TAx4 surface detectors data analysis

. The TAx4 experiment aims to understand UHECR by expanding the observation area of the TA experiment by a factor of 4 and increasing the statistics of UHECR events with energy greater than 10 19 eV. TAx4 consists of newly installed Surface Detectors (SD) and Fluorescence Detectors (FD). The SD was only partially developed before the COVID pandemic and it currently operates with an area 2.5 times TA including the original TA area. The TAx4 SD array has been collecting data since April 2019, and data analysis is underway. In this paper, we will report on the comparison between Monte Carlo simulation and real data acquired by the TAx4 SD array and the preliminary energy spectrum of TAx4 SD array.


Introduction
Telescope Array (TA) experiment, located in Utah, USA, aims to reveal the origin of Ultra-High-Energy Cosmic Rays (UHECR) by observing extensive air showers using both Surface Detectors (SD) and Fluorescence Detectors (FD) and covering about 700 km 2 [1]. TA experiment has observed an indication for a cluster of arrival directions of cosmic rays above 57 EeV within a 20 • circle with 5 years data which is known as the Hot Spot. The posterior chance probability to observe the excess anywhere in the field of view with 5 years exposure is 3.4σ [2].
TAx4 experiment was proposed to confirm the Hot Spot by increasing the aperture. The detectors have been deployed to the northern side and southern side of TA SDs as shown in Fig 1. Currently, TAx4 experiment consists of 257 TAx4 SDs [3] deployed on a square grid with 2.08 km spacing, which is different from TA SD spacing(1.2 km). TAx4 SDs plus the original TA SDs cover about 2.5 times the area of the original TA SD. TAx4 SDs began the data taking in April 2019.
In this paper, we show current analysis results of TAx4 SD using 1.5 years data for TAx4 SD northern array and 2 years data for TAx4 SD southern array. Monte Carlo (MC) simulation is compared with the observation, and we show they agree within statistical uncertainty for energy greater than 10 EeV. A preliminary energy spectrum observed by TAx4 SD array is also discussed. The TAx4 SD energy spectrum is consistent with the TA SD standard spectrum measured with 11 years of data [4].

MC simulation
We use the same MC simulation method as TA SD [5]. The method is as follows : (i) showers are generated by the CORSIKA program [6] using QGSJET II-04 [7] for * e-mail: fujisue@icrr.u-tokyo.ac.jp * * Full author list: http://www.telescopearray.org/research/collaborators high energy hadronic interaction (for TA SD, QGSJET II-03 was used), FLUKA [8] is used for low energy hadronic interaction, and EGS4 [9] for electromagnetic interaction. The energy range generated goes from 10 17.5 eV up to 10 20.5 eV, and 200 showers are generated for each ∆log 10 (E/eV) = 0.1 bin. Zenith angles(θ) are simulated following a sin θ cos θ distribution at the detector level, which means isotropic arrival direction of cosmic rays. Primary particle generated for this study were all proton.
(ii) After the shower generation by CORSIKA, all shower particles at ground level are divided spatially into square tiles with 6 m length per side and temporally into 20 ns time bins. Energy deposit to an SD which is virtually located at the center of the square tile for each 20 ns time bin is calculated using a detector response table developed using GEANT4 [10] package. (iii) Energy deposit is converted to ADC counts considering PMT response, electronics response and so on. In this step, real time calibration data is used, so that the simulated air shower events are comparable with observed air shower events. By selecting appropriate tiles and calibration data, we can simulate for various shower core positions, azimuthal angles and event times.

Data/MC comparison
Comparison between observed real events and simulated events is needed to confirm that the MC simulation accurately reproduces real data. To this aim the distributions of reconstructed parameters of the observed events and those of the MC simulation are here compared.

Event selection
The following 7 conditions are required for events (both in data and simulation) in this analysis : (1) at least 5 SDs are used in reconstruction, (2) the reconstructed core position is at least 400 meters away from the border of the array, (3) the reconstructed zenith angle is less than 55 degrees, (4) the reduced chi square of the reconstruction fit is less than 4, (5) the uncertainty of reconstructed direction is less than 8 degrees, (6) the relative uncertainty of S800 (the density of shower particles at a lateral distance of 800 meters from the shower axis) is less than 0.5 and (7) the reconstructed energy without energy scaling is less than 10 19 eV.

