GRB Afterglow Spectra

1
GRB Afterglow Spectra

• Daniel Perley
• Astro 250
• 19 September 2005

International Talk Like a Pirate Day
2
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
tcool gmec / sTcß2ge2g2(B2/8p) gc
6p mec
sTg B2 t
'critical' e- t tcool
ge gc
tcool a 1 / ge gc a 1 / t
1/2
-(p1)/2
log Pn
nm
3
npk (gi) a gi2
Remember, Pnpk is const, so constant amount of
energy is emitted at all ginm lt n lt ne

4
Title
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Subject
Daniel Perley
19 September 2005
GRB Afterglow Spectra
5
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
The GRB Standard Model
Background
ISM
Shocked Gas
SHOCK
Earth
Daniel Perley
19 September 2005
GRB Afterglow Spectra
6
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Relativistic Shock
Background
From Brians lecture
ISM
Deceleration by factor v 2
g G v2
G
SHOCK
number density no energy density Eo no mp
c2 energy per particle Eo/no mp c2
n' 4 g no E' 4 g2 no mp c2E'/n' g mp c2
gtCompressionlt by 4 g
Energy Increase by factor g
Daniel Perley
19 September 2005
GRB Afterglow Spectra
7
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Energy Deposition
Energy Deposition
Where does the energy go?
Protons Electrons Magnetic field Other
particles?
Ep ep E' Ee ee E' B eB E'
Daniel Perley
19 September 2005
GRB Afterglow Spectra
8
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Proton/Electron Energy
Energy Deposition
Particle energy deposited in random motions.
ISM
Shocked Gas
SHOCK
g
G
Bulk motion of shocked gas relative to observer
Extreme (relativistic) temperature of shocked
gas described by gp, ge
Daniel Perley
19 September 2005
GRB Afterglow Spectra
9
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Proton Energy
Energy Deposition
Not particularly interesting on its own. Protons
necessarily drag electrons with them at the same
bulk velocity. Share energy with electrons
electron g factors necessarily much higher.
Daniel Perley
19 September 2005
GRB Afterglow Spectra
10
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Electron Energy
Energy Deposition
Faster-moving electrons will radiate more
efficiently by all important processes.
ge
Daniel Perley
19 September 2005
GRB Afterglow Spectra
11
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Electron Energy Distribution
Energy Deposition
Q How is electron energy distributed?
A



?
Hypothesis Power-law?
(Seen in SNe, NR shocks)
Daniel Perley
19 September 2005
GRB Afterglow Spectra
12
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Electron Energy Distribution
Energy Deposition
Model as power-law
N a Complicated
N a g -p
Log N
Log g
Daniel Perley
19 September 2005
GRB Afterglow Spectra
13
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Electron Energy Distribution
Energy Deposition
Simplify cut-off power law at minimum energy
Minimum energy
Daniel Perley
19 September 2005
GRB Afterglow Spectra
14
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Electron Energy Distribution
Energy Deposition
Mimimum energy determined by total energy density
ge 1-p
ge Ng
E
gm
ge
Infinite if plt2
n ? Nge dge
Ee me c2 ? ge Nge dge
me c2 C gm2-p
C gm1-p
me c2 gm n
C (1-p) gmp-1 n
Ee
mp
p-2
gm
g
g
ee

610 ee g
n me c2
me
p-1
Daniel Perley
19 September 2005
GRB Afterglow Spectra
15
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Electron Energy Distribution
Energy Deposition
Limits on p
N a g 1-p
g -p
g N
N
gm
gm
ge
ge
E me c2 ? g Nge dge me c2 2-p

