Antarctic Radio Frequency Albedo and Implications for Cosmic Ray Reconstruction

0.93 MB·English

by  D. Z. Besson

Antarctic Radio Frequency Albedo and Implications for Cosmic Ray Reconstruction
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D.Z.Bessona,J.Stockhama,M.Sullivana,P.Allisonb,e,S.W.Barwickd,B.M.Baughmane,J.J.Beattye,K.Belovc,S.Bevanf,
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W.R.Binnsg,C.Chenh,P.Chenh,J.M.Clemi,A.Connollye,D.DeMarcoi,P.F.Dowkonttg,M.DuVernoisb,D.Goldsteind,P.
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W.Gorhamb,E.W.Grashorne,B.Hillb,S.Hooverc,k,l,M.Huangj,M.H.Israelg,A.Javaidi,J.Kowalskib,J.Learnedb,K.M.
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Liewerj,S.Matsunob,B.C.Mercurioe,C.Mikib,M.Mottramf,J.Namd,h,C.J.Naudetj,R.J.Nicholf,K.Palladinoe,A.
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Romero-Wolfb,j,L.Ruckmanb,D.Saltzbergc,D.Seckeli,R.Y.Shangh,M.Stockhama,G.S.Varnerb,A.G.Viereggc,m,andY.
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Wangh
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8 aDepartmentofPhysicsandAstronomy,UniversityofKansas,Lawrence,Kansas66045,USA
9 bDept.ofPhysicsandAstronomy,UniversityofHawaiiatManoa,Honolulu,HI96822.
10 cDept.ofPhysicsandAstronomy,UniversityofCalifornia,LosAngeles,CA90095.
11 dDepartmentofPhysics,UniversityofCalifornia,Irvine,California92697,USA
12 eDepartmentofPhysics,OhioStateUniversity,Columbus,Ohio43210,USA
13 fDepartmentofPhysicsandAstronomy,UniversityCollegeLondon,London,UnitedKingdom
14 gDepartmentofPhysics,WashingtonUniversityinSt.Louis,Missouri63130,USA
15 hDepartmentofPhysics,NationalTaiwanUniversity,Taipei,Taiwan10617
16 iDepartmentofPhysics,UniversityofDelaware,Newark,Delaware19716,USA
17 jJetPropulsionLaboratory,Pasadena,California91109,USA
18 kKavliInstituteforCosmologicalPhysics,UniversityofChicago,5640SouthEllisAvenue,Chicago,IL60637
319 lEnricoFermiInstitute,UniversityofChicago,5640SouthEllisAvenue,Chicago,IL60637
120 mHarvard-SmithsonianCenterforAstrophysics,Cambridge,Massachusetts02138,USA
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Abstract
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8 From an elevation of ∼38 km, the balloon-borne ANtarctic Impulsive Transient Antenna (ANITA) is designed to detect the up-
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coming radio frequency (RF) signal resulting from a sub-surface neutrino-nucleon collision. Although no neutrinos have been
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discovered thus far, ANITA is nevertheless the only experiment to self-trigger on radio frequency emissions from cosmic-ray
]24
M inducedatmosphericairshowers. Inthemajorityofthosecases,down-comingRFsignalsareobservedviatheirreflectionfrom
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theAntarcticicesheetandbackuptotheANITAinterferometer. Estimatingtheenergyscaleoftheincidentcosmicraystherefore
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. requiresanestimateofthefractionalpowerreflectedattheair-iceinterface.Similarly,inferringtheenergyofneutrinosinteracting
h27
in-icefromobservationsoftheupwards-directedsignalrefractingouttoANITAalsorequiresconsiderationofsignalcoherence
p28
-29 acrosstheinterface. BycomparingthedirectSolarRFsignalintensitymeasuredwithANITAtothesurface-reflectedSolarsignal
o intensity, as a function of incident elevation angle relative to the surface θ, we estimate the power reflection coefficients R(θ).
r30 i i
t WefindgeneralconsistencybetweenouraveragemeasurementsandthevaluesofR(θ)expectedfromtheFresnelequations[1],
s31 i
a32 separatelyforhorizontal-vs. vertical-polarizations(“HPol”and“VPol”,respectively).
