Michael Kachelrieß NTNU, Trondheimweb.phys.ntnu.no/~mika/gausdal1.pdf · 2.nd order Fermi...
Transcript of Michael Kachelrieß NTNU, Trondheimweb.phys.ntnu.no/~mika/gausdal1.pdf · 2.nd order Fermi...
[]
Astroparticle Physics
Michael Kachelrieß
NTNU, Trondheim
Plan of the lectures:
Today: High energy astrophysics
Cosmic rays
Observations
Acceleration, possible sources
High energy photons and neutrinos
TeV Blazars
Elmag. cascades, EBL and primordial B fields
diffuse neutrino flux limits, point sources
Wednesday: Dark matter
particle candidates
detection: direct and indirect
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
1910: Father Wulf measures ionizing radiation in Paris
80m: flux/2
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
1910: Father Wulf measures ionizing radiation in Paris
80m: flux/2
300m: flux/2
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
1912: Victor Hess discovers cosmic rays
-10
0
20
40
60
80
1 2 3 4 5 6 7 8 9
exce
ss io
niza
tion
altitude/1000m
Hess’ and Kolhoerster’s results:
“The results are most easily ex-plained by the assumption that ra-diation with very high penetratingpower enters the atmosphere fromabove; the Sun can hardly be con-sidered as the source.”
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
What do we know 98 years later?
sola
rm
odula
tion
→
LHC ⇑
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
What do we know 98 years later?
sola
rm
odula
tion
→
LHC ⇑
only three bits of information?
exponent α of dN/dE ∝ 1/Eα
chemical composition for E <∼ 1017 eV
isotropic flux for E <∼ 1019 eV
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
What do we know 98 years later?
sola
rm
odula
tion
→
LHC ⇑
only three bits of information?
exponent α of dN/dE ∝ 1/E α
chemical composition for E <∼ 1017 eV
isotropic flux for E <∼ few × 1019 eV
anything more?
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Observing gamma-rays or cosmic rays: GeV-TeV
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Observing gamma-rays or cosmic rays: around TeV
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Pierre Auger Observatory:
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Pierre Auger Observatory:
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Three options for HE astronomy:
High-energy photons:IACT’s (HESS, MAGIC, Veritas) extremely successfulnew sources, extragal. backgrounds, evidence for hadronicaccelerators, M87, . . .synergy with Fermi-LATnext generation experiment CTA on the way
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
HESS observations of M87:
Dec
linat
ion
(d
eg)
12.2
12.4
12.6
-ray
exc
ess
even
tsγ
TeV
0
100
200
Right Ascension (hours)
m30h12m31h12m32h12
PSF
AM 87 (H.E.S.S.)
Dec
linat
ion
(d
eg)
12.3
12.4
12.5
Right Ascension (hours)
s30m30h12s00m31h12
B
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
HESS observations of M87:
Date12/1998 12/2000 12/2002 12/2004 12/2006
)-1
s-2
(E>7
30G
eV)
(cm
Φ
0.0
0.5
1.0
1.5
-1210×
)-1
s-2
f(0.
2-6
keV
) (e
rg c
m
0
20
40
-1210×
2003
2004
2005
2006
H.E.S.S.
average
HEGRA
Chandra (HST-1)
Chandra (nucleus)
B
09/Feb 16/Feb
)-1
s-2
(E>7
30G
eV)
(cm
Φ
0
2
4
6
-1210×Feb. 2005
A
09/Mar 16/Mar
March 2005
30/Mar 06/Apr
April 2005
Date04/May 11/May
May 2005
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
HESS observations of M87:
Date12/1998 12/2000 12/2002 12/2004 12/2006
)-1
s-2
(E>7
30G
eV)
(cm
Φ
0.0
0.5
1.0
1.5
-1210×
)-1
s-2
f(0.
2-6
keV
) (e
rg c
m
0
20
40
-1210×
2003
2004
2005
2006
H.E.S.S.
