Introduction

Telescope Array (TA) is a detector for Extremely High Energy Cosmic Rays (EHECRs) constructed in the west desert of Utah, USA. It is a hybrid detector consisting of an air shourer array and air fluorescence telescopes (see Fig.1(left)). The air shower array uses 507 surface detectors (SDs) deployed in a grid of. 1.2 km spacing, covering the ground area of ~700 km(2). The fluorescence telescopes consists of 38 fluorescence detectors (FDs) distributed over 3 stations surrounding the a,rrey.

The measured energy spectrum of EHECR is different in the AGASA experiment and the HiRes experiment, i.e., the AGASA's spectrum is extended toward higher energies without indicating the flux suppression, whereas the HiRes's spectrum demonstrates a cutoff structure at ~10(19.7) eV which can be explained by the Greisen-Zatsepin-Kuzmin (GZK) effect: an energy loss of UHECRs caused by the interaction with cosmic microwave background (CMB). The Pierre Auger Observatory (Auger) recently reported a strong flux suppression as well. The spectra of AGASA, HiRes and Augerwere obtained by different detector techniques, i.e., a plastic scintillator a,rray for AGASA, air fluorescence telescopes for HiRes, and a water tank array for Auger.

The TA's SD (TASD) uses the plastic scintillator for particle detection same as AGASA. Two layers of scintillators (thickness, 1.2 cm; surface area, 3 m(2)) are used for TASD, and a single layer (thickness, 5cm; area, 2m(2)) is used for AGASA. The TASD covers the ground area of 680 km(2) (altitude, 1380m; latitude, 39.3 degrees North) with 1.2 km spacing, whereas the AGASA's SD covers the 100 km(2) (altitude, 900m; Iatitude, 35.8 degrees North) with ~1.0 km spacing. For the AGASA, the scintillation light was directly detected by the photomultiplier tube (PMT) and its integrated pulse height and the Ieading edge timing were read out. For the TASD, the scintillation light was detected by the PMT via wavelength shifting fiber, and the complete waveforms were recorded by the flash ADC (EADC).

The subject of this thesis is to measure the energy spectrum of UHECRs via TASD with more detailed information, higher statistics, and better calibration than the AGASA had done. We also developed an independent data analysis method for the TASD with a help of intense Monte Carlo (MC) simulation of the air shower event.

TASD array

One of the deployed TASD in the field is shown in Fig.1(right). We developed an electronics which enabled a local recording of the waveform (EADC) and the time (GPS) of the SD generated by the air shower events. It also recorded and histogrammed the pulse heights for all the penetrating cosmic rays (CR"), mostly muons, at the rate of ~750 Hz. All the SDs were equipped with this electronics and were operated standalone in the fleld via solar power system. The trigger and data acquisition was performed using a wireless communication system (IEEE802.11). The CR histogram was read out every 10 minutes, and it was used as a precise real-time calibration in the data analysis. The construction of the TASD was completed in March 2008, and the observation started in May 2008 after 2 months of commissioning.

We recoustructed the energy and the arrival direction of air showers by fitting the observed pattern of SD hit timings and deposited energies with an expectation obtained from the air shower and the detector response simulation programs (COSMOS and GEANT4). The expected distribution was formulated as an air shower model function, which gives the average and the width of individual SD hits depending on the energr and arrival direction of primary Cft"s, and the information of the SD locations with respect to the shower a,nis, i.e., the impact parameter and the rotational angle. This method of reconstruction allowed us to determine the zenith angle attenuation of expected energy deposit without using a traditional constant intensity cut (CIC) method. The CIC, which was used for the AGASA data analysis, is based on the assumption that the zenith angle attenuation of the SD energy deposit stays constant with the primary CR energy, which is not supported by the results of our simulation.

Data analysis

We analyzed a total of 393,509 TASD events collected from May 2008 to September 2010 using our reconstruction program. Following cuts are applied to select events used for the spectrum measurement.

・ 5 or more than 5 adjacent SD hits with energy deposition ) 0.4MeV are required for good reconstruction (145,243 events left).

・ 4 or more than 4 good SD (141,857 events left).

・ 4 or more than 4 good SD hits with energy deposition ) 2.4MeV (93,572 events left).

