Journal ArticleWe report a measurement of the ultrahigh-energy cosmic-ray spectrum using an atmospheric fluorescence technique for extensive-air-shower detection. The differential spectrum between 0.1 and 10 EeV (1 EeV = 10^18 eV) is well fitted by a power law with slope 2.94 ±0.02. Above 10 EeV evidence is presented for the development of a spectral " bump " followed by a cutoff at 70 EeV

Baltrusaitis, R. M.

Sokolsky, Pierre

English

The University of Utah: J. Willard Marriott Digital Library

VOLUME 54, NUMBER 16 PHYSICAL REVIEW LETTERS 22 APRIL 1985 Evidence for a High-Energy Cosmic-Ray Spectrum Cutoff R. M. Baltrusaitis, R. Cady, (a) G. L. Cassiday, R. Cooper, J. W. Elbert, P. R. Gerhardy, S. Ko, E. C. Loh, Y. Mizumoto, M. Salamon, (b) P. Sokolsky, and D. Steck Department of Physics, University of Utah, Salt Lake City, Utah 84112 (Received 11 February 1985) We report a measurement of the ultrahigh-energy cosmic-ray spectrum using an atmospheric fluorescence technique for extensive-air-shower detection. The differential spectrum between 0.1 and 10 EeV (1 EeV = 1018 eV) is well fitted by a power law with slope 2.94 ± 0.02. Above 10 EeV evidence is presented for the development of a spectral "bump" followed by a cutoff at 70 EeV. PACS numbers: 98.60.Ce In 1966, Roll and Wilkinson I reported the first con-firmation that the intense isotropic radiation observed earlier by Penzias and Wilson2 was thermal in nature and all pervasive, characteristic of a universe cooled to a temperature of 2.7 K. Given the previous report by Linsley3 of the detection of a primary cosmic ray with an energy estimated to be in excess of 100 Ee V, Greisen4 astutely realized that the spectrum of such energetic cosmic-ray primaries, if their sources were predominantly of extragalactic origin, should steepen abruptly. Such a steepening results naturally from the rapid onset of opacity to passage through the universe of ultrahigh-energy cosmic rays due to energy degrada-tion from photopion production off the 2.7 -K black-body radiation. Thus, the cosmic-ray spectrum would appear to terminate at energies near production thresh-old at 60 EeV. Here we present evidence confirming the early prediction of Greisen and the more recent calculations of Hill and Schramm5 which indicate the development of a spectral "bump," due to pileup of the recoil protons, prior to the onset of the "Greisen cutoff. " We report here the energy spectrum obtained using the Fly's Eye detector situated at 41 0 N latitude in the western Utah desert at an atmospheric depth of 852 g cm - 2. The detector differs from conventional extensive-air-shower (EAS) detectors in that it is essentially a calorimetric device which observes the passage of EAS through the atmosphere by means of the nitrogen fluorescence light given off upon ioniza-tion and excitation by the relativisitic charged particles in the shower. 6 Events have been detected with im-pact parameters as far away as 22 km. The effective collecting aperture is thus very large. However, since the apparatus must detect a very low light flux, observ-ing periods are restricted to clear, moonless nights which greatly negates the benefits of large aperture. The data collected for this analysis were obtained dur-ing a total elapsed time of 33 months and an actual live time of 0.145 yr. The duty cycle is 6.3%. The techniques of track reconstruction and conver-sion of measured photoelectron yields into shower size versus atmospheric slant depth have been described elsewhere. 6 Shower energies are assigned by integra-tion of the resultant longitudinal shower development curve to obtain the total track length. Track lengths are then converted into total "electromagnetic" ener-gy via the relation Eem = (e/Xo) f Ne (x)dx, where E/ X 0, the ratio of the critical energy of an elec-tron to its radiation length in air, represents the total rate of energy loss by ionization and excitation.7 We take E = 81 MeV and xo= 37.1 g cm2 giving an energy loss rate of 2.18 MeV/g cm- 2. 8 (Independent esti-mates of this loss rate were made by integration of dE/dX over the energy distribution of electrons in showers calculated by Hillas,9 and a value of 2.24 MeV I g cm - I was obtained.) In order to estimate the total energy of the primary cosmic ray, we correct for undetected energy lost via (1) neutrals that fail to de-cay into detectable charged particles before striking ground, (2) high-energy muons which lose most of their energy in the earth, and (3) nuclear excitations by the hadrons in the shower. The correction factor was obtained by parametrizing the estimates of lost en-ergy derived by LinsleylO by demanding consistency among a wide variety of cosmic electron and muon size measurements. Application of the correction yields total energy estimates which are larger than the derived electromagnetic energy by factors which range from 13% at 0.1 EeV to 5% at 100 EeV. Resultant total energies are statistically accurate to within ± 15%. Systematic inaccuracy is estimated to be less than 15% on the basis of extensive calibration procedures including a detailed analysis of the detec-tion of scattered light generated by nitrogen laser shots used to simulate EAS events. 