MINOS Observations of Shadowing in the Muon Flux Underground
aa r X i v : . [ h e p - e x ] O c t TH I NTERNATIONAL C OSMIC R AY C ONFERENCE
MINOS Observations of Shadowing in the Muon Flux Underground
E.W. G
RASHORN , FOR THE
MINOS C
OLLABORATION Univ. of Minnesota School of Physics & Astronomy, 116 Church St., Minneapolis, MN 55455, USA Abstract:
A high significance observation of two muon signals, the shadow of the sun and moon, havebeen seen by the 5.4 kt MINOS Far Detector, at a depth of 2070 mwe. The distribution of angular separa-tion of muons near the moon was well described by a Gaussian, which was used to determine the angularresolution ( . ◦ ± . ◦ ) and pointing ( . ◦ ± . ◦ ) of the detector. Introduction & Motivation
The MINOS Far Detector is a magnetized scintil-lator and steel calorimeter, located in the SoudanMine in northern Minnesota, USA, at a depth of720 m. While primary function of the Far Detec-tor is to detect neutrinos from Fermilab’s ν µ beam,the great depth and wide acceptance of the detectorcombined with the flat overburden of the Soudansite allow it to serve as a cosmic-ray muon detec-tor as well. The detector is composed of 486 8 moctagonal planes 2.54 cm thick, spaced 5.96 cm.This 5.4 kt detector is 30 m long and has a totalaperture of . × cm sr . MINOS is the firstunderground experiment able to discriminate pos-itively charged particles from those that are neg-atively charged for the purpose of CPT violationinvestigations, but this feature also allows inde-pendent study of positively and negatively chargedcosmic rays.Optical telescopes use a standard catalogue of starsto establish the resolution and pointing reliabil-ity of a new instrument. This is not possiblefor a cosmic ray detector, as there are no cos-mic ray sources available for calibration. Thereare two well observed phenomena in the otherwiseisotropic cosmic ray sky, though they are deficits,not sources. The sun and the moon provide ameans to study the resolution and pointing of a cos-mic ray detector because they absorb incident cos-mic rays, causing deficits from their respective lo- cation. These signals allow a measure of phenom-ena associated with cosmic ray propagation and in-teraction resulting from geomagnetic fields, inter-planetary magnetic fields, multiple Coulomb scat-tering, etc. These extra-terrestrial objects have thesame . ◦ diameter as viewed from Earth, thoughthe sun shadow is more difficult to observe becauseis much farther away and has its own magneticfield that deflects the charged cosmic rays. Thecosmic ray shadow of the moon has been measuredby air shower arrays (CYGNUS [1], CASA [2], Tibet [3] ), as well as underground detectors(Soudan 2 [4], MACRO [5, 6], L3+C [7]). Data
This analysis encompassed events recorded over1339 days, from 1 August 2003 - 31 March 2007,for a total of 1194 live-days, and includes 51.41million cosmic ray induced muon tracks. Cos-mic ray muons were triggered by recording hitson 4/5 planes or exceeding a pulse-height thresh-old and were written to a temporary disk at Soudanand later sent to Fermilab for reconstruction. Sev-eral cuts were required to ensure only well recon-structed tracks were included in the analysis. Pre-analysis and run cuts include: failure of demulti-plexing figure of merit and data taking quality [8].Analysis cuts include: track length less than 2 m,number of planes less than 20, χ reco /ndf > . ,and either track vertex or end point outside of the BSERVATION OF S HADOWING ... fiducial volume of the detector. A total of 30.52million events survived these cuts for the combinedsample.The background for this analysis was calculatedusing a simple Monte Carlo simulation that ex-ploits two key features of the muons induced bycosmic ray primaries: the time between consecu-tive cosmic ray arrivals follows a well known dis-tribution [9] and the cosmic ray sky is isotropic,Thus, a bootstrap method that independentlychooses the arrival time and location in space ef-ficiently simulates a cosmic ray muon. This sim-ulation chose a muon out of the known distribu-tion of events in the detector (in horizon coordi-nates), paired it with a random time chosen fromthe known time distribution, and found the muon’slocation in celestial coordinates. This was donefor every muon to create one background sample;500 background samples were simulated for a highstatistics background distribution.
