Ryo Yamazaki(Hiroshima University)

Contents
1. GRB 080916C in the Fermi era
2. Afterglows before Swift Era
3. Afterglows in the Swift Era
4. Possible theoretical interpretation

Fermi LAT detection of GRB 080916C
First “GeV” γ detection ofa GRB with known redshift.
* High-z, bright event:z = 4.35±0.15
Eiso (10keV-10GeV)= 8.8x1055erg~ 5 Msunc2=> Jet collimation* GeV photons avoiding
pair-creation annihilation=> Relativistic motion:
Γ > 890±20 (bin “b”)
Fermi LAT collaboration (2009)Effect of high bulk Γ
青：ジェットを正面からみたイベント (detected)
緑：ジェットをoff-beamでみたイベント (detected)
赤：non-detection

Γ = 100

Γ = 300

THVOA 1Donaghy (2006)

THVOA2

Contents
1. GRB 080916C in the Fermi era
2. Afterglows before Swift Era
3. Afterglows in the Swift Era
4. Possible theoretical interpretation

Internal-external shock scenario
External shock
Internal shock
ISMExternal shock
γ線放射後のshellの進化幾つもあったShell は一つに合体し、星間ガス中を進む⇒ external shock⇒ 星間ガスによって減速:γ ∝ T-3/8 , (T: 観測者時間)
シンクロトロン放射の特徴的振動数：hνsyn ∝ γ４ ∝ T-3/2⇒ 時間がたつにつれて、X線→ 光学→電波という順番で afterglow(残光) が生じる。
加速された電子のスペクトルをとおいてスペクトル＆時間変化を理論的に計算。
⇒ 観測結果と見事に合う。

Spectrum of synchrotron radiation

Sari et al.(98)Galama et al. (98)

理論に出てくるパラメータ： E, n, εe , εB
観測されるスペクトルのパラメータ：νc , νm , νa , Fν, max⇒ 理論と観測の比較により、

E 〜 1051-54erg, n 〜 0.1-30 cm-3,εe〜 0.1, εB〜 0.01

Relations among spectral/temporal indicesFν ∝ T α ν β( α : spectral index, β : temporal decay index)

加速された電子のスペクトルをとすると、ISM model, 典型的なパラメータに対して、可視光： αopt = − (3p−3) /4, β opt = − (p−1)/2X線 ： αx = − (3p−2) /4,β x = − p/2=> p を消去して、“α−β relation” : αx = (3βx +1)/2=> 観測と比較。
他の例： αopt = 3βopt /2,αopt − αx = 1/4

Zhang & Meszaros (03)Fν ∝ T α ν βLight curve Fitting in the pre-Swift era

Panaitescu & Kumar (01)Afterglow Light curves
For uniform ISM
Fν

Fν

FS

RS

FS
T-2

T-1
T-1/2

T-1
T-2

T-2
X-ray
102 103

Optical
104
[sec]

105

106

102 103104[sec]

105106Theory of Jetted Afterglow
Light curve breaks at γ −1 ∼ Δθ due to shock
deceleration caused by sideway expansion.
Δθ ∝ Tjet3/8 n1/8 E-1/8

GRB 990510

2 Δθ
Break timeγ 〜 102γ 〜 10Harrison et al. (1999)

Epeak [keV] : spectral peak energy

Ghirlanda ( Epeak – Egamma ) relation

Epeak ∝ Eiso0.56 0.02
Egamma = Eiso(Δθ)2/2
Epeak ∝ Egamma0.69 0.04
Ghirlanda et al. 05

Contents
1. GRB 080916C in the Fermi era
2. Afterglows before Swift Era
3. Afterglows in the Swift Era
4. Possible theoretical interpretation

Swift 時代の残光観測の結果
Pre-swift era に確立したと思われた理論の予言通りにはならなかった。
Swift 衛星 (2004.11~)

Pre-Swift (prediction)(T>~0.1-1day)T-1 decaying X-ray afterglow******
Bright optical flashes?
(coming from reverse shock)

Swift era
(T>~100sec)
Steep/shallow decaying X-rays
X-ray flares
Many optically dark events(no evidence for the reverse shock?)******

Prompt optical/IR emissions

Achromatic jet breaks(Ghirlanda relation)

No jet breaks for a fraction of events(Ghirlanda outliers)
Achromatic/Chromatic jet breaks

X-ray afterglow in the Pre-Swift era

log [Rest-frame Time (s)]X-ray afterglow in the Swift era

Chincarini et al. (2005)
log [Rest-frame Time (s)]Optical Afterglow in the pre-Swift era

Nardini et al. 2006

Optical Afterglow in the Swift era
Light curves with measured redshifts

arXiv:0803.1872

X-ray/Optical 同時観測の時代

“Canonical” behavior of X-ray Afterglow

X-ray flux

Expectation: Simple T-1 decay

ExpectedGRBT-1
Ever observedTime

unlike optical afterglow(absorption, reverse shock,density fluctuation, SN,…)X-ray flux

