1. The signature of a wind reverse shock in GRB’s Afterglows
Asaf Pe’er Ralph A.M.J. Wijers (Amsterdam)
ApJ., 543, 1036
astro-ph/
June 06

2. 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

3. 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:
ISM
nISM~103 cm-3
Stellar wind
Shocked stellar wind
Massive star
(reverse) shock wave
(forward) shock wave
Contact discontinuity

4. Graph #1: Density profile
Pb>>Pa rb=4ra(r=R0)
Castor et. al., 1975
Weaver et. al., 1977

5. Density profile numerical simulation by Chevalier, Li & Fransson (2004)

6. Blast wave propagation in region a: density profile
Dr(ã)ob. ~ r/4G2
Blandford & McKee (1976) : n(r) r-2  G(r) r-1/2

7. GRB blast wave propagation in region a
(relativistically-) shocked stellar wind
(hot: Gmc2 per particle)
Region a:
Stellar wind
(cold)
Region b:
Shocked stellar wind
G(r)
Compressed:
Dr(ã)ob. ~ r/4G2
Relativistic blast wave
Wind reverse shock

8. Interaction of shock waves
Region ã
Region a
Region b
Wind reverse shock
G(r)
(downstream)
r<R0
G(r)
Region b ~
Region c ~
Region ã:
Region b
G1G(r=R0)
(upstream)
GRS<G1
r>R0
New blast wave
reverse shock
New blast wave
forward shock
Contact discontinuity

9. Calculation of plasma properties during interaction
Problem: reverse shock propagates into hot medium  not strong !
Region b:
Region ã:
Region b ~
Region c
GRS<G1=?
G1G(r=R0)
G2=?
We know:
Boundary conditions: G1, nã, nb
We find:
Reverse shock jump conditions:
- Conservation of particle number flux: [nGb]
- Energy flux – [wG2b]
- Momentum flux: [wG2b2 + P]

10. 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 G1  conditions in other regions are time independent !

11. Graph #2: Evolution of blast wave Lorentz factor
G(r) r-1/2
G(r) r-3/2
R1 = 1.06R0 = radius where the reverse shock crossed region ã

12. Light curves calculations
Synchrotron emission spectrum
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) ~

13. 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

14. Comparison with data: GRB030329
R-band afterglow of GRB (corrected for the contribution of SN2003dh)
(Taken from Lipkin et.al., 2004)

15. 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