E - Institut für Physik

Transcription

Astroparticle Physics
- an introduction with a focus on galactic cosmic rays
Christian Stegmann
ECAP, Erlangen
Graduate school, Berlin, October 2010
1/43
Über Beobachtungen der durchdringenden
Strahlung bei sieben Freiballonfahrten
Von V. F. Hess
(Physik. Zeitschr. 14, 1084, 1912)
[...]
Die Ergebnisse der vorliegenden Beobachtungen scheinen am ehesten durch die Annahme erklärt
werden zu können, daß eine eine Strahlung von sehr hoher Durchdringungskraft von oben her in
unsere Atmosphäre eindringt und auch noch in den untersten Schichten einen Teil der in
geschlossenen Gefäßen beobachteten Ionisation hervorruft.
[...]
2/43
The fifth ballon flight
3/43
1 Introduction
Cosmic rays is all radiation consisting of charged relativistic particles impinging on the
Earth' atmosphere
High energy cosmic rays: E > 1 GeV
Gamma-ray and neutrinos
• created as secondaries of high energy cosmic rays
•
help to learn more about cosmic rays and their sources (“multi-messenger”)
4/43
Cosmic Ray Spectrum
• nearly featureless
•
extending over eleven orders of
magnitude from
a few GeV to a few · 1020 eV
Many more known (later)
5/43
Historical Remarks
1912
1929
Victor Hess discovered cosmic rays
Skobelzyn observed first cosmic ray in cloud chamber; Bothe & Kohlhörster
showed that tracks are curved in a magnetic field
1928
Clay observed latitude effect
1932
Anderson discovered the positron in cosmic rays
1932
Raged debate in USA about sources of cosmic rays
1934
The sign of the east-west asymmetry showed that cosmic rays are positively
charged
1934/1938 Rossi and Auger discovered extensive air showers
1934
Bethe and Heitler developed the electromagnetic cascade theory
1949
Fermi proposed that cosmic rays are accelerated by bouncing off magnetic clouds
1952/1954 First human accelerator reaching p > 1 GeV
1972
Launch of the SAS-2 satellite marked the start of high energy gamma-ray
astronomy
1976
Start of the first prototype of a large scale underwater detector for high energy
neutrino astronomy, DUMAND, in Hawaii
1989
First detection of the Crab Nebula in very high energy gamma-rays (E>100 GeV)
1998
Superkamiokande found first convincing evidence for massive neutrinos
...
6/43
Aspects of Cosmic Ray Physics
• Astrophysical aspects
◦ What are the sources?
◦ How do they accelerate cosmic rays?
◦ What happens during the journey of cosmic rays to Earth?
• Interactions of particles in the atmosphere
• Experimental methods to detect cosmic rays, gamma rays,
neutrinos
• Connections between cosmic ray physics and searches for
physics beyond the Standard Model
7/43
Our Milky Way
8/43
Our Milky Way
• Average magnetic field
B=3 G
RL
• Lamour radius
3 G
cp
E
RL =
≈ 100 pc
ze B
B Z⋅1018 eV
• E =1018 eV marks the transition from difuse to rectilinear
propagation of cosmic rays
9/43
Basic notation of particle physics – a reminder
• Optical/interaction depth
N
= n l  =  = optical depth
A
• Absorption
dI =−I d =−I n  dl
I =I 0 exp − or
• Slant depth