Combined Muon Calibration
A further cut, excluding tracks with p <
30 GeV / c , was required to reject muons that weregreatly affected by energy dependent processes.The final data set included 20.17 million muons.To find the one dimensional space angle separationfrom the moon and the sun for each muon track, alist of the celestial body’s location in celestial coor-dinates in one hour increments was obtained fromthe JPL HORIZONS [10] ephemeris database forMay 1, 2003 until May 1, 2007. The ephemerisdata was referenced to the location of the detec-tor in latitude, longitude, and distance below sealevel. A function was written that interpolated thecelestial body’s location at the time a particularmuon is seen in the detector. Then the particu-lar muon’s arrival direction was compared to thecelestial body’s location at that time. The one di-mensional space angle separation was found usingthe Haversine formula, published in Sky and Tele-scope [ ? ]. The muons were binned in S bin = 0 . ◦ increments, and since radial distance from the cen-ter of the celestial body is measured over a twodimensional projection, the bin solid angle of bin(i) increases when moving out from the center as ∆Ω i = (2 i − ∗ S bin π . Weighting the number of events in each bin by the reciprocal of the arearesulted in the distribution N i / ∆Ω i , the differen-tial muon density. The ∆ θ distribution is shown inFig. 1 (l); from the sun, Fig. 1 (r), with statisticalerror bars displayed. There is a very clear deviationfrom a flat distribution in both plots as θ → , andthat deviation is attributed to muons blocked by themoon and sun, respectively. The background wascalculated using the method described in Sec. 2.As expected, the backgrounds are nearly flat, witha fit value of χ /ndf = 0 . / for the moon and χ /ndf = 0 . / for the sun . This MonteCarlois consistent with the premise of a sourceless cos-mic ray sky. The significance of the shadow can befound by fitting to the distribution a function of theform [4]: ∆ N µ ∆Ω = λ (1 − ( R m /σ ) e − θ / σ ) (1)where λ is the average differential muon flux, σ ac-counts for smearing from detector resolution, mul-tiple coulomb scattering and geomagnetic deflec-tion, and R m = 0 . ◦ , the angular radius of themoon. A fit to eq. 1 yields χ /ndf = 37 . / , animprovement of 16.4 over the liner fit ( χ /ndf =54 . / ), with parameters λ = 483 . ± . and σ = 0 . ◦ ± . ◦ . The change in χ over 38degrees of freedom for the moon corresponds toa − chance probability. The improvement of χ probability for the sun corresponds to a − chance probability. These results are summarizedin Table 1.Since the tracks of dimuon events, muons that areinduced by the same cosmic ray primary, are nearlyparallel when they are created, they can be used tofind the MINOS Point Spread Function. To quan-tify the absolute pointing of the Far Detector, theMINOS Point Spread Function will be used to findthe two dimensional contours of the most signifi-cant muon deficit caused by the moon. This anal-ysis is not complete at the time of this writing,however, so in its stead a simple approximationwas used on the one dimensional moon shadowto place an quantify the pointing of the detector.A significant shadow pointing to the apparent lo-cation of the moon was found using a one di-mensional space angle separation, a convolution of ∆ RA, ∆ Dec . Since the moon’s radius is . ◦ ,we can approximate the absolute pointing of thedetector as . ◦ ± . ◦ , with the error given by TH I NTERNATIONAL C OSMIC R AY C ONFERENCE (deg) qD ) (deg W dN/d MINOS PRELIMINARY (deg) qD ) (deg W (dN/d MINOS PRELIMINARY
Figure 1:
The differential muon flux with respect to displacement from the moon’s (l), and sun’s (r) location,binned in . o . The dashed curve is the calculated background, while the solid curve is the best fit from eq. 1. one half the bin width in theta. This analysis as-sumes that the pointing is reliable to begin with, somore precise analysis is still to be performed. Charge-Separated Analysis
