Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
High Energy Radiation Processes
Dmitry Khangulyan
Institute of Space and Astronautical Science, Tokyo, Japan
Dublin Summer School on High Energy Astrophysics
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Outline
Introduction
Particle distribution
Efficiency of the radiation processes
Klein-Nishina Regime
Example
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
What this talk is about
Malcolm’s Talk: Radiation Processes in High Energy
Astrophysics
A Physical Approach with Applications
Bremsstralung, Synchrotron, inverse Compton (Thomson limit)
This talk: High Energy Radiation Processes
One Zone Modelling
Synchrotron, inverse Compton (Klein-Nishina limit)
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
The talk is biased towards
made with http://www.wordle.net/
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Particle Distribution
Microscopical Description
dN(qi , pi , t) = f (qi , pi , t)dqi dpi
f is the distribution function
qi and pi are some coordinates in the phase space
f = e.g.
dN
dV
or
dN
d3 xd3 p
One Zone Modeling typically implies
f =
dN
dE
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Particle Distribution
Microscopical Description
Boltzmann Equation
∂f
∂f
∂f
∂f
+v +F
=
∂t
∂r
∂p
∂t col
Collision integral ∂f
∂t col accounts for many processes: particle
injection, acceleration, scattering, energy losses, etc
In the case of injection/cooling problems, the problem may be
significantly simplified under the continue loss approximation
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Significant simplification in the case of
energy losses
Cont. Loss Approx.
Z∞
F (E, t) =
f (E 0 , t)dE 0
E
F (E + Ėdt, t + dt) =
Z∞
F (E, t)+dt
q(E 0 , t)dE 0
E
Fokker-Planck Equation
Distribution function & Injection
dN = f (E, t)dE
dN = q(E, t)dEdt
∂f
∂(Ėf )
+
= q(E, t)
∂t
∂E
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Significant simplification in the case of
energy losses
Z∞
F (E + Ėdt, t + dt) = F (E, t) + dt
q(E 0 , t)dE 0
E
∂F
∂F
dt = F (E, t) + dt
F (E, t) +
Ėdt +
∂E
∂t
Z∞
q(E 0 , t)dE 0
E
accounting for
∂F
∂E
= −f
∂
=⇒
∂E
R∞
∂
∂E
q(E 0 , t)dE 0 = −q
E
∂f
∂(Ėf )
+
= q(E, t)
∂t
∂E
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Particle Energy Distribution
Fokker-Planck Equation Solution
f (E, t) =
1
Ė
ZEeff
dE 0 q(E 0 ),
ZEeff
where t =
E
E
dE 0
Ė 0
Ė = Ėsyn + Ėic + Ėad + etc/Ėsyn + Ėpp + Ėpγ + etc
Fast Cooling (Saturation)
Eeff → ∞
f (E) =
1
Ė
Slow Cooling
t E/Ė
Z∞
dE 0 q(E 0 )
f (E, t) = q(E) · t
E
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Some Remarks
Used simplifications
Acceleration and Losses are treated independently
High energy cut-off depends on loss rate
Some acceleration processes cannot be treated in this way, e.g.
converter mechanism by Derishev
Particles lose energy by small fractions, which is not true for
some processes, e.g. IC in the Klein-Nishina regime
Transport Equation with Diffusion and Escape
∂f
∂(Ėf )
f
+
+ ∇ (D∇f ) + = q(E, t)
∂t
∂E
τ
also can be solved analytically, see e.g. Ginzburg’s
"Astrophysics of Cosmic Rays"
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Some Remarks
Klein-Nishina and Continues Loss approximation
Particles lose energy by small
fractions, which is not true for
some processes, e.g. IC in
the Klein-Nishina regime
Solid line: cσic f (γ) = q(γ) + c
R∞
γ
Dash-dotted line: f (γ) =
1
Ėic
R∞
dσ
dγ 0 f (γ 0 ) dE
(γ 0 , γ 0 − γ)
γ
dγ 0 q(γ 0 )
γ
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Some Remarks
High Acceleration Cut-Off
Acceleration Time
Cooling Time
tacc = 0.1ηETeV BG−1 s (where η > 1)
tcool = E/Ė
tacc < tcool
Dominant Synchrotron Losses
−1/2 −1/2
γ < 108 BG
η
~ω < 100η −1 MeV
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
An Extreme Accelerator?
Crab Nebula
Broad Band Spectrum
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
νFν peak gives the luminosity
νFν peaking distribution
νFν = Eγ2
dNγ
dEγ
Z
Lγ =
ZE0
Emin
dEγ Eγ
dEγ Eγ1−α
dNγ
=
dEγ
E
Zmax
dEγ Eγ1−β
+
E0
Emin E0 Emax
1
1
+
Lγ = L0
2−α β−2
For α = 1.5 and β = 2.5
Lγ = 4L0
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
νFν peak gives order of magnitude estimate
of the luminosity
Fermi/LAT observations of
PSR B1259-63
Detailed information about the
pulsar spin-down luminosity
provides very precise information
about the available energetics
LSD = 8.3 × 1035 erg s−1
LLAT = 8 × 10
35
D
2.3kpc
2
erg s−1
Even in this case, there are
unavoidable uncertainties related
to the distance to the source...
