1 Physics of GRB Prompt emission Asaf Pe’er University of Amsterdam September 2005.
Transcript of 1 Physics of GRB Prompt emission Asaf Pe’er University of Amsterdam September 2005.
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Physics of GRB Prompt emission
Asaf Pe’er
University of Amsterdam
September 2005
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Outline
Dynamics Basic facts Why relativistic expansion ? Constraints on the expansion Lorentz factor Fireball hydrodynamics: Time evolution The 4 different phases
Radiative Processes Spectrum I: Simplified analysis Complexities Spectrum II: Modified analysis Some open issues
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Basic Facts
- ray flux: f ~ 10-7 -10-5 erg cm-2 s-1
ob. MeV
Cosmological distance: z=1 dL = 1028 cm
Liso, = 4 f dL2 1050 – 1052 erg s-1
Duration: few sec.
Variability: t~ ms
Example of a lightcurve
(Thanks to Klaas Wiersema)
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Why relativistic expansion?
♦ Variability: t ~ 1ms Source size: R0 = ct ~ 107 cm
♦ Number density of photons at MeV:
♦ Optical depth for pair production e±:
cR
Ln
204
1MeV
16
0
TT0 10
4~
cR
LnR
Creation of e±, fireball !
-152 s erg10L
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Why relativistic expansion ?
► Photons accelerate the fireball.
► In comoving frame: co. = ob./
►Photons don’t have enough energy to produce pairs.
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Estimate of
Mean free path for pair production ) e±( by photon of comoving energy
,,(') 1
2
11
Th dd
ndddl
:/' 11
100 MeV photons were observed
Idea: Optical depth to ~100 MeV photons ≤ 1
22 BATSEU
d
dn
T1 16
3(,,)
221
T11
()2
'
16
3
2
1(')
cm
Ul
e
BATSE
The )comoving( energy density in the BATSE range )20 keV – 2 MeV(: cR
LU BATSE 224
1
2
'
()
cos1
2 2
cme
Th
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Estimate of (2)
Constraint on source size in expanding plasma:
22
(cos1)2
2
RRRR
R
-
1
c
Rt
22
tcmc
L
e
6222
1T
()512
3
6/112
152, MeV100
250
tL
RRco
1
Rt relation:
l
RcocRcm
Ll
e2222
1T1
1
4()2
'
16
3
2
1(')
QxQ/10x
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Some complexities
♦ The observed spectrum is NOT quasi-thermal
♦ Small baryon load )enough >10-8 M( High optical depth to scattering
Conclusion: Explosion energy is converted to baryons kinetic energy,
which then dissipates to produce -rays.
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Stages in dynamics of fireball evolution
Acceleration Coasting Self-similar:
(Forward )shock
Dissipation )Internal collisions,Shock waves(
Transition)Rev. Shock(
R
R-3/2 )R-1/2(
R0
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Stages in dynamics of fireball evolution
Acceleration Coasting Self-similar:
(Forward )shock
Dissipation )Internal collisions,Shock waves(
Transition)Rev. Shock(
R
R-3/2 )R-1/2(
R0
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Scaling law for an expanding plasma: I. Expansion phase
Conservation of entropy in adiabatic expansion:
Conservation of energy )obs. Frame(:
Combined together:
.
3
4 ()
30
2
4
02
ConstTRR
Tu
p
RRVT
puVS co
co
.40
2
..
ConstTRR
uVE cocoob
33
11 ;()()
;()
RnRV
RRRT
RR
coco
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Stages in dynamics of fireball evolution
Acceleration Coasting Self-similar:
(Forward )shock
Dissipation )Internal collisions,Shock waves(
Transition)Rev. Shock(
R
R-3/2 )R-1/2(
R0
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Scaling law for an expanding plasma: II. Coasting phase
Fraction of energy carried by baryons:
Baryons kinetic energy:
Entropy conservation equation- holds
1/21 EcM b
0
2
RR
EcME
s
bk
2
3/2
30
2
;()
()
Rn
RRT
ConstR
ConstTRR
co
024 RRVco
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Extended emission: Shells collisions
cRtTGRB /0
22 22
c~v~For
c
The kinetic energy must dissipate. e.g.:
Magnetic reconnection
Internal collisions (among the propagating shells)
External collisions (with the surrounding matter)
Slow heating Expansion as a collection of shells each of thickness R0
cm1062 22
2122
ttcRcollisions
R0=ct
v1, 1 v2,2
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Stages in dynamics of fireball evolution
Acceleration Coasting Self-similar:
(Forward )shock
Dissipation )Internal collisions,Shock waves(
Transition)Rev. Shock(
R
R-3/2 )R-1/2(
R0
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Radiation
─ Characteristic )synchrotron( observed energy -
─ Characteristic inverse Compton )IC( energy-
cR
LuuB iso
B 222/1
4 ;(8)
MeV1.0
2
3
13
22
2/152,
2/15.0,
25.0,
2.
tL
cm
qB
isoBe
me
obsyn
fm
m
e
pem
1
.2. obsynm
obIC
f~few
Dissipation process: Unknown physics !!!