l
I l = I 0 exp −∫ dl n 
0
l
A

l
X l=∫ dl ' l ' 
0
measures the weight per area of the material crossed
10/43
Galactic Cosmic Rays – Basic observations
∞
●
Integral intensity I E =∫ d E ' I  E ' 
E
●
Flux  =
∫ d  I  E cos 
=
2
/ 2
0
0
I  E  ∫ d  ∫ d sin  cos 
/2
=  I  E  ∫ d  sin 2 = I  E 
for isotropic intensity
●
0
(differential) number density of particles with velocity v
4
n E =
I E
v
11/43
More general
4
d N
I=
d A dt d  dE
d N = f  x , pd 3 x d 3 p
with f  x , p = phase space distribution
⇒ I  x , p ,  , =v p
2
dp
2
f  x , p= p f  x , p
dE
12/43
Abundances
• Nuclei
• Electrons
98%
1%
Nuclei
• Protons
• He
• heavier nuclei
87%
12%
~1%
Above a few GeV
− particles
I  E ~1.8 E
2
cm s sr GeV
13/43
Abundances
n LiBeB
≈0.25
measured ratio
n CNO
14/43
Cascade equation for two species of particles
d np
np
d ns
ns
np
= −
= −  p sp
and
dX
dX
s
p
p
X
=
∫ dl l 
i = m/ i
p sp =  sp / tot
measures the amount of transversed matter
2
interaction lengths (in gr /cm )
spallation probability
[ 
 ]
ns
s
X X
= p sp
exp
−
−1 for n s 0=0
Solution
np
s − p
 p s
15/43
[ 
 ]
ns
s
X X
= p sp
exp
−
−1
np
s − p
 p s
s=LiBeB with s ≈10 g /cm 2
p=CNO
 
ns
np
 sp
with  p≈6.7 g /cm and p sp =
≈0.35
 tot
2
≈ 0.25
meas
⇒ fits for X ≈0.56 g /cm
2
Slant depth of the Milky Way X =m H n H h≈10−3 g / cm2
⇒ propagation of cosmic rays resembles a random-walk.
We can describe Cosmic Rays in the Milky Way as fluid!
16/43
Diffusion-equation
 E
dE
x
∂
dE
∂E
x 
i
i
∂
dx
∂ xi i
E
d xi
n i  E , r , t 
= electron density
d2 N
=
, dV =d x 1 d x 2 d x 3
dV d E
 E  E , r , t  = energy flux per volume
 x  E ,r , t  = spatial flux per energy interval
i
Q  E , r , t 
= production rate of e ± per volume per energy interval
17/43
∂
n  E , r , t d E dV
∂t
= Q  E , r , t d E dV

[
3

∑
i=1
⇒

∂n
  − ∂  E Q
=− ∇
r
∂t
∂E
[
∂n 
 n – ∂  E Q.
=∇  D ∇
∂t
∂E

 x  E , r , t −  x  E , r , t 
i
Flux ~ gradient of the concentration ⇒
⇒
]
∂ E
 E  E ,r , t −  E  E , r , t 
d E dV
∂E
i
 x = Dij
i
∂ x
∂ xi
i
]
d xi d E
dV
d xi
∂n
∂xj
D= Dij =Diffusion tensor
Loss rate due to energy loss mechanisms
dE
dE
−
≡b  E ⇒ n  E 
= E =−b  E  n  E 
dt
dt
18/43
Diffusion loss equation
∂n 
∂

= ∇  D ∇ n
[ b E  n E  ]Q  E 
∂t
∂E
Isotrope medium ⇒
⇒
D= Skalar, no spacial extension
 D ∇
 n=D ∇ 2 n
∇
19/43
Energy loss mechanisms for electrons
dE
,
dt
E
Cooling times =
d E /d t 
Energy loss rate
Ionisation
 
Hydrogen −
Thus
 
dE
dt
−15
=7.64⋅10
ion
 
nH
−3
m
 3 ln 19.8  eV s−1

relativistic rise (Bethe-Bloch)
 
nH
dE
≈10−5 −3
eV Jahr−1 and ~ E n−1
H
dt
m
20/43
Bremsstrahlung (interaction with nuclei)
Hydrogen
H-plasma
 
 
dE
dt
dE
dt
 
 
=3.66⋅10−22
brems
−23
=7.0⋅10
brems
nH
−3
m
nH
−3
m
E s−1
−1
ln 0.36 E s
−1
⇒ ~n H
Adiabatic losses
Adiabatic extension of a source (e.g. SNR)
dU =− p dV
(Expansion of a volume → work → loss of inner energy)
  
e.g. homogenously expanding sphere −
dE
dt
=
ad

1 dR
E
R dt
⇒ ~const
21/43
Synchrotron-radiation
Source: high energy electrons/positrons in B-field
Basics: Radiation in rest frame of the charge (Lamor Formula)
2
2
q ∣̈r∣
dE
dE
−
=
is lorentz-invariant)
3 (
d t 6  0 c
dt
Dipol-radiation: ∣ 
E∣~∣sin ∣
2
I ~sin 
Polarisation: 
E ∥r at large distance
⊥
diplo axis
Example: Motion in a constant B-field
v ⊥ =v sin  , v∥=cos 

