux are setfor each ANITA event where possible using the prompt andsteady analyses (Figure 2). To calculate upper limits, loca-tions are sampled according to the per-event PDFs reportedby ANITA, injecting the same level of flux at each sampledlocation, and running each iteration through the full analysisprocedure which maximizes the joint likelihood at all loca-tions on the sky. This allows us to place upper limits onpoint-sources whose locations are distributed according tothe per-event PDF reported by ANITA. We set these limitsfor an assumed spectrum given by

Φ(E, t) =dNνµ+νµ

dE dAdt= Φ0

( EE0

)−2, (8)

where Φ0 is a normalization constant on a point-source flux,which carries units of GeV−1cm−2s−1. We constrain the time-integrated muon neutrino flux, E2F , where

E2F = E2∫

Φ(E, t)dt . (9)

All of the limits we calculate are provided in Table 2. Inthe case that an upper limit fluctuates below the sensitivity,we conservatively set the upper limit to the sensitivity value.Prompt limits are placed at the specified time windows foremission centered on the ANITA event times, whereas limitsfrom the steady analysis are for emission over the livetime ofour data sample. This hard spectrum was chosen conserva-tively because with the observation of EeV events by ANITA,if the underlying spectrum is softer, then the expected num-ber of observable neutrinos for IceCube would increase. Asthe time-integrated flux sensitivity for the triggered analysisbegins to worsen past 105 s, upper limits for ∆t > 105 s areonly set using the time-integrated approach.

5. DISCUSSION

For many astrophysical sources, power-law spectra in pho-tons are common over finite energy ranges. Additionally, dif-fusive shock acceleration models suggest that the neutrinospectrum, as well as gamma rays from pion decay, shouldfollow a power-law spectrum, justifying the choice of test-ing power-laws for corresponding neutrino spectra. How-ever, for the ANITA events, interpolating a power law be-tween the energy range at which IceCube is sensitive to thebest-fit ANITA event energies could pose a problem. For softspectra, events detected by ANITA would suggest that manyevents would be detectable at IceCube. For hard spectra, ex-trapolating between IceCube and ANITA would imply dra-matic bolometric neutrino luminosities for any point source.

However even in the case of non-power-law neutrino emis-sion, the limits we can set on muon neutrinos in the TeV-PeVenergy range can constrain generic fluxes of incident tau neu-trinos with EeV energies. As has been shown in (Safa et al.2020), any incident flux with an EeV ντ component that tra-verses large Earth chord lengths will result in a secondaryflux of lower energy neutrinos, to which IceCube would besensitive. We use the same prescription here to analyze howconstraining our limits are on a generic point source flux thatincludes EeV neutrinos.

For any incident flux of neutrinos from the northern sky,Φ(Eν , t), the number of expected detected tau neutrino in-duced muon events at IceCube is given by

〈NµIceCube〉 =

∫dEµ

∫dEτ

∫dEνΦ (Eν , t)Psurv

τ (Eν)dNτ (Eτ )

dEτ

Γτ→µ

Γtotal

dNµ

dEµ

(Eτ ,Eµ

)Aµ

e f f

(Eµ

)∆T (10)

+

∫dEµ

∫dEτ

∫dE ′ν

∫dEνΦ (Eν , t)Pν

(Eν ,E ′ν

) dNν

dE ′ν

(E ′ν)

N p (E ′ν) dNτ

dEτ

(E ′ν ;Eτ

) Γτ→µ

Γtotal

dNµ

dEµ

(Eτ ;Eµ

)Aµ

e f f

(Eµ

)∆T ,

where the first contribution is from emerging tau-leptons thatwould decay to muons and then pass an IceCube event selec-

tion. The second contribution is from the remaining ντ flux,

8 M. AARTSEN ET AL.

Table 2. Analysis results and upper limits. Upper limits (90% C.L) are on the time-integrated νµ + νµ power law flux (E−2 ) from a point-sourcefollowing the spatial probability distribution provided by ANITA. Limits are set assuming constant emission over a fixed time window. As thetemporal profile of emission is fit for in the rolling analysis, no upper limits are placed from that analysis. Time windows for the steady androlling analyses are listed as the IceCube seasons analyzed, where IC86-I contains 2.88×107 s of data and 1.90×108 s for IC86-II - IC86-VII.

Event Analysis Time Window p-value Upper limit (GeV · cm−2)

AAE-061228Steady IC86-I - IC86-VII 0.606 0.195

RollingIC86-I 0.562 -

IC86-II - IC86-VII 0.208 -

AAE-141220

10s 1.0 -Prompt 103s 1.0 0.053

105s 1.0 0.051Steady IC86-I - IC86-VII 0.081 0.401

RollingIC86-I 0.342 -

IC86-II - IC86-VII 0.224 -

AAC-150108

10s 1.0 0.040Prompt 103s 1.0 0.041

105s 1.0 0.032Steady IC86-I - IC86-VII 0.210 0.278

RollingIC86-I 0.636 -

IC86-II - IC86-VII 0.512 -

2 3 4 5 6 7

log (Eµ

GeV)

105

106

Aµ eff

(m2)

Figure 3. Effective area of the IceCube event selection to muonsfrom the northern sky, incident on a volume 1.5 km away from theedge of the detector. Eµ is the muon energy incident on this volume.

the majority of which has cascaded down in energy. N p(Eν)is the number of targets effectively seen by an incident neu-trino with energy Eν . The effective area of this event selec-tion to muons incident on the detector is displayed in Fig-ure 3. Psurv

τ (Eν) and Pν(Eν) represent the survival probabil-ity of a τ -lepton and ντ , given an incident neutrino energy,respectively, and Γτ→µ

/Γtotal represents the branching ratio

for the tau-decay to muon channel, which is approximately18%.

