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Comparing Simulated Showers to Data

Comparing Simulated Showers to Data. Gordon Thomson Rutgers University. Outline. Introduction: using simulations in FD analysis. Comparing Xmax means and widths. Comparing longitudinal shower profiles. Conclusions. Simulations Play a Crucial Role in FD Analysis.

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Comparing Simulated Showers to Data

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  1. Comparing Simulated Showers to Data Gordon Thomson Rutgers University INR Workshop, May 2008

  2. Outline • Introduction: using simulations in FD analysis. • Comparing Xmax means and widths. • Comparing longitudinal shower profiles. • Conclusions.

  3. Simulations Play a Crucial Role in FD Analysis • Calculate aperture for spectrum • 1018 eV limit is 10 km, for HiRes, Auger, HEAT, NOT TA/TALE • 1019 eV limit is 22 km • 1020 eV limit is 35 km, set by 1° pixel size (1.5° for Auger and HEAT) • Unfolding correction (necessary for SD also) • Understand biases for <Xmax> analysis • Most Important: understand your detector • Know inputs to MC; develop so MC is just like data;  Understand how detector / experiment / UHECR’s work

  4. HiRes Data / MC Comparisons TA/TALE will make plots like these. I hope someday Auger will also.

  5. “31° Bias”, for HiRes, Auger, NOT TA • Must see Xmax to measure E accurately. • For E < 1018 eV, events have to be close, and Xmax occurs above 31° in elevation. • Dangerous bias is present; enters into both spectrum and <Xmax> determination MC events must have same Xmax distribution as data.

  6. Requirements for Shower Simulation • <Xmax> must follow data • Make models (QGSJet, Sibyll, etc.) yield correct <Xmax>(E): Simulate a mixture of protons and iron • 80/20 for QGSJet01; 60/40 for Sibyll • Put real Corsika showers into MC.

  7. Results for <Xmax>, Xmax Distribution • The <Xmax> measurements of Fly’s Eye, HiRes/MIA, and HiRes stereo are shown. • Red = HiRes simulation • Blue = Fly’s Eye simulation • Black points = HiRes data • Simulation of HiRes/MIA + HiRes stereo <Xmax> works. • <Xmax> simulation agrees with data. • Xmax distribution does also.

  8. Accurate Aperture Calculation? • QGSJet01 works; Sibyll works; any reasonable model will work.  An accurate aperture calculation can be performed, with no model dependence.

  9. Study of Longitudinal Shower Profile Shapes • Previous work: • HiRes/MIA Prototype • T. Abu-Zayyad et al., A Measurement of the average Longitudinal Development Profile of CR Air showers, Astropart. Phys., 16, 1 (2001) • Now: • HiRes2 monocular data, work by Gareth Hughes • More statistics • Improved Monte Carlo • 2 orders of magnitude higher in energy range

  10. Shower Displayed in x (g/cm2) • Make quality cuts: • well defined showers • Standard spectrum cuts • Track length > 200g/cm2 •  < 110o • Extra Bracketing -50g/cm2 • Cerenkov Fraction < 0.35 • Fit to Gaisser-Hillas formula

  11. Shower Displayed in s (age) • Gaisser-Hillas: • With 2 free parameters: • Gaussian in Age: • One free parameter: •  = Shower Width • Symmetric about s=1

  12. Average Shower: Data • Black points mean of the blue • Gaussian fits in bins of age • Fit black points to normalized • Gaisser-Hillas • Gaussian in Age

  13. Average Shower: Monte Carlo • Corsika shower library • QGSJET Proton and Iron • Put through detailed Detector Simulation • Resolution

  14. Data – Monte Carlo Comparison • Top: Good agreement between Data and Monte Carlo • Black: Data • Red: Monte Carlo • Bottom: Ratio of Data/Monte Carlo • Flat from 0.6 to 1.3 in Age E > 1018.5eV

  15. Resolution in  • Energy dependant  resolution • effects profile reconstruction • Geometric bias • Top and Bottom of mirrors • Mirror edges • Compare Monte Carlo reconstructed with ‘True’ value of  and Rp • Shows us age range we can fit

  16. Fits to Average Showers • Black points mean of the blue • Gaussian fits in bins of age • Make average showers for half decade bins in energy • Good fits above 1018.5eV • 2/dof ~ few

  17. Average Shower Widths , Monte Carlo only • CORSIKA(QGSJET) • 80% Proton and 20% Iron • Get back what we put in • Consistent across all energies

  18. Data and Monte Carlo Results • Good agreement • Same falling behavior • Within errors • 3.5 difference in highest energy bin. What is this? • Low statistics (10 data events)

  19. Conclusions • Simulating UHECR showers is a crucial step in any experiment. • Both shower and apparatus simulation are important. • It is possible to perform an excellent simulation of UHECR experiments (both aperture and resolution). • One can simulate both <Xmax> and Xmax distributions to agree well with data. • We have a developed a method to study the average longitudinal profiles of showers. • Good fit for Gaisser-Hillas, and Gaussian in age. • Compared shower profile widths, in data to QGSJet01-based Monte Carlo: Shows good agreement.

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