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Kunihito IOKA (Osaka Univ.)6. Central engine7. Links with other fields8. Luminosity-lag9. X-ray flash10. Summary
1. Observation2. Fireball3. Internal shock4. Afterglow5. Jet
1. ObservationGamma-Ray Burst
Brightest object 15210 −≈ s ergs
Vela satellites in 1967
Origin has been a puzzle
IsotropicAngular distribution
～1000 events/yr
Spatial distribution Inhomogeneous
( ) 3 2N P P−> ∝Homogeneous in Euclidean
max 0.330 0.010V V = ±
Duration
Long-softShort-hard
Long burstShort burst
SpectrumBand spectrum
Non-thermal
Afterglow Beppo-SAX in 1997
X-ray
Radio
Redshift Optical → Redshift
Summary of observation>msec
LuminosityRedshift
AfterglowGRBX-rayOpticalRadio
～1000 events/yrIsotropic, Inhomogeneous～200 keV10-3s～103s : short, long
Time
2. FireballCompactness problem
( )810 10ms cmR c T Tδ δ≈ ≈2 49
7 2810 ergE FD F D−≈ ≈e eγγ + −→2 22
133 2 7 210
10 erg cm 3Gpc 10msTe
FD F D TRR m c
δτ σ−
− −
! !
MeVEγ ≥
Optically thick Non-thermal⇔
1−ΓRelativistic motion
2R Γ!Eγ
N4 6.5Bβτ − + −∝ Γ Γ!
210Γ≥Γ×MeVMeV
FireballiRE
1 4 3 452 ,710 MeVi iT E R−!
3 3entropy const constT R⇒ =
( )2exp 20keV:thine B pn m c k T T± ∝ − ⇒ ≈
( ) 9 1 4 1 452 ,76 10 cmi p i iR T T R E R± = ≈ ×
4 3energy const const iT R R Rγ γ⇒ = ⇒ ! obs iT T Tγ! !
+Baryon3
bn R−∝ 14 1 2 1 252 21 10 cmthinR E η −×!
2E Mcη =
92 ,71 10 cm : Matter dominantmatter i iR R Rη η= = × 2E Mcγ!
Thermal
10 5 10
5
10 :Pure radiation 10 < <10 :Electron dominated1< <10 :Relativistic baryon <1: Newtonian
η ηη η
<
Ｃｅｎｔｒａｌ ｅｎｇｉｎｅ
Ｏｐｔｉｃａｌｌｙ ｔｈｉｃｋ ｒｅｇｉｏｎ
Ｉｎｔｅｒｎａｌ ｓｈｏｃｋｓ
Ｅｘｔｅｒｎａｌ ｓｈｏｃｋｓ
？
ＩＳＭ
1−Γ 1−Γ
−+→ eeγγ
Internal-External shock model
Kinetic energy
Shock dissipation⇓
Luminosity
time
3. Internal shock
rγ
Two shell collision
sγ mγ
rm sm mm
( )
( )
2 2
2
1 1
1
r r s s r s m m
r r s s
r s m m
m m m m E
m m
m m E
γ γ γ
γ γ
γ
• + = + +
• − + −
= + + −
( )efficiency : 1 r s m
r r s s
m mm m
γε
γ γ+
= −+
: 0.5 when 13.9r s r sm m ε γ γ= > >
Many shell
Kobayashi,Piran&Sari(97)
Time scale
2γ γ
c Tδ
2 1310 cmR c Tγ δ! ! 1−Γ
2R γ!
2
R Tc
δγ
!
γ γ2γ2γ
c Tδ
Pulse intervalTδ
Nakar&Piran(02)
Pulse width
4. Afterglow
rγ
External shock
mγ
rm sm mm
2m r s r rm mγ γ γ= ⇒ ≈34
3s pm R nmπ=
2 3 2 243r r p rE m c R nm cπγ γ= =
16 1 3 2 3 1 351 2 010 cmR E nγ − −!
Hydrodynamics3 2 24
3 pE R nm cπ γ!n2T R γ!
3 8Tγ −∝R
Relativistic shock
n2 ,n U
( )( )
2
2
4 3
1 p
n n
U nm c
γ
γ
= +
= −Jump condition
① Electron Fermi acceleration( ) ( ) 2.21 , (Fermi acc.)e e e eU U O Nε γ γ −= ∝!
( )1B BU U Oε = !
Electron synchrotron emission1 / 3ν∝
Fν
ν
( )
( )
22 2
22
43 8e T e
e ee
BF c
qBm c
νν γ σ γ γπ
ν γ γ γ
=
=
② Magnetic field
{ }
{ },max
, , ,
, , ,
e B
a m c
E n
Fν
ε ε
ν ν νc
Spectrum
52
3
10 erg0.1 50cm0.10.01
e
B
Enεε
−−!
!
!
!
