High Energy Astrophysics

Kunihito IOKA (KEK)井岡　邦仁

§ Radiative Processes

2

Radiative ProcessesInternalShock

ExternalShock

Acceleration ofRelativistic Jet

G>>1

ISMWindSN

Synchrotron Inverse Compton Bremss, e±, … Hadron

GRB PromptAGN Blazar

g-spheret~1

GRB AfterglowAGN HotspotMicroquasarPWN, SNR

3

Synchrotron Sources

GRB afterglow

Galama 98; Panaitescu & Kumar 00; Yost+ 03; Price+ 03; De Pasquale+ 10; many others

4

Synchrotron Sources

AGN Blazar & Hotspot

Fossati+ 97, 98; Kubo+ 98; Donato+ 01; Kino & Takahara 04, Stawarz+ 07; many others

5

Synchrotron Sources

Pulsar Wind Nebula

Aharonian+ 98; Meyer+ 10; Tanaka & Takahara10, 11; many others

6

Synchrotron Sources

Supernova Remnant

Giordano+ 11, Ohira+ 11; Abdo+ 10; many others

7

Synchrotron Characteristic Frequency

€

meγ edvdt

= qcv×B

meγ ev

R v~ q

cvB

Eq. of motion

Period

€

T ~ Rv

~ γ emecqB

ωB ~ qBγ emec

€

ν obs ~ ωBγ e3 ~ qB

mecγ e

2 ~ 2 ×107Hz BGγ e2

€

2γ e

€

~ 2Rγ e

× 12γ e

2

€

~ 2Rγ e

unobservable

8

Power & Spectrum

€

P erg s−1[ ] = 43

σ Tc B2

8πγ e

2β e2

Spectrum

€

Pν = dPdν

€

ν

€

ν1 3

€

exp −ν( )

€

ν obs

BsT

Energy densityVolume/Time

Power

ThompsonCross Section

9

Electron Distribution

€

Ne γ e( )Number

per unit ge

€

ge− p

€

ge

€

gm

€

Ne = Ne γ e( )dγ e∫∝ γ m

− p +1 p >1( )

Ee = mec2 γ eNe γ e( )dγ e∫

∝ γ m− p +2 p > 2( )

€

ν1 3

€

Pν

€

∝ Pν∝ Ne × Power

ν∝ γ e

− p +1 × γ e2

γ e2

∝ γ e− p +1 ∝ν

−p−12

€

νm

€

ν

(p=2: Equal E per log bin)

10

Lorentz Boost

€

νm = qBmec

γ m2 • Γ

Fν ,max =Ne ⋅

43

σ Tc B2

8πγ m

2 • Γ2

4πdL2 ⋅ qB

mecγ m

2 • Γ= Neσ T mec

2B24π 2qdL

2 • Γ

€

erg s−1 cm−1 Hz−1[ ]€

Hz[ ]

€

ν1 3

€

Fν

€

νm

€

ν€

ν−

p−12

Blueshift

Blueshift

Lab time tCom. t’=t/GObs. tobs=t/G2E/tobs=GE’/(t’/G)

Next we needG, Ne, B, gm

∝ gm0

11

GRB Afterglow G (Bulk Lorentz factor)– Adiabatic, n=const, spherical:

Ne (Electron number)–

B (Magnetic field)– Shock jump condition– A fraction of energy ⇒ B

€

G∝T− 3

8 E18n

−18

€

Ne = 43

πR3n ∝ Γ 2T( )3n

€

n2 = 4Γne2 = 4Γ 2nmpc

2

⎧ ⎨ ⎩

€

B2

8π= εB × e2

⇒ B = Γ 32πεB nmpc2 Given: T, E, n, dL, ee, eB

12

GRB Afterglow gm (Minimum Lorentz factor)– Shock jump condition– A fraction of energy ⇒ Electron

