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
Contents
Introduction Measurement method Data sample Average development profile Uncertainty analysis Discussion and Conclusion
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
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
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
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
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)
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
The average profile
The average shower longitudinal development profile (the dots) and fitting functions.
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
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
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%
Discussion: energy resolution
Energy resolution has improvement, especially the big tail vanished
Discussion: shower width vs. Energy
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
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
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
Gaussian-in-Age function
2
2
( 1)
2( )s
n s k e
where σ is the width of shower
