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

(at rest)

ISMExpandingshell

Reverse Shock: 1-D Cartoon

ISMExpandingshell

Reverse Shock: 1-D Cartoon

ISMExpandingshell

Reverse Shock: 1-D Cartoon

ISMExpandingshell

Reverse Shock: 1-D Cartoon

ISMExpandingshell

Reverse Shock: 1-D Cartoon

Reverse shock crosses the shell

ISMExpandingshell

Hydrodynamics

Region 4:Unshocked

shell

Region 3:Shocked

shell

Region 2:Shocked

ISM

Region 1:Unshocked

ISM

Reverseshock

Contactdiscontinuity

Forwardshock

(at rest)

Hydrodynamics: Simulation

(from Kobayashi & Sari 2000)

slows

heats

compacts

Region 4 Region 3 Region 2 Region 1

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: EnergeticsThe reverse shock emission is from region 3:

Light Curve: EnergeticsThe reverse shock emission is from region 3:

IR !!!

(can in general be as high as optical, sincesensitive 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

(from Kobayashi 2000)

In all four cases, flux fades by ~ t-2 after the critical time

Light Curve: Combined Afterglows

(from Zhang, et al. 2003)

Light Curve: Combined Afterglows

(from Zhang, et al. 2003)

Reverseshock

componentForward

shockcomponent

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 triggerwhich matched the expected flux in that band

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 !

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

(Vestrand, et al. 2005)

Optical lightcurvessuperimposed on gamma-rays

Seems to be adefinite relationshiphere!

Not an extensionof the GRB

GRB041219a: Other Weirdness

(Blake, et al. 2005)

GRB041219a: Other Weirdness

(Blake, et al. 2005)

t-2 ? t+1/2 ?

GRB041219a: Other Weirdness

(Blake, et al. 2005)

What is this?!

t-2 ? t+1/2 ?

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