[
Keywords: radioglaciology,interferometry,cosmicrays
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v
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1. Introduction
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1.1. TheANITAExperiment
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. Initiatedin2003, theAntarcticImpulsiveTransientAntenna(ANITA)isaballoon-borneantennaarrayprimarilydesignedto
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detect radio wave pulses caused by neutrino collisions with ice[2]. The basic instrument consists of a suite of 40 quad-ridged
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338 hornantennas,optimizedoverthefrequencyrange200-1200MHz,withseparateoutputsforverticallyvs. horizontally-polarized
1 incident radio frequency signals, mounted to a high-altitude balloon. From an elevation of ∼38 km, the payload observes the
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v:40 Antarctic continent in a circumpolar trajectory. Two one-month long missions (ANITA-I; Dec. 2006-Jan. 2007 and ANITA-II;
i Dec. 2008-Jan. 2009) have yielded world’s-best limits to the flux of Ultra-High Energy (“UHE”, corresponding to energies in
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excessof1019 eV)neutrinosintheenergyrangetowhichANITAissensitive[4,5]. Nevertheless,model-dependentcalculations
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r ofsurfaceeffectsshowconsiderablevariationinthefractionofsignalpoweremergingfromwithinthedenseicetargetmedium
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andacrosstheinterfacetothereceiver;thisisalsotrueforexperimentsseekingtomeasureneutrinointeractionswithinthelunar
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regolith[6, 7, 8, 9]. An interferometric analysis of the ANITA-I data sample provided a statistically large (16 events) sample
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of radio frequency signals attributed to the geomagnetic + Askaryan radiation associated with cosmic-ray induced extensive air
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showers[12](EAS);thoseeventsmarkedthefirstself-triggereddetectionofEASviatheirradioemissions.
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TheanalysisdescribedbelowisbasedonANITA-IIdata. AfterlaunchingfromMcMurdoStationinDecember,2008,ANITA-
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IIwasaloftforaperiodof31dayswithatypicalinstantaneousdutycycleexceeding95%. Althoughtheexternalexperimental
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conditions(livetimeandflightpath)weremorefavorableforANITA-IIthanforANITA-I,thesampleofdetectedextensiveair-
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shower(EAS)eventswassomewhatsmallerforANITA-II,primarilyowingtoamodificationtothetriggerthatfavoredneutrino
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detection, but, as realizedexpost facto, dis-favoredEAS detection[10]. TheANITA-IIIlaunch, scheduledforDecember, 2013,
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is expected to result in an improvement by a factor of ∼100 in the number of detected air shower events relative to ANITA-I.
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Correspondingly,wehavesoughttodeterminethesurfacereflectivityinadvanceofthatupcomingANITA-IIImission.
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PreprintsubmittedtoAstroparticlePhysics January21,2013
1.2. ANITADataAcquisitionandSignalReceptionChain
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TheANITAdetectorisdesignedtoefficientlycollectradiosignalovera1GHzbandwidth,withelectronicsandtriggerconfig-
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uredtoproducetheminimumpossibleenergythreshold. Thefront-endSeaveyquad-ridgeantennasprovidethefirstelementin
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theANITAradiowavesignalprocessingchain. ThesehornantennashaveseparateVPolvs. HPolsignalpolarizationreadouts,
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andeachhasafield-of-viewofapproximately25◦half-width-half-maximum(FWHM)inbothazimuthangle(φ)andzenithangle
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(θ). Following the Seavey antennas, high- and low-pass filtering restricts the system bandpass to 200–1200 MHz, after which
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signalsaresplitintoa‘trigger’pathconsistingofaheirarchyoftriggerconditions(“levels”)anda‘digitization’path. Ifalllevels
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ofthethree-tiered,heirarchicaltriggeraresatisfied,thedigitizedsignals,consistingof256voltagessampledforeachantennaat
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2.6GSa/s,arethenstoredtodisk. DuringtypicalANITA-IIdata-takingconditions,datawerewrittenatarateofapproximately
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10Hz. Theoverwhelmingmajorityofthesetriggersareduetoupwardexcursionsofthethermalradiophotosphere.