・ Events were passed for the reconstruction program (93,566 events reconstructed).

・ 4 or more than 4 good SD hits with energy deposition > 2.4MeV (93,572 events left).

・ 4 or more than 4 good SD hits between 500m and 3000m from core position and slower than light speed (59,159 events left).

・ The distance from the reconstructed shouier core position to the boarder of the SD array is larger than 1.2 km (48,289 events left).

・ Reconstructed zenith angle is smaller than 45 degrees (39,305 events left).

・ Reconstructed primary energy is larger than 10(18.8)eV (2,032 events left).

・ X(2)/DoF for the lateral distribution of energy deposit is less than 3 (2,019 events left).

・ X(2)/DoF for the timing distribution of shower front is less than 10 (2,011 events left).

To evaluate reconstruction efEciency and energ'resolution, we generated simulated events and reconstructed them. The simulated events were generated implementing the real detector conditions such as the calibrations, dead time, and offiine (truned off) SDs. They v/ere generated at fixed energies be. tween lgta'o urr6 1920'0 eV and with uniform arrival directions. The exposure of the measurement was calculated by processing the simulated events in the same manner as the data. As seen in Fig.2 (left), the exposure above 101eeV is nearly constant. The value of ~5.3x10(16) [m(2) s sr] is approximately the same as that obtained hy AGASA for 13 years.

The energy resolution was estimated using the simulated event: it is 17% at 10(19) eV and 12% at 10(20) eV (see Fig.2(right)). A systematic shift of up to 10% was observed in the reconstructed energy of MC events, and the same amount was corrected for the reconstructed energy of the observed event. The systematic uncertainty of the energy scale is estimated to be +9%, -13% at 10(19) eV and +LTYI, -30% at 10(20) eV. The largest contribution comes from the unknown primary composition of the UHECRs (proton or iron)

Results and discussion

The obtained energy spectrum is shown in Fig.3(left) after a small smearing effect by the energy resolution is corrected. It is also plotted in Figure a (left) together with the data from other experiments. The same set of data is plotted in Figure a (right) with energy scales of each experiment adjusted by a constant amount: -5% (AGASA), +16% (HiRes), and +34% (Auger). Theses energy scales are calculated from average flux between 10(18.8)eV and 10(19.2)eV to agree for all experiments. As seen in Figure 4(right), the observed spectrum by TASD is consistent with existing measurements in the energy range between 10(18) eV-10(19.8) eV.

To evaluate the structure of the observed energy spectrum, we fitted the spectrum by double povrer law model and triple power law model. The result is shorvn in Fig.3 (left). The parameters obtained by the fit are listed in Table-1.

The observed second breakpoint energy E(2) is 10(19.72)eV for the triple power law model. We observed 18 events above 10(19.72)eV whereas the expected number of events is 48.5 for the triple power law model (shown in dashed line in Fig.3), and is 36.1 for the double povier law model. The probability to observe LB events or less when 36.1 (48.5) events are expected is 6.8x10(-4) (4.7x10(-7)), or 3.2 (4.9) sigma.

The obtained energy spectrum of TASD is compared with the theoretical expectation. We calculated the expected energy spectrum assuming that the CR acceleration sources are distributed uniformly in the extragalactic space, and the protons originating from the source propagate to the Earth rectilinearly experiencing the interaction with the CMB. The calculated spectrum is plotted in Figure 3 (right) in solid green curve. The fit to the observed spectrum was made by the constraint that the integral flux for energies over 10(18.8)eV is the same for the data and the expected spectrum, and by optimizing the power law index of CR generation at the source. The best fit was obtained at r= 2.65 +- 0.05 with x(2)/DoF:1G.6/13. It is noted that the observed cutofi energy (E(1/2)=10(19.70+0.05-0.08)eV) agrees well with the expectation (10(19.72)eV) for the proton spectrum. For the case of iron acceleration at the source, acceptable fits were obtained only by excluding the data below 101e eV, and by assuming unexpectedly hard spectrum (r=2.1) at the source.

Conclusion

We measured the energy spectrum of UHECRs using the air shoryer array of TA for energies above 10(18.8) eV. The extended spectrum of AGASA (without cutoff) was dismissed at the CL level of 3.2 sigma or Iarger. The observed spectrum is well represented by the expected spectrum for the extra-galactic proton experiencing the interaction with the CMB during its propagation to the Earth.

