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