€

mec2 γ ene γ e( )dγ e

γ m

∫ = εe × e2

ne γ e( )dγ eγ m

∫ = n2

⎧

⎨ ⎪

⎩ ⎪

⇒ mec2 p −1

p − 2γ m = εeΓmpc

2

⇒ γ m = εep − 2p −1

mp

me

Γ

€

n2 = 4Γne2 = 4Γ 2nmpc

2

⎧ ⎨ ⎩

€

νm ∝ Bγ m2 Γ ∝εe

2εB

12 E

12T

−32

Fν ,max ∝NeBΓ

dL2 ∝εB

12 En

12dL

−2

Given: T, E, n, dL, ee, eB

13

GRB Afterglow Evolution

€

νm = 6 ×1014 Hz εB1 2εe

2E521 2Td

−3 2

Fν ,max =1×105μJy εB1 2E52n

1 2dL ,28−2

€

Jy =10−23erg s−1 cm−2 Hz−1

€

Fν

€

νm

€

νm

€

ν

€

Fν ν > ν m( ) = Fν ,maxν

ν m

⎛ ⎝ ⎜

⎞ ⎠ ⎟−

p−12

∝T−

3 p−1( )4 ~ T−1 p = 2.2( )

~Observations

14

Jet Break Adiabatic, n=const, jet

€

⇒νm ∝ Bγ m

2 Γ ∝T−2

Fν ,max ∝NeBΓ

dL2 ∝T−1

⎧ ⎨ ⎪

⎩ ⎪€

R ~ const, Γ ∝T−1 2

€

Fν ν > ν m( ) = Fν ,maxν

ν m

⎛ ⎝ ⎜

⎞ ⎠ ⎟− p−1

2

∝T−1 ⋅T− p +1 ~ T− p8181

52,83 057.0~ nEt isoday

Harrison+ 99

Break time ⇒ Opening angle

AchromaticBreak

15

Cooling

€

Ne γ e( )

€

Fν

€

ν

€

ge

€

gm

€

gc

€

νm

€

ν c

€

ge− p

€

ge− p−1

€

ν−

p−12

€

ν13

€

tcool = γ emec2

P= γ emec

2

43

σ Tc B2

8πγ e

2∝ 1

γ e

Ne ∝Q • tcool ∝ γ e− p 1

γ e

∝ γ e− p−1

Electrons lose energy by synchrotron

Injection rate of eSecond derivation

€

Total energyFrequency

∝ γ e− p +2

γ e2 ∝ γ e

− p ∝ν− p

2

€

ν−

p2

16

Fast Cooling

€

Ne γ e( )

€

Fν

€

ν

€

ge

€

gm

€

gc

€

νm

€

ν c

€

ge− p−1

€

ge−2

€

ν13

€

tcool = γ emec2

P= γ emec

2

43

σ Tc B2

8πγ e

2∝ 1

γ e

Ne γ e( )dγ eγ e

∫tcool

~ const ⇒ Ne ∝ γ e−2

Electrons lose energy by synchrotron

Second derivation

€

Total energyFrequency

∝ γ e

γ e2 ∝ν

− 12

€

ν−

p2

(stationary)

€

ν−

12

⇔ Slow coolingin previous case

17

Self-absorption

€

Fν

€

ν

€

ge

€

νm

€

ν 2

€

Fν

€

ν−

p−12

€

νm

€

ν c

€

ν−

p2

€

ν13

€

ν 2

€

ν a

Black body

€

Fν = 2ν 2

c 2 kT ⋅SSurface area

€

Case 1: kT ~ γ mmec2

€

ν−

p−12

€

ν c

€

ν−

p2

€

ν52

€

ν a

€

Case 2 : kT ∝ γ e ∝ν 1 2

Fν ∝ν 2kT ∝ν 5 2

18

Cooling & Self-absorption ν

€

′ t = γ cmec2

43

σ Tc B2

8πγ c

2

ν c = qBmec

γ c2 ⋅Γ

= qmecσ T

2B3 ′ t 2 ⋅Γ

= qmecσ T

2B3T 2Γ 2 ⋅Γ

∝ 1B3T 2Γ

€

2ν a2

c 2 kT ⋅S ~ Fν ,maxν a

ν m

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1 3 ~GcT

€

gmmec2Γ

€

GcT( )2

4πd2

€

ν a5 3 ⋅γ mΓ 3T 2d−2 ∝NeBΓd−2 ⋅B−1 3γ m

−2 3Γ−1 3

⇒ ν a5 3 ∝ γ m

−5 3Γ−7 3T−2B2 3

⇒ ν a ∝ γ m−1Γ−7 5T−6 5B2 5

(Fν,max, νa, νm, νc) ⇒ (E, n, ee, eB)

