A Study of Depth of Shower Maximum of Simulated Air Shower Longitudinal profile 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

Nuclear Cascadep, n, Π0, Π+ , K +, K0, …[decay]High Energy: COLLISIONLow Energy: DECAY

Electromagnetic CascadePair Creation e+ + e-

Bremsstrahlung

Primary particle ⇾Air ⇾

Observation ⇾

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 fluorescent detector.The integral of the profile 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 coefficient ‘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 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.

M.C.Simulation

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

QGSJET01Proton, He, O , Mg,Fe

(1015-1019) 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 profile can be fitted by Gaussian distribution and here we study the dependence of the shape of the profile 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 Ɣ3=<(x -<x>)3>/σx3

Another measure of asymmetry is kurtosis whether the data are peaked or flat are peaked or flat 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 flat 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-Ɣ4=<(x-<x>)4>/σx4

Results from the simulation

CORSIKA QGSJET 01

Distribution of Xmax at 1015 ev

Distribution of Xmax at 1016 ev

CORSIKA QGSJET 01

Distribution of Xmax at 1017 ev

CORSIKA QGSJET 01

Distribution of Xmax at 1018 ev

CORSIKA QGSJET 01

Distribution of Xmax at 1019 ev

CORSIKA QGSJET 01

CORSIKA QGSJET 01

Distribution of Nmax at 1 Eev

CORSIKA 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

<Xmax> =C1logE + C2logA+C3

Red =1015ev,Green =1016ev,Blue=1017ev,purple=1018ev,Black=1019ev

This shows a very smooth dependence of <Xmax> onprimary mass.

CORSIKA QGSJET 01

Parametrization

32.609-20.682939.04291019

32.578-22.222638.25411018

32.5437-24.707437.47621017

32.4956-28.346936.54731016

32.3833-31.220134.75021015

C3C2C1E(ev)

Degree of skewness as function of primary energy

CORSIKA QGSJET 01

In this figure it is seen that the skewness of <Xmax> distributions varies little with energy.

CORSIKA QGSJET 01

Degree of Skewness as function of particle mass

CORSIKA QGSJET 01CORSIKA

QGSJET 01

In the figure Full lines show the fitted function.This figure shows a dependence ofskewness with primary mass. From the figure we can say that skewness decreasesexponentially with primary mass.

γ3=C4*exp(-A/C5)+C6

Parametrization

0.0726011.78250.55551019

0.0573526.43130.7306581018

0.1790814.51490.5432311017

C 6C 5C 4Energy(ev)

γ3=C4*exp(-A/C5)+C6

Kurtosis as function of primary energy

CORSIKA QGSJET 01

This figure describes that Kurtosis fluctuate with energy .We cannot infer anysmooth change with energy.

Kurtosis as function of primary mass

CORSIKA QGSJET 01

γ4=C7*exp(-A/C8)+C9

This figure shows a dependence of kurtosis with primary mass. From the figure wecan say that kurtosis decreases exponentially with primary mass.

γ4=C7*exp(-A/C8)+C9

Parametrization

2.7521216.5240.605001019

2.795645.87861.278161018

2.8418126.78220.918281017

C 9C 8C7Energy(ev)

γ4=C7*exp(-A/C8)+C9

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