Cosmic Rays above the Knee RegionCosmic Rays above the Knee Region

33rdrd School on Cosmic Rays and Astrophysics School on Cosmic Rays and Astrophysics

Paul SommersPaul Sommers

Penn State UniversityPenn State University

Lecture 1Science issues and open questions. Observational evidence.

Lecture 2 Air shower physics.Measurement techniques.

Air shower means “particle cascade”

An energetic cosmic ray collides with air nucleus and produces lots of secondary particles. (See image of a particle collision in the Star detector at RHIC.) Each of them produces more particles. An energetic air shower can have many billions of particles at ground level.

Why not measure the cosmic rays directly?

At 1019 eV (1.6 Joule) the rate is 1 cosmic ray per year per square kilometer!

Satellite and balloon payloads are far too small to make measurements.

Take advantage of the atmosphere. Use it as transducer and amplifier.

For high energy cosmic ray observations (unlike conventional astronomy) the atmosphere is a blessing, not a curse.

The billions of secondary particles are easy to detect.

The Auger Observatory, for example, measures every high energy cosmic ray that arrives in a 3000 km2 area in Argentina (an area equal to that of Rhode Island).

The challenge is to “reconstruct” the properties of the primary cosmic ray by detecting some of the secondaries.

The properties we want to measure are

Arrival direction

Energy

Particle type, mass

Thousands of particles produced in the collision of two gold nuclei at RHIC

Air Shower Physics

The actors:

Nuclei composed of nucleons N (p,n)

Pions: π+, π-, π0

Muons: μ+, μ-

Electrons, positrons: e+, e-

Gamma rays [photons]: γ

The actions:

N + N lots of hadronic particles and anti-particles (mostly pions, equal mix of π+,π-,π0)π±+ N lots of hadronic particles and anti-particles (mostly pions, equal mix of π+,π-,π0)π± μ± + ν (decay lifetime is 1/100 muon lifetime)π0 γ + γ immediate decay (10-16 sec)γ e+ + e- (and recoiling nucleus) [“pair production”] e± e± + γ (and recoiling nucleus) [“bremsstrahlung” or “brake radiation”]

Air shower building block:

The electromagnetic cascade

Pair production and bremsstrahlung

In this simplified picture, the

particle number doubles in each

generation.

Each generation takes one

radiation length (37 g/cm2 in air).

The cascade continues to grow until the average energy per particle is less than an electron loses to ionization in one radiation length (81 MeV). It is then at its maximum “size,” and the number of particles then decreases.

γ

e+ e-

e+ γ γ e-

e+ e+γ γe-e-e-e+

Each π0 decay produces two photons (γ’s), which transfers energy from the “hadronic cascade” to the “electromagnetic cascade.”

The electromagnetic cascade “longitudinal profile”

“Greisen Function” (depends only on the energy E)

Shower size (number of particles)

Slant depth

Π0 decays take energy from the hadronic cascade. Approximately 90% of the total energy is dissipated by the electromagnetic cascade (ionization of air nuclei).

Decays of π+ and π- particles to μ+ and μ- cause most of the remaining energy to go into the Earth as muons.

The number of muons in the shower depends on how much energy is left in the hadronic cascade when the average energy per pion is reduced to the level where decay is more probable than interaction.

If the mean pion energy is reduced to that level in relatively few generations (n), then relatively more of the energy is available for making muons: (2/3)nE.

A heavy nucleus produces more muons than a light nucleus of the same energy.

Higher inelasticity and multiplicity in hadronic interactions also causes fewer generations and therefore more muons.

Measurements (Overview)Arrival direction (can be very accurate, in principle)

SD: Arrival times at different stations

Hybrid: Shower detector plane, and pixel/tank times.

Energy (measurements subject to ~10% uncertainty due to fluctuations in shower developments)

SD: Secondary particle density 1000 meters from the core.

Hybrid: Total fluorescence light.

Particle type (not determined shower-by-shower in most cases)

Nuclear mass A: large A means maximum size occurs relatively high in

the atmosphere, and also relatively many muons.

Photons: maximum development deeper than for hadronic showers.

Neutrinos: recognized as a young shower (lots of e±) at very great

slant depth.

Arrival direction using a surface detector

Shower plane arrives to different stations at different times.

Time separation Δt between tanks separated by D gives

sin(θ) = Δt c/D.