€

νm ∝ Bγ m2 Γ

Fν ,max ∝NeBΓ

dL2

19

Synchrotron Shock ModelSari, Piran & Narayan 98

(Fν,max, νa, νm, νc) ⇒ (E, n, ee, eB)

20Zhang &

Meszaros 03

21

Min. Energy Requirement

€

Lν ∝Ne ⋅σ Tc B2

8πγ e

2

qBmec

γ e2

⋅Γ

ν = qBmec

γ e2Γ

⎧

⎨

⎪ ⎪ ⎪

⎩

⎪ ⎪ ⎪

€

E = Γ Neγ emec2 + B2

8πV

⎛ ⎝ ⎜

⎞ ⎠ ⎟

= ...( )Lν

Bν 1 2

B1 2Γ1 2 + ...( )ΓVB2

Synchrotron observables

Total Energy

€

Emin ≈ 8 ×1014 erg Lν4 7ν 2 7V 3 7Γ1 7

Bmin ≈1×108G Lν2 7ν 1 7V −2 7Γ−2 7€

B

€

B− 3

2€

B2

€

Emin

€

Bmin

useful for limited observations

22

Reverse Shock Emission

p, e

G

Radius

Radius

Ejecta ISMCo

ntac

t Disc

ontin

uity

Reve

rse

Shoc

k

Forw

ard

Shoc

k

4 3 2 1

€

νm,r

ν m, f

=

qBr

mecγ m,r

2 Γ3

qB f

mecγ m, f

2 Γ2

~γ m,r

2

γ m, f2 ~ Γ34

2

Γ22

€

n2 ≈ 4Γ2n1, e2 ≈ Γ2n2mpc2

n3 = 4Γ34 + 3( )n4, e3 = Γ34 −1( )n3mpc2

€

e2 = e3, Γ2 = Γ3

G2>>1, if G34~1 ⇒ RS emission is soft(Density is high at RS ⇒ Low temperature)while e2=e3 ⇒ Total energy is similar

23

Sari & Piran 99

Zhang+ 03

GRB990123

Fox+ 03GRB021211

９等Optical Flash

Provide information

on ejecta⇒ G0, B0

But somehowrare

24

Electron DistributionBlazar/Hotspot

p~1.4-1.8 (<2)⇒ Need gmax or gbr

€

Ne γ e( )

€

ge− p

€

ge

€

gmax

~104-105

to determine Etot

€

gbr

~103-104

Pulsar Wind Nebulap~1-1.6 (<2)⇒ Need gmax or gbr

€

Ne γ e( )

€

ge− p

€

ge

€

gmax

~109€

gbr

~106

p~2-3 p~2-3

to determine Etot

⇒ Pulsar Wind G~106

p~1-2 p~1-2

25

Synchrotron Model for GRB Prompt?

€

gm ~ εe

mp

me

4πR2c B2

8πΓ 2 = εB L = εB

Lγ

εe

Internal Shock⇒ 1. Electron 2. Magnetic Field⇒ Synchrotron

€

νm = qBmec

γ m2 Γ ≈1 MeV εe

3 2εB1 2 Lγ ,52

1 2

Γ2.52 Δt−2

€

R ~ 2Γ2cΔt( )

c/s w/ observed Yonetoku relation?But DG usually destroy correlations

26

Amati/Yonetoku Relation

Amati 02Yonetoku+KI 03

Ep~600keV L531/2

Large DG/Gusually destroys

a correlation~Typical g Energy

27

Synchrotron Death line

ForbiddenSuperposition

of syn-spectrumFν

ν1/3

ν

dynnsynchrotro

eecool t

Pcmt

2g

ν-1/2

w/ cooling (fast)