n ? Nge dge 1 1-p
C gm2-p
C gm1-p
C (1-p) n gm1-p
Daniel Perley
19 September 2005
GRB Afterglow Spectra
16
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Magnetic Energy
Energy Deposition
Strong post-shock magnetic field expected from
equipartition. Generation mechanism
unknown/complicated various plasma effects
B
B2
eB E'
8p
eB 4 g2 no mp c2
32p eB g2 no mp c2
B2
32p eB no mp g c
B
no
(0.4 gauss) eB1/2 ( )1/2 g
cm-3
Daniel Perley
19 September 2005
GRB Afterglow Spectra
17
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
Emission Mechanisms
How does it cool?
Bremsstrahlung P a ge3/2 n2 Inverse Compton P
sTcß2ge2Uph Synchrotron P sTcß2ge2UB
Daniel Perley
19 September 2005
GRB Afterglow Spectra
18
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
Relativistic Cyclotron
Relativistic modification to cyclotron frequency
Most emission is not at this frequency.
Daniel Perley
19 September 2005
GRB Afterglow Spectra
19
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
Synchrotron Beaming
Emission is highly pulsed we see emission for
only 1/g2 of total emission time.
- One factor of g from beaming angle-
Additional factor of g from "Doppler" boost
1/g
1/g
1/?cyc
1/g2?cyc
Daniel Perley
19 September 2005
GRB Afterglow Spectra
20
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
1e- Synchrotron Spectrum


21
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
1e- Synchrotron Spectrum
Fourier transformed
g2?cyc

E
t

d(?-n?cyc)

E
t
?cyc
g2?cyc
g2?cyc
g2?cyc
22
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
1e- Synchrotron Spectrum
More precisely
e-n/?cyc n 1/2
n 1/3
log Pn
log n
npk
Total Power P sTcß2g2UB a g2UB Peak
Freq. npk g2?cyc
Daniel Perley
19 September 2005
GRB Afterglow Spectra
23
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
1e- Synchrotron Spectrum
More precisely
e-n/?cyc n 1/2
n 1/3
log Pn
log n
npk
Shocked frame
a ge2 a ge2 a const
Total Power P sTcß2ge2UB Peak Freq.
npk ge2?cyc / 2p Peak Power Pnpk P / npk
Daniel Perley
19 September 2005
GRB Afterglow Spectra
24
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
1e- Synchrotron Spectrum
e-n/?cyc n 1/2
n 1/3
log Pn
log n
npk
npk
Shocked frame
a ge2 a ge2 a const
Total Power P sTcß2ge2UB Peak Freq.
npk ge2?cyc / 2p Peak Power Pnpk P / npk
Daniel Perley
19 September 2005
GRB Afterglow Spectra
25
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
1e- Synchrotron Spectrum
e-n/?cyc n 1/2
n 1/3
log Pn
log n
npk
npk
Observer frame
Total Power P sTcß2ge2g2UB Peak Freq.
npk ge2g?cyc / 2p Peak Power Pnpk P /
npk
a ge2g2 a ge2g a g
Daniel Perley
19 September 2005
GRB Afterglow Spectra
26
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Sychrotron
Uncooled Multi-e- Spectrum
Material contains many electrons at different
velocities (ge) true spectrum is a combination
of individual spectra, according to electron
energy distribution.
Electron distribution
Electron spectrum
Daniel Perley
19 September 2005
GRB Afterglow Spectra
27
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
Uncooled Multi-e- Spectrum
Can just do a weighted sum (convolution) but
need to convert x-axis from ge to npk.
-(p-1)/2
log Nn
From before, npk a ge2
log npk
nm
ge
a
Electron distribution
e- distribution Ng a ge-p
Solve Nn Ng(n) a ge-p
ge-1 a n-(p1)/2
Sign error??
Daniel Perley
19 September 2005
GRB Afterglow Spectra
28
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
Uncooled Multi-e- Spectrum
-(p-1)/2
log Nn
log npk
nm
Electron distribution
Electron spectrum
Total Spectrum
Daniel Perley
19 September 2005
GRB Afterglow Spectra
29
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
Uncooled Multi-e- Spectrum
exp
1/3
log Pn
log n
npk
1/3
-(p-1)/2
log Pn
nm
30
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Uncooled Synchrotron
Uncooled Multi-e- Spectrum
1/3
-(p-1)/2
log Pn
log npk
nm
"Broken" Power law Below nm, emission
dominated by low-g e- Above nm, emission from
electrons with npeak(g) nm
31
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Characteristic Cooling Time
1/3
-(p-1)/2
log Pn
log npk
nm
This analysis is too simplistic for
GRBs. Calculate characteristic cooling time
Potentially much shorter than time since GRB
(shock passage)
tcool E / P gmec / sTcß2g2UB
4 10-3 s ( )-2 g-1
32
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling e- Spectrum
If an electron's energy changes significantly
over the time since the energy injection, use an
"averaged" spectrum for that electron.
ge Initial electron energy (at injection) gc
Final electron energy (after cooling)
Energy of the highest-g e- that hasn't cooled
Determined by observational timescale tobs
gcmec / sTcß2gc2UBgc
6p mec
sTB2tobs
Daniel Perley
19 September 2005
GRB Afterglow Spectra
33
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling e- Spectrum
Electron radiates as it cools, with a simple
synchrotron spectrum corresponding to the
instantaneous energy gi .
ge Initial electron energy gc Final
electron energy
gi
Instantaneous spectrum
Daniel Perley
19 September 2005
GRB Afterglow Spectra
34
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling e- Spectrum
Peak power radiated at each gi is the same
ge Initial electron energy gc Final
electron energy
gi
P(gi) const
Electron evolution
Instantaneous spectrum
exp
1/3