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Radiation Production
Single particle spectra:
Emission of a Particle (two
channels)
dNi
= Ki (Eγ , E0 )
dEγ
Total luminosity:
L = Ė1 + Ė2
Luminosity per channel:
Li =
Ėi
Ė1 + Ė2
L
Ratio of the humps:
Ė1
L1
=
L2
Ė2
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Comparison of Radiation Mechanisms
Radiation Efficiency
Escape Time: tesc = min(tdiff , tad )
tdiff =
R2
2
∼ 2 · 104 ζ −1 R12
B1 E1−1 s,
2D
tad =
Energy Transfer: µ =
ζ=
D
DBohm
R
−1
∼ 102 R12 V10
s
Vbulk
Eγ
E0
Radiation Efficiency: κ = µ min(1, tesc /tint )
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Radiation Mechanism in BS
Inverse Compton Scattering
Cooling Time:
tic = 40
L
38
10 erg/s
−1 2 R
1012 cm
T
3 · 104 K
1.7
0.7
ETeV
s
Energy Transfer:
(
Eγ =
Ee ,
Ee2
,
m2 c 4
E m2 c 4
E m2 c 4
Radiation Efficiency
κ∼1
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Radiation Mechanism in BS
Proton-proton interaction
Cooling Time:
tpp = 106
−1
np
s
109 cm−3
Energy Transfer:
Eγ ∼ 0.1 Ep
Radiation Efficiency
κ = 10−3
np
tesc
104 s 109 cm−3
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Radiation Mechanism in BS
Photo-meson production
Cooling Time:
tpγ = 3 · 104
L
1038 erg/s
−1 R
2 1012 cm
T
3 · 104 K
s
Energy Transfer:
Eγ ∼ 0.1 Ep
Radiation Efficiency
tesc
L
κ = 0.03 4
10 s 1038 erg/s
R
1012 cm
−2 T
3 · 104 K
−1
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Radiation Mechanism in BS
Photo-disintegration (see Bosch-Ramon&Khangulyan,
2009)
Cooling Time:
tpd ∼ 3 · 103
L
1038 erg/s
−1 T
3 · 104 K
2
R
1012 cm
s
Energy Transfer:
Eγ ∼ 0.01 EN
Radiation Efficiency
tesc
L
κ = 0.03 4
10 s 1038 erg/s
R
1012 cm
−2 T
3 · 104 K
−1
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
The most Favorable Emission Process in BS
Radiation Processes
Proc.
IC
pp
Eγ /E0
1
0.1
κ
1
n
p
tesc
10−3 10
4
9
−3
“ s 10 cm
”−2 “
pγ
0.1
tesc
L
0.03 10
4 s 1038 erg/s
Photo-des.
0.01
tesc
L
0.03 10
4 s 1038 erg/s
R
1012 cm
“
R
1012 cm
”−2 “
T
3·104 K
T
3·104 K
”−1
”−1
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Proton Synchrotron
Electrons
−1 −2
Cooling: tcool = 400ETeV
BG s
Photon Energy:
2
~ω = 20ETeV
BG keV
Highest Energy Cooling:
−3/2
tcool = 6η 1/2 BG
s
Highest Energy Photons:
~ω = 100η −1 MeV
Protons
Cooling:
−1 −2
tcool = 400ETeV
BG
mp
me
4
s
Photon Energy:~ω =
3
me
2
20ETeV
BG m
keV
p
Highest Energy Cooling:
2
−3/2 mp
tcool = 6η 1/2 BG
s
me
Highest Energy
Photons:
m
~ω = 100η −1 mpe MeV
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Synchrotron-IC Model
Very similar processes
Energy Losses
4
ĖIC = − Uph cγ 2
3
Mean Energy
4
~ω =
~ω0 γ 2
3
Lsyn
UB
=
Lic
Uph
4
Ėsyn = − UB cγ 2
3
~ω =
eB~
2πme c
~ωsyn
=
~ωic
γ2
eB~
2πme c
4
3 ~ω0
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Synchrotron-IC Model
Ratio of the peaks
Two identical humps?
