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Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition

• S. P

. Knurenko1 and A. Sabourov2

1s.p.knurenko@ikfia.ysn.ru, 2tema@ikfia.ysn.ru

• Yu. G. Shafer Institute of cosmophysical research and aeronomy

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 1

• 1. Introduction

The Yakutsk EAS array is designed for detection of cosmic rays (CR) with energy 1015 − 1019 eV. It provides measurements of main components of extensive air showers (EAS): electrons, muons and Cherenkov light

• emission. Recently, experiments on radio-emission

detection have been re-initiated. The array itself consists of several instruments, combined in a single system (see next two slides): the main array, small Cherenkov array, Cherenkov tracking detector based on camera-obscura, large muon detector, weather-station and a λ = 532 nm lidar to measure atmosphere parameters.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 2

1.1 The schematics of Yakutsk EAS array network

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 3

1.2 The Yakutsk EAS array layout

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 4

• 2. Energy spectrum

The readings of light-integrating Cherenkov detectors can be analyzed separately from

• ther detectors. The energy of CR particle initiating air shower is determined in almost

model independent way involving Cherenkov light measurements. The depth shower maximum xmax is derived from observations of Cherenkov light lateral distribution. Knowing the xmax for protons and iron nuclei from simulations (QGSJET01), the mean logarithmic mass can be derived from measured xmax: ln A = xmax − xp

max

xFe

max − xp max

·

• ln AFe

The experimental data set (∼ 75000 events at E0 > 1017 eV) is considered within two, dip and ankle scenarios. In both cases low energy part of CR spectrum J(E) is produced in supernova remnants (SNRs). The galactic part of spectrum Jg(E) and composition are calculated within kinetic nonlinear theory (Berezhko and Völk (2007)).

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 5

2.1 The dip-scenario:

The second CR component Jeg(E) is produced by extragalactic sources assuming that they produce CR spectrum Jeg

s /E−2.7 at E > 1018 eV and taking into account

the modification of this spectrum due to the propagation effects in the intergalactic space (Aloisio et al (2007)). On the next slide: The dip-scenario compared to with several experiments. The dashed line represents the Galactic component. The dash-dotted line represents the assumed extragalactic component. It is seen, that experimental CR in a satisfactory way is consistent with theoretically expected spectrum within the dip scenario.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 6

2.1 The dip-scenario:

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 7

2.2 The ankle scenario:

In the ankle scenario the extragalactic source spectrum is assumed to be much harder Jeg

s /E−2: Jeg(E) becomes dominant above 1019 eV and therefore the observed CR

spectrum needs the third component — reacceleration mechanism (spiral shocks in the galactic wind, pulsar vicinity (Völk & Zirakishvili (2004), Bell (1992), Berezhko (1994))). Instead of Jg

Z(E) for every element with nuclear charge number Z we use J′g Z (E) which

coincides with Jg

Z(E) at E < Emax1 and at E > Emax2:

J′g

Z (E) = Jg Z(E)

• EZ

max1

• ·
• E

EZ

max1

−γ · exp

• −E

EZ

max2

• where EZ

max1 — minimal energy of particles involved into reacceleration process and

EZ

max2 — maximal particle energy achieved in reacceleration.

On the next slide: The ankle scenario compared to experimental data. Dashed line — galactic component (including SNRs and reaccelerated CRs). Dash-dotted line — extragalactic component (corresponding to Jeg

s /E−2).

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 8

2.2 The ankle scenario:

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 9

2.3 Mean CR atomic number

Due to dependence of maximal (cutoff) energy of CR produced in SNRs Emax ≃ 3 · Z · 1015 eV on the atomic charge number Z CR composition becomes progressively heavier as the energy increases from E ∼ 1015 eV to E ≃ 1016 eV, where iron nuclei become dominant. At higher energies within the dip scenario the contribution

• f extragalactic CR becomes essential, therefore ln A goes down with the increase of

the energy towards the value ln A ≃ 1.5. Completely different CR composition is expected at E > 1016 eV within the ankle scenario is expected at E > 1016 within the ankle scenario. Due to reacceleration heavy CR with dominant CR iron nuclei extend from ∼ 1015 eV to about ∼ 1019 eV (see next slide). In this case the transition towards lighter extragalactic component occurs at E ∼ 1019 eV. Next slide: Mean logarithm of the CR nucleus atomic number as a function of energy calculated within the dip and ankle scenario are represented by solid and dashed lines

• respectively. Experimental data obtained at ATIC-2, JACEE, KASCADE, HiRes, PAO and

Yakutsk EAS experiments. It follows that the Yakutsk EAS array data better agree with the ankle scenario.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 10