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1.3. ANITAinterferometry
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Beginningwiththeeighty100-nsdurationvoltagewaveformswhicharetakenduringanANITAeventtrigger(40antennas×2
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polarizationsperantenna),familiarradiointerferometrytechniquesareusedtoidentifylocalizedradiosources. Todeterminethe
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directionofanexternalimpulsivesource,thefullsolidangleisfirstdividedintoanN ×N grid(typically,180×360)inelevation
68 θ φ
andazimuth,respectively. Next,aninter-channelcross-correlationsumiscalculatedforeachpointinthegrid,byshiftingcross-
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correlatedwaveformsbytherelativepropagationtimedelaysthatwouldbeincurred,channel-by-channel,foraputativesourceat
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that(θ,φ)gridpoint.Formally,thecross-correlationC,fortwochannelsiand jcanbewrittenasthedotproductofthevoltagetime
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seriesforchanneliV(t)andthevoltagetimeseriesforchanneljV (t),shiftedbythecalculatedtimedelayδtS(θ,φ)corresponding
72 i j ij
totheputativesourceS at(θ,φ),fortheNsamplesinthedotproduct(equaltothenumberofsamplesinthewaveformminusthe
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numberoftimesamplescorrespondingtothetimeshiftδt ). Tominimizesensitivitytochannel-dependentgainvariations, this
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cross-correlationcoefficientisnormalizedrelativetothermsvoltagesinthetwochannelsσ(V)andσ(V ):
75 i j
(cid:88)N (cid:113)
c = VS(t )VS(t +δtS)/ σ(V)σ(V ) (1)
ij i n j n ij i j
n=1
Inthelimitofastrongsourcewhichdominatesthe100-nswaveform,thecross-correlationriseslinearlywithsignalvoltageVS,
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since σ(V) ∼ VS. In the limit of a very weak source, σ(V) is largely independent of VS and the cross-correlation increases
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quadraticallywithsignalvoltage. Thehighsignal-to-noise(SNR)eventsthatcomprisetheANITAEASsamplecorrespondtothe
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formercase. TheSolarsignaldescribedbelowcorrespondstothelattercase, andtherefore, inthecaseofsignalsfromtheSun,
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thecross-correlationcoefficientscaleswiththeradiopowerreceived. Thetotalcross-correlationCiscalculatedbysummingover
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all independent (i, j) pairs. The polar and azimuthal angles of a putative source are then assigned to that grid pixel giving the
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highest total cross-correlation C. More extensive details on the construction of the ANITAinterferometric map can be found in
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theliterature[11].
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An obvious design goal of ANITA is to localize sources with the best-possible pointing resolution. Unlike source vertexing
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algorithms using hit-time assignments from threshold-crossings, interferometry is particularly suited for continuous-wave (CW)
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sources. As illustrated by Monte Carlo simulations (Fig. 1), the interferometric reconstruction resolution improves, roughly
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linearly,withthefrequencyofthesource. Alternately,theangularsizeoftheinterferometricimageprovidesinformationonthe
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sourcefrequencycontent,withwiderimagesimplyingpowerspectraweightedpreferentiallytolowerfrequencies.
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Adisconetransmitter,buriedapproximately100mintotheicesheetataremotesitenearTaylorDome,hasbeenusedtoassess
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theinteferometricsourcereconstructionresolutionforsignalswithbroadfrequencycontent. Forthattransmitter,weobtainvalues
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of0.25degreesinelevationand0.56degreesinazimuthfortheANITA-IIflight. Forcomparison,theintrinsicSolarradiosource
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sizeisoforder1degreeinthesky.
