Transcript Long GRBs

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
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
Tagliaferri et al. 2005
GRB 050502B
Falcone et al. 2006
O’Brien et al. 2006
Observational Motivation
O’Brien et al. 2006
Tagliaferri et al. 2005
a.
b.
c.
Importance
Central Engine Physics
Diagnostic of Central Engine Activity
or Properties of External Medium
Predictions for g-ray and n telescopes
1. 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
1. Proton synchrotron
2. Photopair production
3. Photopion production
•
Escape from blast wave shell
p  B  p g


p g  p  e  e
p g  N 
Photopion Production
1.
2.
Resonance Production
D+(1232), N+(1440),…
Direct Production
pgn+
, pg
,
D++ -
Mücke et al. 1999
Threshold  m  150 MeV
pgD0+
3.
4.
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
 ( Er )  340b, 200 MeV  Er  500 MeV , K1  0.2
120b, Er  500 MeV , K2  0.6
Kin ( Er )  ˆ  70b, Er  200 MeV
(useful for energyloss rate estimates)
Photopion Processes in a GRB Blast Wave
Threshold : g pe   m  400
e  hn / me c
2
Threshold energy E p of protons interacting with photons
with energy epk (as measured by outside observer)
E p  mp c2g p
fe  nFn
Fast cooling
f e pk
Protons with E > E p interact with
photons with e < epk, and vice versa
Describe nFn spectrum as a broken
power law
a= 1/2
4/3
3
eabs ec
b = (2-p)/2  -0.5
s=2
g0= gc
g1= gmin
e min
 e pk
e2
e
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/x22)
Calculate comoving rate t´-1f(Ep) = rf in comoving frame
using photopion (f) cross-section approximation
 Ep
rf
(0  a  1)
Kf
 Ep
All factors can be easily derived
from blast-wave physics (in the
external shock model)
1 a
1b
Ep
Ep
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
(Böttcher and Dermer 2000)
3 5 7
Deceleration length
Deceleration timescale
1 s 10 s
Why these parameters?
(see Dermer, Chiang, and Mitman 2000)
Energies and Fluxes for Standard Parameters
Standard parameter set: z = 1
nFn flux ~ 10-6 ergs cm-2 s1
Duration ~ 30 s
Requires very energetic
protons (> 1015 eV) to
interact with peak of the
synchrotron spectrum
-1
Comoving Rates (s )
Characteristic hard-to-soft
evolution
10
Standard Parameters
1
r
-1
10
10
10
E (10 eV)
p
1/t'
10
18
acc
ava
f
-3
-6
E (MeV)
-5
r
pk
esc
r
-7
f
r
p,syn
-9
1
10
100
1000
Observer time t(s)
10
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
Energies and fluxes
Epk ~ 200 keV at start of
GRB
10
Photopion Rate vs. Available Time for Standard Parameters
Standard parameter set: z = 1
-1
Comoving Rates (s )
Unless the rate is greater
than the inverse of the
available time, then no
significant losses
10
10
Standard Parameters
1
r
-1
1/t'
10
10
10
10
18
acc
E (10 eV)
p
ava
f
-3
-6
E (MeV)
-5
r
pk
esc
r
-7
f
r
p,syn
-9
1
10
100
1000
Observer time t(s)
10
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
Energies and fluxes
Photopion rate increases
with time for protons
with energy Ep that have
photopion interactions
with photons with epk
Acceleration Rate vs. Available Time for Standard Parameters
Standard parameter set: z = 1
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
-1
Comoving Rates (s )
Take zacc = 10: no problem
to accelerate protons to Ep
10
10
Standard Parameters
1
r
1/t'
10
10
10
10
18
acc
-1
E (10 eV)
p
ava
f
-3
-6
E (MeV)
-5
r
pk
esc
r
-7
f
r
p,syn
-9
1
10
100
1000
Observer time t(s)
10
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
Energies and fluxes
Assume Fermi acceleration
mechanism; acceleration
timescale = factor zacc
greater than the Larmor
timescale t´L = mcg´p/eB
Escape Rate vs. Available Time for Standard Parameters
Standard parameter set: z = 1
Diffusive escape from blast
wave with comoving width
<x> = x/(12).
No significant escape for
protons with energy Ep until
>>103 s
-1
Comoving Rates (s )
10
Standard Parameters
1
r
-1
1/t'
10
10
10
10
18
acc
E (10 eV)
p
ava
f
-3
-5
r
-6
E (MeV)
pk
esc
r
-7
f
r
p,syn
-9
1
10
100
1000
Observer time t(s)
10
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
Energies and fluxes
Calculate escape timescale
using Bohm diffusion
approximation
10
Proton Synchrotron Loss Rate vs. Available Time
Standard parameter set: z = 1
Proton synchrotron energyloss rate:
-1
No significant proton
sychrotron energy loss for
protons with energy Ep
10
Standard Parameters
1
r
-1
1/t'
10
10
10
18
acc
E (10 eV)
p
ava
f
-3
-6
E (MeV)
-5
r
pk
esc
r
-7
f
r
p,syn
10
-9
1
10
100
1000
Observer time t(s)
10
3
10
2
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
Energies and fluxes
Comoving Rates (s )
10
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)
Rates for 1020 eV Protons
Standard parameter set: z = 1
-2
10
Calculated at E =10
p
1/t'
-3
-1
Comovin Rates (s )
For these parameters, it
takes too long to accelerate
particles before undergoing
photopion losses or
escaping.
10
r
10
eV
ava
r
-4
20
esc
acc
-5
r
10
r
-6
10
f
p,syn
-7
10
1
10
100
1000
Observer time t(s)
10
4
Rates for 1020 eV Protons with Equipartition Parameters
Equipartition parameter set with density = 1000 cm-3, z = 1
10
-2
r
Calculated at E =10
20
p
esc
eV
-1
Comovin Rates (s )
Within the available time,
photopion losses and
escape cause a discharge of
the proton energy several
hundred seconds after GRB
10
-3
r
r
10
-4
10
-5
1
1/t'
acc
ava
p,syn
r
10
100
Observer time t(s)
1000
f
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
-2
Calculated at E =10
20
1/t'
-1
Comoving Rates (s )
p
10
ava
-3
r
acc
r
10
-4
r
r
10
f
esc
p,syn
-5
1
10
100
Observer time t(s)
1000
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 emissions
from blast wave, limited
by curvature relation
f e (t )  e
1
(t  t0 )
Kumar and Panaitescu (2000),
Dermer (2004)
2 
Rapidly Declining X-ray Emission Observed with Swift
How to turn emission off?
Fn  n 
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
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?
Neutron Escape and g-Ray Production
through Photopion Processes
• Photopion production
Decay lifetime  900 gn seconds
Neutron production rate more rapid than photopion energy loss (by a
factor  2 )
Cascade radiation, including proton synchrotron radiation, forms a new gray emission component
GRB 940217
Long (>90 min) g-ray emission
(Hurley et al. 1994)
Anomalous High-Energy Emission Components in GRBs
Evidence for Second Component from BATSE/TASC Analysis
−18 s – 14 s
1 MeV
14 s – 47 s
47 s – 80 s
80 s – 113 s
Hard (-1 photon spectral
index) spectrum during
delayed phase
113 s – 211
s
GRB 941017
(González et al. 2003)
(see talk by Peter Mészáros)
100
MeV
2. X-ray Flares with External Shocks
Making the GRB Prompt Emission and X-ray Flares
ncl
Dcl
0
E0
x0
D(x)
Thick Column: D cl 
E0
4 x02m p c 2 02ncl
Short timescale variability
requires existence of clouds
with typical sizes << x/0
and thick columns
Dermer and Mitman (1999, 2004)
Require Strong Forward Shock to make
Bright, Rapidly Variable GRB Emission
ncl
0
Dcl
Shell width: D(x)  D0, x < 02D0 = xspr
D(x)  hx/02 , x > xspr
Shell density: n( x ) 
x0
E0
4 x 2m p c 2 02 D( x )
1. Nonrelativistic reverse shock:
D cl 
2. Thick Column:
D(x)
h << 1: a requirement on
the external shock model
3. STV: Dcl << x/0
n(x0) >> 02 ncl
D( x0 )n( x0 )
ncl
1. + 2.  D cl  02 D( x0 )
With 3. and shell-width relation 
unless h << 1
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
Collision Phase 1
F  n( x0 ) / ncl
Sari and Piran 1995
Kobayashi et al. 1997
Panaitescu and Mészáros (1999)
Penetration Phase 2
(deceleration shock)
RS crosses shell before
FS crosses cloud
fe (t )  (2d L )
2 1
i  cl
FS crosses cloud before
RS crosses shell


