AFTERGLOW PHYSICS

Alin Panaitescu Los Alamos National Laboratory

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{

Power-law decay indices F

tfor RS and FS light-curves

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

Optical light-curve breaks in pre-Swift afterglows

Zeh, Klose & Kann 06

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

Swift X-ray afterglows: three phases

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

Jet-breaks = achromatic (late and followed by steep decay)

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

rel. boost of specific flux and photon energy by &

Bulk-scattering - relativistic effects

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)