average
HEGRA
Chandra (HST-1)
Chandra (nucleus)
B
09/Feb 16/Feb
)-1
s-2
(E>7
30G
eV)
(cm
Φ
0
2
4
6
-1210×Feb. 2005
A
09/Mar 16/Mar
March 2005
30/Mar 06/Apr
April 2005
Date04/May 11/May
May 2005
fast variability excludes acceleration along kpc jet
acceleration in hot spots marginally okay
favors acceleration close to SMBH
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Three options for HE astronomy:
VHE photons: successful, but restricted to few Mpc
10
12
14
16
18
20
22
Gpc100Mpc10MpcMpc100kpc10kpckpc
log1
0(E
/eV
)
photon horizon γγ → e+e− CMB
IR
radio
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Three options for HE astronomy:
VHE photons: successful, but restricted to few Mpchadronic photons vs. synchtrotron/Compton photons
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Three options for HE astronomy:
astronomy with VHE photons restricted to few Mpc
astronomy with HE neutrinos:
smoking gun for hadrons but challenging
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Three options for HE astronomy:
astronomy with VHE photons restricted to few Mpc
astronomy with HE neutrinos:
smoking gun for hadrons but challenging
large λν , but also large uncertainty 〈δϑ〉 >∼ 1
small event numbers: <∼ few/yr for PAO or ICECUBE
identification of steady sources challenging without additionalinput
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Three options for HE astronomy:
astronomy with VHE photons restricted to few Mpc
astronomy with HE neutrinos:
smoking gun for hadrons but challenging
large λν , but also large uncertainty 〈δϑ〉 >∼ 1
small event numbers: <∼ few/yr for PAO or ICECUBE
identification of steady sources challenging without additionalinput
Alternative:
is astronomy with charged particles possible?
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Three options for HE astronomy:
10
12
14
16
18
20
22
Gpc100Mpc10MpcMpc100kpc10kpckpc
log1
0(E
/eV
)
proton horizon
photon horizon γγ → e+e− CMB
IR
Virgo ⇓
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Three options for HE astronomy:
10
12
14
16
18
20
22
Gpc100Mpc10MpcMpc100kpc10kpckpc
log1
0(E
/eV
)
proton horizon
photon horizon γγ → e+e− CMB
IR
Virgo ⇓
if UHECRs are protons:
deflections may be small
use larger statistics of UHECRs
well-suited horizon scale
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Possible sources and the Hillas plot:
pulsars
Galactic halo
AGN cores
GRB
cluster
SNR
radio galaxies
AU Mpckpcpc
−9
−7
−5
−3
−1
1
3
5
7
9
11
13
0 2 4 6 8 10 12 14 16 18 20 22log(R/km)
log(
B/G
)
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Possible sources and the Hillas plot:
pulsars
Galactic halo
AGN cores
GRB
cluster
SNR
radio galaxies
AU Mpckpcpc
−9
−7
−5
−3
−1
1
3
5
7
9
11
13
0 2 4 6 8 10 12 14 16 18 20 22log(R/km)
log(
B/G
)
contains only size constraint; additionally
age limitation: SNR, galaxy clusters
energy losses: pulsars, AGN
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
[]
Standard Galactic source: SNRs
energetics:sources are SNRs:kinetic energy output of SNe:10M⊙ ejected with v ∼ 5 × 108 cm/s every 30 yr⇒ LSN,kin ∼ 3 × 1042 erg/s
explains local energy density of CR ǫCR ∼ 1 eV/cm3 for aescape time from disc τesc ∼ 6 × 106 yr and efficieny ∼ 1%
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Standard Galactic source: SNRs
energetics:sources are SNRs:kinetic energy output of SNe:10M⊙ ejected with v ∼ 5 × 108 cm/s every 30 yr⇒ LSN,kin ∼ 3 × 1042 erg/s
explains local energy density of CR ǫCR ∼ 1 eV/cm3 for aescape time from disc τesc ∼ 6 × 106 yr and efficieny ∼ 1%
1.order Fermi shock acceleration ⇒ dN/dE ∝ E−γ withγ = 2.0 − 2.2
diffusion in GMF with D(E) ∝ τesc(E) ∼ E−δ and δ ∼ 0.5explains observed spectrum E−2.6
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Standard Galactic source: SNRs
energetics:sources are SNRs:kinetic energy output of SNe:10M⊙ ejected with v ∼ 5 × 108 cm/s every 30 yr⇒ LSN,kin ∼ 3 × 1042 erg/s
explains local energy density of CR ǫCR ∼ 1 eV/cm3 for aescape time from disc τesc ∼ 6 × 106 yr and efficieny ∼ 1%
1.order Fermi shock acceleration ⇒ dN/dE ∝ E−γ withγ = 2.0 − 2.2
diffusion in GMF with D(E) ∝ τesc(E) ∼ E−δ and δ ∼ 0.5explains observed spectrum E−2.6
Problems:
maximal energy Emax too low
anisotropy too large
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
2.nd order Fermi acceleration
consider CR with initial energy E1 “scattering” at a “cloud”moving with velocity V :
V
E p
E p
θ θ
1 1
2 2
1 2
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy gain ξ ≡ (E2 − E1)/E1?
