grb afterglow spectra daniel perley astro 250 19 september* 2005 * international talk like a pirate...
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GRB Afterglow Spectra
Daniel Perley
Astro 250
19 September* 2005
* International Talk Like a Pirate Day
Background
Daniel Perley 19 September 2005GRB Afterglow Spectra
The GRB Standard Model
ISM
Shocked Gas
Earth
SH
OC
KS
HO
CK
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
Background
Daniel Perley 19 September 2005GRB Afterglow Spectra
Relativistic Shock
SH
OC
KS
HO
CK
ISM
Γ
number density
no
energy density
Eo = no mp c2
energy per particle
Eo/no = mp c2
From Brian’s lecture…
n′ = 4 no
E′ = 4 2no mp
c2
E′/n′ = mp c2
= Γ √2
>Compression< by 4
Energy Increase by factor
Deceleration by factor √ 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Energy Deposition
Where does the energy go?
energy per particle
Eo/no = mp c2E′/n′ = mp c2 Energy Increase
by factor
• Protons
• Electrons
• Magnetic field
• Other particles?
Ep = εp E′
Ee = εe E′
B = εB E′
Energy DepositionBackground 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Proton/Electron Energy
SH
OC
KS
HO
CK
ISMShocked Gas
Γ
e
Extreme (relativistic) ‘temperature’ of shocked gas described by p, e
Bulk motion of shocked gas relative to observer
Particle energy deposited in random motions.
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Proton Energy
Not particularly interesting on its own.
Protons necessarily drag electrons with them at the same bulk velocity.
Share energy with electrons: electron factors necessarily much higher.
Energy DepositionBackground 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Electron Energy
Faster-moving electrons will radiate more efficiently by all important processes.
e
Energy DepositionBackground 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Electron Energy Distribution
Q: How is electron energy distributed?
A:
…
…
…
?
Hypothesis: Power-law? (Seen in SNe, NR shocks)
Energy DepositionBackground 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Log
N
Log
N α -p
N α [Complicated]
Model as power-law:
Energy Deposition Electron Energy DistributionBackground 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Electron Energy Distribution
Simplify: cut-off power law at minimum energy
Log
N
Log
N α -
p
N α [Complicated]
m
Minimum energy
Energy DepositionBackground 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Electron Energy Distribution
Mimimum energy determined by total energy density:
n = ∫ Ne de Ee = me c2 ∫ e Ne
de
= C m1-p = me c2 C m
2-p
Infinite if p<2
N
e
e-p
m
n
eN
e
m
e1-p
E
11-p
C = (1-p) mp-1 n
12-p
= me c2 m n1-p2-p
m p-2p-1
Ee
n me c2
p-2p-1
mp
me εe ≈ 610 εe
Energy DepositionBackground 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Magnetic Energy
Strong post-shock magnetic field expected from equipartition.
Generation mechanism unknown/complicated – various plasma effects
B2
8π= εB E′
= εB 4 2no mp c2
= 32π εB 2no mp
c2
B2
B = 32π εB no mp c
≈ (0.4 gauss) εB1/2 ( )1/2
no
cm-3
B
Energy DepositionBackground 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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Emission Mechanisms
How does it cool?
Bremsstrahlung
P α e3/2 n2
Inverse Compton
P = σTcβ2e2Uph
SynchrotronP = σTcβ2e
2UB
Uncooled Synchrotron
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
43
43
Daniel Perley 19 September 2005GRB Afterglow Spectra
Relativistic Cyclotron
Relativistic modification to cyclotron frequency:
ωcyc = e B
m c
Most emission is not at this frequency.
Uncooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Synchrotron Beaming
Emission is highly pulsed – we see emission for only 1/2 of total emission time.
