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Understanding Reverse Shocks in Gamma-Ray Bursts

This article explores the significance of reverse shocks in GRBs, the process by which internal energy converts shell kinetic energy, with emphasis on the shock's importance and energetics. It also delves into the light curve characteristics and observations of reverse shock components.

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Understanding Reverse Shocks in Gamma-Ray Bursts

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  1. Reverse Shocks and Prompt Emission Mark Bandstra Astro 250 050926

  2. 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)

  3. 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

  4. Reverse Shock: 1-D Cartoon Expanding shell ISM (at rest)

  5. Reverse Shock: 1-D Cartoon Expanding shell ISM

  6. Reverse Shock: 1-D Cartoon Expanding shell ISM

  7. Reverse Shock: 1-D Cartoon Expanding shell ISM

  8. Reverse Shock: 1-D Cartoon Expanding shell ISM

  9. Reverse Shock: 1-D Cartoon Expanding shell ISM Reverse shock crosses the shell

  10. Hydrodynamics Region 4: Unshocked shell Region 3: Shocked shell Region 2: Shocked ISM Region 1: Unshocked ISM (at rest) Forward shock Reverse shock Contact discontinuity

  11. Hydrodynamics: Simulation Region 4 Region 3 Region 2 Region 1 slows heats compacts (from Kobayashi & Sari 2000)

  12. 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

  13. 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 )

  14. 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)

  15. 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:

  16. 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

  17. 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…

  18. 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:

  19. Light Curve: Energetics • Forward shock is from region 2:

  20. Light Curve: Energetics • Forward shock is from region 2: X-rays!!!

  21. Light Curve: Energetics The reverse shock emission is from region 3:

  22. 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)

  23. Light Curve: Scaling relations • One important scaling relationship: t-2 after the shock crosses • From the Blandford-McKee blast wave: • Spectral properties:

  24. Light Curve Examples In all four cases, flux fades by ~ t-2 after the critical time (from Kobayashi 2000)

  25. Light Curve: Combined Afterglows (from Zhang, et al. 2003)

  26. Light Curve: Combined Afterglows Reverse shock component Forward shock component (from Zhang, et al. 2003)

  27. Observations: GRB990123 (ROTSE images, from Akerlof, et al. 1999) • Observation starting 22 sec after BATSE trigger • Peaked at 9th magnitude 50 sec after trigger

  28. Observations: GRB990123 ROTSE lightcurve with GRB inset, from Akerlof, et al. 1999 Optical flash is not simply low-frequency extension of the GRB!

  29. 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

  30. 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

  31. 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

  32. 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)

  33. GRB041219a: Other Weirdness (Blake, et al. 2005)

  34. GRB041219a: Other Weirdness t+1/2 ? t-2 ? (Blake, et al. 2005)

  35. GRB041219a: Other Weirdness What is this?! t+1/2 ? t-2 ? (Blake, et al. 2005)

  36. 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)

  37. 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

  38. Hope you enjoyed the ride

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