Cyclotron-frequency  m ̇v=q v × B
g =
1 qB
2 m
22/43
q=e , m=me
v g =2.8  MHz  B /1 G   Radio
−1
∣
a∣=∣v̇⊥∣=
eB
v sin  Zentripetal acceleration in B-System (Laboratory)
 me
2
∣
a '∣= ∣a∣ in current rest frame
Lamor-Formula
2
2
  
4
e ∣̈r∣
dE
e
−
=
=s
2 4 2
d t 6  0 c3
6  0 c me
2
U mag
T
4
2
v
B
2
2
c
 sin 
c
2 0
2
e
B
2
T =
,
U
=
,


=1/
c
0
0
mag
2 4
2 0
6 0 c me
⇒
 

2
dE
v
2
2
−
=2  T c U mag
 sin 
c
dt
23/43
Average over isotropical velocity distribution
1
1
〈 sin  〉= 12 ∫ d cos  sin 2 = 12 ∫ du 1−u 2 = 23
−1
−1
2
〈 〉
dE
−
dt

2
4
v
2
= T c U mag

3
c
−14
=1.058⋅10
2
 B / T  2  2 W
for particles with an isotropical velocity distribution
2
3


E
1 TeV
⇒
steepening of the electron spectrum
3 me c
B
10
=4⋅10
Cooling time sy =
4  T U mag E
100  G
Cooling is more efficient for higher energies
−2

−1
s
24/43
Inverse Compton-effect
Compton effect
Kinematics

ℏ
= 1−cos  , =

me c 2
Dynamics: Klein-Nishima
 KN
{[
]
 r 2e
21
1 4
1
=
1−
ln 2 1  −
2  22 12


{
}
 T 1−2 
≪1(Thomson-Grenzfall)
≈
1
1
 r 2e ln 2   ≫1(ultrarelativistisch)
2

25/43
Inverse Compton-effect
Energy loss rate of electrons
U rad≡ energy density of the isotropical radiation field with  ℏ ≪me c 2
〈 〉

dE 4
v
−
=  T c U rad
3
c
dt
2
2 (see sychrotron radiation)
2
3

3 me c
E
13
Cooling time sy =
=4⋅10
1 TeV
4  T U rad E

−1
3
s for U CMB =0.25 eV / cm
Diffusion lost equation
∂n 
∂

= ∇  D ∇ n
[ b E  n E  ]Q  E 
∂t
∂E
26/43
How to solve?
• define source distribtution
• define boundary conditions
Most simple example
• infinite, homogeneous source distribution
Injection spectrum Q  E =K⋅E − x
• steady state
•
∂n
 n= 
=0, ∇
0
∂t
d
⇒
[b  E  n  E ]=−Q  E 
dE
1
K
−x1
⇒ n E =−
⋅
E

b  E  1−x
⇒
const

=0, because lim n  E =0
E∞
− x−1
K E
⇒ n E =
x−1 b E 
27/43
Ansatz for b E =−
dE
: (leading orders in E )
dt
E
19,8  A2 E
 A3 E 2
2
me c



Ionisation
Bremsstrahlung
Synchrotron, I.C.
(+adiabatic losses)
b  E = A 1 2 ln
− x −1
Ionisation dominates
⇒ n E ~E
Bremsstrahlung dominates
⇒ n E ~E ~Q  E 
− x 1 Q  E 
⇒ n E ~E
~
E
Synchrotron radiation + I.C. dominates
~E⋅Q  E 
−x
28/43
Simple description of the diffusion („Leaky box type“)
 E  = life time in „galactic confinement volume“
• D = 0 in confinement volume
•
loss term =
nE
 E 
Comparison of cooling times

