Particle Astrophysics Lecture 3
Cosmic Rays
Kael HANSON
Université Libre de Bruxelles
Service de physique des particules élémentaires
ULB Particle Astrophysics
Cosmic Rays
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Cosmic rays mostly protons accelerated at sites within the galaxy.
I
As they are charged and thus deviated in galactic and inter-galactic and solar and
terrestrial magnetic fields, it is extremely difficult to point observed events back
to sources. Charged particle astronomy only possible for E > 1019 eV
I
At this point,interactions with CMBR limit horizon to only nearby sources within
tens or hundreds of Mpc.
I
One century after discovery, origins of cosmic rays, in particular UHECR, remain
unknown.
I
Field of high-energy gamma rays identifies point sources where acceleration of
EM components at least is taking place - still not clear if hadrons are involved in
some of these accelerators.
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Hadronic acceleration would lead to production of chargeless neutrinos which if
detected would be smoking gun of hadronic particle accelerators.
Larmor Radius and Rigidity
Larmor radius, or gyroradius, rL , is the radius of the orbit of a charged particle moving
in a uniform, perpendicular magnetic field, obtained by simply equating the Lorentz
force with the centripetal force:
qvB =
p
mv2
⇒ rL =
rL
ZeB
(1)
where p has replaced mv in the classical limit. However, this also holds for the
relativistic generalization by considering p to be the relativistic 3-momentum. There
are several adaptations of this formula, tuned to units natural to various scenarios.
One such is
1
G
p
rL = 33.36 km
GeV/c
Z
B
In cosmic ray physics, one often sees references in the literature to the rigidity of a
particle, defined as
pc
R ≡ rL Bc =
(2)
Ze
which has units Volts! A 10 GeV proton has a rigidity of 10 GV, etc ...
Hillas Plots
Hilla s -p lo t
(c a n d id a te s ite s fo r E=100 Ee V a n d E=1 Ze V)
15
Hillas[?] arguing that in order for it to
accelerate CR particles to high
energies, the size of the acceleration
region must be at least twice the
Larmor radius:
Size (m)
3 × 1022
2 × 1017
1019
109
108
Emax
1019
log(Magnetic field, gauss)
Field (G)
10−8
10−6
10−6
0.5
50
GRB
Protons
(100 EeV)
9
Protons
(1 ZeV)
White
dwarf
3
nuclei
Fe (100 EeV)
ve s
ti ie
Ac lax
ga
Source
IGM
Gal. Disk
Gal. Halo
Ter. Field
Fridge
Magnet
GRB
Neutron
star
jets
hot-spots
lobes
-3
Colliding
galaxies
SNR
Clusters
Galactic disk
halo
-9
3 × 1021
3
6
9
12
1 au
15
1 pc
1 kpc
18
21
1 Mpc
log(size, km)
(Fermi)
E max~ ZBL
E max~ ZBL K (Ultra-relativistic shocks-GRB)
Fermi Shock Acceleration
I
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Fermi’s original 2nd-order Fermi acceleration (referring to the dependence on
β2 ) involved randomly moving magnetic clouds that swept up charged particles in
the ISM. This mechanism is not efficient at energy transfer and has trouble even
explaining intermediate-energy CRs,
Later, he and others hypothesized that shock waves expanding from SNe can give
rise to first-order acceleration sometimes diffusive acceleration - energy gain
proportional to β which can extend acceleration to higher energies. A simplified
model is
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Particle moves along +x with energy E, shock is moving opposite with velocity
β 1. The CR particle is reflected back and gains an energy (prove this!)
∆E
'β
E
(3)
Particle is somehow reflected back, either by magnetic cloud or outer shock shell
moving with lower velocity than the inner shell. The particle may lose energy here.
At each cycle particle gains fractional energy α, thus, after n cycles the particle will
have energy E = E0 (1 + α)n , alternatively
n=
I
ln(E/E0 )
ln(1 + α)
(4)
At each cycle there is a probability, P, that the CR does not escape. Realistically
P = P(E), and you are encouraged to model this general case numerically. However,
to make the math tractable, let’s assume P is fixed. So the fraction of particles left
after n cycles is expressed as
N
= Pn
N0
(5)
Fermi Acceleration
Continued
If one takes the logarithm of both sides of Eq. 5 and insert n from Eq. 4 one can find
the power-law behavior typical of Fermi acceleration:
ln(E/E0 ) ln P
N
ln
= n ln P =
⇒
N0
ln(1 + α)
ln P
= s ln(E/E0 ), s ≡
⇒
ln(1 + α)
N(> E) ∝ Es
which, when turned into a differential flux, becomes,
dN(E)
∝ E−γ , γ = 1 − s
dE
(6)
As we shall see in a bit, the observed value for γ is 2.7 so taking a typical shock wave
velocity of 10,000 km/s gives an escape probability 1 − P = 0.05.
