A Study of Depth of Shower Maximum of Simulated Air Shower - - PowerPoint PPT Presentation

A Study of Depth of Shower Maximum

• f 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

• f 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 Cascade p, n, Π0, Π+ , K +, K0, … [decay] High Energy: COLLISION Low Energy: DECAY Electromagnetic Cascade Pair 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 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

• f 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 QGSJET01 Proton, 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 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 Ɣ3=<(x -<x>)3>/σx3

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- 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



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> on primary mass.

CORSIKA

 QGSJET 01

Parametrization

32.609

• 20.6829

39.0429 1019 32.578

• 22.2226

38.2541 1018 32.5437

• 24.7074

37.4762 1017 32.4956

• 28.3469

36.5473 1016 32.3833

• 31.2201

34.7502 1015 C3 C2 C1 E(ev)

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



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.

γ3=C4*exp(-A/C5)+C6

Parametrization

0.07260 11.7825 0.5555 1019 0.05735 26.4313 0.730658 1018 0.17908 14.5149 0.543231 1017 C 6 C 5 C 4 Energy (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 any smooth 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 we can say that kurtosis decreases exponentially with primary mass.

γ

Parametrization

2.75212 16.524 0.60500 1019 2.79564 5.8786 1.27816 1018 2.84181 26.7822 0.91828 1017 C 9 C 8 C7 Energy (ev)

γ4=C7*exp(-A/C8)+C9

Conclusion

Here we have parametarised the moments

• f 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