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 Talk1. Highly Radiative Blastwave Phase Explains the

Rapid X-ray Declines in Swift GRB Light Curves

Tagliaferri et al. 2005

a. Blast-wave physics with hadrons and leptonsb. External shock analysis of timescalesc. Evolution toward highly radiative regime in the

early afterglow

2. X-ray Flares with External Shocks a. Complete analysis of blast wave/cloud interactionb. Calculation of SEDs and light curvesc. Frozen pulse requirement

GRB 050502B

Falcone et al. 2006 O’Brien et al. 2006

Observational Motivation

Tagliaferri et al. 2005

O’Brien et al. 2006

Importance

a. Central Engine Physicsb. Diagnostic of Central Engine Activity

or Properties of External Mediumc. Predictions for -ray and telescopes

Blast Wave Physics with Leptons and HadronsElectrons

• 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

pBp eepp

Np

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

pn+, p ++- , p0+

3. Multi-pion productionQCD fragmentation models

4. DiffractionCouples photons with 0,

2.0,500200,340)( 1 KMeVEMeVbE rr

Mücke et al. 1999

r

Two-Step Function Approximation for Photopion Cross SectionAtoyan and Dermer 2003

6.0,500,120 2 KMeVEb rMeVEbEK rrin 200,70ˆ)( (useful for energy-

loss rate estimates)

Er

Photopion Processes in a GRB Blast Wave

400: mThreshold p

Fast cooling

s = 2

c

= c

= min

abs

4/3

a= 1/2 b = (2-p)/2 -0.5

3

pkf

Ff

pk

min

Threshold energy of protons interacting with photons with energy pk (as measured by outside observer)

2/ cmh e

ppp cmE 2

pE

Describe F spectrum as a brokenpower law

Protons with E > interact with photons with < pk, and vice versa

pE

Photopion Energy Loss Rate in a GRB Blast Wave

Relate F spectrum to comoving photon density nph(´) for blast-wave geometry (´2nph(´)dL

2f/x22) Calculate comoving rate t´-1

(Ep) = r in comoving frame using photopion () cross-section approximation

pEpE

r

bpE 1

apE 1

)10( aK

All factors can be easily derivedfrom blast-wave physics (in the external shock model)

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

Why these parameters?(see Dermer, Chiang, and Mitman 2000)

(Böttcher and Dermer 2000)

1 s 10 s

3 5 7

10-9

10-7

10-5

10-3

10-1

101

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

1 10 100 1000

Standard Parameters

Com

ovi

ng R

ate

s (s

-1) E

ne

rgies a

nd

fluxes

Observer time t(s)

racc

1/t'ava

r

resc

Epk

(MeV)

Ep(1018eV)

rp,syn

f-6

Energies and Fluxes for Standard ParametersStandard parameter set: z = 1

F 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

Photopion Rate vs. Available Time for Standard ParametersStandard parameter set: z = 1

Photopion rate increases with time for protons with energy Ep that have photopion interactions with photons with pk

Unless the rate is greater than the inverse of the available time, then no significant losses

10-9

10-7

10-5

10-3

10-1

101

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

1 10 100 1000

Standard Parameters

Com

ovi

ng R

ate

s (s

-1) E

ne

rgies a

nd

fluxes

Observer time t(s)

racc

1/t'ava

r

resc

Epk

(MeV)

Ep(1018eV)

rp,syn

f-6

Acceleration Rate vs. Available Time for Standard ParametersStandard 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 Ep

Implicitly assumes Type 2 Fermi acceleration, through gyroresonant interactions in blast wave shell

Makes very hard proton spectrum n´(´p) 1/´p

10-9

10-7

10-5

10-3

10-1

101

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

1 10 100 1000

Standard Parameters

Com

ovi

ng R

ate

s (s

-1) E

ne

rgies a

nd

fluxes

Observer time t(s)

racc

1/t'ava

r

resc

Epk

(MeV)

Ep(1018eV)

rp,syn

f-6

Dermer and Humi 2001

Escape Rate vs. Available Time for Standard ParametersStandard parameter set: z = 1

Diffusive escape from blast wave with comoving width <x> = x/(12).

Calculate escape timescale using Bohm diffusion approximation

No significant escape for protons with energy Ep until >>103 s

10-9

10-7

10-5

10-3

10-1

101

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

1 10 100 1000

Standard Parameters

Com

ovi

ng R

ate

s (s

-1) E

ne

rgies a

nd

fluxes

Observer time t(s)

racc

1/t'ava

r

resc

Epk

(MeV)

Ep(1018eV)

rp,syn

f-6

Proton Synchrotron Loss Rate vs. Available TimeStandard parameter set: z = 1

Proton synchrotron energy-loss rate:

No significant proton sychrotron energy loss for protons with energy Ep

10-9

10-7

10-5

10-3

10-1

101

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

1 10 100 1000

Standard Parameters

Com

ovi

ng R

ate

s (s

-1) E

ne

rgies a

nd

fluxes

Observer time t(s)

racc

1/t'ava

r

resc

Epk

(MeV)

Ep(1018eV)

rp,syn

f-6

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 > 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)

Rates for 1020 eV ProtonsStandard parameter set: z = 1

For these parameters, it takes too long to accelerate particles before undergoing photopion losses or escaping.

