Theory and Phenomenology of Extensive Air Showers
Ralph Engel
Forschungszentrum Karlsruhe, Germany
Ralph Engel, 13 March 2005 Outline
Basics of extensive air showers (EAS)
Electromagnetic EAS - Heitler's model, cascade theory - Landau-Pomeranchuk-Migdal effect - Magnetic bremsstrahlung and pair-production
Hadron-induced EAS - Extension of Heitler's model, superposition model - Hadronic interaction models - Predictions and model dependence
Summary & outlook
Ralph Engel, 13 March 2005 Cosmic ray interactions
high energy:
extensive air shower
low- and medium energy: inclusive flux Typical energies in of secondary atmosphere: particles ch.π's: ~150 GeV kaons: ~600 GeV neu.π's: ~109 GeV
Ralph Engel, 13 March 2005 Cosmic ray flux and energy scales
Ralph Engel, 13 March 2005 Measurement techniques
Example: Pierre Auger Observatory
E ~ 1020 eV
time bins (100 ns)
Lateral distance (m)
Ralph Engel, 13 March 2005 Characterization of extensive air showers
Atmospheric depth: ∞ ∫ l dl= X h h
Shower particles: mainly e±,γ 80 – 95% of primary energy converted to ionization energy Up to 1011 charged particles
Ralph Engel, 13 March 2005 Electromagnetic showers
Ralph Engel, 13 March 2005 Heitler's model of em. showers
E0 Primary particle: photon Number of particles N(X)
λ 2n particles after n interactions
n = X /
) 2 n X m . . . . N X = 2 = 2 /
g/c
( X / E X = E0 /2
X Assumption:
epth shower maximum reached if E(X) = Ec
d
c
i
pher
os N max = E0 / Ec X max~ lnE0 / Ec
atm
Ralph Engel, 13 March 2005 Quantitative treatment: cascade Eqs.
Energy loss dE E Critical energy: of electron: = − − dX X 0 Ec = X 0 ~ 80 MeV
Cascade equations (Rossi & Greisen Rev.Mod.Phys. 13, 1940) d E E0 e = − E E P E , E d E dX e e ∫E e e e e
E0 ∂ E E P E , E d E − e ∫E e ∂ E
0.31 E0 X X ln E E N max ≈ max ≈ 0 0 / c E lnE0 / Ec−0.33 c
Ralph Engel, 13 March 2005 Photon shower: long. shower profile
E = 1014 eV
Cascade Eqs.: CONEX (mean shower profile)
Photons: pair production, Compton scattering Electrons: bremsstrahlung, Moller scattering (Pierog et al., astro-ph/0411260) Positons: bremsstrahlung, Bhabha scattering E = 1016 eV
Monte Carlo: CORSIKA (average over many showers)
EGS4 adapted to air with variable density
Ralph Engel, 13 March 2005 Photon shower: energy distribution
Photons: Number infinite photons Carry finite fraction of total energy
electrons Electrons & positions: Number finite Excess: ~20-30% more electrons than positons
Energy (GeV) Ralph Engel, 13 March 2005 Landau-Pomeranchuk-Migdal effect
Pair production 17
y (sea level, E ~10 eV)
5x1016 eV LPM
/d
σ d
5x1017 eV E y E
5x1018 eV
(Risse et al., Astropart Phys 21, 2004) Energy fraction y
no LPM
E LPM S ~ LPM supp y1− y E
Example: photon 3x1020 eV
Ralph Engel, 13 March 2005 Pre-showering in geomag. field
Interaction probability (strong field)
(Homola et al. astro-ph/0311442)
zenith 80° 70° 60° 50° 40° 30° Unique signature of photons 20° 10°
Ralph Engel, 13 March 2005 Highest energy Fly's Eye event
LPM+pre-shower Energy: ~3.2x1020 eV LPM
(Risse et al., Astropart Phys 21, 2004)
Chance probability: ~ 13% (1.5 σ)
Ralph Engel, 13 March 2005 Hadron-induced showers
Ralph Engel, 13 March 2005 Muon production in had. showers
Primary particle: proton
π0 decay immediately
Only charged pions initiate new hadronic cascades
Cascade ends with decay at energy Edec
n E X = E0 /ntot = Edec
n N = nch
E ln n N = 0 , = ch ≈ 0.82...0.95 E ln n dec tot Ralph Engel, 13 March 2005 Application: superposition model
Proton shower characteristics:
N E E E0 max = 0 / c N = E dec X max = e ln E0
Assumption: nucleus of mass A and energy E0 acts like A independent nucleons with energy En = E0/A
A N max = A En/ Ec = E0 / Ec A E0 / A 1− N = A = A N A E dec X max ~ e ln E0 / A
Ralph Engel, 13 March 2005 Toy model parameters
Hadronic interaction model interaction cross section multiplicity of secondary particles ratio of neutral to charged pion multiplicity
Atmosphere as target and calorimeter critical energy typical pion decay energy
Number of shower particles proportional to energy
Ralph Engel, 13 March 2005 Comparison of energies
Ralph Engel, 13 March 2005 Hadronic interaction models
Requirements:
simulation of π, K, p, n, ...., Fe collisions with air nuclei (C,N,O, Ar) coverage of full energy range from production threshold to √s ~ 400,000 GeV minimum bias event simulation - central and peripheral collisions - diffractive and non-diffractive interactions optimal description of high-energy secondary particles