log Pg
log Pn
log gi
log n
ge
gc
npk(gi)
Daniel Perley
19 September 2005
GRB Afterglow Spectra
35
ne
2
ni
log npk
nm
gi
gm
ge
Electron distribution
Electron spectrum
36
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling e- Spectrum
Another convolution - need to transform ge to npk.
-1/2
log Pn
From before, npk a ge2
nc
ne
ge
a
Electron evolution
Power distribution Pg const
const
Solve Pn Pg(n) g-1
n-1/2
log Pg
log gi
gc
ge
Daniel Perley
19 September 2005
GRB Afterglow Spectra
37
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling e- Spectrum
-1/2
log Pn
nc
ne
Instantaneous spectrum
Electron evolution
Daniel Perley
19 September 2005
GRB Afterglow Spectra
38
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling e- Spectrum
-1/2
exp
1/3
log Pn
log Pn
nc
log n
ne
npk
Instantaneous spectrum
Electron evolution
1/3
-1/2
log Pn
Daniel Perley
19 September 2005
GRB Afterglow Spectra
39
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling e- Spectrum
-1/2
1/3
log Pn
log n
nc
ne
Broken power law n gt ne Exponential
cut-off (model as no emission) nc lt n lt ne
Instantaneous emission when electron
passed through appropriate g n lt nc
Post-cooling emission
Daniel Perley
19 September 2005
GRB Afterglow Spectra
40
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling e- Spectrum
-1/2
1/3
log Pn
log n
nm
ne
Higher initial energy simply extends the curve to
higher frequencies.
Daniel Perley
19 September 2005
GRB Afterglow Spectra
41
Cooled Synchrotron
Cooling e- Spectrum
So for nc lt n lt ne Pn n-1/2
'critical' e- t tcool
ge gc
tcool a 1 / ge gc a 1 / t
Daniel Perley
19 September 2005
GRB Afterglow Spectra
42
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling Regimes
Two possibilities for multi-electron spectra
gc lt gm
-p
log Ng
ALL electrons will cool on given timescale Fast
cooling
log ge
gm
gc
gc gt gm
-p
log Ng
SOME electrons will cool on given timescale
Slow cooling
log ge
gm
gc
43
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Fast Cooling
gc lt gm
-p
log Ng
ALL electrons will cool on given timescale Fast
cooling
log ge
gm
gc
44
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Fast Cooling
Sum for multi-e- using the new spectrum
-1/2
1/3
-(p-1)/2
log Nn
log Pn
log ne
nm
nc
nc
ne
Cooled synchrotron spectrum
Electron distribution
1/3
-1/2
Fractionof Nn gt n
n-1/2
log Pn
-p/2
-(p-2)/2 ??
log n
nc
nm
45
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Fast Cooling
1/3
-1/2
log Pn
-p/2
log n
nc
nm
Broken power law n gt nm Emission from
electrons with ge gt g(n) , during passage through
appropriate g nc lt n lt nm Emission from all
electrons, during passage through appropriate g
n lt nc Emission from all electrons at all
times
Daniel Perley
19 September 2005
GRB Afterglow Spectra
46
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Slow Cooling
gc gt gm
-p
log Ng
SOME electrons will cool on given timescale
Slow cooling
log ge
gm
gc
47
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Slow Cooling
Fast-cooling electrons have fast-cooling
spectrum, but with effective gm ? gc (no -1/2
segment)
-p
log Ng
log ge
gm
gc
1/3