ωcyc = e B
m c
E
t
1/ωcyc
1/2ωcyc
- One factor of from beaming angle
- Additional factor of from "Doppler" boost 1/
1/
Uncooled Synchrotron
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
1e- Synchrotron Spectrum
E
t
1/ωcyc
1/2ωcyc
= E
t
δ(t-n/ωcyc)
=
Uncooled Synchrotron
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
1e- Synchrotron Spectrum
E
t
= E
t
δ(ω-nωcyc)^
^
Fourier transformed:
ωcyc
2ωcyc
2ωcyc
2ωcyc
2ωcyc
Uncooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
1e- Synchrotron Spectrum
log
P
1/3 e-/ωcyc 1/2
pk log
More precisely…
Shocked frame:
α e2
α e2
α const
Total Power: P = σTcβ2e2UB
Peak Freq.: pk ≈ e2ωcyc / 2π
Peak Power: Ppk ≈ P / pk
43
Uncooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
1e- Synchrotron Spectrum
log
P
log
1/3 e-/ωcyc 1/2
pk pk
Shocked frame:
α e2
α e2
α const
Total Power: P = σTcβ2e2UB
Peak Freq.: pk ≈ e2ωcyc / 2π
Peak Power: Ppk ≈ P / pk
43
Uncooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
1e- Synchrotron Spectrum
log
P
log
1/3 e-/ωcyc 1/2
pk pk
Total Power: P = σTcβ2e22UB
Peak Freq.: pk ≈ e2ωcyc / 2π
Peak Power: Ppk ≈ P / pk
Observer frame:
α e22
α e2
α
43
Uncooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Uncooled Multi-e- Spectrum
log
P
log
1/3
pk
exp
Material contains many electrons at different velocities (e) – true spectrum is a combination of individual spectra, according to electron energy distribution.
log
N
log e
-p
m
Electron distributionElectron spectrum
Uncooled Sychrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Uncooled Multi-e- Spectrum
Can just do a weighted sum (convolution) – but need to convert x-axis from e to pk.
log
N
log e
-p
m
Electron distribution
From before,
pk α e2
log
N
log pkm
e- distribution:
Nα e-p
Solve:
N = N
α e-p e
-1
α -(p+1)/2
dd
dd α e
-(p-1)/2
Sign error??
Uncooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Uncooled Multi-e- Spectrum
Electron distribution
log
N
log pkm
-(p-1)/2
log
P
log
1/3
pk
exp
Electron spectrum
Total Spectrum
Uncooled Synchrotron
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 Multi-e- Spectrum
log
N
log pkm
-(p-1)/2
log
P
log
1/3
pk
exp
log
P
1/3
Daniel Perley 19 September 2005GRB Afterglow Spectra
-(p-1)/2
m
Uncooled Synchrotron
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 Multi-e- Spectrum
Daniel Perley 19 September 2005GRB Afterglow Spectra
"Broken" Power law:
• Below m, emission dominated by low- e-
• Above m, emission from electrons with peak() = m
log
P
1/3 -(p-1)/2
m log pk
Uncooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
This analysis is too simplistic for GRBs.
Calculate characteristic cooling time:
log
P
1/3 -(p-1)/2
m
tcool = E / P = mec / σTcβ22UB
≈ 4 × 10-3 s ( )-2 -1
43
Bgauss
Potentially much shorter than time since GRB (shock passage)
log pk
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Cooling e- Spectrum
If an electron's energy changes significantly over the time since the energy injection, use an "averaged" spectrum for that electron.
e = Initial electron energy (at injection)
c ≡ Final electron energy (after cooling) ≈ Energy of the highest-e- that hasn't cooled
Determined by observational timescale: tobs = cmec / σTcβ2c
2UB
c =
43
6π mecσTB2tobs
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Cooling e- Spectrum
Electron radiates as it cools, with a simple synchrotron spectrum corresponding to the instantaneous energy i .
e = Initial electron energy
c ≡ Final electron energy
log
P
log
1/3
pk
exp
Instantaneous spectrum
i
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Cooling e- Spectrum
Peak power radiated at each i is the same:
log
P
log
1/3
pk(i)
exp
Instantaneous spectrum
e = Initial electron energy
c ≡ Final electron energy
i P(i) = const
log
P
ec
Electron evolution
log i
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Cooling e- Spectrum
From before,
pk α e2
Power distribution:
P= const
Solve:
P = P
= -1
= -1/2
dd
dd α e
log
P
ec
Another convolution - need to transform e to pk.