2.3 Mean CR atomic number

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 11

• 3. Longitudinal distribution

It is known fact that the depth of shower maximum (xmax) and fluctuations in EAS development are sensitive to atomic number of primary particle and for this reason they are used to estimate the CR mass composition (Efimov et al (1987)), Dyakonov et al (1989), Knurenko et al (2005)). Here we present the data on longitudinal EAS development reconstructed from Cherenkov emission data. These data were obtained after modernization of the Yakutsk array when the accuracy of main EAS characteristics increased as compared to previous series of observations. It is important to consider not

• nly mean EAS parameters, e.g xmax, muon content ρµ/ρch but also their fluctuations in

given energy intervals. In order to minimize the latter, it is also a good idea to analyze them at fixed energies.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 12

3.1 Technical aspects

Determination of xmax in individual shower is based on methods developed at the Yakutsk array and utilize the measurements of EAS Cherenkov light emission at different core distances. the xmax is determined by parameter p = lg Q200/Q550 (a relation of Cherenkov light fluxes at 200 and 550 m from the core); involving the reconstruction of EAS development cascade curve, using Cherenkov light lateral distribution function and a reverse solving (Knurenko et al (2001); based on half-width and half-height of Cherenkov light pulse recorded at 200 m from the core; fourth method includes recording of Cherenkov track with several detectors based

• n camera-obscura located at 300 − 500 m from the array center (Petrov et al

(2008)). Following slides: examples demonstrating these techniques for xmax estimation.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 13

3.1.1 Estimation by parameter p = lg Q200/Q550

106 107 108 109 1010 100 1000 Q (R ), photon/m2 core distance, m E0 = 1.3×1019 eV; θ = 25°; xmax = 738 g/cm2

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 14

3.1.2 Estimation by the shape of Cherenkov pulse

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 15

3.1.3 Estimation with Cherenkov tracking detector

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 16

3.1 Technical aspects

The accuracy of xmax determination in individual showers was estimated in simulation of EAS characteristics measurements at the array involving Monte-Carlo methods and amounted to 30 − 45 g/cm2, 35 − 55 g/cm2, 15 − 25 g/cm2, 35 − 55 g/cm2 accordingly for first, second, third and fourth methods. Total error of xmax estimation included errors associated with core location, atmospheric transparency during observational period, hardware fluctuations and mathematical methods used to calculate main parameters.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 17

3.2 Mean depth of maximal shower development

300 400 500 600 700 800 900 1000 106 107 108 109 xmax, g/cm2 Q (R ), photon/m2

A cloud of points in xmax distribution for showers with energy above 1017 eV. These data were obtained using all four methods and reflect an alteration of xmax towards lower atmosphere depths with growth of energy.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 18

3.2 Mean depth of maximal shower development

Next figure shows xmax values averaged over energy intervals together with the data from other experiments. On the same picture results of different hadron models calculations are shown. All experimental data coincide within experimental errors and demonstrate irregular shift with energy. Up to 3 × 1018 eV E.R. has value 60 − 80 g/cm2 and within the interval of 3 × 1018 − 5 × 1019 eV it equals to 40 − 60 g/cm2. This might be interpreted as a possible alteration in mass composition at very high energies. A comparison with calculations revels the tendency of light nuclei abundance starting from 5 × 1017 eV to 2 × 1019 eV and some abundance above 2 × 1019 eV. Next slide: Filled circles represent Yakutsk data open circles — CASA-MIA, squares — AUGER data, blue triangles — preliminary results of the Telescope Array experiment. Solid lines — results obtained with QGSJet II, dashed — EPOS 1.6, point line — SIBYLL 1.62.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 19

3.2 Mean depth of maximal shower development

550 600 650 700 750 800 850 1017 1018 1019 1020 〈xmax 〉, g/cm2 E0, eV

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 20

3.3 Fluctuations of xmax

Fluctuations of xmax play a huge role in EAS longitudinal development as they are associated with the point of first interaction (and, hence, with cross-section of inelastic interaction, σA-air), energy transfer to secondary hadron particle (inelastic coefficient Kinel) and, to a great extend, depend on the kind of primary particle initiating a shower. So, the amount of fluctuations measured in different energy intervals could characterize CR mass composition at given energy and on the whole determine the dynamics of its change with the energy of primary particle. Next figure demonstrates energy dependence of σ(xmax) obtained at the Yakutsk array. To compare with, the same figure shows HiRes data (Abbasi et al (2009)). The data from HiRes experiment virtually reproduce the data from Yakutsk but have a slight tendency of σ(xmax) change: a small increase in the region of 1017 − 1018 eV and decrease at 2 × 1018 − 5 × 1019 eV. The curves representing simulation results, obtained with QGSJet01, QGSJet II and SIBYLL models, are also shown on this figure. Next figure: filled squares — Yakutsk data, open squares — HiRes data, open triangles — data from Pierre Auger Observatory. Straight line — results obtained with QGSJet01, dashed line — QGSJet II, dotted line — SIBYLL 1.62 for various primary nuclei.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 21

