the measurement of the average shower development profile 高能所:张丙开...
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The measurement of the average shower development profile
高能所:张丙开
导师:曹臻、王焕玉
南京 Apr. 28, 2008
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Contents
Introduction Measurement method Data sample Average development profile Uncertainty analysis Discussion and Conclusion
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Introduction : EAS
Anatomy of an air shower initiated by a high energy proton
Nmax
Xmax
A simulated shower longitudinal development profile
To measure shower longitudinal development profile with HiRes stereo data
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Introduction: Motivation• The shower shape of development profile is very important
for energy reconstruction
• Empirical shower development function are based on data at lower energy or based on theoretical electromagnetic cascade calculation
• None of them has been experimentally tested at these energies in the atmosphere (above 1018eV)
• The profile with energy between 1017-1018eV has been tested by HiRes/MIA experiment
• It is necessary to measure the profile at higher energy with HiRes stereo data
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The HiRes experiment
HiRes1 & HiRes: 22 (42) Mirrors azimuth angle: 0-3600, elevation angle: 3-17 (3-3
1) electronics: H&S (FADC) began operation in June, 1
997 (Dec 1999). End : Apr. 2006
HiRes experiment:
– located at the U.S. Army Dugway proving grounds in Utah
– A fluorescence detector
– Two sites: HiRes1 & HiRe2
– Data analysis mode: • Monocular and stereo
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Method• So, Cerenkov light is not proportional
to the number of charge particles in each step
• Subtract the Cerenkov light, convert the signals into shower sizes (correction).
• Measured signals: – Fluorescence light
• proportional to the number of charge particles & isotropy
– Direct Cerenkov light• Mainly along with shower direction• Accumulated
– Scattered Cerenkov light (Cerenkov beam)• Rayleigh scatter• Mie scatter
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Measurement method
• Determine Xmax and Nmax by a local fit
• Normalize showers & align them together according to shower ages
• Average shower sizes in age bins
Size(X) = size(X) / Nmax
s = 3X/(X+2Xmax)
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Data sample
HiRes stereo data:– 1999.12-2005.11
• Cuts are used as following: – ψ angle: ψ> 135o – Zenith angle: θ > 60o – Shower slant depth span: Δdepth < 250g/cm2
– Shower Xmax is not seen by the detector
• 2095 events are survived with clear profiles & minimum Cherenkov light contaminations
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The average profile
The average shower longitudinal development profile (the dots) and fitting functions.
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X0 is the initial point, Nm is the shower maximum,Xm is shower maximum location,λ is the shower decay length
Tm = Xm/ λ, T0 = X0/ λ
Where y = Xm/L0, T = X/L0, L0 is the radiation length, about 36.66g/cm2
2 3(1 ln )
3 20.31( )
sy s
sn s k ey
2
2
( 1)
2( )s
n s k e
Gaisser-Hillas function
Greisen function
Gaussian-in-Age function
where σ is the width of shower
X sN/Nm n
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Uncertainty analysis
• Cherenkov light subtraction: – assuming a Cherenkov light
contamination of 4.0% and 8.0% in the first bin
• Atmospheric condition: – average atmospheric condition
– Daily atmospheric parameters
The shape of profile has no noticeable change
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Discussion: shower width vs. Xmax
Shower widths dependence on shower Xmax
DATAMC
Sigma=-0.021*xmax/100+0.356Sigma=-0.018*xmax/100+0.339
Sigma=-0.015*xmax/100+0.312
Correlation coefficient: 88%
Correlation coefficient: 27% Correlation coefficient: 50%
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Discussion: energy resolution
Energy resolution has improvement, especially the big tail vanished
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Discussion: shower width vs. Energy
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Conclusion Conclusion
• Gaisser-Hillas, Greisen and Gaussian-in-Age functions describe the average profile equally well.
• The integrals of three functions are all lower than that of data by about 1.5%.
• The widths of showers have dependence on their Xmax
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Gaisser-Hillas function
Where X0 is the initial point, Nm is the shower maximumXm is shower maximum locationλ is the shower decay length
X sN/Nm n
Tm = Xm/ λ, T0 = X0/ λ
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Greisen function
Greisen function describes the development of a pure electromagnetic air shower
Where y = Xm/L0, T = X/L0, L0 is the radiation length, about 36.66g/cm2
2 3(1 ln )
3 20.31( )
sy s
sn s k ey
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Gaussian-in-Age function
2
2
( 1)
2( )s
n s k e
where σ is the width of shower