TA Spectrum

The Telescope Array (TA) experiment is measuring cosmic rays of energies from PeV to 100 EeV and higher in the Northern hemisphere. TA has two parts: main TA and the TA low energy extension (TALE). Main TA is a hybrid detector that consists of 507 plastic scintillation counters on a 1200m spaced square grid that are overlooked by three fluorescence detector stations. TALE is also a hybrid detector that consists of additional fluorescence telescopes arranged to view higher elevations and an infill array of 103 plastic scintillation counters. In this work, we describe the combined TA surface detector (SD) and TALE fluorescence detector spectrum, check the calculation of the TA SD spectrum at the highest energies using an alternative, Constant Intensity Cut, method and discuss the declination dependence of the TA SD spectrum at the highest energies. Details of the TALE spectrum calculation have been presented in a separate work at this conference.


Introduction
Energy spectrum is an important tool in cosmic ray physics. Spectral features including the knee at ∼ 10 15.5 eV, the ankle near ∼ 10 18.5 eV, the cutoff near ∼ 10 19.5 eV, and, recently measured, the second knee at ∼ 10 17.0 eV and the low energy ankle at ∼ 10 16.2 eV [3], as well as the corresponding spectral indices, provide information about the nature of the cosmic ray sources and the effects of the cosmic ray propagation. The Telescope Array (TA) is a modern cosmic ray detector, which is sensitive over a wide range of energies and which sees these features.
In this paper, we discuss the combined TA energy spectrum measurement, ranging from a couple of PeV to hundreds of EeV and higher, and focus on the recent developments of the TA surface detector (SD) spectrum analysis at the highest energies: a declination dependence of the TA SD spectrum above 10 19 eV, a discrepancy in the spectrum measurement between the TA and Auger experiments above 10 19 eV, and an important check of the TA SD spectrum calculation using the Constant Intensity Cut [1] analysis, which is an alternative model-independent reconstruction technique for TA. Current details of the TALE spectrum measurement and interpretation can be found in [2], [3], and [4].

TA Data
TA is located in the desert of Millard County, UT, USA at an altitude of ∼ 1400m above sea level, which corresponds to ∼ 880g/cm 2 vertical mass overburden. TA is designed to measure cosmic rays using the ground array and air fluorescence detection techniques. The main TA, which has * e-mail: dmiivanov@gmail.com been in operation since 2008, consists of a surface detector array of 507 plastic scintillation counters deployed on a square grid of 1200 m spacing [5], which is overlooked by 3 fluorescence detector (FD) stations [6,7]. Each TA SD counter uses 2 layers of 3m 2 × 1.2cm plastic scintillator.
The TA low energy extension (TALE) consists of 10 additional fluorescence telescopes at the Northern TA fluorescence detector site, called the TA Middle Drum (MD), and an infill array of 103 counters of 400 and 600 m spacing in front of the TA MD site. The TALE fluorescence telescopes extend the TA FD field of view from the originally designed range of 3 to 33 o in elevation to 57 o in elevation. This allows a reconstruction of lower energy cosmic rays in fluorescence andČerenkov mode by the TA FD, thus extending the sensitivity of the TA experiment from the original design range of 1 EeV and higher down to a couple of PeV [3]. The TALE FD has been taking data since 2014. Figure 1 shows the combined TA energy spectrum using black filled circles. The spectra of the KASCADE-Grande [8] and the Pierre Auger Observatory [9] have been superimposed using red squares and green triangles, respectively. The combined TA spectrum, shown at the UHECR 2018 conference, consists of the 9 year TA surface detector spectrum [10] and the recently published 22 month TALE monocular spectrum, [3]. After rescaling of the Auger energies by a constant factor of +10.2%, there is a visible agreement among the three experiments, for the energies below 10 19.4 eV. A significant discrepancy between TA and Auger occurs at the highest energies. We investigate this discrepancy in two ways: first, following the recent efforts of the TA-Auger spectrum working group [11,12], we restrict the TA SD spectrum measurement to the declination  [3], while the TA SD measurement [10] starts at 10 18.2 eV and extends to 10 20 eV and higher. Superimposed are the Auger combined spectrum [9], with the Auger energies rescaled by +10.2% (red squares), and the KASCADE-Grande spectrum [8] (green triangles).

Combined TA Spectrum
band that is within the field of view of the Auger, and second, we check the TA SD spectrum calculation using the Constant Intensity Cut [1] energy reconstruction technique, implemented in a way similar to that of the Pierre Auger experiment. Figure 2 shows the TA SD spectrum calculated for the lower and higher declination bands, which correspond to −15.7 • < δ < 24.8 • and 24.8 • < δ < 90 • , respectively. In the lower declination band, −15.7 • < δ < 24.8 • , which is visible to the Auger experiment, the cutoff energy of the TA spectrum occurs at a significantly lower energy of 10 19.59 +0.05 −0.07 eV, which is well within 1σ of the Auger result, 10 19.62±0.02 eV [11,12]. The global chance probability of this effect has been evaluated using the Monte Carlo to be 3.5σ.