6 Confidence that our analysis procedure leads to correct energy assignments can be gained by noting that our measured values of ratio of total energy to maximum shower size, E / N max' and equivalent Gauss-ian width (T of the shower at E = 1.0 EeV are 1.3 ± 0.18 Ge V I electron and 220 ± 33 g cm - 2, respective-ly. These values agree favorably with estimates made by LinsleylO on the basis of cosmic ray data and by Hil-las ll on the basis of Monte Carlo simulations of © 1985 The American Physical Society 1875 VOLUME 54, NUMBER 16 PHYSICAL REVIEW LETTERS 22 APRIL 1985 shower development which incorporate radial scaling and measured high-energy cross sections at accelera-tors suitably extrapolated to EAS energies. Differential spectra are calculated in the usual way, j(E)= [fA fl(E)]-ldN/dE, where A fl (E) is the efficiency-corrected acceptance in km2 sr) for events with energy between E and E + dE. The acceptance has been calculated from a Monte Carlo simulation of the Fly's Eye experiment in which an isotropic cosmic-ray flux incident upon a model atmosphere is generated from quasirandomly selected trajectories and depths of first interactions. The shapes of the Monte Carlo showers are based upon those obtained from the real data sample in order to ensure self-consistency between the Monte Carlo-derived and the real, but unknown, acceptance. The high degree of success which the Monte Carlo simulation has attained in correctly representing real data distributions has been described elsewhere. 6 The resultant acceptance, obtained from the calculated detection efficiency of the isotropic flux on the simu-lated experiment and suitably corrected for track reconstruction and longitudinal development fitting ef-ficiencies, is shown in Fig. 1. Overall reconstruction and fitting efficiencies vary from factors of roughly 50% at E = 0.1 EeV to 70% at E = 100 EeV so that the basic shape of the plotted acceptance is that of the simulated detection efficiency. At the highest energies the acceptance for events in excess of 100 EeV is close to 1000 km2 sr. Accumulated total Fly's Eye exposure for such events is thus far about 145 km2 sr yr. The derived differential spectrum is shown in Fig. 2(a) plotted as E 3j (E). It is essentially flat with the appearance of a bump roughly between 10 and 50 EeV. lei 3 .. 102 .. N Il "" 101 Izl ~ 0< 10° -1 10 0.1 , .' I , Fly's Eye Acceptance 10 100 E(EeV) FIG. l. Fly's Eye acceptance A n (£) for events with en-ergy between E and £ + dE. Acceptance is based on trigger-ing efficiencies obtained from a Monte Carlo simulation of the Fly's Eye experiment (Ref. 6) and then corrected for track reconstruction and longitudinal development fitting ef-ficiencies. 1876 The number of events in that interval is 62. If the spectrum continued with the same slope ('Y = 2.94 ± 0.02) as obtained for energies < 10 EeV, the number of events between 10 and 50 EeV would be 46. The uncertainty in the extrapolated value is small, and hence the significance of the bump is roughly 16/.J46 = 2.4IT. We also note that the spec-trum between 10 and 50 EeV exhibits a slope of 2.42 ± 0.27 which is about 2IT flatter than the lower energy value. In order to compare our results with those of previ-ous experiments lO, 12, 13 we plot our derived integral spectrum in Fig. 2(b) as ELSI( > E). At energies ranging from 1 to 50 EeV the overall agreement between our data and that of the Haverah Park experi-ment is quite good. Below 1 EeV and above 50 EeV there is disagreement. We note that a shift in energy scale cannot be invoked to raise the lower-energy points relative to the higher-energy ones. The spectral (a) N :> Q) (b) '7 .. ..... ' .. .. ~ iii ~ :> Q) _ Fly's Eye I---T T TTl -Differential Spectrum ~ E 3 I I _L 0.1 10 10 16 _ 0 --A_ 0 !. 0 E(EeV) -A Fly's Eye Yokutsk o Haverah Pork I ---100 1015 'Of l'D'lYi1~qf It 1014 Intelpal 0.1 10 E(EeV) 100 FIG. 2. (a) Differential spectrum j (E) plotted as £3j (E). A power-law best fit of the form j (E) = aE - y yields a = 109.6 ±2.2 EeV- 1 km- 2 sr- 1 yr- 1 and y=2.94 ±0.02 for events at E < 10 EeV. Between 10 and 50 EeV we ob-tain a = 34 ± 17 EeV- 1 km- 2 sr- 1 yr- I and y = 2.42 ± 0.27. The lack of events above 50 EeV indicates that the flattened slope does not continue. (b) Integral spectrum I ( > E) plotted as E L5J( > E). Data from both Haverah Park and Yakutsk (Refs. 10, 12, and 13) experiments are also shown. VOLUME 54, NUMBER 16 PHYSICAL REVIEW LETTERS 22 APRIL 1985 90 80 70 t t CI) 60 E-< tt z 50 J"I Tf+ > 40 J"I "" 30 20 ++ 10 ,+,+ .. ' 1.0 FIG. 3. Monte Carlo response function (Ein-Eout)!Ein. Virtually no systematic shift is indicated between Monte Carlo assigned energies E in and analyzed energies E out. Resolution of ± 15% is identical with assessed resolution of real data and exhibits almost no energy dependence. shape is invariant under a scale change since the scales of both the event energy and energy-dependent accep-tance would change coherently. Only an unknown discrepancy between the Monte Carlo and real-data en-ergy assignments could result in a spectral index shift. This possibility has been tested by subjecting the Monte Carlo data to the same analysis as the real data. The resulting energy response function (energy "out" versus energy "in") of Fig. 3 shows excellent agree-ment between the two energy scales. 