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1.4. ANITARadioAirShowerObservations
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A maximum likelihood analysis of the 16 ANITA-I EAS detections implied a mean energy of 1.5±0.4(stat)+2.0(sys)×1019
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eV for the cosmic ray primary[12], with the highest primary estimated at an energy approximately equal to the GZK-scale[13]
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of ∼ 6 × 1019eV. Agreement in the spectral characteristics between the two cosmic rays incident in the six degree elevation
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rangebetweenpayloadhorizontalθP=0andtheEarth’shorizonatθP = −6◦,comparedtothe14cosmicraysobservedviatheir
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reflections,indicatethatsurfaceroughnesseffectsarenotlarge,albeitwithverylimitedstatistics. Thatsamplewassupplemented
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with an additional four reflected events observed with ANITA-II. Interestingly, two of the ANITA-II events featured reflection
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pointsconsistentwithseaice, forwhichthedielectriccontrastrelativetotheair, andthereforethefractionalreflectedpower, is
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expectedtobelargercomparedtoreflectionsfromsheetice. Usingthecoordinateconventiontobefollowedlaterinthispaperfor
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comparingintensitymeasurementstoexpectationsfromtheFresnelequations,withthesignalangleofincidenceθ definedrelative
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toatangentonthesurface, theincidenceanglesfortheANITAradio-reflectedEASsampleisshowninFigure2. Fromsimple
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solid angle considerations (dΩ ∼ cosθdθ), we expect the acceptance to decrease with elevation angle. Additionally, since the
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antennasarecantedat-10degreesrelativetothepayloadhorizontal,largevaluesofθareincreasinglyexperimentallysuppressed.
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Correspondingly,theobservedEASsampleisprimarilydetectedintheangularrangeθ(cid:46)25degrees.
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Figure1:Interferometricmapforsimulated200,400,600,and800MHzcontinuous-wavesourceat(θSP,φS=0,0).
Figure2:Elevationangleθi,relativetothehorizon,forthe14ANITA-I,and4ANITA-IIcosmicrayeventsobservedviatheirradioemissions.Indicateddistances
areestimated.
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2. SurfaceRoughness,GeneralConsiderations
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AccordingtotheRayleighcriterion,themagnitudeofvariationinsurfaceheighth,asmeasuredalongthelineoftheincoming
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radar must satisfy the condition hcos(φ) < 0.125 (φ here denotes the “look angle”) for the surface to be considered ’smooth’.
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Inthelimitofperfectsmoothness(h → 0,correspondingto“specularreflection”),theFresnelequationsprescribethefractional
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reflectedsignalintensity,asafunctionofincidenceangleθ. Deviationsfromsmoothnessresultinaθ-dependentredistribution
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of the reflected signal power. Depending on the geometry of the surface features, the wavelength, and the dielectric constrast
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acrossasurface,surfaceroughnesscantranslateintoeitheranenhancement,orreductioninthemagnitudeofreflectedpower,and
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correspondinglyananti-correlatedreductionorenhancementintheamountofpowertransmittedacrossthesurface.
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3. AntarcticSurfaceReflectivity
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3.1. VisibleFrequencies
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The polar albedo is one of the crucial inputs to climate models, given its importance in determining the thermal equilibrium
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between Earth and Sun. Since the Solar power spectrum peaks in the visible, measurements of Solar reflectivity have typically
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focusedonthe3900-6600Åregime[14]. Atsuchscales,sastrugieffectsdominate,asafunctionoflookangleφ relativetothe
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sastrugialignment. Long-termstudies(particularlyatSouthPoleStation)haveestablishedperiodicvariationsintheSolaralbedo
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inthevisiblewavelengthinterval,over∼5yeartimescales[15].Suchmeasurementscanalsobeusedasaproxyforwinddirection
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measurements[16],totheextentthatalbedoobservationsprobewind-blownsastrugiorientation.
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3.2. PriorMeasurementsatLowerFrequencies
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The Earth has, to date, been extensively mapped in the Ku-band (12-18 GHz)[17, 18] and also in the lower-frequency C-
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band(2–4GHz),mostrecently,andmostcomprehensivelybytheCanadian-basedRADARSATsatellites. Theserelativelyhigh
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frequencies,andcorrespondinglysmallwavelengthscomparedtothetypicalscaleofsurfacefeaturesprobenotonlypure‘surface’
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features,butalsosub-surfacevolumetricscatteringdueto,e.g.,buriedsastrugi. Theabsolute(/relative)RADARSATsignalreturn
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strength calibration of 2 dB(/1 dB) is sufficient to map the backscattering power across the Antarctic continent (Fig. 3), which
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exhibits variations of order 20 dB. Those results are qualitatively consistent with the Envisat satellite Ku-band backscatter[19],
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albeitwithsomelargedeviations,particularlyaroundtheRossIceShelf.
