Download - Reverse Shocks and Prompt Emission
![Page 1: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/1.jpg)
Reverse Shocks and Prompt Emission
Mark BandstraAstro 250050926
![Page 2: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/2.jpg)
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)
![Page 3: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/3.jpg)
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
![Page 4: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/4.jpg)
Reverse Shock: 1-D Cartoon
(at rest)
ISMExpandingshell
![Page 5: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/5.jpg)
Reverse Shock: 1-D Cartoon
ISMExpandingshell
![Page 6: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/6.jpg)
Reverse Shock: 1-D Cartoon
ISMExpandingshell
![Page 7: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/7.jpg)
Reverse Shock: 1-D Cartoon
ISMExpandingshell
![Page 8: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/8.jpg)
Reverse Shock: 1-D Cartoon
ISMExpandingshell
![Page 9: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/9.jpg)
Reverse Shock: 1-D Cartoon
Reverse shock crosses the shell
ISMExpandingshell
![Page 10: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/10.jpg)
Hydrodynamics
Region 4:Unshocked
shell
Region 3:Shocked
shell
Region 2:Shocked
ISM
Region 1:Unshocked
ISM
Reverseshock
Contactdiscontinuity
Forwardshock
(at rest)
![Page 11: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/11.jpg)
Hydrodynamics: Simulation
(from Kobayashi & Sari 2000)
slows
heats
compacts
Region 4 Region 3 Region 2 Region 1
![Page 12: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/12.jpg)
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
![Page 13: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/13.jpg)
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 )
![Page 14: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/14.jpg)
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)
![Page 15: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/15.jpg)
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:
![Page 16: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/16.jpg)
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
![Page 17: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/17.jpg)
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…
![Page 18: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/18.jpg)
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:
![Page 19: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/19.jpg)
Light Curve: Energetics• Forward shock is from region 2:
![Page 20: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/20.jpg)
Light Curve: Energetics• Forward shock is from region 2:
X-rays!!!
![Page 21: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/21.jpg)
Light Curve: EnergeticsThe reverse shock emission is from region 3:
![Page 22: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/22.jpg)
Light Curve: EnergeticsThe reverse shock emission is from region 3:
IR !!!(can in general be as high as optical, sincesensitive to B and e)
![Page 23: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/23.jpg)
Light Curve: Scaling relations• One important scaling relationship: t-2 after the shock crosses• From the Blandford-McKee blast wave:
• Spectral properties:
![Page 24: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/24.jpg)
Light Curve Examples
(from Kobayashi 2000)
In all four cases, flux fades by ~ t-2 after the critical time
![Page 25: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/25.jpg)
Light Curve: Combined Afterglows
(from Zhang, et al. 2003)
![Page 26: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/26.jpg)
Light Curve: Combined Afterglows
(from Zhang, et al. 2003)
Reverseshock
componentForward
shockcomponent
![Page 27: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/27.jpg)
Observations: GRB990123
(ROTSE images, from Akerlof, et al. 1999)•Observation starting 22 sec after BATSE trigger•Peaked at 9th magnitude 50 sec after trigger
![Page 28: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/28.jpg)
Observations: GRB990123
ROTSE lightcurve with GRB inset, from Akerlof, et al. 1999
Optical flash is not simply low-frequency extension of the GRB!
![Page 29: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/29.jpg)
Observations: GRB990123
An interpretation of the data by Sari & Piran 1999
There was also a radio detection ~ 1 day after triggerwhich matched the expected flux in that band
![Page 30: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/30.jpg)
Observations: GRB990123
An interpretation of the data by Sari & Piran 1999
There was also a radio detection ~ 1 day after triggerwhich matched the expected flux in that band
Good! t-2 !
![Page 31: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/31.jpg)
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
![Page 32: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/32.jpg)
GRB041219a vs. GRB990123
(Vestrand, et al. 2005)
Optical lightcurvessuperimposed on gamma-rays
Seems to be adefinite relationshiphere!
Not an extensionof the GRB
![Page 33: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/33.jpg)
GRB041219a: Other Weirdness
(Blake, et al. 2005)
![Page 34: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/34.jpg)
GRB041219a: Other Weirdness
(Blake, et al. 2005)
t-2 ? t+1/2 ?
![Page 35: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/35.jpg)
GRB041219a: Other Weirdness
(Blake, et al. 2005)
What is this?!
t-2 ? t+1/2 ?
![Page 36: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/36.jpg)
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)
![Page 37: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/37.jpg)
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
![Page 38: Reverse Shocks and Prompt Emission](https://reader030.vdocuments.net/reader030/viewer/2022013004/56816844550346895dde1cc8/html5/thumbnails/38.jpg)
Hope you enjoyed the ride