Modeling the Early Afterglow Swift and GRBs Venice, Italy, June 5-9, 2006

1. Modeling the Early Afterglow Swift and GRBsVenice, Italy, June 5-9, 2006 Chuck Dermer US Naval Research Laboratory Armen Atoyan U. de Montréal Markus Böttcher Ohio University Jim Chiang UMBC/GSFC

2. Highly Radiative Blastwave Phase Explains the Rapid X-ray Declines in Swift GRB Light Curves Outline of Talk • Blast-wave physics with hadrons and leptons • External shock analysis of timescales • Evolution toward highly radiative regime in the • early afterglow 2. X-ray Flares with External Shocks • Complete analysis of blast wave/cloud interaction • Calculation of SEDs and light curves • Frozen pulse requirement Tagliaferri et al. 2005 GRB 050502B Falcone et al. 2006 O’Brien et al. 2006

3. Observational Motivation O’Brien et al. 2006 Tagliaferri et al. 2005 Importance • Central Engine Physics • Diagnostic of Central Engine Activity • or Properties of External Medium • c. Predictions for g-ray and n telescopes

4. Highly Radiative Blastwave Phase Explains the Rapid X-ray Declines in Swift GRB Light Curves Blast Wave Physics with Leptons and Hadrons Electrons • Acceleration by Fermi Processes • Energy in electrons and magnetic field determined by ee and eB parameters • Radiative cooling by synchrotron and Compton Processes Protons • Acceleration by Fermi processes • Energy content in protons determined by ee parameter • Radiative cooling by • Escape from blast wave shell • Proton synchrotron • Photopair production • Photopion production

5. Photopion Production Threshold  mp  150 MeV Mücke et al. 1999 • Resonance Production • D+(1232), N+(1440),… • Direct Production • pgnp+, pg D++p- , pgD0p+ • Multi-pion production • QCD fragmentation models • Diffraction • Couples photons with r0, w Er r Two-Step Function Approximation for Photopion Cross Section Atoyan and Dermer 2003 (useful for energy-loss rate estimates)

6. Photopion Processes in a GRB Blast Wave Threshold energy of protons interacting with photons with energy epk (as measured by outside observer) Fast cooling a= 1/2 b = (2-p)/2  -0.5 s = 2 Protons with E > interact with photons with e < epk, and vice versa 4/3 g0= gc g1= gmin 3 e eabs ec e2 Describe nFn spectrum as a broken power law

7. Photopion Energy Loss Rate in a GRB Blast Wave Relate nFn spectrum to comoving photon density nph(e´) for blast-wave geometry (e´2nph(e´)dL2fe/x2G2) Calculate comoving rate t´-1fp(Ep) = rfp in comoving frame using photopion (fp) cross-section approximation rfp Kfp All factors can be easily derived from blast-wave physics (in the external shock model)

8. Choose Blast-Wave Physics Model Adiabatic blast wave with apparent total isotropic energy release 1054 E54 ergs (cf. Friedman and Bloom 2004) Assume uniform surrounding medium with density 100 n2 cm-3 Relativistic adiabatic blast wave decelerates according to the relation Deceleration length Deceleration timescale (Böttcher and Dermer 2000) 3 5 7 1 s 10 s Why these parameters? (see Dermer, Chiang, and Mitman 2000)

9. Energies and Fluxes for Standard Parameters Standard parameter set: z = 1 nFn flux ~ 10-6 ergs cm-2 s-1 Epk ~ 200 keV at start of GRB Characteristic hard-to-soft evolution Duration ~ 30 s Requires very energetic protons (> 1015 eV) to interact with peak of the synchrotron spectrum

10. Photopion Rate vs. Available Time for Standard Parameters Standard parameter set: z = 1 Photopion rate increases with time for protons with energy Ep that have photopion interactions with photons with epk Unless the rate is greater than the inverse of the available time, then no significant losses

11. Acceleration Rate vs. Available Time for Standard Parameters Standard parameter set: z = 1 Assume Fermi acceleration mechanism; acceleration timescale = factor zacc greater than the Larmor timescale t´L = mcg´p/eB Take zacc = 10: no problem to accelerate protons to Ep Implicitly assumes Type 2 Fermi acceleration, through gyroresonant interactions in blast wave shell Makes very hard proton spectrum n´(g´p)  1/g´p Dermer and Humi 2001

