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High Energy Astrophysics. § Radiative Processes. Kunihito IOKA (KEK) 井岡 邦仁. Radiative Processes. ISM Wind SN. Acceleration of Relativistic Jet G >>1. External Shock. Internal Shock. g -sphere t ~1. GRB Prompt AGN Blazar. Synchrotron Inverse Compton Bremss , e ± , … - PowerPoint PPT Presentation
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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