afterglow physics - 京都大学 · 1. dynamics of shocked gas (n e, ... jet dynamics - (r) ......
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Relativistic blast-wave model for GRB afterglows
Rel. outflow 0~100-500
Interaction with CBM
Reverse shock into ejecta(Sari&Piran 99, Meszaros&Rees 99, Kobayashi 00)
Forward shock into ambient medium(Rhoads&Paczynski 93, Meszaros & Rees 97)
RS FS
R-1/2, wind CBM nR−2
R-3/2, homogeneous CBM+ F
F
t−(;s,e,...)
Afterglow radiation mechanism: synchrotron (inverse-Compton much less)
Even if EB ~ E initially, B is too weak at 1017 cm
Origin of magnetic field and relativistic electrons: 1. magnetic dissipation in Poynting outflow (Rees & Meszaros 97, Lyutikov & Blandford 2000) 2. dissipation of ejecta energy by interaction with CBM (Rees & Meszaros 1994, 1997) + plasma instability (e.g. Weibel – Medvedev 2001) or Fermi acceleration (electrons)
Afterglow light-curve depends on 1. dynamics of shocked gas (N
e,
e for FS; B, Lorentz boost)
2. distribution with energy of radiating electrons (sets synchrotron spectrum) & 3. distribution of incoming ejecta (sets N
e,
e for RS)
{ {Power-law spectrumPower-law light-curve{
Multi-wavelength afterglow observations
RADIO
OPTICAL
X-RAY
ls -
ls -l
ATCA VLA OVRO
MDM VLT HST
BSAX CXO SWIFT
Parameters of forward-shock
emission
up to 4 constraints (a,
p,
c,F
p)
4 parameters blast-wave kinetic energy E~1053 erg/sr medium density n~0.1-1 cm-3 micro parameters
B~10-3
&
e~10-2
970805-Wijers & Galama 98 030329
Collimated outflow
if > -1 (spherical) → = 1.5+(-.5,0,.5)
if < → = 2, 2+1
Flux dimming is faster after = because
1. lack of emitting fluid at angle >
coll
= 1/2(wind), 3/4 (homogeneous)
2. jet lateral spreading :faster deceleration
t-1/4(-3/8) → t-1/2 , spread
<1/2
1/
OB
S
emitting surface
Kulkarni et al 99: GRB 90123
Jet dynamics -(r),(r) - and emission - F(t) - calculated numerically + data fit determine jet parameters and medium
comparable fits – Jet model homog. better fit than wind – Jet model homog. better fit than wind – SO model
Best fit parameters for uniform jets from fits to multiwavelength afterglow data
Results: - high GRB efficiency (10-80%) - narrow jets (2-3 deg) - initial jet kinetic energy comparable with that of SNe - wind density parameter consistent with Galactic WRs - non-universal microphysical parameters
Numerical modeling of broadband emission of 10 GRB afterglows:
Jet/Struct.outflow model – uniform CBM fits better than wind: 7-1(2)/6-1(3)
→ why is ambient medium homogeneous if progenitor is Wolf-Rayet star ?