28

Inverse Compton

Electron

Photon

νge

~ge2ν Comoving Frame

~geν~geνThompson scattering

change E littleObviously νIC<gemec2

(Energy conservation)

€

ν IC ~ γ e2ν

€

νB ~ qBmec

γ e2

Blumenthal & Gold 70

29

Cross Section

ν

€

s ≈sT s ≡ ν

mec2 <<1

⎛ ⎝ ⎜

⎞ ⎠ ⎟

σ T

ss ≡ ν

mec2 >>1

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪s [cm2]

In e-moving frame,

€

s = γ eνmec

2

Klein-Nishina Formula/Suppression

€

sT = 8π3

e2

mec2

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

≈ 6.7 ×10−25cm2

30

IC Power

€

P erg s−1[ ] = 43

σ TcUγ γ e2β e

2

BsT

Energy densityVolume/Time

Power

ThompsonCross Section€

PIC

PB

=Uγ

UB

Ratio to synchrotron

e

Syncrotron IC

e

€

⊗

31

IC+Syn Cooling

€

Ne γ e( )

€

Fν

€

ν

€

ge

€

gm

€

gc

€

νm

€

ν c

€

ge− p

€

ge− p−1

€

ν−

p−12

€

ν13

€

tcool = γ emec2

43

σ Tc Uγ + B2

8π

⎛ ⎝ ⎜

⎞ ⎠ ⎟γ e

2

∝ 1γ e

Ne ∝Q • tcool ∝ γ e− p 1

γ e

∝ γ e− p−1

Electrons lose energy by IC & Synchrotron

Injection rate of eSecond derivation

€

Total energyFrequency

∝ γ e− p +2

γ e2 ∝ γ e

− p ∝ν− p

2

€

ν−

p2

32

SSC (SynchrotronSelf-Compton)

Syn IC Syn-emitting electronsupscatter syn-photonsν

νFν

€

x ≡ LIC

Lsyn

=Uγ

UB

=Usyn

UB

=η γUe 1+ x( )

UB

=η γεe

εB 1+ x( )

x =−1+ 1+ 4η γεe εB

2=

η γεe

εB

η γεe

εB

<<1 ⎛ ⎝ ⎜

⎞ ⎠ ⎟

η γεe

εB

⎛ ⎝ ⎜

⎞ ⎠ ⎟

1 2 η γεe

εB

>>1 ⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎧

⎨ ⎪ ⎪

⎩ ⎪ ⎪

IC-to-Syn ratiofraction of Ue that is radiated

Ratio x ⇒ Unique UB & Ue

33

SSC Spectrum

€

Ne γ e( )dγ e

€

Fν

€

ge

€

gm

€

gc

€

νm

€

ν c

€

ge− p +1

€

ge− p

€

ν−p +1

2

€

ν13

€

ν−

p2

€

ν

€

gm2ν m€

ν syn ∝ γ e2B, ν IC ~ γ e

2ν

€

gc2ν c

€

gm2ν c

γ c2ν m

Copy ×gm2

Copy ×gc2

Coincide€

FνIC ∝ σFν

synN γ e( )∫ dγ e

34

SSC Maximum Frequency

€

Ne γ e( )dγ e

€

Fν

€

ge

€

gm

€

gc

€

νm

€

ν c

€

ge− p +1

€

ge− p

€

ν−p +1

2

€

ν13

€

ν−

p2

€

ν

€

gm2ν m

€

gc2ν c

€

gm2ν c

γ c2ν m

Copy ×gm2

Copy ×gc2

€

ν SSC ,max ≈ Γγ maxmec2

€

gmax

35

Klein-Nishina Suppression

€

Ne γ e( )dγ e

€

Fν

€

ge

€

gm

€

gc

€

νm

€

ν c

€

ge− p +1

€

ge− p

€

ν−p +1

2

€

ν13

€

ν−

p2

€

ν

Copy ×gm2

Copy ×gc2

€

gmax

E.g., if

€

gmν m > Γmec2

€

s ~ σ T

ss ≡ γ eν

Γmec2 >>1

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⇒ Softer by ν-1

36

External Compton

Sikora+ 94

€

′ u γ = Γ 2uγ

′ ν = Γν

Assume isotropic diffuse radiationIn jet-comoving,

⇒ Enhance IC Bulk Compton by cold electron

€

ν bulk ≈ Γ 2ν

37

Nonthermal from Thermal Electrons w/ temperature kT (>mec2) Photon energy amplification per scattering