12. Escape Rate vs. Available Time for Standard Parameters Standard parameter set: z = 1 Diffusive escape from blast wave with comoving width <x> = x/(12G). Calculate escape timescale using Bohm diffusion approximation No significant escape for protons with energy Ep until >>103 s

13. Proton Synchrotron Loss Rate vs. Available Time Standard parameter set: z = 1 Proton synchrotron energy-loss rate: No significant proton sychrotron energy loss for protons with energy Ep

14. Gamma-Ray Bursts as Sources of High-Energy Cosmic Rays Solution to Problem of the Origin of Ultra-High Energy Cosmic Rays (Waxman 1995, Vietri 1995, Dermer 2002) Hypothesis requires that GRBs can accelerate cosmic rays to energies > 1020 eV Injection rate density determined by GRB formation rate (= SFR?) GZK cutoff from photopion processes with CMBR Pair production effects for ankle (Berezinsky and Grigoreva 1988) (Wick, Dermer, and Atoyan 2004)

15. Rates for 1020 eV Protons Standard parameter set: z = 1 For these parameters, it takes too long to accelerate particles before undergoing photopion losses or escaping.

16. Rates for 1020 eV Protons with Equipartition Parameters Equipartition parameter set with density = 1000 cm-3, z = 1 Within the available time, photopion losses and escape cause a discharge of the proton energy several hundred seconds after GRB

17. Rates for 1020 eV Protons with Different Parameter Set New parameter set with density = 1000 cm-3, z = 1 Escape from the blast wave also allows internal energy to be rapidly lost (if more diffusive, more escape)

18. Blast Wave Evolution with Loss of Hadronic Internal Energy Assume blast wave loses 0, 25, 50, 75, 90, and 95% of its energy at x = 6x1016 cm. Transition to radiative solution Rapid reduction in blast wave Lorentz factor G = (P2 +1)1/2 Rapid decay in emissions from blast wave, limited by curvature relation Kumar and Panaitescu (2000), Dermer (2004)

19. How to turn emission off? Rapidly Declining X-ray Emission Observed with Swift Zhang et al. 2005 Rising phase of light curve shorter than declining phase in colliding shell emission Difficult for superposition of colliding-shell emissions to explain Swift observations of rapid X-ray decay

20. Rapid X-ray Decays in Short Hard Gamma-Ray Bursts GRB 050724 Barthelmy et al. (2005) Loss of internal energy through ultra-high energy particle escape. (Conditions on parameters relaxed if more diffusive than Bohm diffusion approx.) UHECRs from SGRBs?

21. Neutron Escape and g-Ray Production through Photopion Processes • Photopion production Neutron production rate more rapid than photopion energy loss (by a factor  2 ) Cascade radiation, including proton synchrotron radiation, forms a new g-ray emission component Decay lifetime  900 gn seconds

22. GRB 940217 Long (>90 min) g-ray emission (Hurley et al. 1994)

23. Anomalous High-Energy Emission Components in GRBs Evidence for Second Component from BATSE/TASC Analysis −18 s – 14 s 1 MeV 100 MeV 14 s – 47 s 47 s – 80 s Hard (-1 photon spectral index) spectrum during delayed phase 80 s – 113 s 113 s – 211 s GRB 941017 (González et al. 2003) (see talk by Peter Mészáros)

24. 2. X-ray Flares with External Shocks Making the GRB Prompt Emission and X-ray Flares ncl Dcl E0 G0 x0 Short timescale variability requires existence of clouds with typical sizes << x/G0 and thick columns D(x) Thick Column: Dermer and Mitman (1999, 2004)

25. Require Strong Forward Shock to make Bright, Rapidly Variable GRB Emission Shell width: D(x)  0, x < G02D0 = xspr D(x)  hx/G02, x > xspr ncl G0 Dcl Shell density: x0 1. Nonrelativistic reverse shock: n(x0) >> G02 ncl 2. Thick Column: D(x) 3. STV:Dcl << x/G0 1. + 2.  h << 1: a requirement on the external shock model With 3. and shell-width relation  unless h << 1

26. Blast-Wave Shell/Cloud Physics: The Elementary Interaction • Cloud = SN Remnant/Circumburst Material • Blast Wave/Jet Shell • Serves as a basis for complete analysis of internal shell collisions