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The Envisat C-band backscattering results generally follow the trend shown in Figure 4, but with the C-band backscattering
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strengthoverWestAntarcticareducedby∼2-5dB;thebackscatteringsignalinEastAntarcticaisingeneralagreementwiththe
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Ku-bandscatteringtowithin2-3dB.
Figure 3: RADARSAT Ku-band backscattering coefficient σ0.
Maximumcontrastcorrespondstoavariationofalmost20dBin
measuredreflectedpower[17]. Nocorrectionshavebeenmadefor
lookangleeffects.
Figure4:EvisatKu-bandbackscatteringcoefficient[19],inunitsof
dB.Nocorrectionshavebeenmadeforlookangleeffects.
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Comparable data are not readily available at the higher frequencies of interest to the ANITA mission, although the precision
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of three-dimensional satellite maps of the entire Antarctic continent, such as those provided by LandSat, is now approaching
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dekameterscales.ProposalsarenowunderconsiderationtoconvertphotographicimagescollectedduringtraversesoftheAntarctic
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interiorintosurfaceroughnessmaps,althoughthosewouldalsosampleonlyaverylimitedfractionoftheAntarcticterrain.
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Using the dedicated Taylor Dome discone transmitter, a previous ANITA-I study found reasonable agreement between the
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measuredradiofrequencysignalstrengthatthegondolaandtheexpectationfromSnell’sLaw,knowingtherelativegeometryof
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ANITA-I and the Taylor Dome calibration pulser (Figure 5), albeit over a very limited angular range. That study indicates that
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Figure5: MeasuredANITA-Icalibrationpulserreceivedsignalvoltage(datapoints),comparedtosignalvoltageswithoutinclusionofFresnelfactors(labeled
“a/r”and“A0/r”),andwithinclusionofestimatedFresneltransmissioncoefficientacrossice-airinterface((A0/r)*Fresnel).
surface roughness effects within that range, and in that portion of the continent, are not large. A direct measurement of surface
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heightvariation[2]attheTaylorDomecalibrationpulsersite,aswellasstudiesoflocalradio-frequencypropagationthroughthe
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surface[3],alsoimpliedonlymodestsurfaceroughnessRFeffects,forthatonegeographicallylimitedsite.
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4. InterferometryAppliedtoSolarImaging
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Absentburstsorflares,theSunconvenientlyprovidestheANITAmissionanuninterrupted,unpolarized,(relatively)constant
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powercalibrationsource. However, sincetheSolaremissionsintheANITAbandpassaretypicallysub-thresholdrelativetothe
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ANITAtriggerrequirements, theSolarimageisonlyclearlyvisibleafteraddingmanyinterferometricimagesinanheliocentric
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coordinatesystem. Forourcurrentanalysis,weadd∼103−104events,excludingtriggerscontaininghighsignal-to-noisesources
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toelucidatetheSolarsignal.
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Toillustratetheexpectedsignals,Figures6and7showsimulatedinterferometricmaps,forwhichasinglepointsource,with
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a flat frequency spectrum, has been modeled at the indicated elevation angle. Although reflection effects are absent from these
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maps,weneverthelessobservesomefringingcharacteristicofANITAinterferograms,andresultingfromregularlateralorvertical
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spacing of the ANITA horn receiver antennas. We note that for a source at a payload elevation θP, fringing tends to produce
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an enhancement at an elevation angle typically a few degrees below −θP and therefore contributes some contamination to our
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measured reflection power, with a magnitude that grows with θP, requiring a small correction to our raw, extracted reflection
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signals.