Similarly, for ANITA, the number of expected events fromupgoing τ -leptons is given by

〈NτANITA〉 =

∫∫dEν dE ′νΦ (Eν , t)

dN(E ′ν)

dE ′νξacc(E ′ν)

∆T ,

where ξacc represents ANITA’s acceptance to τ -lepton airshowers, and is taken from (Romero-Wolf et al. 2018). Val-ues for the acceptance at angles which would require an in-cident neutrino to traverse a large column depth are set to theacceptance at the horizon. This removes absorption effectsin the reported acceptance, which is accounted for separatelywith the code used to propagate these fluxes, TauRunner,described in (Safa et al. 2020, 2019). We focus our analy-sis to the non-observation of coincident events in IceCube at∆T = 103 s. A similar procedure can be applied to longertime windows. Qualitatively, it would result in similar limitsup to the lifetime of the ANITA flight. For longer emissiontime-scales, limits from IceCube become even more con-straining as the implied normalization on the ANITA fluxwould have to increase to compensate for the fraction of timeduring which ANITA was not taking data.

To make as conservative a statement as possible, we in-ject fluxes described by delta-functions in energy, Φ(Eν , t) =Φ0δ(Eν − E0), where now the normalization carries units ofcm−2s−1. After propagating these mono-energetic fluxes, werecord what fraction of the incident flux results in a de-tectable signal at ANITA. We repeat this procedure for avariety of injected initial neutrino energies, so that we canfind the energy which yields the maximum probability of aτ -lepton arriving at ANITA with an energy within the quotedreconstructed energy bounds. We find that the optimal flux

ICECUBE-ANITA POINT SOURCE SEARCH 9

6 8 10 12log(Eτ/GeV)

10−10

10−9

10−8

10−7

10−6

10−5P

(Eτ>E

)

109 GeV

1010 GeV

1011 GeV

1012 GeV

1013 GeV

AAE-141220

Figure 4. Normalized cumulative distributions for Earth-emergingtau-leptons. Colors correspond to the incoming tau-neutrino energy,and the gray band is the 95% containment on the error of the recon-structed shower energy of AAE-141220.

for ANITA corresponds to an injected ντ flux with E0 = 1EeV. Normalized cumulative distributions from secondary τ -leptons are shown in Figure 4, for injected neutrinos at anglescorresponding to the best-fit reconstructed direction of AAE-141220.

We next inject a flux of EeV tau neutrinos, and find thespectral shape of the secondary ντ flux which would be in-cident on IceCube. As we observed 0 coincident events inthe time window of 103 s around AAE-141220 in the promptanalysis, we calculate the maximum allowed flux normaliza-tion (at 90% confidence level) on the primary flux that wouldevade this non-observation. The results are displayed in Fig-ure 5.

Although IceCube’s sensitivity is peaked many orders ofmagnitude below the reconstructed energies of the ANITAevents, the limits set on any potential neutrino source that cre-ated AAE-141220 are more constraining by several orders ofmagnitude than the implied flux by the ANITA observations.If one considers constant emission over the entire livetimeof the IceCube event selection, then the time-integrated fluxlimit set by the IceCube non-observation of AAE-141220 be-comes around one order of magnitude less constraining, as itis apparent in the steady limits in Figure 2. However, forthe implied normalization placed by ANITA observations,this value would increase by approximately two orders ofmagnitude, due to the limited livetime of the ANITA flight.This has the overall effect of increasing the tension betweenthese two normalizations by approximately one more orderof magnitude than for the 103 s followup shown in Figure 5.

6. CONCLUSION

Recent detections of events of interest by ANITA are con-sidered anomalous due to the small survival probability of