≪ E ≪ 
1 2 
k n


relevant energy
loss mechanisms
 steady state solution
not relevant
particles escape
before loosing energy
without diffusion
29/43
Example
Typical for nuclei: ≃1⋯3⋅107 years
Assumption:  similar for e ±
6
−3
E=300 MeV , n H =10 m
E=3 GeV ,
E=10 GeV ,
7
 ionisation≃3⋅10 Jahre
Ionisation relevant for E ≤300 MeV
− x−1
 n  E ~ E
6 −3
7
n H =10 m
 brems≃5⋅10 Jahre
Bremsstrahlung relevant around E ≃1 GeV
−x
 n  E ~ E
−10
5
B=6⋅10 T  synchr≃3⋅10 Jahre≃O IC 
Synchr. + I.C. relevant for E10 GeV
 n  E ~ E − x1
 O 100 pc
30/43
31/43
Diffusion of nuclei
Galactic gamma-rays
Direct measurement of the radiation power in the Milky Way L   E  100 MeV≈1032 W
32/43
Inelastic cross-section for p Nuclei  X
 pp≈ [ 31.50.46 ln  E /50 GeV  ] mb 1 mb=10 m 
 pA / pp≈ A 2/3  1.30.15 log 10 A 
good for A > 7
−31
2
Interaction probability P=
Interaction length =
1
n
2
N
! dl
=n dl =
A

6
3
n H =12⋅10 1/m 
Interaction rate WW =c/= n c
±
0
pp   ,  ,
   dominant for  -Spectrum for E 100 MeV

Neutrino source
2
1
±
0
Isospinsymmetrie ⇒ ≈ E in  ,≈ in    
3
3
33/43
Test of the 0    hypothesis
L ≈WW  pp⋅
∑
i (CR in Galaxy)
CR
nH
 pp
V Galaxy
⇒
Ei 1
=  pp n H c CR⋅V Galaxy
3 3
=energy density of charged CR≈ protonen
≈106 eV m−3
≈106 m−3
≈32⋅10−31 m2
≈400 pc⋅⋅8 kpc2≈2⋅1060 m3
L   ≈1.3⋅1032 W
Measured
32
L  E 100 MeV ≈10 W
34/43
Diffusion equation for nuclei
∂ ni 
 n  ∂ [ b  E  n  E  ]Q  E − n i ∑ P n j
=∇  D ∇
i
i
ij
∂t
∂E
i
j
j
ni
= Number density of nuclei i
i  E  = Lifetime for spallation from nuclei i
P ij  E  = Mean number of nuclei i per spallation from nuclei j
( P ij ≠0 only for A nuclei i  Anuclei j 
Simple approximation for light nuclei in isotropic medium
•
diffusion small compared to spallation loss ⇒
•
mnuclei ≫me ⇒ n no energy losss ⇒ b  E ≈0
•
light nuclei: Li, Be, B rare ⇒
D≈0
Q i  E ≈0
35/43
Where are we – a short summary
• Cosmic rays are messengers from the high energy Universe
• The cosmic rays we measure on Earth are typical for the cosmic rays population in our
Milky Way
• Cosmic-ray propagation can be described by a diffusion equation, i.e. cosmic rays
behave like a fluid in a box
• Next steps (today)
◦ Age of cosmic rays → sources must be active now
Energy dependent propagation → source spectra are power laws dn / dE ~E −2
◦ Acceleration of cosmic rays
◦
◦ Source detection?
36/43
Simplest assumption
All CR have the same fixed age  after injection when observed on Earth
⇒ ⇒
d ni
n 
n  with n  observed on Earth
=− i ∑ P ij j
d
i
j
j
L-Kerne (L = light): Li, Be, B; n L 0=0 Injection time (there are no sources
M-Kerne (M = medium): C, N, O most abundant primary nuclei, n M 0≠0
Fragmentationswahrscheinlichkeit
Spallation ML, M P ML≈
0.28

