The signature of a wind reverse shock in GRB’s Afterglows
Asaf Pe’er Ralph A.M.J. Wijers
(Amsterdam)
June 06
ApJ., 543, 1036
astro-ph/0511508
Outline
Motivation: massive stars as GRB progenitors
Complexities of the ambient density profile
Interaction of relativistic blast wave and wind termination shock
Plasma dynamics
Resulting light curves
Motivation: wind from massive star
Massive stars are progenitors of Long GRB’s (GRB-SN Ic connection, GRB’s in star forming regions..)
Massive stars emit supersonic wind:
Massive star
ISMnISM~103 cm-3
(forward) shock wave
Stellar wind
Shocked stellar wind
(reverse) shock wave
Contact discontinuity
Graph #1: Density profile
cm
106.15/2
6,10/310/1
8,10/3
6
18
3,
tnvM
R
ISMw
RS
cm 106.1 5/36,
5/15/28,
5/16
19
3,
tnvMRISMwFS
Castor et. al., 1975
Weaver et. al., 1977
t
n
v
:parametersfree
ISM
w
M
Pb>>Pab=4a(r=R0)
Density profile numerical simulation by Chevalier, Li & Fransson (2004)
Blast wave propagation in region a: density profile
Blandford & McKee (1976) : n(r) r-2 (r) r-1/2
r(ã)ob. ~ r/42
GRB blast wave propagation in region a
Region b:
Shocked stellar wind
Wind reverse shock
Region a:
Stellar wind
(cold)
Relativistic blast wave
(r)
Region ã:
(relativistically-) shocked stellar wind
(hot: mc2 per particle)
Compressed:
r(ã)ob. ~ r/42
Interaction of shock waves
Region b
Region aRegion ã
(r)
Region b
New blast wave
forward shock
(r)
(r=R0
)
Region ã:
New blast wave
reverse shock
RS<
Contact discontinuity
Region b~
Region c~
r<R0
r>R0
Wind reverse shock(downstream)
(upstream)
Calculation of plasma properties during interaction
Problem: reverse shock propagates into hot medium not strong !
Region b:Region ã: Region b~ Region c~
RS<=?(r=R0
)
2=?
We know:
Boundary conditions: 1, nã, nb
Reverse shock jump conditions:
- Conservation of particle number flux: [n]
- Energy flux – []
- Momentum flux: [ + P]
We find:
ab
ab
RS
nn
~~
~~
1
12
1.2
3
43.0
725.0
Schematic density profile during the existence of the reverse shock
As long as the reverse shock exists – plasma in region ã is upstream continues to move at 1 conditions in other regions are time independent !
Graph #2: Evolution of blast wave Lorentz factor
(r) r-1/2
(r) r-3/2
R1 = 1.06R0 = radius where the reverse shock crossed region ã
Light curves calculations
Calculation in 3 different regimes:(a) r < R0 Emission from region ã
(b) R0<r<R1 Emission from regions ã , b, c
(c) r>R1 Emission from region c
(Sari, Piran & Narayan, 1998)
Synchrotron emission spectrum
~~
~
Graph #3: Resulting light curve
Model predictions: (1) Jump in the light curve by a factor ~2 after ~day; (2) Change of spectral slopes at late times (3) Late times afterglow looks like explosion into constant density
Comparison with data: GRB030329
R-band afterglow of GRB030329 (corrected for the contribution of SN2003dh)
(Taken from Lipkin et.al., 2004)
Summary
Wind of massive star results in complex density structure
GRB blast wave splits at R0, change its r- dependence
Light curve is complex: shows jump by a factor of ~2 after ~ day, and change slope at late times