EeV tau-neutrinos through long chord lengths. The eventsare known to be inconsistent with a cosmogenic interpreta-tion, but could have been produced by cosmic accelerators,specifically those with short characteristic timescales. Weshow here that for timescales as small as 103 s, assumingAAE-141220 as originating from a neutrino source, limitsset using IceCube data are more than four orders of magni-tude in tension with the point source flux required to detectone event at ANITA. These limits are constraining for a va-riety of flux models, from simple power laws to any genericmodel that includes a component at or above EeV energies.In addition to the anomalous events, we also find no evi-dence for a neutrino source in the direction of the neutrinocandidate event from a search for Askaryan emission duringANITA-III. These new limits, in conjunction with the incon-sistency of isotropic flux interpretations, leave no room foran astrophysical interpretation of the AAE in the context ofthe Standard Model. However, it has been shown that theseevents can be explained using physics Beyond the StandardModel, as many models suggest that the AAE lend supportfor axionic dark matter, sterile neutrinos, supersymmetry, orheavy dark matter (Cherry & Shoemaker 2019; Anchordo-qui et al. 2018; Huang 2018; Dudas et al. 2018; Connollyet al. 2018; Fox et al. 2018; Collins et al. 2019; Esteban et al.2019). With the exception of the axionic dark matter expla-nation, all of these proposed models can be constrained bythis non-observation at IceCube, and dedicated tests to quan-tify these constraints will be the focus of another work. Inaddition to explanations that incite new physics, it has re-cently been suggested that the AAE could be explained bydownward-going CR-induced EAS that reflected off of sub-surface features in the Antarctic ice (Shoemaker et al. 2019).Another possible explanation could be coherent transition ra-diation from the geomagnetically-induced air shower current,which could mimic an upgoing air shower (de Vries & Pro-hira 2019). Explaining these anomalous events with system-atic effects or confirming the need for new physics requires adeeper understanding of ANITA’s detection volume. Effortssuch as the HiCal radio frequency pulser, which has flownalongside ANITA in the last two flights (Prohira et al. 2018),are already underway to try to characterize the various prop-erties of the Antarctic ice surface.

ACKNOWLEDGEMENTS

The IceCube collaboration acknowledges the significantcontributions to this manuscript from Anastasia Barbano,Alex Pizzuto, and Ibrahim Safa. The authors gratefully ac-knowledge the support from the following agencies and insti-tutions: USA – U.S. National Science Foundation-Office ofPolar Programs, U.S. National Science Foundation-PhysicsDivision, Wisconsin Alumni Research Foundation, Cen-ter for High Throughput Computing (CHTC) at the Uni-

10 M. AARTSEN ET AL.

103 104 105 106 107 108 109 1010

Eν (GeV)

10−2

100

102

104

106

108

1010

E2 νΦν∆T

(GeV

cm−

2)

Secondary ντ flux

EνΦ0∆T : IceCube 90% UL (ντ)

EνΦ0∆T : ANITA Event (ντ)

Prompt Followup 90% UL (νµ)

Figure 5. Upper limits (90% C.L.) placed by calculating the secondary neutrino flux (purple histogram) from an incident flux of EeV neutrinosassuming constant emission over 103 s and comparing to the non-observation of IceCube events in the prompt analysis described in Sect. 3.1for AAE-141220. The flux implied by the ANITA observations (black), represented in this figure as EνΦ0∆T = Eν∆T

∫Φ(Eν , t)dEν , using

information about ANITA’s acceptance (Romero-Wolf et al. 2018) overshoots this upper limit (purple arrow) by many orders of magnitude. Forcomparison, upper limits on the time-integrated muon-neutrino flux from the prompt analysis are shown in blue. All fluxes are per flavor ν + ν.

versity of Wisconsin-Madison, Open Science Grid (OSG),Extreme Science and Engineering Discovery Environment(XSEDE), U.S. Department of Energy-National Energy Re-search Scientific Computing Center, Particle astrophysicsresearch computing center at the University of Maryland,Institute for Cyber-Enabled Research at Michigan State Uni-versity, and Astroparticle physics computational facility atMarquette University; Belgium – Funds for Scientific Re-search (FRS-FNRS and FWO), FWO Odysseus and BigScience programmes, and Belgian Federal Science PolicyOffice (Belspo); Germany – Bundesministerium für Bildungund Forschung (BMBF), Deutsche Forschungsgemeinschaft(DFG), Helmholtz Alliance for Astroparticle Physics (HAP),Initiative and Networking Fund of the Helmholtz Associa-tion, Deutsches Elektronen Synchrotron (DESY), and HighPerformance Computing cluster of the RWTH Aachen; Swe-

den – Swedish Research Council, Swedish Polar ResearchSecretariat, Swedish National Infrastructure for Comput-ing (SNIC), and Knut and Alice Wallenberg Foundation;Australia – Australian Research Council; Canada – Natu-ral Sciences and Engineering Research Council of Canada,Calcul Québec, Compute Ontario, Canada Foundation forInnovation, WestGrid, and Compute Canada; Denmark – Vil-lum Fonden, Danish National Research Foundation (DNRF),Carlsberg Foundation; New Zealand – Marsden Fund; Japan– Japan Society for Promotion of Science (JSPS) and Insti-tute for Global Prominent Research (IGPR) of Chiba Univer-sity; Korea – National Research Foundation of Korea (NRF);Switzerland – Swiss National Science Foundation (SNSF);United Kingdom – Department of Physics, University ofOxford.

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Figure 6. (Top two rows) Skymaps and TS distributions from all three analyses for AAC-150108. For AAE-061228, IceCube was not in afull detector configuration at the time of the event, and thus only the steady and rolling analyses were used to search for neutrino emission.Skymaps and TS distributions for these analyses are displayed in the bottom two rows.