Cosmic ray mass composition measurement with the TALE hybrid detector

. The Telescope Array (TA) located in the State of Utah in the US is the largest ultra-high energy cosmic rays observatory in the northern hemisphere. The Telescope Array Low-energy Extension (TALE) detector was constructed to study the transition of cosmic rays from Galactic to extra-galactic origin. The TALE detector consists of a Fluorescence Detector (FD) station with 10 high elevation telescopes located at the TA Middle Drum FD Station (itself made up of 14 FD telescopes), and a Surface Detector (SD) array made up of 80 scintillation counters, including 40 with 400 m spacing and 40 with 600 m spacing. We have continued stable observation with hybrid mode since 2017. In this contribution, we present the latest result of the cosmic ray mass composition measurement using almost 4 years of TALE hybrid data.


Introduction
The Telescope Array (TA) cosmic ray observatory is the largest hybrid cosmic ray detector in the northern hemisphere in Millard Country, Utah St. The main part of the experiment consists of a surface detector (SD) array that is overlooked by 3 fluorescence detector (FD) stations. The TA SD consists of 507 scintillation counters with 1.2 km spacing and covering a total of ∼ 700 km 2 area on the ground. The three TA FD stations are located at Black Rock Mesa (BRM), Long Ridge (LR), and Middle Drum (MD), and these are overlooking the area of SD array. The Telescope Array Low-energy Extension(TALE), located at the north part of the TA experiment site, is aimed at measuring the energy spectrum and the mass composition of very high energy cosmic rays above 10 16 eV. The TALE detector consists of one FD station with ten fluorescence telescopes and an array of 80 scintillation surface detectors, which were deployed to cover a total area of approximately 20 km 2 . All 10 telescopes were refurbished from components previously used by HiRes [1], and view 31 • to 59 • in elevation, directly above the field of view of the MD telescopes. The TALE FD began operation in 2013 at the MD station. On the other hand, the TALE SD consists of 40 scintillation counters with 400 m and 40 counters with 600 m spacing, and started observation from 2017. In addition, an external trigger from the TALE FD to the TALE SD to detect low energy cosmic rays, so-called hybrid trigger system, was installed in 2018. The full details of the TALE detectors are found in [2] [3]. In this contribution, we report on the performance of the TALE hybrid detector and present preliminary results of mass composition measurements using 4 years of the TALE hybrid data. * e-mail: kfujita@icrr.u-tokyo.ac.jp

Event Reconstruction
The reconstruction process for the hybrid events is composed of the following 3 steps: the PMT selection for FD side, the determination of shower detector plane (SDP), which is the plane including the shower axis and the FD location, and the profile constrained geometry fit (PCGF) [4]. At first PMTs to be used in the reconstruction are selected by rejecting those that are spatially and temporally isolated from the shower image. After the good PMTs are selected, the SDP is determined from the pointing direction vectors of the selected PMTs. Once the SDP is determined, we perform the PCGF reconstruction that simultaneously reconstruct the shower geometry and the shower profile. So far the PCGF reconstruction is applied to the FD monocular data, and we perform it in hybrid data. Technically, for each given ψ angle, which is the shower inclination angle in the SDP as shown in Fig. 1, the shower geometry is calculated by a time vs angle fit that uses the pointing directions and timings of the PMTs and the one SD. This SD information provides us with more accurate shower geometry than monocular mode. Then the shower profile is fitted in given shower geometry using the Gaisser-Hillas parameterization formula [5] where N(x) is the number of charged particles at a given slant depth, x, X max is the depth of shower maximum, N max is the maximum number of particles at X max , X 0 is the depth of the first interaction, and λ is the interaction length of shower particles. For each trial, a combined χ 2 com = χ 2 geo + χ 2 pfl is evaluated, and the best expectation of the shower geometry and energy deposit profile from a cosmic ray shower is chosen. All reconstructed events are processed to apply the quality cuts summarized in Table. 1. The obtained shower parameter resolutions energies above 10 16.5 eV are ∼ 3 % in R p , ∼ 1 • in ψ angle, ∼ 30 g/cm 2 in X max and ∼ 10 % in energy (Fig. 2, 3). Figure 1: The schematics of the monocular and the hybrid shower geometry reconstruction. The relations between the measured values, which are t exp,i , α i and the fitting parameters, which are t core , r core and ψ. In the hybrid analysis, the two observable, t SD and r SD , are added to the relation of the monocular analysis, and as a result the number of the fitting parameter is reduced to two and the geometry determination accuracy is improved.

Composition Analysis
We presented the preliminary results of a measurement of the cosmic rays mass composition in the energy range of 10 16.5 -10 18.4 eV. The result of the mean of the shower maximum, X max , and the width of the observed X max distributions, σ(X max ) as a function of the logarithmic shower energy are presented in Fig. 4. For the comparison, the pure proton and pure iron predictions calculated by our Monte-Carlo simulation are also shown beside the observed ones. In the left panel of Fig. 4, the observed elongation rate shows clearly a break, where the energy is just above 10 17 eV. A linear fit has been rejected with a p−value of 2.5 × 10 −7 . The elongation rate before the break energy is 16 ± 5 g/cm 2 /decade and after the break energy is 97 ± 4 g/cm 2 /decade, while the pure proton and iron ones are 68 ± 2 g/cm 2 /decade and 62 ± 2 g/cm 2 /decade, respectively. On the other hand, the σ(X max ) is compatible or wider than pure proton composition in whole energies. These results indicate that the mass     composition at around 10 17 eV, i.e. around the well known 2nd knee in the cosmic ray spectrum, is consistent with mixed composition, and the average mass of cosmic ray increases up to the break energy, then changing to lighter composition with increasing energies.
The left panel of Fig. 5 is a comparison of X max with other fluorescence measurements, with systematic error denoted by gray band. The contributions of the various source on the X max measurement are listed in further comparison with particle detection based experiments, we display a mean logarithmic mass plot. From the observed X max , the mean lnA can be calculated by: where X data max is the mean X max observed by experiments, X proton/iron max are the mean X max for the proton and the iron primaries obtained by MC simulation, and lnA iron is the natural logarithm of the iron atomic mass. The right panel of Fig. 5 shows the lnA as a function of energy. The lnA values measured by the TALE hybrid detector are shown as black dots with systematic error denoted by gray band.   [6], TA [7,8], HiRes/MIA [9] measurements. Bottom: Comparison of lnA as a function of energy with various measurements. For comparison, two interpretations by KASCADE [10], IceTop [11], Tunka [12], Yakutsk [13], Auger [6], and 8.5 yrs TA BRM/LR hybrid [7] results are shown. The gray band in both figures represents the systematic uncertainty on X max measurement.

Sources
X max Photonic Scale 5 g/cm 2 Relative Time of FD and SD 3.5 g/cm 2 Fluorescence yield 5 to 1 g/cm 2 Cherenkov model 11 to 3 g/cm 2 Atmosphere 1.4 g/cm 2 Missing energy 3 g/cm 2 Total 13.8 to 7.1 g/cm 2 Table 2: Summary of systematic uncertainties on the X max measurements. Lines with multiple entries represent the values at the low and high end of the considered energy range ( 10 16.5 eV and 10 18.5 eV, respectively).

Conclusion
We report on the preliminary result of the mass composition measurement obtained by using 4 years of TALE hybrid data. In this contribution, we present the measured X max and σ(X max ) as a function of primary energy. The X max elongation rate shows a change in the slope at the energy just above ∼ 10 17 eV. This break in the elongation rate is likely correlated with the observed break in the cosmic ray energy spectrum by the TALE FD monocular measurement [3].