Lorentz transformation 1: lab (unprimed) → cloud (primed)
E′1 = γE1(1 − β cos ϑ1) where β = V/c and γ = 1/
√
1 − β2
Lorentz transformation 2: cloud → lab
E2 = γE′2(1 + β cos ϑ′
2)
scattering off magnetic irregularities is collisionless, the cloudis very massive
⇒ E′2 = E′
1
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy gain ξ ≡ (E2 − E1)/E1?
⇒ E′2 = E′
1:
• Lorentz transformation 1: lab → cloud
E′1 = γE1(1 − β cos ϑ1)
︸ ︷︷ ︸where β = V/c and γ = 1/
√
1 − β2
• Lorentz transformation 2: cloud → lab
E2 = γE′2(1 + β cos ϑ′
2)
⇒ ξ =E2 − E1
E1
=1 − β cos ϑ1 + β cos ϑ′
2 − β2 cos ϑ1 cos ϑ′2
1 − β2− 1.
we need average values of cos ϑ1 and cos ϑ′2:
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Assume: CR scatters off magnetic irregularities many times in cloud⇒ its direction is randomized,
〈cos ϑ′2〉 = 0.
collision rate CR–cloud: proportional to their relative velocity(v − V cos ϑ1):⇒ for ultrarelativistic particles, v = c,
dn
dΩ1
∝ (1 − β cos ϑ1),
and we obtain
〈cos ϑ1〉 =
∫
cos ϑ1dn
dΩ1
dΩ1/
∫dn
dΩ1
dΩ1= −β
3
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy gain ξ for 2.nd order Fermi:
Plugging 〈cos ϑ′2〉 = 0 and 〈cos ϑ1〉 = −β
3into formula for ξ gives
ξ =1 + β2/3
1 − β2− 1 ≃
4
3β2
since β ≪ 1.
ξ ∝ β2 > 0 ⇒ energy gain
– O(ξ) = β2,because β ≪ 1: average energy gain is very small
– ξ depends on drift velocity of “clouds”
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
[]
Diffusive shock acceleration
consider CR with initial energy E1 “scattering” at a shock movingwith velocity Vs:
shock
V
EEE
E
E
E E
θV
V
11
1
1
2
22
1
θ2
p
p s
E2
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
same discussion, but now different angular averages:
projection of istropic flux on planar shock:
dn
d cos ϑ1
=
2 cos ϑ1 cos ϑ1 < 00 cos ϑ1 > 0
thus 〈cos ϑ1〉 = −23
and 〈cos ϑ2〉 = 23
⇒ ξ ≈4
3β =
4
3(u1 − u2)
+ ξ ∝ β: “efficient”+ test particle approximation: universal spectrum
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy spectrum
• energy after n acceleration cycles
En = E0(1 + ξ)n
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy spectrum
• energy after n acceleration cycles
En = E0(1 + ξ)n
• if escape probability per encounter is pesc, then probability tostay in acceleration region after n encounters is (1 − pesc)
n
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy spectrum
• energy after n acceleration cycles
En = E0(1 + ξ)n
• if escape probability per encounter is pesc, then probability tostay in acceleration region after n encounters is (1 − pesc)
n
• number of encounters needed to reach En is
n = ln
(En
E0
)
/ ln (1 + ξ)
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy spectrum
• energy after n acceleration cycles
En = E0(1 + ξ)n
• if escape probability per encounter is pesc, then probability tostay in acceleration region after n encounters is (1 − pesc)
n
• number of encounters needed to reach En is
n = ln
(En
E0
)
/ ln (1 + ξ)
• fraction of particles with energy > En is
f(> En) =∞∑
m=n
(1 − pesc)m =
(1 − pesc)n
pesc
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy spectrum
• number of encounters needed to reach E is
n = ln
(E
E0
)
/ ln (1 + ξ)
︸ ︷︷ ︸
• fraction with energy > E is
f(> E) =(1 − pesc)
n
pesc
∝1
pesc
(E
E0
)γ
where
γ = ln
(1
1 − pesc
)
/ ln(1 + ξ) ≈ pesc/ξ
shock: pesc ∝ u2 ⇒ γ ≈ pesc/ξ ≈ 3u1/u2−1
strong shock: R ≡ u1/u2 = 4 and dN/dE ∝ E−2
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Maximal energy of SNR: Lagage-Cesarsky limit
acceleration rate
βacc =dE
dt
∣∣∣∣acc
=3Ev2
sh
ζD(E), ζ ∼ 8 − 20
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Maximal energy of SNR: Lagage-Cesarsky limit
acceleration rate
βacc =dE
dt
∣∣∣∣acc
=3Ev2
sh
ζD(E), ζ ∼ 8 − 20
assume Bohm diffusion D(E) = cRL/3 ∝ E and B ∼ µG
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Maximal energy of SNR: Lagage-Cesarsky limit
acceleration rate
βacc =dE
dt
∣∣∣∣acc
=3Ev2
sh
ζD(E), ζ ∼ 8 − 20
assume Bohm diffusion D(E) = cRL/3 ∝ E and B ∼ µG
⇒ Emax ∼ 1013—1014 eV
