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

Outline of Talk 1.Highly Radiative Blastwave Phase Explains the Rapid X-ray Declines in Swift GRB Light Curves Tagliaferri et al a.Blast-wave physics with hadrons and leptons b.External shock analysis of timescales c.Evolution toward highly radiative regime in the early afterglow 2.X-ray Flares with External Shocks a.Complete analysis of blast wave/cloud interaction b.Calculation of SEDs and light curves c.Frozen pulse requirement GRB B Falcone et al O’Brien et al. 2006

Observational Motivation Tagliaferri et al O’Brien et al Importance a.Central Engine Physics b.Diagnostic of Central Engine Activity or Properties of External Medium c.Predictions for  -ray and telescopes

Blast Wave Physics with Leptons and Hadrons Electrons Acceleration by Fermi Processes Energy in electrons and magnetic field determined by  e and  B parameters Radiative cooling by synchrotron and Compton Processes Protons Acceleration by Fermi processes Energy content in protons determined by  e parameter Radiative cooling by Escape from blast wave shell 1.Proton synchrotron 2.Photopair production 3.Photopion production 1.Highly Radiative Blastwave Phase Explains the Rapid X-ray Declines in Swift GRB Light Curves

Photopion Production Threshold  m   150 MeV 1.Resonance Production  + (1232), N + (1440),… 2.Direct Production p  n  +, p   ++  -, p   0  + 3.Multi-pion production QCD fragmentation models 4.Diffraction Couples photons with  0,  Mücke et al r Two-Step Function Approximation for Photopion Cross Section Atoyan and Dermer 2003 (useful for energy- loss rate estimates) ErEr

Photopion Processes in a GRB Blast Wave Fast cooling s = 2 cc   =  c   =  min    abs 4/3 a= 1/2 b = (2-p)/2  Threshold energy of protons interacting with photons with energy  pk (as measured by outside observer) Describe F spectrum as a broken power law Protons with E > interact with photons with  <  pk, and vice versa

Photopion Energy Loss Rate in a GRB Blast Wave Relate F spectrum to comoving photon density n ph (  ´) for blast-wave geometry (  ´2n ph (  ´)  d L 2 f  /x 2  2 ) Calculate comoving rate t´ -1  (E p ) = r  in comoving frame using photopion (  ) cross-section approximation r  K  All factors can be easily derived from blast-wave physics (in the external shock model)

Choose Blast-Wave Physics Model Adiabatic blast wave with apparent total isotropic energy release E 54 ergs (cf. Friedman and Bloom 2004) Assume uniform surrounding medium with density 100 n 2 cm -3 Relativistic adiabatic blast wave decelerates according to the relation Deceleration length Deceleration timescale Why these parameters? (see Dermer, Chiang, and Mitman 2000) (Böttcher and Dermer 2000) 1 s10 s 3 5 7

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

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

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

Escape Rate vs. Available Time for Standard Parameters Standard parameter set: z = 1 Diffusive escape from blast wave with comoving width = x/(12  ). Calculate escape timescale using Bohm diffusion approximation No significant escape for protons with energy E p until >>10 3 s

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 E p

Gamma-Ray Bursts as Sources of High-Energy Cosmic Rays Solution to Problem of the Origin of Ultra-High Energy Cosmic Rays (Wick, Dermer, and Atoyan 2004) (Waxman 1995, Vietri 1995, Dermer 2002) Hypothesis requires that GRBs can accelerate cosmic rays to energies > 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)

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

Rates for 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

Rates for 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)

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 = 6x10 16 cm. Transition to radiative solution Rapid reduction in blast wave Lorentz factor  = (P 2 +1) 1/2 Rapid decay in emissions from blast wave, limited by curvature relation Kumar and Panaitescu (2000), Dermer (2004)

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

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

Neutron Escape and  -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  - ray emission component Decay lifetime  900  n seconds

GRB Long (>90 min)  -ray emission (Hurley et al. 1994)

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

Making the GRB Prompt Emission and X-ray Flares Short timescale variability requires existence of clouds with typical sizes << x/  0 and thick columns Thick Column: 00 n cl E0E0 Dermer and Mitman (1999, 2004)  (x)  cl 2.X-ray Flares with External Shocks x0x0

Require Strong Forward Shock to make Bright, Rapidly Variable GRB Emission  (x)  cl Shell width:  (x)   0, x <  0   0 = x spr  x    x/   , x > x spr 00 n cl 1. Nonrelativistic reverse shock: n(x 0 ) >>    n cl 3. STV:  cl << x/   2. Thick Column: Shell density: x0x  With 3. and shell-width relation  unless  << 1  << 1 : a requirement on the external shock model

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

Analysis of the Interaction Assumption: x 2 –x 0 << x 0 Collision Phase 1 Sari and Piran 1995 Kobayashi et al Panaitescu and Mészáros (1999)

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

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

Standard Parameters E ergs   0 3x10 7 cm z1.0 n cl 10 3 cm -3 x cm x x10 15 cm  cl 0.01  i 0.0  e 0.1 p2.5 Light curves at 511 keV Assume same parameters for forward, reverse, and deceleration-shocked fluids  = 1/  0

Blastwave/Cloud SED: Standard parameters  = 1/ ,  cl = 0.01,  i = 0 Solid curves: forward shock emissions Dashed curves: reverse shock Dotted curves: deceleration shock

Model Pulses for Small Cloud Standard parameters except where noted  = 1/  0 Clouds nearly along the line-of-sight to the observer make brightest, shortest pulses Small mass in clouds

Model X-ray Flares in the Frozen Pulse Approximation  0  0 =10 9 cm, z = 2 x 0 = cm  0 =100, E 0 =10 54 ergs If the frozen pulse approximation is allowed, no difficulty to explain the  -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)

GRB Model: Two-Step Collapse Process 56 Ni 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 Soderberg et al 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  factors Introduces new problems: E pk distribution Pulse duration Short delay Vietri-Stella supranova model

Summary Highly radiative phase in blastwave evolution explains rapid X-ray declines Predictions: 1.Blast wave in fast cooling regime 2.Temporally evolving E pk 3.Hadronic  -ray light consisting of cascading photopion and proton synchrotron radiation varying independently of leptonic synchrotron 4.Strong GeV-TeV radiation and/or ultra-high energy (>10 17 eV) neutrinos correlated with rapidly decaying X-ray emission 5.UHECR emissivity following the GRB formation rate history of the universe External shocks explain  -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 make Long Duration GRBs

Photon and Neutrino Fluence during Prompt Phase Hard  -ray emission component from hadronic cascade radiation inside GRB blast wave Second component from outflowing high-energy neutral beam of neutrons,  -rays, and neutrinos Nonthermal Baryon Loading Factor f b = 1 Requires large baryon load to explain GRB  tot = 3  ergs cm -2  = 100

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

Photon attenuation strongly dependent on  and t var in collapsar model  Optical Depth   evolves in collapsar model due to evolving Doppler factor and internal radiation field Dermer & Atoyan, 2003

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

Two-Step Collapse (Short-Delay Supranova) Model 1.Standard SNIb/c ( 56 Ni production) 2.Magnetar Wind Evacuates Poles 3.GRB in collapse of NS to BH 4.Prompt Phase due to External Shocks with Shell/Circumburst Material 5.Standard Energy Reservoir (NS collapse to BH) 6.Beaming from mechanical/B-field collimation Delay time ~< 1 day (GRB )