Note that ponderance of the problem immediately preceeding Eq. 3 leads to
realization of favorable energetics of extremely relativistic acceleration regions such as
those thought to exist in jets of galactic or extragalactic objects. Instead of energy
gain which goes as β one profits from γ (usu. Γ for some reason).
Galactic Sources
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Supernova remnants (SNR) remain the most
likely candidates for CR acceleration up to at
least 1014 eV via the Fermi shock mechanism.
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Neutron stars Neutron stars, especially young
fast-rotating pulsars and magnetars possess
extreme magnetic fields (up to 1012 G in the
case of magnetars) with complex structure
that could accelerate CR up to the highest
energies. These objects are far rarer than
SNRs, however, only a dozen magnetars are
known in the Milky Way, although many could
exist in the local neighborhood.
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Microquasars are radio-intense X-ray binary
stars with companion orbiting an accreting
black hole. They are particularly interesting
particle accelerators due to observation of VHE
gamma ray emission and highly relativistic jets
which could provide energy for UHECR.
Extragalactic Sources
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Active Galaxies (AGN) are radio loud
galaxies with SMBH at center and often
some jet structure, observed or not. Blazars
are subclass of AGN with jet pointed in
direction of observation. Blazars often have
highly time-variable structure with eruptions
in radio, optical, gamma. Jets are highly
relativistic and, especially those pointed at
observer are ideal candidates for particle
acceleration.
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Gamma Ray Bursts (GRB) are among the
most violent events known in universe and
have been hypothesized by Waxman-Bahcall
to be potentially the only source of UHECR
in the universe. They are extremely distant
objects with redshifts ranging from minimum
of 0.05 to most of order unity.
Intergalactic Propagation
On larger distance scales, other effects become important:
I
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On scales where redshift is signficant, CR energies are red-shifted down in energy:
E → E/(1 + z).
At energies above ∼ 1015 eV the pair-production process
p + γCMB → p + e+ + e−
(7)
becomes possible. Because the fraction of energy lost in each interaction is small
the effective interaction distance is still quite large:
R=
I
mp
1
' 600 Mpc
2me σpγ nCMB
At energies above 1020 eV pion production becomes possible
p + π0 + X
p + γCMB →
n + π+ + X
(8)
(9)
This interaction, called GZK, dominates in this energy regime, and ultimately
limits observation of the extreme energy universe to
R=
mp
1
' 100 Mpc
2mπ σpγ nCMB
(10)
Intergalactic Propagation
Continued
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For heavier nuclei the dominant loss mechanism at UHE is photo-disintegration
A + γ → (A − 1) + N
which for He begins at 3 × 1019 eV and for Fe at 8 × 1019 eV.
A summary plot showing the effective charged particle horizon for UHE protons is
given below (thick solid line / thin solid line is pion / pair production).
Astronomy with Charged Particles
Shown is a map of magnetic deviations
in degrees as indicated by color bar for
particles of rigidity 40 EV in galactic
coordinates (galactic center at center
of Aitoff projection, galactic disk in
line that bisects projection).
In fact, galactic magnetic fields are not
well understood especially outside of
the galactic disc, and models of such
should be judged as being very
speculative.
Solar Modulation
I
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CR below several TeV are affected
by solar wind which varies on
11-year solar cycle. At times of
peak intensity the wind CR
Figure: Oxygen component of CR during
different phases of solar cycle
There is also dip in CR intensity
following CME - the following
plot demonstrates this "Forbush
Decrease" following a solar flare
event in 2006
Figure: Forbush decrease event observed
simultaneously in August 2005 in IceTop
tanks as well as NM16 and NMD neutron
monitors at South Pole
Terrestrial Effects
I
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Earth’s magnetic field well-modeled as dipole of moment M = 8 × 1022 A · m,
giving rise to equatorial field
µ M
0
(11)
B=
4π r3
of approximate intensity 0.3 to 0.6 G at the surface of the Earth.