Most commonly used model:Synchrotron + inverse Compton )IC(
A fraction e of the energy is transferred to electronsB - to magnetic field
Characteristic electrons Lorentz factor:
magnetic field:
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Example of expected spectrum- optically thin case
Synchrotron component
Inverse-Compton Component
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Some complexities…
• Clustering of the peak energy
• Steep slopes at low energies
Observational:
• Dissipation at mild optical depth ?
• Contribution from other radiative sources .
• Unknown shock microphysics )e,B…(
Theoretical:
From Preece et. al., 2000
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“The compactness problem”
3'
cRm
Ll
e
T
55.2
145.0,52250'
tLl e
1
11'
sc
l
Optically thin Synchrotron – IC emission model is incomplete ! Synchrotron spectrum extends above ob.
syn~0.1 MeV Possibility of pair production
Compactness parameter:
High compactness Large optical depth
T2'
. ()' cmnRl eco
MeV1.0 14
25.2
2/152
2/15.0,
25.0,
.
tLBe
obsyn
15.0,
35.0,
15.24
2.MeV1.0,250'
Be
obsyn tl
MeV250
'1.0 5/32/1
5.0,5/8
5.0,10/1
5/2.
452
tL
lBe
obsyn
Put numbers:
Or: ob.syn~0.1 MeV
High Compactness !!
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Example of optically thin spectrum
Synchrotron component
Inverse-Compton Component
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Physical processes – dissipation phase:
Electrons cool fast by Synchrotron and IC scattering –
♦ Synchrotron )cyclotron(
♦ Synchrotron self absorption
♦ Inverse )+ direct !( Compton
♦ Pair creation: e±
♦ Pair annihilation: e+ + e-
♦ Contribution of protons – production )’, high energy photons(
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Estimate of scattering optical depth by pairs
Balance between pair production and annihilation
Pair production rate – from energy considerations:
dyne
e
tcmcR
L
dt
dn222
od.Pr
1
4
T2
Ann.
cndt
dn
At steady state: 2/1T. 'lnRco
Pair annihilation rate:
Conclusion: optical depth of (at least)±≥ few is expected due to pairs!
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Spectrum at mild- high optical depth
IC scattering by pairs:
Steep slopes in keV – MeV : 0.5 < peak ~ MeVHigh optical depth Sharp cutoff at mec2 100 MeV
250'l
2500'l
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Electron distribution: high compactness
=0.08
Low energy distribution: quasi )but not( Maxwellian
Steep power law above .1/1' pe nnfl
l’ = 250
= elec. temp. )in units of mec2(
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Spectrum as a function of compactness
500100log100()
log()
1
()3
4exp()
.2
.
.
.2
..
in
sc
el
sc
scelinsc
nn
nn
Spectrum dependence on the Optical depth Compactness
± < few, l’≤few Optically thin spectrum
± >500, l’>105 Spectrum approach thermal
Characteristic values – in between !!
Estimate number of scattering required for thermalization:
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Summary
Dynamical evolution of GRB’s: different phases
Resulting spectrum : Complicated Low compactness High compactness
Acceleration Coasting Self-similar:
Dissipation
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Estimate of Full calculation(
• Given: Photons observed up to 1~100 MeV
2
2
2
2~10log
BATSE
BATSE
U
d
dn
AAd
dndU
Ad
dn
d
dndd
dd
dnddl
(cos)16
3
2
1
(,,)(')
T
111
221
T
221
T
2T11
()2
'
16
3
2
1
(cos)1(cos)()2
'
216
3
2
1
2(cos)
16
3
2
1(')
cm
U
dcm
U
Uddl
e
BATSE
e
BATSE
BATSE
TH
T1 16
3(,,)
Photons in the BATSE range )20 keV – 2 MeV(: above MeV
6/112
152,
6222
1T
221
T
MeV100250
1()512
3
()2
'
16
3
2
1
2
tL
tcmc
L
cm
UR
l
R
ee
BATSEco