Chevalier, Li & Fransson 04
1. termination shock of free WR wind with radius smaller than R
aglow = 0.4 (E
53tday
/no)1/4pc
2. peculiar motion (~vshock
~50 km/s)
of WR star → smaller Rshock
3. faster & tenuous wind (expelled in the last < 1000 yrs before core-collapse) interacting with WR wind R
shock
Jet-breaks in X-ray light-curves (Swift)
1/3 of Swift X-ray afterglows display breaks 0.5 <
x < 1.5 to 1.5 < x < 2.5 at 0.5-10 d
1/3 may also have a break at 1-10 d
1/3 do not have a break until > 10 d
while
~75% of pre-Swift optical afterglows display a break at 0.3-3 d Reason: Swift “sees” dimmer afterglows from wider jets, whose lc breaks occur later
red = light-curves with breakspurple = lcs without breaks until ~10 d
Flux & jet-break time dep on j
if jet energy were universal
F dE/dj-2
tbreak
(dE/dj4
j2
F tbreak
means that afterglows with earlier jet-breaks are brighterb
X-ray plateaus (100-600s → 1-10 ks) no spectral evolution at plateau end
x1
=x2
→ no spectral break crosses X-ray
Plateaus require a departure from assumptions of
standard blast-wave model:
1. constant kinetic energy
(but variable before deceleration or if ejecta are anisotropic)
2. constant micro-physical parameters (contrived)
plateau
1. energy injection (Nousek et al 06, Zhang et al 06, AP et al 06)
Plateaus from increasing average dE/d over visible 1/ area
2. structured outflow (e.g. Eichler & Granot 06)
Plateaus from increasing average dE/d over visible 1/ area
d(dE/d)/dt>0 model
decoupled optical & X-ray light-curves cannot be explained by energy injection alone because EI alters dynamics of forward-shock, hence resulting light-curve features should be achromatic
Possible reasons for X-ray and optical decoupled light-curves
1. X-ray = reprocessed synchrotron forward-shock emission
scattered in another part of rel. outflow = bulk-scattering (to be continued)
2. X-ray (& optical ?) emission is (are) from
2a. a long-lived reverse shock (Uhm & Beloborodov 07 ) 2b. long-lived internal shocks (Ghisellini et al 07)
Note: All require long-lived engine, producing rel. outflow for tsource
~ taglow
>106 s
Unifying forward-shock model for X-ray plateaus
Plateaus require existence of an outflow behind forward-shock (FS) either for energy injection or for scattering
Scattering negligible rel to FS Scattering dominant rel to FS achromatic light-curve breaks chromatic light-curve breaks
O=Synchrotron, X=Sy
O=Sy, X=inverse-Compton O&X decays well correlated O&X decays correlated O&X decays decoupled
Early optical emission from reverse shock (RS))
excess emission from RSduring early afterglow
sy-FS
Ejecta energized by RS, followed by adiabatic cooling: F−t−() with = (0.67/0.80) + (1.19/1.47)
= 2.5 for =1.5 (homogeneous CBM) or =1.2 (wind) (but optical at 100-1000s not known for 990123 & 021211)
first optical flash (1999)AP & Meszaros (1998)
Measurements of optical spectral slope during early afterglow enable test of RS expectation : = 3/4 + 4/3
2=0.76
2=0.50?
1=1.96
1=0.89 ?
2=1.23(.02)
2=0.0+0.2*log(t/1ks)
080319B: Wozniak et al 08, Bloom et al 08
hardening hardening softening
061126: Perley et al 07
1=2.53
1=0.63
1& 1 consistent with RS model early decay too fast for RS model
Note: fast-decaying early emission is softer than slower-decaying late emission, indicating different origins (early=RS, late=FS)
CONCLUSIONS
1. Confirmed predictions of relativistic blast-wave model (RS or FS)
a. power-law afterglow spectra F− (seen in optical and X-ray)
b. power-law flux decay Ft−() (seen in radio, optical and X-ray)
c. optical flashes from RS (very rare, RS emission present until 1ks, afterwards FS) d. light-curve jet breaks (achromatic breaks, very few cases)
2. Early (<10 ks) X-ray LC breaks at end of plateau due to
a. achromatic breaks: long-lived injection of energy into FS b. chromatic X-ray LC breaks: “external” scattering in outflow inner to FS or “central engine” (e.g. internal shocks) emission dominant over FS
X-ray plateaus and chromatic lc breaks from reverse-shock
Genet et al 07(
p between O & X)
Uhm & Beloborodov 07 (c between O & X)
distribution of ejecta mass with LF resulting lcs
X
O
O
X
in contradiction with hardening of optical emission of 061126 & 080319B at B/C (suggesting differentemission mechanisms at A-B and B-D)