CR below several tens of GeV are affected by the terrestrial magnetic field: a
cutoff which deflects particles of rigidity less than
Rmin =
[1 +
59.6 cos4 λ
GV
1 − sin θ cos3 λ]2
√
(12)
where λ is the magnetic latitude (recall that currently the magnetic North Pole is
Canada at 75◦ N, 101◦ W, and θ is the "East-West" angle: particles from the
East, West, and vertical have sin θ = 1, sin θ = −1 and sin θ = 0.
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Straighforward subsitution of values at the magnetic equator in Eq. 12 gives a
rigidity cutoff of 59.6 GV for particles from the East, 10.2 GV from the West, and
14.9 GV for vertically incident particles. This gives rise to the "East-West" effect:
due to the steep spectrum of cosmic rays many more particles arrive from the
West than from the East.
I
The latitude effect is apparent by examination of Eq. 12 dependence on λ: at
magnetic poles the geomagnetic cutoff vanishes, however low energy CR are still
cutoff by atmospheric thickness.
Toy Simulation
Here’s what 63 lines of Python can do - simple simulation of rays in magnetic
equatorial plane launched from x = 10rE and various ordinates. You are looking at
the South Pole so eastbound rays are coming in counter-clockwise.
Toy Simulation
Continued
Same but rigidity increased to allow vertically incident rays.
The All-Particle Cosmic Ray Spectrum
I
The flux CR particles at the top of the
Earth’s atmosphere is very nearly a perfect
power law spectrum from several tens of
GeV to roughly 5 PeV following the flux
dN
1.8 × 104 (E/GeV)−α
=
dE
m2 · s · sr · GeV
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Composition
I
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H and He form 85% and 12%,
respectively of all CR, with contribution
from Z > 3 only at 3%.
CR relative abundances follow closely
those found natively in Solar System with
exception of elements Li, Be, B which are
comparatively rare output of stars but are
formed in CR spallations with C and O
nuclei.
100
-2 -1
-1
E dN/dE, m s sr GeV
2
Cosmic Ray Electrons
positron/electron ratio
10
0.10
3
0.05
0.02
1
1
10
100
Energy, GeV
1000
10000
UHECR
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CR leaking from galaxy
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Dominance of another source or
sources
The observed behavior of the UHECR
spectrum above 1019 eV has been
contested by HiRes / Akeno groups.
New high-statistics PAO measurement
seems to indicate a real cutoff at
1020 eV.
10 5
Knee
E 2.7F(E) [GeV1.7 m−2 s−1 sr−1]
For log1 0E/eV > 15.7 (CR "knee")
the CR spectrum steepens to spectral
index of -3.0 from -2.7 and steepens
even further. The causes for these
phenomena are not well understood:
10 4
10 3
10 13
2nd Knee
Grigorov
JACEE
MGU
TienShan
Tibet07
Akeno
CASA/MIA
Hegra
Flys Eye
Agasa
HiRes1
HiRes2
Auger SD
Auger hybrid
Kascade
10 14
10 15
Ankle
10 16
10 17
E [eV]
10 18
10 19
10 20
Composition of UHECR
I
The CR composition above the
knee must be measured using
indirect techniques which must be
modelled using Monte Carlo
techniques. These are subject to
large theoretical errors due to lack
of knowledge of cross-section
behaviors in the extreme forward
region x 10− 8.
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Composition using these
techniques involves only two
archetypes: light nuclei (protons)
and heavy nuclei (iron).
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The panels at left show Auger /
HiRes measurements near GZK
cutoff, all favoring at least a
mixed composition tending toward
heavy at the higher energies.
Intermediate-Energy CR Anisotropies
The terrestrial, solar, and galactic fields do a good job of isotropizing the CR flux at
Earth. However, small anisotropies remain which Tibet Air Shower Array, Milagro, and
IceCube-22 have all measured. For case of IceCube, the a sample of 5 billion muons
collected during 2007 with median energy per cosmic ray of 20 TeV were plotted
against the southern sky with anisotropies of order 0.2% being observed. Explanation
due to Compton-Getting effect of our movement through bulk CR fluid has been
rejected to high confidence. Explanations still unknown.
Anisotropies at UHE
Structure of the Atmosphere
I
Atmosphere below 86 km is to
very good approximation an ideal
gas composed of 0.78 N2 and
0.21 O2 :
P=
ρRT
M0
(13)
where M0 is the mean molar
mass of the air: 28.5 g/mol and
R = 8.31 J/mol · K
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In this model the pressure P(h)
and the thickness X(h) are
roughly exponential functions of
the height:
P(h) = P0 exp(−h/h0 )
(14)
X(h) = X0 exp(−h/h0 )
(15)
where the scale height
h0 = 6.5 km, P0 = 101 kPa, and
X0 = 1000 g/cm2 .