6 Errors in recon-struction and fitting efficiency estimates in the lower energy region E < 1 EeV where the acceptance is rap-idly changing could account for the differences ob-served there between our results and those of the Haverah Park group. Such a possibility is currently under investigation although the outcome will not af-fect our conclusion regarding the discrepancy which appears to be developing in the energy region E > 50 EeV where we have detected only one event. An ex-trapolation of our measured differential spectrum between 10 and 50 EeV indicates that we should have seen 11 ± 5 events at E > 50 EeV. Based upon the Haverah Park spectrum we should have detected 7 ± 2 events at E > 50 EeV with 2 of them at E > 100 EeV. Thus, the discrepancy between detected and anticipat-ed numbers of events above 50 EeV is 20' below our own expectations if the flattened spectrum continued and 30' below those based upon the Haverah Park data. We consider whether or not the apparent termina-tion of the spectrum could be accounted for by a failure of the detector to register events at E > 50 EeV. The estimate of numbers of events which should have been detected at E > 50 EeV is based on the acceptance at 50 EeV where excellent agreement is obtained between our measured differential spectrum and that of Haverah Park.12 About 80% of the "missed" events at E > 50 EeV should have fallen within the 50-EeV acceptance where they would have been detected with even greater probability than the ones actually registered because of the increased brightness of the resultant EAS. We also consider whether or not the appearance of a bump or an ankle in our data at the tail end of a steep-ly falling spectrum could result from a response func-tion that varied with energy. We have extensively in-vestigated the distribution of errors in energy assess-ment and find no significant behavioral differences between the low-energy and high-energy populations. Hence, it is our conclusion that the "ankle" in the cosmic-ray spectrum at 10 EeV is most propably a "bump" as predicted by Hill and Schramm5 which is followed by a spectral "cutoff" at about 70 EeV as ori-ginally predicted by Greisen. 3 We note that these spectral features imply that ultrahigh-energy cosmic rays are of extragalactic origin and have traveled dis-tances on the order of 70-150 Mpc or roughly the scale of intercluster spacing. Unequivocal verification of this result requires better statistics and should be augmented by both anisotropy and compositional stud-ies. Such efforts are in progress. We gratefully acknowledge the support of our research by the National Science Foundation. (a)Present address: Department of Physics, University of Hawaii, Honolulu, Haw. 96822. (b)Present address: Department of Physics, University of California, Berkeley, Cal. 94720. Ip. G. Roll and D. T. Wilkinson, Phys. Rev. Lett. 16, 405 (1966) . 2A. A. Penzias and R. W. Wilson, Astrophys. J. 142,419 (1965). 3J. Linsley, Phys. Rev. Lett. 10, 146 (1963). 4K. Greisen, Phys. Rev. Lett. 16, 748 (1966). 5c. T. Hill and D. N. Schramm, Phys. Rev. D 31, 564 (1984), and Phys. Lett. 131B, 247 (1983). 6R. M. Baltrusaitis et al., Nucl. lnstrum. Methods (to be published) . 7B. Rossi, High Energy Particles (Prentice-Hall, Englewood Cliffs, N. J., 1952), Chap. 5. 80. I. Dozhenko and A. A. Pomanskii, Zh. Eksp. Teor. Fiz. 45, 268 (1963) [Sov. Phys. JETP 18, 187 (1964»). 9A. M. Hillas, J. Phys. G 8, 1461 (1982). 10J. Linsley, in Proceedings of the Eighteenth International Cosmic Ray Conference, Bangalore, India, edited by P. V. Ra-mana Murthy (Tata Institute of Fundamental Research, Bombay, 1983), Vol. 12, p. 135. "A. M. HilIas, in Proceedings of the Cosmic Ray Workshop, University of Utah, edited by T. K. Gaisser (Bartol Research Foundation of the Franklin Institute, University of De-laware, Newark, Del., 1983). 12G. Cunningham et al., Astrophys. J. Lett. 236, L171 (1980) . 130. S. Diminstein et al., Bull. Naushno-technithekoj In-formasii, Yakutsk, USSR 9,537 (1982). 1877 

Evidence for a high-energy cosmic-ray spectrum cutoff

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Evidence for a high-energy cosmic-ray spectrum cutoff

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