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Fig. 8showstheimageoftheSunbothinverticalandhorizontalpolarizationsindata,afterco-adding10000events,acquired
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over a time of approximately 20 minutes. During that time, the Sun typically moves 0.5 degrees in the sky. As the Sun has no
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intrinsicpolarization,weexpectapproximatelyequalsourceintensitiesineachpolarization,consistentwithobservation. Wenote
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the presence of fringe effects in the interferometric map; such background effects are additionally complicated by the celestial
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proxmityofthegalacticcentertotheSunitself. OverthecourseoftheANITA-IIflight,SagittariusA*isapproximately5degrees
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higher in elevation relative to the Sun, and within 25 degrees in azimuth, crossing the Solar azimuth roughly midway into the
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flight.
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4.1. Cross-checkofmeasurementprocedure
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We have conducted cross-checks to verify the numerical veracity of the interferometric technique, as applied to the Sun, as
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follows.
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4.1.1. VariationofSolarsignalstrengthwithtime
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ForastationarysummerobserveratlatitudesbelowtheAntarcticcircle,theSunisexpectedtotraceasinusoidacrossthesky
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overadiurnalperiod. Weobserveanobvious24-hourcycleofSolarsourceintensity(Figure9),astrackedforan8-dayperiodof
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theflightfollowingtheballoon’slaunchfromMcMurdoStation.
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4.1.2. AntennaGainvs. Elevation
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Overthecourseofatypicalone-monthDec.-Jan. Long-DurationBalloon(LDB)Antarcticmission,theSun’selevationinthe
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sky,relativetothepayload“horizontal”θ ,variesbetween10and40degrees,andthereforeallowsanin-flightdetermination
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ofthepolarbeampatternfortheANITAdual-polarizationquad-ridgedhornantennas. Figure10overlaysthedependenceofthe
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peak interferometric Solar power (defined as the magnitude of the highest-amplitude pixel in the Solar interferometric map) on
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Figure6: Interferometricmapforsimulatedsourceat10,15,and Figure7:Interferometricmapforsimulatedsourceat25,30,and35
20degreepayloadelevations, andprojectionsontoelevationaxis degreepayloadelevations(left),andprojectionsontoelevationaxis
(right).Colorscalehasunitsof(Voltage)2. (right).Colorscalehasunitsof(Voltage)2.
Figure8: Interferograms(top,VPolandbottom,HPol)formedbytrackingthelocationoftheSunfor10000events. Normalizationisidenticalforbothtopand
bottomplots. Forthisplot,weusepayloadcoordinates,forwhichthehorizontalplaneisdefinedas0◦,withelevationanglestowardsthezenith/(nadir)defined
aspositive/(negative). InterferogramsarestackedtoaccountforboththemotionoftheSun,aswellasthetranslationalmotionoftheANITAgondolaacrossthe
Earth’ssurfaceandtherotationalmotionsofANITArelativetoitsverticalandhorizontalaxes.HorizontalfringesmoreevidentinVPolareconsistentwitheffects
duetothewarm/coldice/airdiscontinuityatthehorizon,indicatedbysolidblacklineatθP=−6degrees.
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Figure9:Solarsignalstrengthasafunctionofnumberofhoursintoflight.Normalizationisidenticalforbothtopandbottomplots.
Solar elevation, compared with the expectation from a simple Gaussian parametrization of the Seavey horn beam pattern. We
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observe that the Solar interferometric map can be used, in-flight, to calibrate the off-axis beam pattern to an accuracy of a few
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degrees.
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4.1.3. SolarPowerasafunctionofFrequency
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Figure 11 shows the absolute spectral power measured at two terrestrial observatories[20, 21], averaged over the time period
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comprisedbytheANITA-IImission. OverlaidonthatgraphisthedirectSolarpower,asmeasuredinterferometricallybyANITA-
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II.Weobservereasonableagreementintheshapeofthetwospectra.
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5. MeasurementofSurfaceRadioReflectivityR
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5.1. Geometry
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As indicated in Figure 2, the typical displacement between the ANITA balloon and the surface reflection point is of order
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hundreds of km. For a sub-sample of data spaced out over the duration of the ANITA-II flight, Fig. 12 shows the latitude and
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longitudeofboththegondolaandalsotheicesurfacereflectionlocationontheicesurfacecalculatedusingtheknowngondolaand
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Solarpositionsatthetimeofeacheventtrigger,andtakingintoaccountEarthcurvatureeffects. TheANITAflightpathsamples
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theinterioricesheet,aswellasshelficeandsomeseaiceatlatitudeslowerthantheRossIceShelf.