 d | sin  | dx x e j(e , x; t)
2
i  cl
0
Use Sari, Piran and Narayan (1998)
formalism for phases 1 and 2
Expansion Phase 3
Synchrotron and adiabatic cooling
Conservation of magnetic flux  B
B R||2  const
dg g
g2

 b 4
d 

2

R

B
vt
T 0
||
  1
,b
R||
v 6 mec
4 3
g ( ) 
b( 4  1)  (4 4 / g i )
Take v = c/3
Gupta, Böttcher, and Dermer (2006)
Standard Parameters
E0
0
D0
z
1053 ergs
300
3x107 cm
1.0
ncl
x0
x1
cl
i
103 cm-3
1016 cm
1.02x1015 cm
0.01
0.0
ee
0.1
p
2.5
h = 1/0
Light curves at 511 keV
Assume same parameters for forward,
reverse, and deceleration-shocked fluids
Blastwave/Cloud SED: Standard parameters
Solid curves: forward shock emissions
Dashed curves: reverse shock
Dotted curves: deceleration shock
h = 1/, cl = 0.01, i = 0
Model Pulses
for Small
Cloud
Standard
parameters
except where
noted
h = 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
h 0
D0 =109 cm, z = 2
x0 = 1017cm
0 =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 selfsimilar stage of
blastwave evolution
Gas-dynamical treatment
Mészáros, Laguna, and Rees (1993)
Relativistic hydrodynamic treatment
Cohen, Piran, and Sari (1998)
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  factors
Introduces new problems:
Epk distribution
Pulse duration
Soderberg et al. 2006
Summary
Highly radiative phase in blastwave evolution explains rapid X-ray declines
Predictions:
1. Blast wave in fast cooling regime
2. Temporally evolving Epk
3. Hadronic g-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 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 make Long Duration GRBs
Photon and
Neutrino Fluence
during Prompt
Phase
Nonthermal Baryon
Loading Factor fb = 1
Ftot = 310-4 ergs cm-2
d = 100
Requires large baryon load
to explain GRB 941017
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


pg    e ( n, p,n )
  0  2g  e
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
gg Optical Depth
Photon attenuation strongly dependent on d and tvar in collapsar model
F tot  3  104
ergs cm 2 ,
50 one sec
pulses
gg 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
y
Gamma jet: makes
GRB/X-rays
Outer jet makes optical and plateau
X-ray phase
y
E
 const for   y

Two-Step Collapse (Short-Delay Supranova)
Model
1.
2.
3.
4.
5.
6.
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)
Delay time ~<
Beaming from mechanical/B-field collimation
1 day (GRB 030329)