1. 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

2. Contents Introduction Measurement method Data sample Average development profile Uncertainty analysis Discussion and Conclusion

3. 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

4. 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 10 18 eV) The profile with energy between 10 17 -10 18 eV has been tested by HiRes/MIA experiment It is necessary to measure the profile at higher energy with HiRes stereo data

5. The HiRes experiment  HiRes1 & HiRes:  22 (42) Mirrors  azimuth angle: 0-360 0,  elevation angle: 3-17 (3- 31)  electronics: H&S (FADC)  began operation in June, 1997 (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

6. 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

7. 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) / N max s = 3X/(X+2X max )

8. Data sample HiRes stereo data: – 1999.12-2005.11 Cuts are used as following: – ψ angle: ψ> 135 o – Zenith angle: θ > 60 o – Shower slant depth span: Δdepth < 250g/cm 2 – Shower Xmax is not seen by the detector 2095 events are survived with clear profiles & minimum Cherenkov light contaminations

9. The average profile The average shower longitudinal development profile (the dots) and fitting functions.

10. X 0 is the initial point, N m is the shower maximum, X m is shower maximum location,λ is the shower decay length T m = X m / λ, T 0 = X 0 / λ Where y = X m /L 0, T = X/L 0, L 0 is the radiation length, about 36.66g/cm2 Gaisser-Hillas function Greisen function Gaussian-in-Age function where σ is the width of shower X  s N/Nm  n

11. 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

12. Discussion: shower width vs. Xmax Shower widths dependence on shower Xmax DATA MC Sigma=-0.021*xmax/100+0.356 Sigma=-0.018*xmax/100+0.339 Sigma=-0.015*xmax/100+0.312 Correlation coefficient: 88% Correlation coefficient: 27% Correlation coefficient: 50%

13. Discussion: energy resolution Energy resolution has improvement, especially the big tail vanished

14. Discussion: shower width vs. Energy

15. 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

17. Gaisser-Hillas function Where X 0 is the initial point, N m is the shower maximum X m is shower maximum location λ is the shower decay length X  s N/N m  n T m = X m / λ, T 0 = X 0 / λ

18. Greisen function Greisen function describes the development of a pure electromagnetic air shower Where y = X m /L 0, T = X/L 0, L 0 is the radiation length, about 36.66g/cm2

19. Gaussian-in-Age function where σ is the width of shower