tuned to existing fixed-target and collider data
variable projectile/target combinations variable collision energy fast simulation
Ralph Engel, 13 March 2005 Cosmic ray hadronic interaction models
High energy models: Low/intermediate energy models:
DPMJET II.5 and III (Ranft / GHEISHA (Fesefeldt) Roesler, RE & Ranft) Hillas' splitting algorithm (Hillas) neXus 2.0 and 3.0 (Drescher, Hladik, Ostapchenko, Pierog & FLUKA (Fasso, Ferrari, Ranft & Werner) Sala)
QGSJET 98 and 01 (Kalmykov & UrQMD (Bass, Bleicher et al.) Ostapchenko) TARGET (RE, Gaisser, SIBYLL 1.7 and 2.1 (Engel / RE, Protheroe & Stanev) Fletcher, Gaisser, Lipari & Stanev) HADRIN/NUCRIN (Hänßgen & Ranft)
● Gribov-Regge type models, minijets SOPHIA (Mücke, RE, Rachen, Protheroe, Stanev) ● Parametrizations of data
Ralph Engel, 13 March 2005 Tuning to accelerator data (i)
Proton-antiproton at CERN SPS
Pseudorapidity distribution of charged particles
= −ln tan/2
Ralph Engel, 13 March 2005 Tuning to accelerator data (ii)
Mean charged particle multiplicity
Mean transverse momentum
Proton-antiproton at CERN SPS & Tevatron
Ralph Engel, 13 March 2005 Hadronic interaction model predictions
Production (Heck, 2003) cross section p-air
Secondary particle multiplicity (charged)
Wide range of predictions: ● Air showers rather insensitive ● Correlation of cross section and multiplicity: partial compensation
Ralph Engel, 13 March 2005 Extrapolation of leading particle production
Distribution of momentum fraction of leading baryon
p-air → p/n X
Extremely inelastic events
Nearly elastic events
Energy fraction of leading baryon Ralph Engel, 13 March 2005 Air shower predictions
Ralph Engel, 13 March 2005 Energy/composition: Ne-Nμ correlation
Standard method for surface detector arrays (from lateral distribution)
E N A = A1− 0 E dec
Model dependence increasing with energy
Ralph Engel, 13 March 2005 Energy/composition: shower profile
Detailed MC simulation: 10 showers zenith angle 35°, QGSJET
A A N max = N max , X max ~ e lnE0 / A Ralph Engel, 13 March 2005 Mean depth of shower maximum
(Heck, 2004)
Superposition model:
A X max ~ e ln E0 / A
MC simulation (CORSIKA):
predictions depend on had. interaction model used for simulation
Ralph Engel, 13 March 2005 Fluctuations of depth of maximum
(Pierog et al., astro-ph/0411260)
QGSJET vs. NEXUS:
Mean Xmax very different
Fluctuations show similar structure
Fluctuations almost model-independent and related to mass
Ralph Engel, 13 March 2005 Energy reconstruction: fluorescence technique
Fraction of “unseen” energy Eu
E = EcalEu
QGSJET The higher the energy of the primary particle the smaller the fraction of unseen energy
SIBYLL (Alvarez-Muniz et al., PRD69 (2004) 103003)
Ralph Engel, 13 March 2005 Discrimination potential of LHC
CASTOR CMS TOTEM
● p-p collisions at LHC at √s = 14 TeV ● major experiments consider to do CR relevant measurements (for example, CMS / CASTOR / TOTEM)
Ralph Engel, 13 March 2005 Constraints from cosmic ray data
Difficulties with cosmic ray beams:
no direct measurement of interaction primary energy, particle unknown
Possible methods of constraining models:
comparison of measurements to simulated showers assuming a primary energy spectrum and composition consistency checks within limits given by expected primary composition multiparameter measurements: check of parameter correlations
Model-independent limits on interaction characteristics impossible
Ralph Engel, 13 March 2005 Cross section measurement
Correlation between first interaction point and depth of shower maximum
Slope in Xmax distribution related (Belov, to interaction length HiRes 2004) - selection of proton showers - selection by energy
Ralph Engel, 13 March 2005 HiRes cross section measurement
HiRes result on p-air production cross section
HiRes
(Belov, ISVHECRI04) possible influence of heavier primaries and gamma-rays σ p− Air = ± + − in 456 17(stat) 39(sys) 11(sys) mb
Ralph Engel, 13 March 2005 Summary & outlook
Electromagnetic showers reasonably well understood
Uncertainties due to hadronic interaction models limit energy and composition measurements
Some observables less model dependent - high statistics needed - multi-observable / hybrid measurements
Importance of measurements from accelerator experiments (fixed target and collider)
New hadronic interaction models in preparation (QGSJET II, EPOS, ...)
Studies of systematic uncertainty of CR measurements due to models needed
Ralph Engel, 13 March 2005