A Study of Depth of Shower Maximum of Simulated Air Shower Longitudinal profjle using statistical methods Dipsikha Kalita (Research Scholar) Gauhati University CRIS 2010
Outline - Brief Introduction to Extensive Air Shower - Shower cascade - Why Longitudinal development is important? - Simulation of EAS using CORSIKA -6735 code - Statistical method of analysis - Third moment of distribution - Fourth moment of distribution - Conclusion
Extensive air showers These are the secondary particles resulting from the interaction of the primary particle with air molecules that are detected by the detectors in different arrays. Pierre Auger discovered EAS in1938.
Shower Cascade in the Atmosphere Air Shower Phenomena Primary particle ⇾ Nuclear Cascade Air ⇾ p, n, Π0, Π+ , K +, K0, … Observation ⇾ [decay] High Energy: COLLISION Low Energy: DECAY Electromagnetic Cascade Pair Creation e + + e - Bremsstrahlung
Why we need to study longitudinal development ? The Longitudinal development parameterization yields the position of the shower maximum, Xmax in gm cm−2, which is sensitive to the incident CR particle type: e.g. p, C/N/O, Fe or Ɣ . Xmax can be measured experimentally by optical cherenkov and fmuorescent detector.The integral of the profjle is directly related to the shower energy.
Depth of shower maximum The depth at which a shower reaches its maximum development (Xmax) depends on the mass and energy of incident particle. Xmax = a log(E / A)+b The coeffjcient ‘a’ and ‘b’ depend on the nature of hadronic interactions,most notably on the multiplicity,elasticity and crosssection in ultra-high energy collisions of hadrons with air.
M.C.Simulation M.C Simulations are used to test hadronic interaction models as well as to test astrophysical models predicting different mass compositions at different energies.In order to study primary abundance, a large number of M.C events are to be generated with wide range of primary energy and particle type.
Simulation of EAS CORSIKA 6735 (COsmic Ray SImulations for KAscade) •A Monte Carlo Code to Simulate Extensive Air Showers . •Applies a random seed generator to vary the output data •Primary particles can be protons, light nuclei, and or photons in the code •Particles are tracked through the atmosphere as they decay into unstable secondary •Code Created by D.Heck, J. Knapp, J.N. Capdevielle, G. Schatz and T. Thouw at Karlsruhe, Germany
Simulation of EAS CORSIKA 6735 (COsmic Ray SImulations for KAscade) Here we study Xmax distribution using the following- CORSIKA 6735 QGSJET01 Proton, He, O , Mg,Fe (10 15 -10 19 ) ev
EAS longitudinal development is given by Nishimura and Kamata by solving diffusion equation and Greisen has given the analytical form which is used extensively.The longitudinal profjle can be fjtted by Gaussian distribution and here we study the dependence of the shape of the profjle on the primary particle type.The shape is measured by the higher moments of the distribution ,Viz Skewness and Kurtosis.
Skewness is a measure of asymmetry about the mean . If the distribution has a tail, compared to a normal ditribution , this can be measured by the third moment of the distribution.A positive value means a longer tail towards right.Third moment of the distribution is measured by Ɣ 3 =<(x -<x>) 3 >/ σ x 3
Another measure of asymmetry is kurtosis whether the data are peaked or fmat are peaked or fmat relative to a normal distribution. That is, data sets with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy tails. Data sets with low kurtosis tend to have a fmat top near the mean rather than a sharp peak. A uniform distribution would be the extreme case.The fourth moment of the distribution is measured by- Ɣ 4 =<(x-<x>) 4 >/ σ x 4
Results from the simulation
Distribution of Xmax at 10 15 ev CORSIKA QGSJET 01
Distribution of Xmax at 10 16 ev CORSIKA QGSJET 01
Distribution of Xmax at 10 17 ev CORSIKA QGSJET 01
Distribution of Xmax at 10 18 ev CORSIKA QGSJET 01
Distribution of Xmax at 10 19 ev CORSIKA QGSJET 01
Distribution of Nmax at 1 E ev CORSIKA 01 QGSJET 01
<Xmax> VS Energy CORSIKA QGSJET 01
Comparison of <Xmax> (g/cm2) for p,Fe initiated showers CORSIKA QGSJET 01
<Xmax> as function of particle mass CORSIKA QGSJET 01 <Xmax> =C 1 logE + C 2 logA+C 3 Red =10 15 ev,Green =10 16 ev,Blue=10 17 ev,purple=10 18 ev,Black=10 19 ev This shows a very smooth dependence of <Xmax> on primary mass.
Parametrization E(ev) C 1 C 2 C 3 10 15 34.7502 -31.2201 32.3833 10 16 36.5473 -28.3469 32.4956 10 17 37.4762 -24.7074 32.5437 10 18 38.2541 -22.2226 32.578 10 19 39.0429 -20.6829 32.609
Degree of skewness as function of primary energy CORSIKA QGSJET 01 In this fjgure it is seen that the skewness of <Xmax> distributions varies little with energy.
Degree of Skewness as function of particle mass CORSIKA QGSJET 01 γ 3 =C 4 *exp(-A/C 5 )+C 6 In the figure Full lines show the fitted function.This figure shows a dependence of skewness with primary mass. From the figure we can say that skewness decreases exponentially with primary mass.
Parametrization γ 3 =C 4 *exp(-A/C 5 )+C 6 Energy C 4 C 5 C 6 (ev) 10 17 0.543231 14.5149 0.17908 10 18 0.730658 26.4313 0.05735 10 19 0.5555 11.7825 0.07260
Kurtosis as function of primary energy CORSIKA QGSJET 01 This figure describes that Kurtosis fluctuate with energy .We cannot infer any smooth change with energy.
Kurtosis as function of primary mass CORSIKA QGSJET 01 γ 4 =C 7 *exp(-A/C 8 )+C 9 This figure shows a dependence of kurtosis with primary mass. From the figure we can say that kurtosis decreases exponentially with primary mass.
Parametrization γ 4 =C 7 *exp(-A/C 8 )+C 9 Energy C 7 C 8 C 9 (ev) 10 17 0.91828 26.7822 2.84181 γ 10 18 1.27816 5.8786 2.79564 10 19 0.60500 16.524 2.75212
Conclusion Here we have parametarised the moments of the Xmax distribution for different primary mass compositions and primary energies.In a multiparametric analysis,this will help to make inference about primary mass composition.
Thank you
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