10-7

10-6

10-5

10-4

10-3

10-2

1 10 100 1000 104

Observer time t(s)

Com

ovi

n R

ate

s (s

-1)

racc

1/t'ava

r

rp,syn

resc

Calculated at Ep=1020 eV

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

10-5

10-4

10-3

10-2

1 10 100 1000

Observer time t(s)

Com

ovi

n R

ate

s (s

-1)

racc 1/t'

ava

r

rp,syn

resc

Calculated at Ep=1020 eV

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)

10-5

10-4

10-3

10-2

1 10 100 1000

Observer time t(s)

Com

ovi

ng R

ate

s (s

-1)

racc

1/t'ava

r

rp,syn

resc

Calculated at Ep=1020 eV

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 = (P2 +1)1/2

Rapid decay in emissionsfrom blast wave, limitedby curvature relation

2

01 )()( tttf

Kumar and Panaitescu (2000),

Dermer (2004)

Rapidly Declining X-ray Emission Observed with Swift

Zhang et al. 2005

F

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 050724

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 componentDecay lifetime 900 n seconds

GRB 940217GRB 940217

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 941017(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: clp

cl ncmx

E222

0

0

04

0

ncl

E0

Dermer and Mitman (1999, 2004)

(x)

cl

2. X-ray Flares with External Shocks

x0

Require Strong Forward Shock to make Bright, Rapidly Variable GRB Emission

(x)

cl

Shell width: (x) 0, x < 00 = xspr

xx/

, x > xspr

)(4)(

2220

0xcmx

Exn

p

0ncl

1. Nonrelativistic reverse shock: n(x0) >> ncl

3. STV: cl << x/

2. Thick Column: cl

cl n

xnx )()( 00

Shell density:

x0

1. + 2. )( 020 xcl

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:

x2 –x0 << x0

clnxnF /)( 0

Collision Phase 1

Sari and Piran 1995Kobayashi et al. 1997Panaitescu and Mészáros (1999)

Penetration Phase 2

Use Sari, Piran and Narayan (1998) formalism for phases 1 and 2

0

212 );,(|sin|)2()( txjxdxddtfcli

cli

L

RS crosses shell before FS crosses cloud

FS crosses cloud before RS crosses shell

(deceleration shock)

Expansion Phase 3

Gupta, Böttcher, and Dermer (2006)

4

2

bd

d

cm

B

v

Rb

R

tv

e

T

6

,12

0||

||

)/4()1(

4)(

44

3

ib

Synchrotron and adiabatic cooling

Take v = c/3

Conservation of magnetic flux B

constRB 2||

Standard Parameters

E0 1053 ergs0 3000 3x107 cmz 1.0

ncl 103 cm-3

x0 1016 cmx1 1.02x1015 cmcl 0.01i 0.0

e 0.1p 2.5

Light curves at 511 keVAssume 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 emissionsDashed curves: reverse shockDotted 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

00 =109 cm, z = 2x0 = 1017cm0 =100, E0 =1054 ergsIf 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

• 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

Soderberg et al. 2006

GRB Variability in prompt and early afterglow phase due to external shocks with circumburst material

Avoids colliding shell energy crisisSolution by large contrast in factors

Introduces new problems:Epk distribution

Pulse duration

Short delay Vietri-Stella supranova model

Summary

Highly radiative phase in blastwave evolution explains rapid X-ray declinesPredictions:

1. Blast wave in fast cooling regime2. Temporally evolving Epk

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 (>1017 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

e

pnep

2

),,(0

Nonthermal Baryon

Loading Factor fb = 1

Requires large baryon loadto explain GRB 941017

tot = 310-4 ergs cm-2

= 100

Neutrino Detection from GRBs only with Large Baryon-Loading

(~2/yr)

Nonthermal Baryon Loading Factor fb = 20

Dermer & Atoyan, 2003

see poster by Murase and Nagataki

Photon attenuation strongly dependent on and tvar in collapsar model

Optical Depth

evolves in collapsar model due toevolving Doppler factor and internal radiation field

Dermer & Atoyan, 2003

pulses

one

cmergs

tot

sec50

,

1032

4

GRB Blast Wave Geometry in Accord with Swift Observations

Structured Jet

Gamma jet: makesGRB/X-rays

Outer jet makes optical and plateauX-ray phase

forconst

E

Two-Step Collapse (Short-Delay Supranova) Model

1. Standard SNIb/c (56Ni production)2. Magnetar Wind Evacuates Poles3. GRB in collapse of NS to BH4. Prompt Phase due to External Shocks with

Shell/Circumburst Material5. Standard Energy Reservoir (NS collapse to BH)

6. Beaming from mechanical/B-field collimation

Delay time ~< 1 day (GRB 030329)