Lsyn
UB
=
Lic
Uph
Ratio of the energies
eB~
~ωsyn
2πme c
= 4
~ωic
3 ~ω0
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Kein-Nishina Cut-off
Photon Energy < Electron Energy
4
~ω =
~ω0 γ 2 < γme c 2
3
!
me c 2
γ< 4
3 ~ω0
−1
γ < 5 × 105 ω0,
eV
~ω =
eB~
2πme c
γ<
γ 2 < γme c 2
2πme2 c 3
eB~
γ < 3 × 1014 BG−1
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Some Remarks
High Acceleration Cut-Off
Acceleration Time
Cooling Time
tacc = 0.1ηETeV BG−1 s (where η > 1)
tcool = E/Ė
tacc < tcool
Dominant Synchrotron Losses
−1/2 −1/2
γ < 108 BG
η
~ω < 100η −1 MeV
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Kein-Nishina Cut-off
Photon Energy < Electron Energy
4
~ω =
~ω0 γ 2 < γme c 2
3
!
me c 2
γ< 4
3 ~ω0
−1
γ < 5 × 105 ω0,
eV
~ω =
eB~
2πme c
γ<
γ 2 < γme c 2
2πme2 c 3
eB~
γ < 3 × 1014 BG−1
BG > 1012 η
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Leptonic Radiation Mechanisms
Typical SED
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Synchrotron Radiation
Electrons can interact with B-field
Energy Losses: Ėsyn = − 34 UB cγ 2
eB~
γ2
Mean Energy: ~ω = 2πm
c
e
Single Particle Spectrum:
√ 3
dIsyn
ω
3e B
=
F
2
dω
2π mc
ωc
where ωc =
3eBγ 2
2mc
Useful approximation:
Z∞
F (x) = x
x
K5/3 (x 0 )dx 0 = 1.76 x 0.29 e−x
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Synchrotron Radiation
Approximation for the peak
x 1
F (x) =
π 1/2
2
x 1/2 e−x
x 1
F (x) = √
4π
x 1/3
3Γ(1/3)
Useful approximation (but not an asymptotic):
Z∞
F (x) = x
K5/3 (x 0 )dx 0 = 1.76 x 0.29 e−x
x
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Inverse Compton Radiation
Electrons can interact with photon field
Maximum Energy of Gamma Rays Eγ <
“
γ 1−
1
4γ 2
1
1+ 4γ
”
Single Particle Spectrum:
dσγ
πr 2 2 Eγ
Eγ
ln
= 3 e
+ 4γ 2 − 4γEγ − Eγ
dEγ
γ (γ − Eγ )
γ(γ − Eγ )
2γ 2 − 2γEγ + Eγ2 + Eγ
4Eγ γ(γ − Eγ )
#
Energy Losses for a Planckian photon field:
ln(1 + 0.55γTmcc )
1.4γTmcc
17 3
γ̇IC = 5.5×10 Tmcc γ
s−1 ,
1+
2
1 + 25Tmcc γ
1 + 12γ 2 Tmcc
where Tmcc = kT /me c 2
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Klein-Nishina Effect
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Klein-Nishina Effect
dNe
1
=
dE
Ė
Z∞
dE 0 Q(E)
Ė = Ėsyn + Ėic
E
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Klein-Nishina Effect
X-ray:
hardening
γ-rays: no
Klein-Nishina
cutoff
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Klein-Nishina Effect
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Compton Scattering Spectrum
dNγ
=
dEγ
Z
dEe c(1 − cos θ)nph
dNe dσ
dEe dEγ
Aharonian&Atoyan, 1981
High Energy Radiation Processes
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Introduction
Particle Distribution
dNγ
=
dEγ
Radiation Efficiency
Z
dEe c(1 − cos θ)nph
Klein-Nishina
Example
dNe dσ
dEe dEγ
Anisotropic inverse Compton
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Klein-Nishina Effect
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Klein-Nishina + Anisotropic IC
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Gamma-Gamma Absorption
The KN regime implies importance
of γ-γ absorption
γ > 1
Does KN imply strong attenuation?
Does strong attenuation implies
EMC?
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
LS 5039
Binary Pulsar
Microquasar
From Aharonian et al., 2006
A general study of γ- and X-rays
production in the leptonic scenario
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
X-ray and TeV emission from LS5039
Variable/Periodic
Apparent similarities in
lightcurves
Hard distributions of
parent particles
Takahashi et al., 2009
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
X-ray and TeV emission from LS5039
TeV (Aharonian et al., 2006)
X-ray (Takahashi et al., 2009)
Variable
Variable
Periodic
Seems to be periodic
Strong variability in flux level
Significant variability in flux
level
Significant variability in
photon index
SUPC: lower fluxes and
steeper spectra
INFC: higher fluxes and
harder spectra
Very hard spectra at INFC
Minor variability in photon
index
SUPC: lower fluxes and
steeper spectra
INFC: higher fluxes and
harder spectra
Hard spectra
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Time-scales and Energy Bands (II)
Takahashi et al., 2009
High Energy Radiation Processes
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Introduction
Particle Distribution
Radiation Efficiency
Klein-Nishina
Example
Modeling (results)
Adiabatic cooling rate from
X-ray data
Good agreement with HESS
fluxes
Acceptable agreement with
HESS spectral indexes
Testable prediction for Fermi
High Energy Radiation Processes
Takahashi et al, 2009
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