Transcript Document

Reverse Shocks and Prompt Emission
Mark Bandstra
Astro 250
050926
Where are we?
• During the intermediate “coasting” phase
• Internal shocks create the actual GRB emission
• External forward shocks into the ISM create the afterglow
emission long after the GRB
• A reverse “external” shock forms when the shell hits the
ISM
• Emission from this shock is in optical/IR/radio and is
within seconds of the GRB
• The reverse shock converts the KE of the shell into internal
energy, allowing it to decelerate into the Blandford-McKee
solution (Brian’s talk)
Why is the reverse shock important?
• Allows confirmation of internal/external shocks
scenario
• Allows measurement of initial Lorentz factor of
shell expansion, which the GRB and later
afterglow cannot
• Allows us to probe the magnetic field in the shell
Reverse Shock: 1-D Cartoon
Expanding
shell
ISM
(at rest)
Reverse Shock: 1-D Cartoon
Expanding
shell
ISM
Reverse Shock: 1-D Cartoon
Expanding
shell
ISM
Reverse Shock: 1-D Cartoon
Expanding
shell
ISM
Reverse Shock: 1-D Cartoon
Expanding
shell
ISM
Reverse Shock: 1-D Cartoon
Expanding
shell
Reverse shock crosses the shell
ISM
Hydrodynamics
Region 4:
Unshocked
shell
Region 3:
Shocked
shell
Region 2:
Shocked
ISM
Region 1:
Unshocked
ISM
(at rest)
Reverse
shock
Contact
discontinuity
Forward
shock
Hydrodynamics: Simulation
Region 4
Region 3
Region 2
Region 1
slows
heats
compacts
(from Kobayashi & Sari 2000)
Hydrodynamics: Assumptions
Region 4:
Unshocked
shell
Region 3:
Shocked
shell
Region 2:
Shocked
ISM
Region 1:
Unshocked
ISM
Also, CD means p2=p3 and 2=3
Hydrodynamics: Equations
Region 4:
Unshocked
shell
Region 3:
Shocked
shell
Region 2:
Shocked
ISM
Region 1:
Unshocked
ISM
(The symbol
is 3 in the frame of 4,
and it may be ~1 or >>1 )
Hydrodynamics: Solution
• Solution depends only on f=n4/n1, n1, and 
• Two regimes of the solution:
• 2 >> f (ultrarelativistic reverse shock)
• f >> 2 (“Newtonian” reverse shock)
• The shock begins in the Newtonian regime and
may end up relativistic (we will look at this soon)
Crossing Time
• How long does it take the shock to travel from the
CD to the edge of the shell (in obs. frame)?
• General formula:
• For both cases, the crossing time is about the same:
Distance Scales
•
•
•
•
l: Sedov length
R: forward shock sweeps up M/ of ISM (shell decelerates)
R: reverse shock crosses shell
RN: transition from Newtonian to relativistic reverse shock
Distance Scales: Two cases
• R < R < RN: Newtonian
– Shock crosses shell before transition to the relativistic
case can occur
– But most of these become mildly relativistic by the end
of propagation, with R  R  RN
• RN < R < R: Relativistic
– Transition occurs before crossing
• Apparently, we only expect significant emission
from a relativistic reverse shock…
Light Curve: Energetics
• First of all, what is the characteristic energy of the reverse
shock, compared with the forward shock?
• Relativistic reverse shock case:
• Find f at R:
• Then the gamma factors at R are:
Light Curve: Energetics
• Forward shock is from region 2:
Light Curve: Energetics
• Forward shock is from region 2:
X-rays!!!
Light Curve: Energetics
The reverse shock emission is from region 3:
Light Curve: Energetics
The reverse shock emission is from region 3:
IR !!!
(can in general be as high as optical, since
sensitive to B and e)
Light Curve: Scaling relations
• One important scaling relationship: t-2 after the shock crosses
• From the Blandford-McKee blast wave:
• Spectral properties:
Light Curve Examples
In all four cases, flux fades by ~ t-2 after the critical time
(from Kobayashi 2000)
Light Curve: Combined Afterglows
(from Zhang, et al. 2003)
Light Curve: Combined Afterglows
Reverse
shock
component
Forward
shock
component
(from Zhang, et al. 2003)
Observations: GRB990123
(ROTSE images, from Akerlof, et al. 1999)
•Observation starting 22 sec after BATSE trigger
•Peaked at 9th magnitude 50 sec after trigger
Observations: GRB990123
ROTSE lightcurve with GRB inset, from Akerlof, et al. 1999
Optical flash is not simply low-frequency extension of the GRB!
Observations: GRB990123
An interpretation of the data by Sari & Piran 1999
There was also a radio detection ~ 1 day after trigger
which matched the expected flux in that band
Observations: GRB990123
Good! t-2 !
An interpretation of the data by Sari & Piran 1999
There was also a radio detection ~ 1 day after trigger
which matched the expected flux in that band
So Observations have been a piece of cake, right?
• Prompt optical emission only seen in about four
other GRBs
• GRB041219a
– May have seen the t-2 decrease AND the t1/2 rebrightening
– But, optical light curve tracks the GRB light curve!
– Strange IR feature perhaps related to central engine
GRB041219a vs. GRB990123
Seems to be a
definite relationship
here!
Optical lightcurves
superimposed on
gamma-rays
Not an extension
of the GRB
(Vestrand, et al. 2005)
GRB041219a: Other Weirdness
(Blake, et al. 2005)
GRB041219a: Other Weirdness
t+1/2 ?
t-2 ?
(Blake, et al. 2005)
GRB041219a: Other Weirdness
What is this?!
t+1/2 ?
t-2 ?
(Blake, et al. 2005)
Observations: Other Worries
• People are worried about the lack of more optical flashes
• So much so, that they think that there is some physical
process at work to suppress these afterglows
• “Although host extinction can explain the properties of
some bursts, and the natural range of burst energies and
distances can explain some others, … these considerations
alone cannot explain the full diversity of the burst
population. Instead, one or more mechanisms must act to
suppress the optical flash and provide a significantly
enhanced efficiency of the prompt gamma-ray emission for
some bursts.” (Roming, et al. 2005)
Other Applications
• Determining initial Lorentz factor 
– The peak time of the light curve is sensitive to 3, and
therefore we can estimate 3
– Example: For GRB990123,   270, n1  0.2 cm-3
• Measuring B and e
– Spectral properties also sensitive to these parameters
Hope you enjoyed the ride