Mass composition of cosmic rays with energy above 10**17 eV according to surface detectors of the Yakutsk EAS array
aa r X i v : . [ a s t r o - ph . H E ] N ov Mass composition of cosmic rays with energy above eV according to surfacedetectors of the Yakutsk EAS array A. V. Glushkov and A. Sabourov ∗ Yu. G. Shafer Institute of cosmophysical research and aeronomy and677980, Lenin Ave. 31, Yakutsk, Russia
We discuss the lateral distribution of charged particles in extensive air showers with energy above10 eV measured by surface scintillation detectors of Yakutsk EAS array. The analysis coversthe data obtained during the period from 1977 to 2013. Experimental values are compared totheoretical predictions obtained with the use of corsika code within frameworks of different hadroninteraction models. The best agreement between theory and experiment is observed for QGSJet01dand QGSJet-II-04 models. A change in the cosmic ray mass composition towards proton is observedin the energy range (1 − × eV. Keywords: extensive air showers, cosmic ray mass composition
I. INTRODUCTION
The mass composition of cosmic rays (CR) with energy E ≥ eV is still not known precisely despite thefact that it has been actively studied on world extensive air shower (EAS) arrays for more than 40 years. [1]. Thisresearch is based on various EAS parameters that are sensitive to the CR mass composition. For measurement of theseparameters the Yakutsk experiment utilizes the lateral distribution functions (LDF) of electron, muon and Cherenkovcomponents of EAS (see e.g. [2–6]). One of the key chracteristics that could be estimated on a ground array is thedepth of maximum of a shower cascade curve ( x max ) which is connected with the atomic number A of primary CRparticle with the relation: log A = log 56 · x pmax − x exp.max x pmax − x Femax , (1)where x exp.max is experimentally measured value and x pmax , x Femax are values obtained via calculations performed forprimary protons and iron nuclei. Here, one cannot do without theoretical notion of EAS development. Earlier, thelateral distribution of signal in surface scintillation detectors of the Yakutsk array have been calculated [7]. Thecalculations were performed with the use of corsika code [8] for primary particles with energies E ≥ eVwithin the framework of QGSJet01d [9], QGSJet-II-04 [10], SIBYLL-2.1 [11] and EPOS-LHC [12] models. FLUKApackage [13] was chosen for treatment of low-energy interactions. Further, we compare LDFs predicted by thesemodels with experimental data obtained during the period of continuous observation lasted from 1977 to 2013. II. RESULTS AND DISCUSSION
EAS events covered by the analysis have zenith angles of arrival direction θ ≤ . ◦ ( h cos θ i = 0 . × ) operating in coincidence mode. Accordingto [7], the energy of primary particles was determined by relations: E = (3 . ± . × · ( ρ s, (0 ◦ )) . , eV (2) ρ s, (0 ◦ ) = ρ s, ( θ ) · exp (sec θ − · λ ρ , m − (3) λ ρ = 415 ±
5, g/cm (4)where ρ s, ( θ ) is the density of shower particles measured by surface scintillation detectors at the distance r = 600 mfrom shower axis. The relation (2) unambiguously connects ρ s, (0 ◦ ) with E at any CR composition, since at ∼ ∗ tema@ikfia.sbras.ru -2000-1500-1000-500 0 500 1000 1500 2000 -2000 -1500 -1000 -500 0 500 1000 1500 2000 y , m x , m FIG. 1. The layout of master stations of Yakutsk EAS array. Stations whose indications were used in the analysis are shadedwith gray color. the LDFs of charged particles intercross each other. It is demonstrated on Fig.2 where two simulation results areshown obtained for protons and iron nuclei with E = 10 eV and cos θ = 0 . f s ( r, θ ) = ρ s, ( θ ) · (cid:18)
600 + r r + r (cid:19) a · (cid:18)
600 + r M r + r M (cid:19) b − a , (5)where a = 1, r = 0, r M — is the Moliere radius which depends on the air temperature t ( ◦ C) and air pressure P (mbar): r M = ≃ . × P · t + 273273 , m. (6)The r M value is determined for every registered shower (for Yakutsk h t i ≃ − ◦ C and h r M i ≃
70 m). In equation (5) b is the parameter defined earlier [14]: b = 1 .