Collapsar, Hypernova
ｒｅｖｅｒｓｅ ｓｈｏｃｋ ｆｏｒｗａｒｄ ｓｈｏｃｋ
Shock emission
Optical flash
5. JetJet & Relativistic beaming
1−Γ・ Relativistic beaming・ Jet
1−≈ Γ
Jet in afterglow11 −− ≤⇒+≈ ΓθΓθθ ii ：ｓｉｄｅｗａｙｓ ｅｘｐａｎｓｉｏｎ
Energy, Event rate, Model
iθ
3 2 2 243 pE R nm cπ γ θ!
2 2T R γ γ−! !
Break in afterglow PolarizationA few %
Total
Total energy
5110 ergE ≈
6. Central engine①Ｃｏｌｌａｐｓｅ ｏｆ ｍａｓｓｉｖｅ ｓｔａｒ
② Ｍｅｒｇｅｒｓ ｏｆ ｃｏｍｐａｃｔ ｏｂｊｅｃｔｓ・Ｂａｒｙｏｎ ｆｒｅｅ
・Ｌｏｃａｔｉｏｎ ｗｉｔｈｉｎ ｈｏｓｔ ｇａｌａｘｉｅｓ・ＧＲＢ-Ｓｕｐｅｒｎｏｖａ （ｅ.ｇ.，ＳＮ１９９８ｂｗ）？Ｈｉｇｈ ａｍｂｉｅｎｔ ｇａｓ ｄｅｎｓｉｔｙ
？？
Collapsar, Hypernova
？？
Host galaxy
SN1998bw-GRB980425( ) 46 65.5 0.7 10 erg/s : 10 dimLγ
−± ×! !
Lightcurve Fe line
7. Links with other fieldsCR, HEν, HEγ
44 3
19 21
10 erg/Mpc /yrUHECR (10 - 10 eV)
≈≈
Cosmology
8. Luminosity-lag ApJ,554,L163(01)
peakLＬｕｍｉｎｏｓｉｔｙ
γ:Ｔｉｍｅ
T∆X:
Ｔｉｍｅ
↓⇔↑ T∆ Lpeak ・Ｓｔａｎｄａｒｄ ｃａｎｄｌｅ ？・Ｂｒｉｇｈｔｅｒ ｔｈａｎ ＳＮｅ Ia・Ｌｅｓｓ ｅｘｔｉｎｃｔｉｏｎ
Viewing angle of a single jet？
？
？
⇒Ｌｕｍｉｎｏｓｉｔｙ-ｌａｇ ｒｅｌａｔｉｏｎ ？
Thin jet
( ) ( ) ( ) ( )
( )
�� �
0 0 0ν
vv
v
j r, t A f ν t t r r
cos θ cosθ cosθH θ θ θ H cossinθ sinθ
δ δ
φ
= − −
∆ −× ∆ − − −
Ｅｍｉｓｓｉｖｉｔｙθ∆
vθ
( )( )Bβ -α /sα s� �
�� �0 0
ν νf ν =ν ν
ＢＢ１＋
１＋
～Ｂａｎｄ ｓｐｅｃｔｒｕｍ
Ｓｐｅｃｔｒｕｍ ( )’’ｆ νν
’ν( ) Bαν+
∝2’
( ) Bβν+
∝2’
B B1, 1, 2.5, s 1γ θ α β∆ = = − = − =
( ) ( )( )( )
( )( )
( ) ( )
20 0
ν 22 2
00
∆ T2cA r γF T = f νγ 1 βcosθ TD γ 1 βcosθ T
cβwhere 1 βcosθ T = T Tr
φ − −
− −
v 0θ ! 1v 2θ γ −!
1vθ γ −!
Lag:
Luminosity-Lag Relation
Pulse profile
Luminosity-width
ＦＲＥＤ（Ｆａｓｔ ＲｉｓｅＥｘｐｏｎｅｎｔｉａｌ Ｄｅｃａｙ）
8232
.−≅⇔−≈+−=∝
obs
BκFWHM
peakν
κ: nobservatioακ where WFν
Viewing angle①Ｐｅａｋ ｌｕｍｉｎｏｓｉｔｙ-ｓｐｅｃｔｒａｌ ｌａｇ ｒｅｌａｔｉｏｎ② Ｐｅａｋ ｌｕｍｉｎｏｓｉｔｙ-ｖａｒｉａｂｉｌｉｔｙ ｒｅｌａｔｉｏｎ③ Ｌｕｍｉｎｏｓｉｔｙ-ｗｉｄｔｈ ｒｅｌａｔｉｏｎ
GRB980425Ａ ｔｙｐｉｃａｌ ＧＲＢ⇒Ａｓｓｏｃｉａｔｉｏｎ ｏｆ ＧＲＢｓ ｗｉｔｈ ＳＮｅ
9. X-ray flash
Off-axis GRB
Flux/Fluence RatioApJ,571,L31(02)
3 1 3 2 2 110 yr 5 3 10 yr− − −× × ≈Volume Viewing angle
10. SummaryGRB : Internal shockAfterglow : External shockJetViewing angle
Various relations, X-ray flashCentral engine ???
Collapsar? Merger?CR, HEν, HEγ, GW, Cosmology