L/ M,L P LM=PLL =0
d nM
d
d nL
d
P MM=0
nM 
=−
no refill
M
n  P
=− L  ML nM 
L
M
X-section ⇒
 M≈60 kg/m
2,
 L≈84kg/m
2
(from known X-sections)
37/43
Age of Cosmic Rays
Estimate of the confinement volume
2
6
=  c  with 
 = mean density, =48kg/m ⇒ =3⋅10 years
Extension of a galaxy 1-10 kpc ⇒ escape after 3⋅103 – 3⋅10 4 years
⇒ confinement volume
Improved estimate of the age (confinement time):
Measure radioactive isotopes, half life time 1/2
ui
⇒ additional loss term:
dec i 
dec i =i 1 /2 /ln 2,
i ⇔ time dilatation
38/43
Example
C,O
spallation

7
Be , 9 Be ,
10
Be 10% at birth
10
Be  10 Be e
1 /2=3.9⋅106 years
Measurement
n  10 Be/ n  7 Be , n  10 Be/ n  9 Be ⇒ only 28%
10
Be
⇒ mean age at arrival on Earth= O 10 7 Jahre
Simplified model
Leaky Box:
• D=0
•
loss term = −
ni
e i 
e = local escape time in galaxy
Steady state:
• ṅ i =0
•
no source terms Q i =0 , Be produce alone in spallation of C,O,N
•
no energy loss b  E =0
39/43
⇒
0=−
ni
ni
P ij
−
 ∑
nj
 e i Spali  

j ∈{C,N,O} Spal j
Ci
for
and
⇒
i ∈{ 7 Be , 9 Be}
nk
nk
nk
0=−
−
C k −
e k  Spal k 
 dec k 
für k =10 Be
nk C k
1/e i 1/Spal i 
=
n i C i 1/ e k 1/ Spal k 1 /dec k 
Measurement of n k
ni
⇒e≈10 7 years
with =48 kg/m
⇒ IS≈3⋅105 m3
3
40/43
Die GZK Grenze
Magnetische Einschlussgebiete ↔ Gyroradius
r =R B
Galaktisch: B≈3⋅10
Protonen
● E≈10 eV →
15
●
E10
●
E≈10 18
●
E≈10
15
21
−10
sin 
,
Bc
RB =
pc
Ze
T
pc
≈ Skala der Diffusionsgleichung
⇒ Isotropie
eV → Anisotropie steigt, Entweichzeit sinkt, Diffusion
verliert an Relevanz
eV → r ≤3.6 kpc ≈ Halo-Radius
r ≤0.36
eV → nicht galaktisch eingeschlossen
B≈3⋅10−12 T⇒ r ≤36 Mpc ⇒ lokale Gruppe
Dominate Verlustprozesse höchstenergetischer Strahlung
Kollisionen mit CMB (+IR, V, ...) ⇒ Photoproduktion
a) Schwelle
41/43
{

pCMB  n 0
p   
 s≥ m pm c 2≈1.1 GeV
Labor
 s≈ 2 p p p≈  2 E p E  1cos ≈ 2 E p E 
2
⇒ E p≈
Planck-Spektrum für
b) Erste Resonanz
⇒
T ≈2.73 K
⇒
1.1GeV 
s
≥
2 E
2 E
19
E p ≥5⋅10 eV
GZK-Cut-Off (Greisen, Za....)
{
33.3%
p CMB   n 
0
 p 66.7 %




1
3
   J =
   J P=
2
2
L=0
L=0
2
m p=938 MeV /c m=1232 MeV /c 2
P
Schwelle
  p≈0.1mb  Resonanz   p≈0.6 mb
Resonanzlage
 s=m c 2 , E p≥
m c 2 
2 E
⇒
T =2.73K
E p 6⋅1019 eV
42/43
Reichweite
=  p n −1
n ≈5⋅108 m−3 , 〈   p 〉 ≈0.75 mb
⇒≈3Mpc ,
propagation≈107 Jahre
● Höchstenergetische Protonen (>1020 eV) stammen aus lokaler Gruppe → Abfall des
Spektrums (GZK Cut-Off)
● Beobachtung “Knöchel”, d.h. Ausflachung, Widerspruch?
(Spektrum Auger, Skymap Auger)
● Beschleunigung in AGN?
● Exotische Alternative: Primordiale schwere Teilchen,
m 10 20 eV / c 2
● das wird in den nächsten Jahren noch sehr spannend!!!!
z
43/43

E - Institut für Physik

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