log Pn
-p/2
nc
log n
48
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Slow Cooling
Non-cooling electrons have an uncooled-population
spectrum, but cut off at nc.
-p
log Ng
log ge
gm
gc
1/3
-(p-1)/2
log Pn
nm
nc
log n
49
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Slow Cooling
By their powers combined
-p
log Ng
log ge
gm
gc
1/3
-(p-1)/2
1/3
log Pn
-p/2
nm
nc
log n
50
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Slow Cooling
1/3
-(p-1)/2
log Pn
-p/2
log n
nm
nc
Broken power law n gt nc Emission from
cooling electrons with ge gt g(n) during
passage through appropriate g nm lt n lt nc
Emission from slow electrons with initial
(constant) energy g n lt nm Emission from
slow electrons with min. gm
Daniel Perley
19 September 2005
GRB Afterglow Spectra
51
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Cooling Comparison
1/3
-1/2
Fast cooling
log Pn
-p/2
log n
nc
nm
1/3
-(p-1)/2
Slow cooling
log Pn
-p/2
log n
nm
nc
Daniel Perley
19 September 2005
GRB Afterglow Spectra
52
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Cooled Synchrotron
Synchrotron Self-Absorption
Photon can be re-absorbed to excite an electron
in a magnetic field (inverse of synchrotron
emission.) Synchrotron emission/absorption will
be in equilibrium below a certain frequency na
below this point the shocked gas is optically
thick and will radiate as a blackbody (Pn a n2)
1/3
log Pn
2
log n
na
Daniel Perley
19 September 2005
GRB Afterglow Spectra
53
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Synchrotron Summary
Complete Comparison
1/3
-1/2
Fast cooling
log Pn
2
-p/2
nc
na
nm
log n
1/3
-(p-1)/2
Slow cooling
2
log Pn
-p/2
nm
nc
na
log n
Daniel Perley
19 September 2005
GRB Afterglow Spectra
54
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Theory vs. Observations
Observing
GRB970508 Galama et al. 1998 tburst 12.1
days
0.44
gt1.1
-0.6
-1.12
Daniel Perley
19 September 2005
GRB Afterglow Spectra
55
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Observable Parameters
Subject
An instantaneous spectrum gives several key
pieces of information na nc nm p
Fpk z
ee eB no E'
Daniel Perley
19 September 2005
GRB Afterglow Spectra
56
Background GRB Standard Model Relativistic
Shock Energy Deposition Proton Energy
Electron Energy Electron Distribution
Magnetic Energy Uncooled Synchrotron Emission
Mechanisms Relativistic Cyclotron Synchrotron
Beaming 1e- Spectrum Multi-e- Spectrum Cooled
Synchrotron Cooling Time 1e- Spectrum
Cooling Regimes Fast Cooling Slow Cooling
Cooling Comparison Self-Absorption Complete
Comparison Spectral Observation Observation vs.
Theory Observation Parameters Intervening ISM
Effects
Intervening ISM Effects
Subject
Cosmological redshift will not affect power-law -
all radiation scaled down by (1z)Will see
deviation from power-law in some frequency ranges
in some cases Galactic extinction (can be
calculated/removed) Host extinction (similar
to Galactic, but at higher frequencies,
and cannot be estimated independently of
GRB) Hydrogen absorption features (associated
with high-z)
Daniel Perley
19 September 2005
GRB Afterglow Spectra