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5.2. QuantitativeTechnique
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SimilartoFigure8,wecancreateanenhancedradiofrequencyreflectedSolarimagebyaddingmanyevents.However,whereas
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Figure8isobtainedbycorrectingeachinterferogram,event-by-event,forboththeballoonmotionaswellasthecelestialmotion
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of the Sun to maintain coherence of the direct Solar image, proper accounting of the reflection requires correcting for balloon
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motion as well as the motion of the Solar reflection point across the ice surface. Although the location of the Solar reflection
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onthesurfaceisobviouslycloselycorrelatedtothedirectSolarmotioninazimuth,andalsocloselyanti-correlatedtothedirect
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Solarmotioninelevation,correctionsduetolocalEarthcurvature,surfaceelevationandtheviewinganglerelativetothesurface
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caneasilysmearthereflectionimagebyanamountexceedingtheintrinsicexpectedSolarbeamspotsize(∼1degree)andmust
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thereforebecarefullytrackedasthereflectionimagesarestacked. Wenotethatlarge-scalevariationsinsurfaceslopegradientsin
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Antarcticatypicallyoccuroverhundredsofkm,andconstitute,atmost,a0.1degreesmearingfortheanalysispresentedbelow.
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For this analysis, to determine the relative reflected:direct observed signal strength, we fit the direct and reflected peaks to
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Gaussianfunctions,andtaketheintegralunderourGaussiansignalparametrizationasourprimaryestimateofthesignalpower.
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Figures13and14showthefitstotheone-dimensionalprojectionsofthereflection-stackedinterferometricmapscorrespondingto
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Fig.8,fromwhichweextractsignalestimates. Forsimplicity,wehavecenteredtheSolarimageinthecenterofthegraphsshown.
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As a cross-check, we have also performed a second, independent analysis, which uses the maximum amplitude pixel in the
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interferometricmap,inthevicinityoftheknownSolar,orreflectedlocationinthesky,asameasureofthesignalintensity. This
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technique works well for cases of high signal to noise, which is true for the HPol reflected signal, but becomes decreasingly
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Figure 11: Solar intensities measured at two Solar observatories
inLearmonth, Australia(opencircles)andTrieste, Italy(crosses)
comparedtothefrequencybandedSolarintensitiesretrievedfrom
theinterferograms(Hpol,opentrianglesandVpol,opensquares).
TheTriestedataarecorrectedforlatitudeoftheobservations. The
ANITA data are obtained from interferograms filtered into five
bands (200-400 MHz, 400-600 MHz, 600-800 MHz, 800-1000
Figure10:Parametrizedantennagainofvaryingbeamwidth(lines)
MHz,1000-1200MHz);pointsareplacedatthecenterfrequency
compared to relative Solar intensities extracted from Hpol (top)
ofeachband. Foreachband,weusethesamesampleof8000co-
and Vpol (bottom) interferograms. Color scale indicates number
addedeventtriggers. Normalizationshavebeensettobeapproxi-
ofeventsobservedatagivenpointingraph.
matelyequalat200MHz.
Figure12:IllustrationoftypicalgeometryofANITA-IIgondolarelativetosurfacereflectionpoint.ANITA-IIlocationssampledduringflightareshownforsingle
events.Redpointscorrespondtoballoonlocation;eachassociatedlinepointstothereflectionlocationontheicesurface.