27. Analysis of the Interaction Assumption: x2 –x0 << x0 Collision Phase 1 Sari and Piran 1995 Kobayashi et al. 1997 Panaitescu and Mészáros (1999)

28. Penetration Phase 2 (deceleration shock) RS crosses shell before FS crosses cloud FS crosses cloud before RS crosses shell Use Sari, Piran and Narayan (1998) formalism for phases 1 and 2

29. Expansion Phase 3 Synchrotron and adiabatic cooling Conservation of magnetic flux  B Take v = c/3 Gupta, Böttcher, and Dermer (2006)

30. Standard Parameters E0 1053 ergs G0 300 D0 3x107 cm z 1.0 ncl 103 cm-3 x0 1016 cm x1 1.02x1015 cm qcl 0.01 qi 0.0 ee 0.1 p 2.5 Light curves at 511 keV Assume same parameters for forward, reverse, and deceleration-shocked fluids h = 1/G0

31. Blastwave/Cloud SED: Standard parameters Solid curves: forward shock emissions Dashed curves: reverse shock Dotted curves: deceleration shock h = 1/G, qcl = 0.01, qi = 0

32. Model Pulses for Small Cloud Standard parameters except where noted h = 1/G0 Clouds nearly along the line-of-sight to the observer make brightest, shortest pulses Small mass in clouds

33. Model X-ray Flares in the Frozen Pulse Approximation h  0 D0 =109 cm, z = 2 x0 = 1017cm G0 =100, E0 =1054 ergs If the frozen pulse approximation is allowed, no difficulty to explain the g-ray pulses and X-ray flares in GRBs Before the self-similar stage of blastwave evolution Gas-dynamical treatment Relativistic hydrodynamic treatment Mészáros, Laguna, and Rees (1993) Cohen, Piran, and Sari (1998)

34. Soderberg et al. 2006 GRB Model: Two-Step Collapse Process Short delay Vietri-Stella supranova model • 56Ni Production: • Same distributions (within limited statistics) for GRB SNe and SNe Ib/c • Precursor is first step? • Search for precursors hours to days earlier • Standard Energy Reservoir • Impulsive NS collapse to Black Hole • GRB Variability in prompt and early afterglow phase due to external shocks with circumburst material • Avoids colliding shell energy crisis • Solution by large contrast in G factors • Introduces new problems: • Epk distribution • Pulse duration

35. Highly radiative phase in blastwave evolution explains rapid X-ray declines • Predictions: • Blast wave in fast cooling regime • Temporally evolving Epk • Hadronic g-ray light consisting of cascading photopion and proton synchrotron radiation varying independently of leptonic synchrotron • Strong GeV-TeV radiation and/or ultra-high energy (>1017 eV) neutrinos correlated with rapidly decaying X-ray emission • UHECR emissivity following the GRB formation rate history of the universe • External shocks explain g-ray pulses and X-ray flares in the early afterglow phase (before all parts of the blast wave have reached the self-similar stage of evolution) • Short-delay two-step collapse supranovae makeLong Duration GRBs Summary

36. Photon and Neutrino Fluence during Prompt Phase Hard g-ray emission component from hadronic cascade radiation inside GRB blast wave Second component from outflowing high-energy neutral beam of neutrons, g-rays, and neutrinos Nonthermal Baryon Loading Factor fb = 1 Requires large baryon load to explain GRB 941017 Ftot = 310-4 ergs cm-2 d = 100

37. Neutrino Detection from GRBs only with Large Baryon-Loading Nonthermal Baryon Loading Factor fb = 20 (~2/yr) see poster by Murase and Nagataki Dermer & Atoyan, 2003

38. ggOpticalDepth Photon attenuation strongly dependent on d and tvar in collapsar model tgg evolves in collapsar model due to evolving Doppler factor and internal radiation field Dermer & Atoyan, 2003

39. GRB Blast Wave Geometry in Accord with Swift Observations Structured Jet y Gamma jet: makes GRB/X-rays Outer jet makes optical and plateau X-ray phase yG

40. Two-Step Collapse (Short-Delay Supranova) Model • Standard SNIb/c (56Ni production) • Magnetar Wind Evacuates Poles • GRB in collapse of NS to BH • Prompt Phase due to External Shocks with Shell/Circumburst Material • Standard Energy Reservoir (NS collapse to BH) • Beaming from mechanical/B-field collimation Delay time ~< 1 day (GRB 030329)