38 + 2 . × cos θ + 0 . × log ρ s, ( θ ). (7)The final analysis includes showers whose errors of axis reconstruction do not exceed 20 −
30 m for SM and 50 m —for LM. Mean LDFs were constructed in energy bins with logarithmic step h = ∆ log E = 0 . . h , in order to examine in detail the agreement between the experiment and a given model. Duringconstruction of mean LDFs, particle densities were multiplied by normalization ratio h E i /E ( h E i being the meanenergy in a group) and averaged within radial bins ∆ log r = 0 .
04. Mean particle densities were determined withthe formula: h ρ s ( r i ) i = P Nk =1 ρ k ( r i ) N , (8)where N is the number of readings from detectors within axis distance ranges (log r i , log r i + 0 . -2 -1
100 1000 r s ( m - ) r (m) pFe FIG. 2. LDFs of charged particles in showers with E = 10 eV and cos θ = 0 . The resulting LDFs were approximated with the function ρ s, ( r, θ ) = f s ( r, θ ) · (cid:18)
600 + r r + r (cid:19) , (9)where a = 2, r M = 10, r = 8 and r = 10 m. Here, the r M has become a formal parameter. In the aggregate withother parameters from (9) it provides the best agreement with densities (8) in the whole range 20 − ρ s, ( θ ) and b in individual groups were derived through χ minimization. h s ( - ) E (eV) pFe QGSJet01dQGSJet-II-04SIBYLL-2.1EPOS-LHCaverageYakutsk
FIG. 3. Local steepness of the surface detector response LDF in the distance range (100 − h cos θ i = 0 . The parameter b reflects the steepness of LDF, which is sensitive to CR mass composition. On Fig.3 the localsteepness of LDF is shown η s (100 − ρ s (100) − log ρ s (400)log (400 / −
400 m. Its value is close to b but it can be measured for all energies. During theparametrization of (9), particle densities outside the specified range were omitted. Lines represent expected valuespredicted by four models used in corsika simulations. 200 showers were simulated for each set of primary parameters(mass of primary particle, energy, zenith angle). In order to speed-up the simulation the thin-sampling mechanismwas activated in all versions of corsika code with the following parameters: ǫ i /E ∈ [3 . · − , − ] and w max ∈ [10 , . · ], depending on the primary energy. During calculation of particle density we considered the responseof scintillation detectors from muons, gamma-photons and electrons [7].On Fig.3 the dependency obtained by averaging of predictions of all models is shown with crosses. It is closestto QGSJet01d and QGSJet-II-04 models and provides the possibility to estimate the mass composition of primaryparticles from the relation: h log A i = w p + w Fe · log 56. (11)Here w p = w Fe and w Fe = h log A i / log 56. From this notion we have: w Fe = d exp. − d p d Fe − d p , (12)where d = η s (100 − -2-1 0 1 2 3 410 Æ l og A æ E (eV) KASCADETunka-133YakutskPAOTAHiRes
FIG. 4. Energy dependence of the CR mass composition according to several EAS experiments.
On Fig.4 energy dependencies are shown obtained by various EAS experiments. Dark circles represent our estimationbased on (11) and (12) for averaged dependency shown on Fig.3. Stars represent the data of KASCADE duringthe period from May 1998 to December 1999 [15]. With crosses are denoted the data of Tunka-133 obtained fromCherenkov light LDF [16]. White squares — PAO [17], upward triangles — HiRes [18], downward triangles — TA [19].The last three sets were obtained from the x max values presented in [17–19] according to averaged values h x max ( E ) i for abovementioned hadron interaction models. All results are roughly consistent with each other except for h log A i at E ≥ × eV resulting from the PAO data [17]. III. CONCLUSION
Long-term observation of ultra-high energy cosmic rays at the Yakutsk EAS array and comparison of experimentalresults to simulation [7] have provided the opportunity to estimate the CR mass composition in the energy range E ≃ − eV where experimental data are notably sparse. On Fig.4 a rapid change of the mass compositionwith energy is seen in energy range (1 − × eV towards lighter nuclei. This is probably due to a transitionfrom galactic CR to extragalactic. One may assume that at E ≥ × eV primary particles are mainly protons.However it is a bit premature to make such a strict conclusion. Further research is required to give a definitive answer. ACKNOWLEDGMENTS
Simulations were performed on the
Arian Kuz’min supercomputer of the North-Eastern Federal University(Yakutsk).The work is financially supported by Russian Academy of Science within the program “Fundamental properties ofmatter and astrophysics”, by RFBR grant 13-02-12036 ofi-m-2013 and by grant of President of the Republic Sakha(Yakutia) to young scientists, specialists and students to support research. [1] P. K. F. Greider,
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