For the charge separated sample, a further cutwas required to exclude events with low confi-dence charge sign determination. The curvature ofthe track is used to determine the momentum andcharge of the particle, so this cut was charge overmomentum divided by the error in the determina-tion of charge over momentum ( q/pσ q/p > . ) [ ? ].There are 2.7 million positively charged and 1.9million negatively charged muon in this sample.An analysis similar to what is described in Sec. 3was performed on the charge separated muon sam-ple. The charge separated moon shadow plots canbe seen in Fig. 2 (l), and the sun shadow plotsare shown in Fig. 2 (r). The Gaussian hypothesisgives very little improvement over the flat hypoth-esis, suggesting that the shadow of the moon or sunhas not been seen for the charge separated sample.The strong cut q/pσ q/p reduces the statistics by overfour times, from 20 to 4.6 million, eliminating anobservable deficit in the direction of either sun ormoon. This cut does give a charge ratio of 1.3 forboth sun and moon distribution, which is consis-tent with the published MINOS result. This anal-ysis has provided a flat distribution in the regionapproaching the moon, so given more statistics asignificant shadow should be observed. Conclusions
Using 20.17 million muons accumulated over 1194live-days, the MINOS Far Detector has observedthe cosmic ray shadow of the moon with a high sig-nificance. Despite the inherent fragility of the one-dimensional moon shadow measurement (therewere only nine events in the bin nearest to themoon), the null hypothesis of the muon deficit inthe area near to the apparent location of the moonhas a probability of − .The cosmic ray shadowof the sun over the same time period has a chanceprobability of − The shadow of the moon wasused to approximate both the effective angular res-olution of the detector, . ◦ ± . ◦ , and the ab-solute pointing of the detector, . ◦ ± . ◦ . Inagreement with the expectation, no significant dif-ference was found in the shadowing effects for ei-ther population, save for the charge ratio. Acknowledgments
This work was supported by the U.S. Departmentof Energy and the University of Minnesota. Spe-cial thanks to the mine crew in Soudan for theirtireless effort keeps the detector up and running.
References [1] D. E. Alexandreas et al. Observation of shad-owing of ultrahigh-energy cosmic rays by themoon and the sun.
Phys. Rev. , D43:1735–1738, 1991.
BSERVATION OF S HADOWING ... (deg) qD ) (deg W dN/d MINOS PRELIMINARY (deg) qD ) (deg W dN/d MINOS PRELIMINARY
Figure 2:
The differential muon flux with respect to displacement from the moon’s location (l), and sun’s location(r), binned in 0.1 o increments for µ + (open circles) and µ − , (open triangles). The solid curve is the best fitfrom eq. 1 for µ + ; the dashed curve is for µ − . The fit results are in Table 1. Distribution ∆ χ prob. λ σ moon-total 54.3-37.9 = 16.4 − . ± . . ± . moon- µ + . ± . N/A moon- µ − . ± . N/A sun-total 48.5 - 40.3 = 8.2 − . ± . . ± . sun- µ + . ± . N/A sun- µ − ± . N/A
Table 1:
Significance for the shadowing observed in each distribution, with ∆ χ ≡ χ line − χ gaus [2] A. Borione et al. Observation of the shadowsof the moon and sun using 100- tev cosmicrays. Phys. Rev. , D49:1171–1177, 1994.[3] M. Amenomori et al. Cosmic ray deficit fromthe directions of the moon and the sun de-tected with the tibet air shower array.
Phys.Rev. , D47:2675–2681, 1993.[4] J. H. Cobb et al. The observation of ashadow of the moon in the undergroundmuon flux in the soudan 2 detector.
Phys.Rev. , D61:092002, 2000.[5] M. Ambrosio et al. Observation of the shad-owing of cosmic rays by the moon usinga deep underground detector.
Phys. Rev. ,D59:012003, 1999.[6] M. Ambrosio et al. Moon and sun shadowingeffect in the macro detector.
Astropart. Phys. ,20:145–156, 2003.[7] P. Achard et al. Measurement of the shadow-ing of high-energy cosmic rays by the moon:A search for tev-energy antiprotons.
As-tropart. Phys. , 23:411–434, 2005.[8] S.L. Mufson. Measurement of the atmo- spheric muon charge ratio at tev energies withminos. In
International Cosmic Ray Confer-ence (these proceedings) , 2007.[9] E.W. Grashorn. Observation of seasonal vari-ations with the minos far detector. In
Inter-national Cosmic Ray Conference (these pro-ceedings) , 2007.[10] J.D. Giorgini, D.K. Yeomans, A.B. Cham-berlin, P.W. Chodas, R.A. Jacobson, M.S.Keesey, J.H. Lieske, S.J. Ostro, E.M. Stan-dish, and R.N. Wimberly. Jpl’s on-line solarsystem data service.
Bulletin of the AmericanAstronomical Society , 28(3):1158, 1996., 28(3):1158, 1996.