michael kachelrieß ntnu, trondheimweb.phys.ntnu.no/~mika/gausdal1.pdf · 2.nd order fermi...

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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


1910: Father Wulf measures ionizing radiation in Paris

80m: flux/2

300m: flux/2


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.”


What do we know 98 years later?

sola

rm

odula

tion

→

LHC ⇑



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



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?


Observing gamma-rays or cosmic rays: GeV-TeV


Observing gamma-rays or cosmic rays: around TeV


Pierre Auger Observatory:


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


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



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



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



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



VHE photons: successful, but restricted to few Mpchadronic photons vs. synchtrotron/Compton photons



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






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?



10

12

14

16

18

20

22


log1

0(E

/eV

)

proton horizon


IR

Virgo ⇓



10

12

14

16

18

20

22


log1

0(E

/eV

)

proton horizon


IR

Virgo ⇓

if UHECRs are protons:

deflections may be small

use larger statistics of UHECRs

well-suited horizon scale


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

)


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


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





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


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


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


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:


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


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”


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


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


Energy spectrum

• energy after n acceleration cycles

En = E0(1 + ξ)n


Energy spectrum


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


Energy spectrum


En = E0(1 + ξ)n


n

• number of encounters needed to reach En is

n = ln

(En

E0

)

/ ln (1 + ξ)


Energy spectrum


En = E0(1 + ξ)n


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


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


Maximal energy of SNR: Lagage-Cesarsky limit

acceleration rate

βacc =dE

dt

∣∣∣∣acc

=3Ev2

sh

ζD(E), ζ ∼ 8 − 20



acceleration rate

βacc =dE

dt

∣∣∣∣acc

=3Ev2

sh

ζD(E), ζ ∼ 8 − 20

assume Bohm diffusion D(E) = cRL/3 ∝ E and B ∼ µG



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


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






observational evidence for B ∼ 100µG in young SNR rims

⇒ Emax ∼ 1015—1016 eV


SNR RX J1713.7-3946

/%#;"

7!;"

changes on δt ∼ 1 yr imply B ∼ 1mG


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


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


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


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


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


Deflection of protons in Galactic B-field:


Unified AGN picture


Correlations with AGNs: PAO analysis

27 CRs (⊙) and 472 AGN (∗):


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


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


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


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


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 ]


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






generically: linear terms excluded, but allowed

0 = ω2 − k2 +

(ω2

k2

M2P

)


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


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


michael kachelrieß ntnu, trondheimweb.phys.ntnu.no/~mika/gausdal1.pdf · 2.nd order fermi...

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