(A non-collinear set of tanks determines the 3-dimensional arrival direction.)

Angular resolution is roughly 1˚ for the Auger SD.θ

D

Get the SDP from the angular pattern of hit pixels.

Get the Shower axis within the SDP from theangular motion of the shower front image and at least one tank time.

Resolution is about ½ degree for the SDP and 0.2 degree within the plane.

If two eyes record the event, resolution is roughly 0.3 degrees.

Arrival direction using a hybrid detector

Energy measurement using a hybrid detector

The area under the fitted functional form is E=∫(dE/dX) dX

(This is the “calorimetric” measurement of the electromagnetic cascade energy, which is estimated to

be 90% of the total energy.)

10m

30m

100m

300m

1000m

3km

10km

70% of maximum

Gaisser-Hillas longitudinal profile with NKG lateral distribution function at each age, in Moliere units converted to meters at depth = 850 g/cm2.

Energy measurement using the surface detector: S(1000)

VEM

Meters

The signal at 1000 meters, S(1000), is obtained by interpolating between measured signals, using a prescribed functional form (one or two parameters).

S(1000) is accurately measured. How does it relate to energy?

Two methods which do not rely on (unverifiable) details of hadronic interactions:

1. Calibrate S(1000) using the hybrid data set where S(1000) is measured and the hybrid energy is known.

2. Use “universality” of air showers to determine the average electromagnetic energy for each S(1000).

[Engel, Unger]

With a fixed Xmax determined by hybrid events,

the shape of the electromagnetic attenuation and muon density attenuation have little dependence on the model

used to calculate them.

Universality

The signal attenuation (with grammage) can be measured accurately by the signal at different zenith angles for showers of the same rate (per km2 sr).

A 2-parameter fit gives the electromagnetic part (hence energy) and also the muon richness (of the average shower for that energy).

Tentative indications from preliminary studies:

Higher shower energies than obtained by air fluorescence measurements.

Richer muon content than expected even for iron (using usual models).

Universality

Signal measured in water Cherenkov tanks 1000m from the shower core.

Composition

Showers by relatively heavy showers have relatively smaller Xmax and relatively more muons than showers from relatively light nuclei or

protons.

Superposition model: A nucleus of mass A and energy E produces a shower that is the same as A proton showers of energy E/A superposed together.

Since Xmax for a proton shower grows with energy as dXmax/dLogE~ 55 g/cm2,

the expected Xmax(56) for an iron shower of energy E is the same as Xmax(1) of a proton shower of energy E/56:

Xmax(56) = Xmax(1) – 55*Log(56) ~ Xmax(1)-100 g/cm2

Iron showers reach maximum size about 100 g/cm2 earlier than protons.

Since number of muons Nμ grows with energy in proportion to Eβ (and β<1) for protons, the number of muons in a shower of energy E and mass A is

Nμ(A,E) = A*Nμ(1,E/A) = A*Nμ(1,E)*(1/A)β = Nμ(1,E)*A1-β

Example: A=56, β=.92 Nμ(56,E)/Nμ(1,E) = 1.38

An iron shower has 38% more muons than a proton shower.

Using <Xmax> to estimate nuclear composition

Earth Skimming

Auger exposure to tau Neutrinos

zenith angle ~ 90-92o

Pierre Auger Pierre Auger NeutrinoNeutrino Observatory Observatory

[Olinto]

How can you be sure it was caused by a neutrino?

Nearly-horizontal air showers caused by hadrons or gamma-rays high in the atmosphere are “old” showers:

(1) The shower front has very large radius.

(2) The FADC traces are impulsive, even far from the core.

A young (locally started) electromagnetic cascade would have

(1) a small shower front curvature

(2) broad FADC traces

If you can tell that its elevation angle is negative, what else could it be?

Experience so far indicates that there is no background of spurious young nearly-horizontal air showers.

Photons

Hybrid detection as deeper than normal showers

Surface detection by slow traces (long rise time) and relatively curved shower front.

Summary

Arrival directions are straightforward and, in principle, they can be measured very accurately (arc minute if enough money).

Energy accuracy is limited (shower-by-shower) by fluctuations, but 10% accuracy is quite possible.

Photon showers can be recognized.

Neutrinos can be recognized.

Nuclear mass determination is confused by uncertainty in hadronic interactions, and methods are an active area of research.