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Maximal energy of SNR: [Bell, Luzcek ’02, Bell ’04 ]
(resonant) coupling CR ↔ Alfven waves
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Maximal energy of SNR: [Bell, Luzcek ’02, Bell ’04 ]
(resonant) coupling CR ↔ Alfven waves
non-linear non-resonant magnetic field amplification
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Maximal energy of SNR: [Bell, Luzcek ’02, Bell ’04 ]
(resonant) coupling CR ↔ Alfven waves
non-linear non-resonant magnetic field amplification
requires also D(E) ∼ E0.5 → E
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Maximal energy of SNR: [Bell, Luzcek ’02, Bell ’04 ]
(resonant) coupling CR ↔ Alfven waves
non-linear non-resonant magnetic field amplification
requires also D(E) ∼ E0.5 → E
observational evidence for B ∼ 100µG in young SNR rims
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Maximal energy of SNR: [Bell, Luzcek ’02, Bell ’04 ]
(resonant) coupling CR ↔ Alfven waves
non-linear non-resonant magnetic field amplification
requires also D(E) ∼ E0.5 → E
observational evidence for B ∼ 100µG in young SNR rims
⇒ Emax ∼ 1015—1016 eV
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
SNR RX J1713.7-3946
/%#;"
7!;"
changes on δt ∼ 1 yr imply B ∼ 1mG
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Knee:
106 107 108
102
103Fe
CHe
pp
Fe
CHe
KASCADE
AKENO
E, GeV
J(E
)E2.
5 , m-2s-1
sr-1G
eV1.
5
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Energy losses, the dip and the GZK cutoff
1e-11
1e-10
1e-09
1e-08
1e-07
18 18.5 19 19.5 20 20.5 21 21.5
(1/E
)*d
E/d
t [1
/yr]
log10(E/eV)
pion production
pair production
redshift
at E ∼ 4 × 1019 eV:N + γ3K → ∆ → N + πstarts and reduces freemean path to∼ 20 Mpc
pair production leedsto a dip at ∼ 1019 eV
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
The dip model
1017 1018 1019 1020 1021
10-2
10-1
100
ηtotal
2
1 η
ee
2
1
1: γg=2.7
2: γg=2.0
mod
ifica
tion
fact
or
E, eVNordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
The dip model
1017 1018 1019 1020 1021
10-2
10-1
100
ηtotal
HiRes I - HiRes II
ηee
γg=2.7
mod
ifica
tion
fact
or
E, eVNordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
The dip model
1017 1018 1019 1020 102110-2
10-1
100
ηtotal
ηee
FeAl
red shift
Hep
γg=2.7
m
odifi
catio
n fa
ctor
E, eVNordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
The dip model
1017 1018 1019 1020 1021
10-2
10-1
100
ηtotal
HiRes I - HiRes II
ηee
γg=2.7
mod
ifica
tion
fact
or
E, eV
good fit w. 1 parameter: evidence for protons
transition below E ∼ 1018 eV
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Deflection of protons in Galactic B-field:
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Unified AGN picture
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Correlations with AGNs: PAO analysis
27 CRs (⊙) and 472 AGN (∗):
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Correlations with AGNs: PAO analysis
adding more date:
Total number of events (excluding exploratory scan)10 20 30 40 50
data
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
= 0.21iso
p
Data
68% CL
95% CL
99.7% CL
Total number of events (excluding exploratory scan)10 20 30 40 50
data
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Chemical composition via Xmax:
/decade] 18 19
]2>
[g/c
mm
ax<X
650
700
750
800
850
proton
iron
QGSJET01QGSJETIISibyll2.1EPOSv1.99
Auger 2009
HiRes ApJ 2005
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Chemical composition via RMS(Xmax) from Auger:
E [eV]
1810 1910
E [eV]
1810 1910
]2)
[g/c
mm
axR
MS
(X
10
20
30
40
50
60
70 proton
iron
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Mixed composition:
Mean 744.8RMS 62.02
]2 [g/cmmaxX600 650 700 750 800 850 900 9500
0.02
0.04
0.06
0.08
0.1
0.12
Mean 744.8RMS 62.02
70% proton
30% iron
sum
σ2 =∑
i
fiσ2i +
∑
i<j
fifj(Xmax,i − Xmax,j)2
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Restricting QCD: Color Glass Condensates, . . .