Standard Reconstruction
As it can be seen in [14] and [15], the standard reconstruction of surface detector events in TA is done as follows. First, counter time and pulse height information are fitted to determine the arrival direction of the event. Then, a fit of the counter pulse height information into the AGASA lateral distribution function [16] is performed, to determine S800, which is the signal size 800 m from the shower axis. An initial energy estimate, E MODEL [ S800, sec(θ) ], in terms of the reconstructed S800 and zenith angle, has been derived from a detailed CORSIKA [17] Monte Carlo, that uses proton QGSJET II.3 [18] hadronic interaction model, executed with the optimal thinning approximation [19], and de-thinned [20] to restore the important information on the ground. The final energy has been rescaled to the TA fluorescence detector using well reconstructed hybrid events seen by the TA SD and the TA FD in common: [14]. In other words, in the case of the proton QGSJET II.3 model, the model-derived SD energy is related to the energy given by the fluorescence detector via the calibration factor 1.27: Although the QGSJET II.3 hadronic model is used in the TA SD analysis by default, we have also calculated the SD -FD calibration factors corresponding to other hadronic interaction models, in order to estimate the possible non-linearity effects on the SD energy arising from the use of the hadronic model. The left panel of Figure 3 shows that the SD -FD calibration factor generally varies among the different hadronic interaction models. However, as the right panel of Figure 3 shows, after constant factors are taken out, the non-linearity effect of the most  Figure 2. The TA SD energy spectrum in the two declination bands [13]. Filled red circles correspond to the spectrum in the lower declination band, −15.7 • < δ < 24.8 • , and open black circles represent the spectrum in the higher declination band, 24.8 • < δ < 90 • . Solid lines show the broken power law fits that correspond to each declination band. The cutoff energies (log 10 (E 2 /eV)) are 19.59 +0.05 −0.07 for the lower and 19.85 +0.03 −0.03 for the higher declination bands. The cutoff energies in the two declination bands are 4σ different. extreme case is well within 10% per decade of energy. Finally, we check the non-linearity of the SD energy by directly comparing the reconstructed SD energies (using proton QGSJET II.3 model) with the FD energies using hybrid events. As Figure 4 shows, there is no evidence of a non-linearity of the SD energy with respect to the FD.

Constant Intensity Cut Method
The 100% efficiency plateau of the TA SD occurs near 10 19 eV. In the 9 years of operation, the TA SD has accumulated enough events to allow one to perform the Constant Intensity Cut (CIC) [1] analysis, which is a model-independent way of deriving the attenuation curve of the event S800 with respect to the event zenith angle. The left panel of Figure 5 shows the CIC curve derived from the TA SD data, and the right panel of Figure 5 shows the normalization of the energy estimator S 34 to the FD, from which we obtain the expression for the SD energy: log 10 (E SD CIC /eV) = ([16.2 ± 0.3] + log 10 [S 34 /(VEM m −2 )])/(0.93 ± 0.02). Figure 6 shows the constant intensity cut procedure applied to the TA SD Monte Carlo. The data and Monte Carlo CIC attenuation curves agree, as the left panel of Figure 6 shows, and S 34 versus energy relationship obtained from the TA SD Monte Carlo agrees with that obtained from the data, as it can be seen by comparing the right panels of Figures 5  and 6. Next, Figure 7 shows the comparison of the TA SD energies reconstructed using the TA SD standard recon-struction method described in Section 5.1 and the reconstruction using the CIC method. The two methods, as it can be seen on the right panel of Figure 7, agree at a ∼3% level. Finally, as Figure 8 demonstrates by comparing the SD and FD energies of the hybrid events, the CIC method does not have an energy-dependent reconstruction bias.

Spectrum Comparison
Having described and validated the two independent methods of estimating the energy of the TA SD events, we can now compare the TA SD energy spectra, calculated by these two methods. Figure 9 shows the comparison of the TA SD spectra calculated using both methods in the lower (left panel) and the higher (right panel) declination bands. As it was expected from the energy comparisons of Figure  7, the spectra in Figure 9 are in excellent agreement.

Summary
We have provided a combined TA spectrum measurement using the most recent results of the TA SD and TALE FD. The combined TA spectrum starts at 10 15.3 eV and extends to 10 20.3 eV, covering 5 orders of magnitude in energy. Cosmic ray spectrum features the knee, the low energy ankle, the second knee, the ankle, and the cutoff have all been observed in the TA data.
We have compared the combined TA spectrum to the spectra of the KASCADE-Grande and the Pierre Auger Observatory, and we have found a reasonable agreement over a wide range of energies, excluding the energies above 10 19.4 eV, where the TA and Auger full sky spectra have a significant discrepancy. We have established that this TA and Auger discrepancy can be, in part, explained by the 3.5σ (global significance) declination dependence of the TA SD spectrum: when the Auger and TA spectra are restricted to the commonly seen declinations, their cutoff energies are in a good agreement.
We have taken further steps to verify that the declination dependence of the TA SD spectrum is not an instrumental effect. In addition to the tests already performed in [13], we have re-examined the systematic uncertainties of our standard SD reconstruction by checking the linearity of the SD energy reconstruction with respect to the hadronic models as well as the FD in Section 5.1, and by cross-checking the results of our standard SD reconstruction with the Constant Intensity Cut method in Sections 5.2 and 5.3.
For a more detailed discussion on the recent Auger and TA spectrum comparisons, and the systematic uncertainties of the two experiments, an interested reader should consult the UHECR 2018 TA-Auger energy spectrum working group report [21].

Acknowledgements
The Telescope Array experiment is supported by the Japan Society for the Promotion of Science(JSPS)