Signatures for showers: Shower Characteristics

R. Vazquez, USC

Trasgo meeting, February 2010. Santiago de Compostela

Extensive Air Showers iniated by Cosmic Rays have intrinsic characteristics:

Size, timing, energies, densities, and rates are intrinsic to the shower and must be taken into account in the design of cosmic ray detectors.

The ability to determine physical parameters from extensive air showers depends on the correct interpretation of these characteristics.

Arrival directionEnergyChemical compositionHadronic interactions

Cosmic ray showers: Heitler modelEnergy Number of particles Depth

E 1 0

E/2 2 λ

E/4 4 2 λ

After n steps Ec= E/2n 2n Xmax= n λ

Then : Xmax = λ log(E/Ec) and N ~ E

This simple model works well even for realistic MC.

If the multipliticy depends on energy

δKEµ =

BEEδAX c

Then

+−= )/log()(max 1

However: Assuming perfectscaling.

-Only forward region isrelevant

For a nucleus primary one may apply the superposition model

Nucleus of energy E, mass A = A nucleons of energy E/A

BEλAEEλAEX c +== )log())/(log(),(max

Hadronic model dependenceComposition dependence

J. Knapp

Number of charged particles as a function of energy

Nmax ~ E

Differences between composition and hadronic models

Kascade

Auger

Argo

The altitude of the experiment determine the energy range!!!

Longitudinal profile

Near the maximum fluctuations are smaller. Fluctuations do not scale with energy

15 %

4 %

π0 →γγπ± →µ νMuonic component

π0 decay instantly π± continue the cascade

N= total multiplicityπ0 π±

π0 π±γ N2

3N

)( NN3213 +

32N

2

32 )( N

After n steps, charged pions decay nNN )( 32=±

Wherenc NEE = βN

µ EcEEN ∝= + )log(/)/log()( 321

ββµ EAAEANAEN −== 1)/(),(

9080 .. −≅βFor nucleus

Seen in realisticMC

QGSJET Proton

Slope ≈0.9independent of θ

Casa-MiaData

AGASA

Shower shape depends on the development stage

Lateral Spread of the Shower

t = log(x)y = log(E)

Timing

For muons timing is well understood. It is related to the height production distribution

dN/dt ~ dN/dz

But has an additional R dependence

<t> = 250 ns σ= 210 ns

<t> = 700 ns σ= 350 ns1019 eV Protons

Muon height production depends on the composition. It could be used, in principle, as a handle to determine composition.

However fluctuations are large.

Max = 337 gr/cm2 σ= 158 gr/cm2

Max = 306 gr/cms

1019 eV Shower@ 60 deg.

Max = 448 gr/cm2 σ= 172 gr/cm2

For electrons, the arrival time distribution is poorly understood

Structureon µs scale

E=89 EeV

Θ = 31 deg.

Timing II: Uncertainties Core uncertaintiesinduce timing uncertainties

For r ~ 1000 mh ~ 10 kmd ~ 100 m

Relativistic effects

A muon with E ~ 1 GeVhas γ ~ 10 and 1-β ~ 5 10-3

Then after x = 1000 m

Same effect for relativistic electrons

Rates

Accidental trigger rateThe rate of accidental triggers is R ~ r2 T

Assume a time window T, and a single station accidental rate of r

T must account for inclined shower, for instance T~ d/cThe flux of random muons is given by Φ ~ 100 1/(m2 s sr)

Then R ~ (Φ A)2 d/c for A ~ 1 m2 d ~ 100m

R ~ 300 events/day

Cosmic ray spectrum compilation

γKEdEdN −=

γ~ 2.7

Rates

F ~ E-γ+1

The shower rate is given byR ~ Flux d2

R = B E-γ+1 d2

R ~ 7.4 108 1/s (Eth/1 GeV)-γ+1

R ~ 4 103 events/day Eth = 106 GeV

R ~ 80 events/day Eth = 107 GeV