550
600
650
700
750
800
850
108 109 1010 1011
Xm
ax [g
/cm
2 ]
energy [GeV]
Seneca 1.2
Sibyll (p,Fe)BBL r.c. (p)BBL f.c. (p)
Hires Stereo
[Drescher, Dumitru, Strikman ’04 ]
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Violation of Lorentz invariance (LI)
quantum gravity (“space-time foam”) or dim. reductiond = n > 4 → 4 could induce tiny departures from LI
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Violation of Lorentz invariance (LI)
quantum gravity (“space-time foam”) or dim. reductiond = n > 4 → 4 could induce tiny departures from LI
⇒ non-universal maximal velocities
⇒ changed dispersion relations may allow p → p + γ orγ → e+e−
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Violation of Lorentz invariance (LI)
quantum gravity (“space-time foam”) or dim. reductiond = n > 4 → 4 could induce tiny departures from LI
⇒ non-universal maximal velocities
⇒ changed dispersion relations may allow p → p + γ orγ → e+e−
example: modify
LQED = −1
4ηνρηµσF νµF ρσ
byηνρηµσ → ηνρηµσ + κνρµσ
observation of TeV photons and UHECRs gives|κνρµσ| < 10−18
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Violation of Lorentz invariance (LI)
quantum gravity (“space-time foam”) or dim. reductiond = n > 4 → 4 could induce tiny departures from LI
⇒ non-universal maximal velocities
⇒ changed dispersion relations may allow p → p + γ orγ → e+e−
generically: linear terms excluded, but allowed
0 = ω2 − k2 +
(ω2
k2
M2P
)
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
suppose,cγ − cπ0 = cγ − ce = 10−22
then π0 is stable above E ∼ 1019 eV and photon unstable!
similar in the GZK cutoff reaction p + γ3K → ∆(1232) thresholdcondition for head-on collision changed to
2ω +m2
p
2E≥ (c∆ − cp)E +
M2∆
2E
if c∆ − cp ≥ 2 × 10−25, reaction forbidden
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Summary
qualitative agreement of standard DSA in SNRs picture with data
⇒ requires non-linear field amplification
⇒ quantitative description from first principles in reach?
main experimental question: fixing discrepancies in exp. results forchemical composition
progress in multi-messenger astronomy requires:
go beyond IceCube
better astrophysical understanding of sources
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Summary
qualitative agreement of standard DSA in SNRs picture with data
⇒ requires non-linear field amplification
⇒ quantitative description from first principles in reach?
main experimental question: fixing discrepancies in exp. results forchemical composition
progress in multi-messenger astronomy requires:
go beyond IceCube
better astrophysical understanding of sources
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Summary
qualitative agreement of standard DSA in SNRs picture with data
⇒ requires non-linear field amplification
⇒ quantitative description from first principles in reach?
main experimental question: fixing discrepancies in exp. results forchemical composition
progress in multi-messenger astronomy requires:
go beyond IceCube
better astrophysical understanding of sources
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Summary
qualitative agreement of standard DSA in SNRs picture with data
⇒ requires non-linear field amplification
⇒ quantitative description from first principles in reach?
main experimental question: fixing discrepancies in exp. results forchemical composition
progress in multi-messenger astronomy requires:
go beyond IceCube
better astrophysical understanding of sources
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics
Summary
qualitative agreement of standard DSA in SNRs picture with data
⇒ requires non-linear field amplification
⇒ quantitative description from first principles in reach?
main experimental question: fixing discrepancies in exp. results forchemical composition
progress in multi-messenger astronomy requires:
go beyond IceCube
better astrophysical understanding of sources
Nordic Winterschool, Gausdal 2011 Michael Kachelrieß High Energy Astrophysics