log
P
c
Electron evolution
const
-1/2
e log i
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Cooling e- Spectrum
log
P
ec
log
P
log
1/3
pk
exp
Instantaneous spectrum Electron evolution
-1/2
Cooled Synchrotron
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
Cooling e- Spectrum
log
P
ec
log
P
log
1/3
pk
exp
Instantaneous spectrum Electron evolution
log
P
1/3 -1/2
Daniel Perley 19 September 2005GRB Afterglow Spectra
-1/2
Cooled Synchrotron
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
Cooling e- Spectrum
Daniel Perley 19 September 2005GRB Afterglow Spectra
log
P
1/3-1/2
c e
Broken power law:
• > e : Exponential cut-off (model as no emission)
• c < < e : Instantaneous emission when electron passed through appropriate
• < c : Post-cooling emission
log
Cooled Synchrotron
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
Cooling e- Spectrum
Daniel Perley 19 September 2005GRB Afterglow Spectra
log
P
1/3-1/2
m e
Higher initial energy simply extends the curve to higher frequencies.
log
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Cooling Regimes
Two possibilities for multi-electron spectra:
log
N
log e
-p
m
log
N
log e
-p
m
c < m
c
c
c > m
ALL electrons will cool on given timescale :Fast cooling
SOME electrons will cool on given timescale :Slow cooling
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Fast Cooling
log
N
log e
-p
m
c < m
c
ALL electrons will cool on given timescale :Fast cooling
Cooled Synchrotron
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
Fast Cooling
log
N
log e
-(p-1)/2
mc
log
P
1/3-1/2
Cooled synchrotron spectrum Electron distribution
Sum for multi-e- using the new spectrum:
-p/2
c e
Fractionof N >
log
P
1/3 -1/2
log
Daniel Perley 19 September 2005GRB Afterglow Spectra
c m
-1/2
-(p-2)/2 ??
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Fast Cooling
log
P
1/3 -1/2
c m
-p/2
Broken power law:
• > m : Emission from electrons with e > , during passage through appropriate
• c < < m : Emission from all electrons, during passage through appropriate
• < c : Emission from all electrons at all times
log
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Slow Cooling
log
N
log e
-p
m c
c > m
SOME electrons will cool on given timescale :Slow cooling
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Slow Cooling
Fast-cooling electrons have fast-cooling spectrum, but with effective m → c (no -1/2 segment)
log
N
log e
-p
m c
-p/2
1/3
c
log
P
log
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Slow Cooling
Non-cooling electrons have an uncooled-population spectrum, but cut off at c.
log
N
log e
-p
m c1/3
-(p-1)/2
m c log
log
P
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Slow Cooling
By their powers combined…
log
N
log e
-p
m c1/3
m c
-(p-1)/2
-p/2
1/3
1/3-(p-1)/2
-p/2 log
P
log
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Slow Cooling
log
P
1/3 -(p-1)/2
m c
-p/2
Broken power law:
• > c : Emission from cooling electrons with e > during passage through appropriate
• m < < c : Emission from slow electrons with initial (constant) energy
• < m : Emission from slow electrons with min. m
log
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Cooling Comparison
log
P
1/3 -(p-1)/2
m c
-p/2
log
P
1/3 -1/2
c m
-p/2
Fast cooling
Slow cooling
log
log
Cooled Synchrotron
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
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 a: below this point the shocked gas is optically thick and will radiate as a blackbody (P α 2)
1/3
log
P
log
2
a
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
Daniel Perley 19 September 2005GRB Afterglow Spectra
Complete Comparison
log
P
1/3 -(p-1)/2
m c
-p/2
log
P
1/3 -1/2
c m
-p/2
Fast cooling
Slow cooling
2
2
log
log
a
a
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
Observing
Daniel Perley 19 September 2005GRB Afterglow Spectra
Theory vs. Observations
GRB970508 – Galama et al. 1998 tburst = 12.1 days
-0.6
0.44>1.1
-1.12
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
Subject
Daniel Perley 19 September 2005GRB Afterglow Spectra
Observable Parameters
An instantaneous spectrum gives several key pieces of information:
a
c
m
p Fpk
z
εe εB no
E'
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 2005GRB Afterglow Spectra
Intervening ISM Effects
Cosmological redshift will not affect power-law - all radiation scaled down by (1+z)
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)
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