In this thesis, the energy spectrum of UHECRs (E > 1018.7eV) was measured using the hybrid data from the Telescope Array. For the precise measurement, the analysis method with the hybrid technique was developed.

The Telescope Array (TA) experiment which is located in Utah desert in United States (39.30 Latitude, -112.91 Longitude and 1382m A.S.L.) is the largest stereo-hybrid detector for UHECR observation in the northern hemisphere[1]. The main target of this experiment is precise measurement of the energy spectrum, arrival direction and composition of UHECR through the investigation of the inconsistency about GZK cut off between the results of the AGASA[2] and HiRes[3]. For this subject, the TA uses the hybrid technique with three stations of Fluorescence Detectors (FDs) which are the same as HiRes technique and 507 Surface Detectors (SDs) which are the same as AGASA technique. Each detector measures UHECRs through the observation of the air showers created by the interaction between UHECRs and atmospheric molecules. SD directly observes particles in air shower on the ground and the FD detects fluorescence photons generated by air showers. Since one of the FD stations, which is the northern station called the Middle Drum (MD), is the detector transferred from the HiRes experiment, we can compare the result from the MD site with the Hires result directly.

The ''hybrid'' observation started from March 2008. In this analysis, the hybrid events which are observed both by FD and SD are used to measure the energy spectrum with the developed hybrid reconstruction technique. To carry out this study, the method of the hybrid analysis, in which the timing of SD data is applied to FD monocular reconstruction, is developed. A full hybrid Monte Carlo (MC) simulation with an air shower simulation is developed. The MC simulation includes the Utah atmosphere and the detector response with the time dependence.

The resolutions which are estimated by using the MC simulation are less than 1.1 degrees of the arrival direction and less than 8% of the energy for the observed UHECRs with energies above 1018.7eV, respectively (see Fig.1). This resolution is quite better than that of the FD monocular analysis. The aperture of the hybrid event is also obtained by using MC simulation.

The used term of the data is from May 27, 2008 to September 28, 2009. The exposure is about 3×1015 m2 sr s for at the energy of 1019eV, which is equivalent to 6% of the AGASA exposure. About 2000 hybrid events are found with one FD station (monocular-hybrid events) and about 200 events hybrid events with two FD stations (stereo-hybrid events).

In this hybrid analysis, the main contributions to the systematic uncertainty of energy and flux measurements are the PMT calibration (8%), mirror reflectance (5%), atmospheric attenuation (11%), fluorescence yield (12%). The total systematic error of the energy measurement is estimated to be 19% by a quadratic sum of these factors. The total systematic uncertainty of the flux is estimated to be 12% by the cloud.

The measured energy spectrum with the developed hybrid technique with energies above 1018.7eV is shown in Fig.2. It is consistent with the result of HiRes within the total systematic uncertainty.

By the March of 2011, the systematic uncertainty of the energy will be improved to around 10% level by the absolute calibration with a linear accelerator called Electron Light Source (ELS) and the data selection of the good weather. By the improvement of the SD analysis, the energy scale between FD and SD will be compared by the hybrid analysis as the direct comparison between the AGASA and HiRes results. This work will become the verification of the inconsistency of the result of the GZK cut off. In March of 2011, the exposure of the TA will reach about twice of the AGASA total exposure. The TA will measure the energy spectrum around the GZK cut off with the energy uncertainty of 10% level by the hybrid technique and ELS calibration.

Fig.1. Angular difference between the reconstructed and true arrival directions (left figure) and the ratio of the reconstructed energy to true energy (right figure) for the primary cosmic rays in the MC data. Here we generated MC data with E-3 above 1018.7eV. In the left figure, the peak value is 0.7 degrees and the resolution (68%) is 1.1 degrees. In the right figure, the standard deviation of the energy resolution is 8%.

Fig.2. The cosmic ray flux multiplied by a factor of E3 for each bin by this analysis together with the previously published results by other experiments. The horizontal axis is the energy of the primary cosmic ray and vertical axis is the flux J(E)×E3. The red filled circles represent the result of this analysis. The purple filled triangle represent the result by AGASA[2]. The light red opened circles represent result by Yakutsk[4]. The light green open squares represent the result by HiRes-1[2]. The light filled squares represent the result by HiRes Stereo[3]. The blue filled triangles represent the result by Auger[5].

本論文は13章からなる。第1章はイントロダクションとして、この研究の動機付けを行い、第2章で研究対象となる超高エネルギー宇宙線とは何か、第3章で、それを検出するテレスコ一プアレイと名付けられた測定器について、第4章で、本研究で最も重要な役割を果たす蛍光検出器のエネルギー較正について詳述している。データ解析の詳細は、第5章から第9章にわたって記述され、第10章で本論文の主要結果である宇宙線のエネルギースペクトルが導出されている。第11章は、その結果に含まれる系統誤差、第12章は、結果についての考察と今後の展望について述べている。第13章は結語である。

本論文は、10の19乗電子ボルト(eV)という超高エネルギー宇宙線の起源に迫るための最重要観測データである宇宙線のエネルギー分布、すなわち、エネルギースペクトルを宇宙線が大気と反応して生成する粒子シャワーによって発生する蛍光と、そのシャワー粒子が地表に到達して検出器に残すエネルギー信号との両方を組み合わせて、エネルギーの絶対値に関する系統誤差の小さい観測を行ったものである。これまでの他の実験グループの測定は、どちらか一方の方法だけによるもので、測定した宇宙線エネルギーの値に不定性が大きかった。そのため、特に、GZKカットオラと呼ばれる宇宙線粒子と宇宙背景輻射(絶対温度2.7Kのマイクロ波)との相互作用に起因する、観測される宇宙線エネルギーの上限の存在について決着がついていなかった。GZKカットオッフの存在を確定することは、超高エネルギー宇宙線の起源が宇宙論的存在であるのか、その加速のメカニズムがどのようなものかを知る重要な一歩である。本研究は、エネルギー絶対値の不定性という、超高エネルギー粒子検出最大の技術的困難を新たな手法で克服しようという意欲的な研究で、論文提出者の顕著な寄与によって、エネルギー測定値の系統誤差を19%に抑えることに成功した。論文提出者の得たエネルギースペクトルはGZKカットオフの存在を示している。本研究は、グループ研究であるが、この成果は論文提出者の本質的かつオリジナルな寄与によって得られたものであることを委員会一同確認した。

したがって、博士(理学)の学位を授与できると認める。