The measurement of the average shower development profile

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 Nmax Xmax A simulated shower longitudinal development profile Anatomy of an air shower initiated by a high energy proton 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 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

5. HiRes1 & HiRes: 22 (42) Mirrors azimuth angle: 0-3600, 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 The HiRes experiment

6. 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 Method

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) / Nmax s = 3X/(X+2Xmax)

8. 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

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

10. X  s N/Nm  n Gaisser-Hillas function 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 Greisen function Where y = Xm/L0, T = X/L0, L0 is the radiation length, about 36.66g/cm2 Gaussian-in-Age function where σ is the width of shower

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 MC DATA Correlation coefficient: 88% Correlation coefficient: 50% Correlation coefficient: 27% Sigma=-0.021*xmax/100+0.356 Sigma=-0.015*xmax/100+0.312 Sigma=-0.018*xmax/100+0.339

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 X  s N/Nm  n Where 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

18. 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

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