3.3 Fluctuations of xmax

10 20 30 40 50 60 70 80 1017 1018 1019 1020 RMS(xmax ), g/cm2 E0, eV

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 22

3.3 Fluctuations of xmax

It should be pointed out that according to previous slide, the portion of heavy nuclei in CR flux energy above 2 × 1018 eV is small and helium and CNO-group nuclei might play a significant role. We came to the same conclusion (Knurenko et al (2005)) where the shape of xmax distribution was analyzed within the framework of QGSJet01 model at fixed energies 1018 eV and ∼ 1019 eV (see next slide). Next slide: xmax distribution at fixed energy 1018 eV. Solid line represents Yakutsk data (8 × 1017 < E < 2 × 1018 eV, E = 1.0 × 1018 eV, 857 events); dotted line — QGSJet01 for mixed composition (70 % p, 30 % Fe); dashed line — QGSJet01 for primary protons, solid grey line — QGSJet01 for CNO group nuclei, dash-dotted line — QGSJet01 for iron nuclei (Knurenko et al (2005)).

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 23

3.3 Fluctuations of xmax

50 100 150 200 400 500 600 700 800 900 1000 1100 number of events xmax, g/cm2

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 24

3.4 Cosmic ray mass composition

Next figure displays mean natural logarithm of the CR atomic number ln A concluded from the xmax data from four experiments — Yakutsk, HiRes, Auger and Telescope Array (Tameda et al (2010)). For ln A derivation xmax values were utilized, obtained in simulations within the framework of the QGSJet II models for proton and iron nuclei. At first glance, all data reveal a tendency to alter ln A with energy. For instance, in energy interval 2 × 1017 − 3 × 1018 eV, the value of ln A drops from 3 to 1.3 and above 1018 eV a slight growth is noted. Such a behaviour is close to the dip-scenario (Berezhko (2008)), where two peaks are presented in the energy dependence of ln A. First one, at ∼ 1017 eV, corresponds to the ending of galactic component, second — at 1019 — to the start of CR intensity change due to GZK-cutoff. Next slide: Mean mass number of primary particle as a function of energy. Circles represent Yakutsk data, triangles — HiRes data, squares — results obtained at Auger

• bservatory, blue empty triangles — preliminary data from the Telescope Array

experiment, dotted line — computational results (Berezhko (2008)).

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 25

3.4 Cosmic ray mass composition

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1017 1018 1019 1020 〈ln A〉 E0, eV

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 26

3.4 Cosmic ray mass composition However, there is still a significant data dispersion in this energy region due to poor event statistics. Thus, the reliability of our statement is quite limited. For more precise conclusion on ultra-high cosmic rays origin, a few conditions must be fulfilled: improved statistics, improvement of xmax estimation precision, adaptation of a single hadron interaction model that well describes experimental data and involving several alternative methods for xmax evaluation.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 27

• 4. Muons with εthr ≥ 1 GeV

The next figure shows an example of mean lateral distributions for muons at different

• energies. Muon lateral distribution function (LDF) is significantly lower then that of

charged component and can be effectively measured in individual events at E ≥ 1017 eV within the core distance range 100 − 800 m. Thus, as a classification parameter in this energy region, a parameter ρµ(600) could be used — the density of muon flux at 600 m from shower core. Next slide: Solid and dotted lines on the figure denote computational results obtained with QGSJet(UrQMD) models for proton (solid) and iron (dotted), red line — EPOS+UrQMD for proton, green — carbon, blue — iron. It’s seen that muon LDF from proton is more steep than one from iron nucleus and this difference is especially pronounced at large core distances. Qualitative comparison of computational results with the experiment reveals a better agreement with a heavier component of primary CR at E ≤ 1018 eV and with lighter at E ∼ 1019 eV. This feature could be stressed out if one puts parameter r2 · ρ(r) on the y-axis of a plot instead of simple ρ(r).

