Transcript Slide 1

Cosmic Rays above the Knee Region
3rd School on Cosmic Rays and Astrophysics
Paul Sommers
Penn State University
Lecture 1
Science 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+, eGamma 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”]
Each π0 decay produces two photons (γ’s),
which transfers energy from the “hadronic
cascade” to the “electromagnetic cascade.”
γ
Air shower building block:
e+
The electromagnetic cascade
e-
Pair production and bremsstrahlung
In this simplified picture, the
γ
e+
particle number doubles in each
e-
γ
generation.
Each generation takes one
γ
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.
e+
e-
e+ e+
e-
e-
γ
The electromagnetic cascade “longitudinal profile”
Shower size
(number of
particles)
Slant depth
“Greisen Function” (depends only on the energy E)
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
Arrival direction using a hybrid detector
Get the SDP from the
angular pattern of hit pixels.
Get the Shower axis
within the SDP from the
angular 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.
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.)
Energy measurement using the surface detector: S(1000)
10m
30m
100m
300m
1000m
3km
10km
Gaisser-Hillas longitudinal profile with NKG lateral distribution function at each age,
in Moliere units converted to meters at depth = 850 g/cm2.
70% of maximum
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).
Universality
[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
Signal measured in
water Cherenkov
tanks 1000m from
the shower core.
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).
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
Pierre Auger Neutrino Observatory
Auger exposure to
tau Neutrinos
zenith angle ~ 90-92o
Earth Skimming 


[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.