“Canonical” behavior of X-ray Afterglow

Expected

Nousek et al. ‘05

GRBT-1
Ever observed

TimeChincarini et al. ‘05

“Canonical” behavior of X-ray Afterglow

X-ray flux

T-5〜-2
Steep decay
X-ray flare
Nousek et al. ‘05

T-0.5

GRBShallow decay
T-1
T=102-3 s
T=103-4 s

Time

Chincarini et al. ‘05

Prompt emission tail: initial steep decay

X-ray flux

T-5〜-2
Steep decay
X-ray flare
T-0.5
Shallow decay

GRBT-1
T=102-3 s
T=103-4 s

TimeShallow decay : most mysterious part…

X-ray flux

T-5〜-2
Steep decay
X-ray flare
T-0.5
Shallow decay

GRB

T-1
T=102-3 s
T=103-4 s

Time

Point
あるはずのものがない。
=> 理論に「引き算」を要請。

・Delayed energy injection
・Time-dependent
microphysics
・others…

Late “Normal” decay phase

X-ray flux

T-5〜-2
Steep decay
X-ray flare

Pre-Swift era の残光理論の予言 α−β relation :αx = (3βx +1)/2と無矛盾。

T-0.5
Shallow decay

GRB

T-1
Normal decay
T=102-3 s
T=103-4 sTimeUrata, RY et al. 2007

XRR

XRR

XRR

Normal decay phase の αx − βx relation はOKだが αopt − αx relation
は合わない。また、Outliersはhard GRBに多いか？

-1/4 < αopt − αx <5/4
for 0<s<3.
(1+z)Ep < 100 keV(1+z)Ep =100-300keV(1+z)Ep > 300keV

No Jet Break in X-rays at expected time
Swift時代以前に確立していると思われていた(1) Jet break の理論 (2) Ghirlanda 関係 (Epeak‐Eγ 関係)
から予想される時刻。

050401050416a050525aSato, RY+ ‘07

Contents
1. GRB 080916C in the Fermi era
2. Afterglows before Swift Era
3. Afterglows in the Swift Era
4. Possible theoretical interpretation

Ryo Yamazaki(Hiroshima University)
Ref. Yamazaki (2009), ApJL, 690, L118

Shallow decay : most mysterious part…

X-ray flux

T-5〜-2
Steep decay
X-ray flare
T-0.5
Shallow decay

GRB

T-1
T=102-3 s
T=103-4 s

Time

Point
あるはずのものがない。
=> 理論に「引き算」を要請。

・Delayed energy injection
・Time-dependent
microphysics
・others…

(X-ray flux) ~ εe EK T-1
EK [erg]
1051 1052

X-ray flux1050

εe : fixed

obs. : T-0.5

T-1

Observer time : T(X-ray flux) ~ εe EK T-1
εeΕK : fixed0.1

X-ray flux0.001 0.01

obs. : T-0.5

T-1

Observer time : T

Fitting formula of X-ray afterglow
GRB 061121

f ( T ) = A0 ( T+T0 )−α0+ A1 T−α1
右辺第2項：
steep decay phase
右辺第1項：
plateau + normal phasef t −α0t = T + T0
f (T+T0) −α0

X-ray flux (arbitrary unit)

Simple formula:(For 061121, T0 ∼ 4000 sec.)

observer time: T[sec]Willingale et al. 2007という関数形でほぼすべてのX線残光をフィットできることを示した。

Fitting formulae
Willingale + 07:

with ta = 0.01 sec
Ta = 3x104 sec
αa = 1.0
This work:with T0 = 0.55 Ta
αa = 1.1 αa
A0 = 1.4 Fa
observer time : T[sec]t = T + T0?

L(T0) – T0 relation

L (T )(T+T0) −α0L (T0 )T0 −α0α0 ~ 1.3-1.4 でOK?
LX,endSato+(08)Tbrk

L T0 -1.3-1.4

Dainotti+(08)Implication: two-component modelJet 1:
gamma-ray dim,shallow+normal X-ray AG

観測者

Jet 2 (launched 103-4sec after jet 1):
prompt GRB, steep-decay X-ray AG,
late optical AG (~103-4sec).

X-ray afterglows XRFs and C-GRBs
X-ray flashes

Classical GRBs

Sakamoto, RY+ (08)Afterglows of known-z events(1+z)Ep < 100 keV(1+z)Ep =100-300keV(1+z)Ep > 300keV

Lx

T-0.5
C-GRB

XRF

T-1.5

T-1

T
Sakamoto, RY+ (08)

Possible trend between T0 and Eiso
Nava+ (08) : for 23 GRBs with measured redshifts

Summary
Ref. Yamazaki (2009), ApJL, 690, L118
X-ray AG light curves are well fitted by a simple functional form:f ( T ) = A0 ( T+T0 )−α0 + A1 T−α1 .
Implication: two-component outflow model with predictions:(optical jet break time) < (X-ray jet break time)
T0 : large => distinct plateau phase, bright prompt (long GRB)
: small => no plateau, dim prompt (X-ray flash)No reverse shock associated with prompt GRB jet?
Instead, precursor X-ray/optical emission?
(MAXI, WIDGET, IceCube, Ashra,…)