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 28

4.1 Muon LDF

103 104 105 106 107 10 100 1000 10000 r 2 ⋅ ρµ(r) r, m ∼1017 eV ∼1018 eV ∼1019 eV

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 29

4.2 Muon content

We considered the dependence of ρµ/ρch on the length of shower development after the maximum — ∆λ = x0/ cos θ − xmax. In highly inclined showers muon content increases proportionally to x0/ cos θ value, where x0 = 1020 g/cm2for Yakutsk. It is known fact that the depth of maximum EAS development differs significantly, depending on the kind of primary particle and, hence, this feature could be used in the analysis of the CR mass composition. For instance, by fixating the ∆λ parameter and studying the fluctuations of ρµ/ρch value. This technique is rather similar to one proposed earlier (Atrashkevich et al (1981)).

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 30

4.2 Muon content

Shower parameters calculated with CORSIKA code were modified by applying distortions according to experimental errors. Parameters measured in experiment (e.g. cos θ, xmax, ρch(r), ρµ(r)) for every shower were rolled with the normal distribution with σ parameter according to the experiment: σ(θ) = 3 · sec θ; σ(xmax) = 40g/cm2; σ(ρr) =

• ρ2

r ·

• 0.025 +

1.2 sdet · ρr · cos θ

• where sdet is area of the detector.

Next slides: A dependence of muon portion with εthr ≥ 1 GeV on the length of track in the atmosphere for individual showers with θ = 0 − 50◦ and energy 1018 eV.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 31

4.2 Muon content: QGSJet II+FLUKA

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 300 400 500 600 700 800 900 ρµ / ρch x0 / cos θ - xmax QGSJet II, FLUKA p C Fe Yakutsk

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 32

4.2 Muon content: EPOS+UrQMD

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 300 400 500 600 700 800 900 ρµ / ρch x0 / cos θ - xmax EPOS, UrQMD p C Fe Yakutsk

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 33

4.2 Muon content It is seen from figures that a strong correlation is

• bserved between the muon content and the

length of track in the atmosphere after the shower maximum. It is also seen that experimental data are in a good agreement with simulation results.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 34

4.3 Fluctuations of ρµ/ρch relation

Showers initiated by different nuclei have differing altitudes of the maximum which in turn means that different numbers of muons are generated in these showers. It also means that they cover different paths in the atmosphere. By analyzing the tracks of muons that they pass in the atmosphere after the maximum of shower development we can try to estimate the composition of cosmic rays. With this aim in view, by choosing the mean zenith angle 36◦ (which corresponds to the track length after the maximum ∆λ = 500 g/cm2), let’s normalize the values of muon content to this level and consider their fluctuations. Results are presented on the next slides. There are also shown the computational results obtained with QGSJet II and EPOS models for various nuclei. Obtained results have shown that within this method fluctuations of ρµ(600)/ρch(600) parameters don’t allow to estimate the CR mass composition. However, mean values from different nuclei

• differ. Besides, QGSJet II hints a heavier composition than that of EPOS: according to

first one, the composition of selected showers shifts towards heavier nuclei; according to second one, showers correspond to nuclei of intermediate group. On the whole, both models argue for mixed composition. Next slides: A distribution of the ρµ/ρch relation, normalized to the track length 500 g/cm2.

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 35

4.3 Fluctuations of ρµ/ρch relation: QGSJet II+FLUKA

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 w ρµ / ρch Yakutsk p C Fe

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 36

4.3 Fluctuations of ρµ/ρch relation: EPOS+UrQMD

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 w ρµ / ρch Yakutsk p C Fe

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 37

4.2 Fluctuations of ρµ/ρch relation

However, if one takes into account gamma-photons generated in ground covering muon detectors, the mean value of ρµ(600)/ρch(600) relation decreases and composition shifts towards lighter nuclei (protons-helium-carbon) (Dedenko et al at Moscow CR conference (2010)).

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 38

4.3 Fluctuations of ρµ/ρch relation, normalized to the length of track 500 g/cm2 QGSJet II, FLUKA EPOS, UrQMD Yakutsk Yakutska p C Fe p C Fe ρµ/ρch 0.3145 0.2768 0.2687 0.3025 0.3193 0.2893 0.3170 0.3381 σ 0.0747 0.0657 0.0517 0.0541 0.0536 0.0563 0.0511 0.0539 A comparison of the muon portion distribution with computational results points towards mixed cosmic ray composition near E ≥ 1018 eV. Large fluctuations of the muon portion prevent revealing of a single determined group of nuclei. A more detailed analysis is required, involving possible systematics of muon density measurement in the Yakutsk experiment.

aWith respect to contribution from gammas generated in the shielding of de-

tector (Dedenko, 2010)

Cosmic ray studies at the Yakutsk EAS array: energy spectrum and mass composition – p. 39