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Figure 13: Sample fit to projection of HPol, Sun-centered Solar Figure14: SamplefitofprojectionofVPol,Sun-centeredinterfer-
interferometricmapontoelevationaxis,aftercutting±10degrees ometricmapontoelevationaxis,aftercutting±10degreesaround
around φ = 0. Fit includes two Gaussian-shaped signals, corre- φ = 0. FitincludestwoGaussian-shapedsignals, corresponding
spondingtodirectSolarsignalandreflectedsurfacereflection,plus todirectSolarsignalandreflectedsurfacereflection,plussecond-
second-orderpolynomialtoapproximatenon-zerobackgroundun- orderpolynomialtoapproximatenon-zerobackgroundunderGaus-
derGaussiansignals. siansignals.
reliabile for low signal-to-noise; correspondingly, we have only applied this cross-check to the HPol case. Fig. 15 displays the
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averageratioRoftheSolarradioreflectionpowerrelativetothedirectSolarimage,forbothverticalaswellashorizontalantenna
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polarizations,includingallantennagaincorrections,asafunctionofthereflectionangleoftheSolarimageofftheEarth’ssurface,
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relativetotheballoon. AlsoshowninFig. 15aretheexpectedFresnelreflectionpowercoefficients,assumingspecularreflection
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off the Antarctic surface, and taking the index of refraction of the surface snow to be n = 1.35. We note that the gain
211 surface
correctionsatlargeincidenceanglebecomequitelargeforthedirectSolarsignal,asindicatedinFigure16.
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WealsonotethattheverticalspreadofpointsrelativetotheFresnelexpectationinFigure15isapproximatelyafactorofthree
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largerthantheverticalspreadofpointsshowninFigure10,indicatingthatthesystematicerrorsforextractingthesignalamplitude
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oftheweakersurfacereflectionareconsiderablylargerthanthesignalestimationuncertaintiesinherentintheinterferometricmaps
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themselves.
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5.3. Interpretation
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Overall,weobservereasonableagreementbetweentheexperimentalpointsandtheexpectationforspecularreflection.However,
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we observe an apparent excess, most pronounced for VPol, of the received signal relative to the expectation from the Fresnel
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equations, at higher angles. In particular, we do not observe the predicted signal dimunition (approaching zero signal strength)
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attheBrewsterangle, whichcanbeattributedtosomecombinationofa)theresultofsurfaceroughnesseffects, whichresultin
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non-zero signal at the Brewster angle, b) under-accounting of the effects of fringing, c) the asymmetry in the ANITA-II event
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trigger,whichtendstofavorthermalexcursionsofVPoloverHPol,andd)anunder-accountingofthecross-polarizationisolation
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between VPol and HPol. Such cross-polarization effects are, in principle, accounted for in Figure 15, but with the assumption
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thatthecross-polarizationisconstantasafunctionoffrequencyandoff-boresightangle. Ourresultssuggestthatisolationmaybe
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pooreratlargeoff-boresightanglesandincreasingwithfrequency.
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Rigoroussimulationofsurfaceeffectsisbeyondthescopeofthiscurrentwork,requiringmoreextensivedatasamplesonthe
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centimeter-scale and shape of the surface features, as well as a cpu-intensive integration across the Antarctic surface. We here
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noteonlythatasimple-mindedtwo-dimensionalmodelcomprisinganaveragesurfaceslopeof0.2radianswithaGaussianpower
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spectrumcan,atleast,reproducetheessentialfeaturesofourVPolobservation,favoringaslightdeficitofsignalatlowincident
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anglesrelativetothebaselineexpectation,andanexcessatlargerincidenceangles(Fig. 17).
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5.4. Cross-check: Comparisonofreflectedintensityoverseaicevs. shelfice
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Thereflectedsignalsignalstrengthataninterfacedependsonthedielectriccontrastbetweentheairandthereflectinglayer.The
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Solarimagereflectedoffseaice,havingrelativelyhighersaltcontent,shouldbebrighterthantheSolarimagereflectedoffsheet
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ice. As illustrated in Figure 18, we correspondingly note the largest enhancement in the reflected signal strength in the coastal
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regionbeyondtheRossIceShelf,consistentwithexpectation.
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Figure15:RatioofANITA-IImeasuredreflectedSolarpowertodirectly-receivedSolarpower,asafunctionofincidentelevationangle,forbothHPolandVPol
antennas.OverlaidarealsocalculatedvaluesasobtainedfromdirectapplicationoftheFresnelequationstocalculatetheexpectedreflectedsignalpowerR.
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