After k scattering Probability of k scatterings is ~tk (<1) Emergent spectrum is

Unsaturated Compton; Also nonrelativisitc case

€

A ≡ ε1

ε0

~ 43

γ e2

€

ek ~ ε0Ak

€

Fν εk( ) ~ Fν ε0( )τ k ~ Fν ε0( )εk

ε0

⎛ ⎝ ⎜

⎞ ⎠ ⎟−α

, α ≡ −lnτln A

~kT

38

ThermalizationConsider photons w/ energy E (<<mec2) in electron bath w/ temperature T (<<mec2)How long does it take for thermalization E→kT?

Energy shift per scattering

⇒ Need many scatteringsEven if t>1, non-thermal spec. survives

€

DEE

~ 4kT − Emec

2 <<1E E+DE

kT

39

e± Signatures

by finite-/multi-zone &time-dependence effects

€

˜ ε cut

Γεcut

Γ~ mec

2( )2

Target g energy

€

tgg ≈sT ′ Δ nγ ε > ˜ ε ( )

Gmec2

Optical depth

Not exp. but power-law

Lithwick & Sari 01Murase & KI 08Aoi+ 10

⇒ Information of G

40

CTA ~20GeV-100TeV x10 Sensitivity D~1-2 min FOV~5-10 deg ~20 s slew (LST) ~2015 (?) ~150€

Large Effective Area⇒ 100-10000 of GeV-TeV g

41

Hadronic Emission: pp

€

pp → p,n + π ±,π 0

π 0 → γ + γ

π + → μ + + ν μ

→ e+ + ν e + ν μ + ν μ

π − → μ− + ν μ→ e− + ν e + ν μ + ν μ

€

N p ε p( )∝ ε p−s

€

ν, ε p

€

~ mπ 2~ 67.5 MeV€

× ~ τ pp

∝σ pp ~ const

€

Fν

High energy p collide with ambient p

€

tπ 0 = 8.4 ×10−17s( )

€

tπ ± = 2.6 ×10−8s( )

€

E th = 2mπ c 2 1+ mπ 4mp( ) ≈ 280MeV

42

pp Cross-Section & Multiplicity

€

K pp ~ 0.5

σ pp ~ 3×10−26cm2

Mπ ~ −0.308 + 0.276ln s

PDG

0912.0023

43

Hadronic or Leptonic?

Funk 11Abdo+ 11

44Funk 11Funk 11

45Funk 11Funk 11

46

Hadronic Emission: pg

€

egtargetε p ≈ 0.2Γ2GeV2

εγ ≈ 0.1ε p

εν ≈ 0.05ε p

€

pγ → Δ → nπ +, pπ 0

π 0 → γγ

π + → μ + + ν μ → e+ + ν e + ν μ + ν μ

Bhattacharjee & Sigl 00

d-function approximation

47

Other Processes Photopair process Adiabatic loss Coulomb collision Bremsstrahlung Nuclear g-ray line Photonuclear reactions EM Cascade Proton, muon, … synchrotron High B QED processes, …

48

§ Radiation Processes Synchrotron– νm, νc (fast/slow), νa

– (Fν,max, νa, νm, νc) ⇒ (E, n, ee, eB) Inverse Compton– νIC~g2ν

– PIC/Psyn=Ug/UB (SSC), EC e± signatures Hadronic: pp, pg Problem: Can index Fν

syn~n1/3 change?

Jitter Radiation

50

Backup

51

Mrk 421