Energy scale
The number of simulated events is large enough to minimize statistical uncertainty of MC simulation, so it is necessary to normalize the simulated events to compare them with observed events. The normalization is often done in terms of the number of observed events, i.e. the number of normalized simulated events are the same as that of observed events. In this study, however, we normalize the simulated events in terms the number of expected events, i.e. the number of normalized simulated events is the same as that expected to be observed by TA SD in 11 years [4] with the TAx4 SD exposure calculated by the MC simulation.
Because of the power law property of cosmic ray energy spectrum, the normalization in terms of the number of expected events highly depends on an energy scale which is determined experimentally by using those events simultaneously observed by FD and SD. Conversely, we can temporally determine the energy scaling factor of TAx4 SD with QGSJET II-04 by minimizing the difference be- tween the number of observed events and that of MC simulation events normalized assuming various energy scaling factors despite the low statistics of TAx4 FD-SD simultaneously observed events. Fig 2 shows the relation between energy scaling factors and the ratio of the number of observed events to that of normalized MC simulation events. From this comparison, we use 1.3 as the temporary energy scaling factor for TAx4 SD with QGSJET II-04 in this study. This is almost the same value as TA SD energy scaling factor with QGSJET II-03 (=1.27) [11]. The actual energy scale will be determined experimentally using simultaneously observed events by TAx4 FD and TAx4 SD.

Comparison of parameters
The comparisons for various parameters between observation and simulation are shown in Fig 3, and the p-values of Kolmogorov-Smirnov test [12] are listed in Table 1. As shown in Fig 3 and Table1, the simulation are statistically consistent with the observation. It shows the accuracy of the MC simulation.

Energy spectrum
Using 1.5 years TAx4 northern SD array data and 2 years TAx4 southern SD array data, we calculated the energy spectrum. The energy spectrum for each "i"th energy bin (with ∆log 10 (E/eV) = 0.1 as a bin width) is calculated by the following equation :  ) is the reconstruction efficiency. The numerator is the number of reconstructed (including the event selection) events in MC simulation for each reconstructed energy bin, while the denominator is the number of thrown events in the MC simulation for each generated energy bin. This term includes bin-to-bin migration effect. ∆E gen i is the bin width of the "i"th energy bin.
The effective aperture and the effective exposure of TAx4 SD array calculated by the MC simulation is shown in  Table 2. As shown in Fig 5, the TAx4 energy spectrum is consistent with the TA SD energy spectrum and a cut off structure around E = 10 19.75 eV. The expected number of events above 10 19.84 eV 1 on the assumption that there is no cut off is 27.16, and 10 events have been observed in data. This corresponds to a probability of 1.48 × 10 −4 (approximately 3.6σ). In addition to this, the deviance of the fits D/ndof is 0.62 for the broken power fit and 1.34 for the single power law fit. Both of the fits are acceptable due to the small statistics, however the broken power law fit is preferred.

Summary
To increase the data acquisition rate of UHECRs, TAx4 experiment is being constructed and has started observation in 2019. In this paper, the initial 1.5 years data of TAx4 northern SD array and 2 years data of TAx4 southern SD array are analyzed. The energy scale of TAx4 SD with QGSJET II-04 is temporally determined in terms of the number of events. The MC simulation is compared with the observation, and it is statistically consistent with the observation. We also analyzed the energy spectrum above 10 19 eV using observed data by TAx4 SD array. It is consistent with the TA SD energy spectrum within statistical uncertainty. The significance of the cut off structure of the TAx4 SD energy spectrum is 3.6σ.     Fig 1). The energy is MC generated energy without energy scaling.  Figure 5: The energy spectrum observed by TAx4 SD array is shown by the red points. The TA SD 11 years energy spectrum [11] is also shown in gray points for comparison. The energy scaling factor between the FD and the SD is assumed to be 1.3. The statistical uncertainty according to [13] of the observed events is considered in the TAx4 SD energy spectrum. For 0 events-observed energy bins, 90% upper limits are shown. The energy spectra, multiplied by E 3 , are shown in the right figure. The red solid line and the red dashed line in the right figure are the fits with broken power law function and single power law function respectively.