the measurement of the average shower development profile

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