INR Workshop, May 2008

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

• 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

HiRes Data / MC Comparisons

TA/TALE will make plots like these.

I hope someday Auger will also.

“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.

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.

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.

Accurate Aperture Calculation?

• QGSJet01 works; Sibyll works; any reasonable model will work.

An accurate aperture calculation can be performed, with no model dependence.

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

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

Shower Displayed in s (age)• Gaisser-Hillas:

• With 2 free parameters:

• Gaussian in Age:

• One free parameter: = Shower Width

• Symmetric about s=1

• Black points mean of the blue – Gaussian fits in bins of

age

• Fit black points to normalized– Gaisser-Hillas– Gaussian in Age

Average Shower: Data

Average Shower: Monte Carlo

• Corsika shower library– QGSJET Proton and

Iron

• Put through detailed Detector Simulation– Resolution

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

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 fitLog10(Energy) Resolution

(degrees)Lower Age Upper Age

17.5 – 18.0 10.0 0.85 1.25

18.0 – 18.5 6.1 0.70 1.40

18.5 – 19.0 3.9 0.60 1.35

19.0 – 19.5 2.9 0.45 1.50

19.5 – 20.0 2.7 0.50 1.20

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

Log10(Energy)Gaisser-Hillas

2/DOF

Gaussian in Age

2/DOF

18.5 – 19.0 2.15 1.85

19.0 -19.5 1.76 1.54

19.5 – 20.0 2.15 2.15

18.5 – 20.0 3.15 2.69

Average Shower Widths , Monte Carlo only

• CORSIKA(QGSJET)– 80% Proton and 20% Iron

• Get back what we put in

• Consistent across all energies

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)

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.