Particles in the Atmosphere
Altitude (km)
15
10000
10
5
3
2
1
0
Vertical flux
[m–2 s–1 sr–1]
1000
_
νµ + νµ
µ+ + µ−
100
10
p+n
1
e+ + e−
π+ + π−
0.1
0.01
0
200
400
600
800
1000
Atmospheric depth [g cm–2]
Electromagnetic Showers in the Atmosphere
If EM particle such as photon or electron initiates
shower in atmosphere ...
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Longitudinal development reaches maximum at
depth
ln(E/Ec )
(16)
Xmax =
ln 2
where critical energy Ec ' 100 MeV for air and
Xmathrmmax is given in units of EM radiation
length which is approximately X0 = 40 g/cm2 for
air.
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Lateral development is characterized by Molière
unit equal to approximately 0.2X0 , about 100 m at
sea level.
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Air is calorimeter, that is total integrated track
length of particles (which determines signal
strength in Cherenkov or fluorescence detector)
L∼
E
Ec
Extensive Air Showers
If hadron initiates the cascade ...
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Longitudinal development also reaches shower
maximum, however, in hadronic case it must be
modeled numerically. In general showers max out
deeper in the atmosphere due to longer hadronic
interaction length Xhad ∼ 90 g/cm2
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Hadronic showers are typically muon-rich with both
penetrating muon component and soft EM
component reaching ground level.
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Lateral development is much broader than EM
cascades with sizes reaching km for UHECR
primaries.
Heavier nuclei interations described well by
superposition model: nucleus of A nucleons and
energy E acts like A protons of energy E/A giving
rise to:
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Equivalent total number of charged particles as
proton case
Number of muons increases, weakly, with A
Shower max is achieved at higher altitudes
AMS
The AMS (Alpha Magnetic Spectrometer)
will be deployed on the ISS perhaps
2008/9 and run for 3 years. It is a very
ambitious detector that will measure and
identify in detail the cosmic rays in the
GeV - TeV range. It is looking specifically
for positrons, antiprotons, signs of dark
matter, antimatter in universe. Its detector
systems are:
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Transition radiation detector (TRD):
transition radiation is produced when
ultra-relativistic charged particle travel
through dielectric boundary - emit
X-rays which can be used to measure
directly γ.
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TOF - time-of-flight system
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Silicon tracking magnetic
spectrometer.
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Ring-imaging Cherenkov counter:
particle ID in GeV region.
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Electromagnetic calorimeter (ECAL).
PAMELA
PAMELA was a cheaper and smaller
competitor to AMS which flew as a
secondary payload aboard a Russian
satellite. It was launched in 2006 and has
accumulated an excess of high energy
positrons - above what would be expected
from theoretical model of positrons
produced as secondaries in CR interactions.
The excess has been interpreted as many
things including signal of dark matter. The
source is not settled at this point.
Ballooning
Detectors carried aloft on balloon
payloads, say ballooners at least, are
the most cost-effective
above-the-atmosphere experiments.
They fly at altitudes of 25 - 30 km
where there is very little thickness left.
Mission durations can last, in the case
of ultra-long duration missions around
Antarctica.
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Cosmic Ray Energetics and Mass
(CREAM).
Pierre Auger Observatory
The Pierre Auger Observatory is 4
fluoresence detectors and 1600 water
Cherenkov surface tanks deployed over
area of 3000 km2 in pampas highlands
of Argentina for UHECR study. The
two detector types unite techniques of
AGASA (Akeno) and HiRes into single
site allowing cross calibration on
hybrid events, reducing greatly the
systematic errors.
PAO - Surface Detectors
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Each surface detector is 10 m2
plastic tank filled with water.
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As the charged particles pass
through the water, they emit
Cherenkov light which is picked
up in 3 down-facing PMTs. 1
VEM (vertical equivalent muon the standard calibration unit for
surface detectors) is approx 100
p.e. in the 3 tubes.
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The distance from tank-to-tank is
large - 1.5 km.
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The array is networked to a
central facility using radio uplinks
and each tank is solar powered.
PAO - Flourescence Detectors
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4 FDs - each 12 m2 reflector
telescopes with 400-pixel PMT
camera in the focal plane
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Each camera views about
30◦ × 30◦ patch of sky
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FD can record shower profiles
versus depth and has very good
energy resolution from
measurement of the fluoresence
output of EAS.
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Duty cycle of FD is poor - must
be moonless clear night.