Table 1: Fitted parameters with double/triple power law to TASD, AGASA, HiRes and Auger spectra.

Figure 1: TA detector arrangement (left). black boxes, green boxes, orange circles, blue cross and black arrows represent SDs, FDs, communication towers for SD, central laser facility for FD calibration and FD field of view, respectively. SD and a communication tower (right).

Figure 2: Exposure including total efficiency and utilization ratio (left). Red continuous is fit result. Energy resolution of reconstruction (right). Red circles are for 10(19)eV and green circles are for 10(20)eV. Vertical axis is normalized by total number of simulated events.

Figure 3: Fit results of energy spectrum (left) by TASD (red circles) using U"*; power law model (blue continuous) and triple power law model (green continuous). Green dashed line is the extension of the middle term of triple power low model. Fit result of energy spectrum (right) by TASD (red circles) using proton spectrum (green continuous).

Figure 4: EHECR energy spectra (left) by TASD (red), AGASA (blue) , HiRes-I, HiRes-II (purple) and Auger (green). The etror bars in bins of absent event indicate 90% confidence interval for AGASA, and indicate 68% confidence interval for the others. Right figure is same as left, but energy is scaled -5%, 13% and 31% for AGASA, HiRes and Auger, respectively.

本論文は10章からなる。第1章は序論であり、本論文の目的が書かれている。1020eV 以上の極高エネルギー宇宙線は宇宙背景輻射との相互作用によりエネルギーを失い、スペクトルにカットオフ(GZK カットオフ)があると予想されている。これまでの実験で、カットオフが無いという結果とカットオフがあるとう矛盾する実験結果が報告されている。カットオフが無ければ、未知の大質量素粒子の存在の可能性など新しい物理があることになり極めて興味深い。本論文は、この問題に決着をつけようというものである。本論文で用いたテレスコープアレー検出器の地表シンチレータ検出器は、GZK カットオフが無いと言っている実験と、同様の検出技術であり直接の比較が可能となる。第2章は極高エネルギー宇宙線物理学についてのべられている。ここで、本論文を考察する上での宇宙線物理学の基礎がまとめられている。第3章から第5章までは測定装置についての説明である。ここでは、論文提出者が中心となっておこなった、地表検出器トリガーDAQ システム及びモニタリングシステム、ミュー粒子を用いた地表検出器の較正法が詳述されている。測定装置の開発研究・製作における論文提出者の寄与は大きいものであると評価された。第6章は、本論文の基幹をなす章であり、空気シャワーのモデル化に関する説明である。シミュレーション時間を短縮するためのシャワーの間引き法(シニング)の開発、そして、これまでの実験では考慮されていなかった空気シャワーの減衰に対するエネルギー依存性を考慮した新たなシャワーモデルの構築が説明されている。これらは、論文提出者自身によるもので高く評価された。第7章は、この新たな空気シャワーモデルを用いた宇宙線事象の再構成法の説明である。第8章において,これまでに収集された極高エネルギー宇宙線データ解析の結果が示された。結果は1019.7 eV 以上の高エネルギー側で、有為なカットオフが見られている。カットオフがないという仮定は、解析の手法により有為さの幅はあるが、3.2σ~4.7σで棄却された。特筆すべきことは、これまで、カットオフがないということを言っていた実験と同様の手法により棄却したことであり、長年にわたる論争であったカットオフの有無に最終的な決着をつけたことになる。したがって、この結果は、高く評価される。第9章の議論では、加速源での宇宙線核種が陽子の場合と鉄の場合で予想されるスペクトルを計算し、データと比較している。陽子起源と良く合っていることが示されている。これは、極高エネルギー宇宙線がどこでどのように作られているかという、宇宙線の起源に迫る重要なデータを提供するものである。

なお、本論文は、テレスコープアレー実験グループとしての共同研究の一部であるが、上述しているように、第4章、第5章の測定器の開発研究、そして、本論文の根幹とも言うべき新しいシャワーモデルの構築、データ解析と結果の導出は、論文提出者がおこなったものである。論文提出者の寄与は十分であると判断する。

したがって、博士(理学)の学位を授与できると認める