radiative processes in high energy astrophysical...
TRANSCRIPT
Radiative processes inhigh energy
astrophysical plasmasÉcole de physique des Houches
23 Février-8 Mars 2013
R. Belmont
Why radiation?
✓Why is radiation so important to understand?✓ Light is a tracer of the emitting media
✓ Geometry, evolution, energy, magnetic field...
✓ Light can influence the source properties✓ cooling/heating, radiation pressure...
✓ Light can be modified after its emission
✓Why are high energy plasmas so important to study?✓ High energy particles are the most efficient emitters✓ They emit over an extremely wide range of frequencies
2
Outline
✓Goals of this course: ✓ Review the main high energy processes for continuum emission
✓ Assumptions, approximations, properties
✓ Show how they can be used to constrain the physics of astrophysical sources
✓Main books/reviews: ✓ Rybicki G.B. & Lightman A.P., 1979, Radiative processes in astrophysics,
New York, Wiley-Interscience✓ Jauch J.M. & Rohrlich F., 1980, The theory of photons and electrons (2nd
edition), Berlin, Springer✓ Aharonian F. A., 2004, Very High energy cosmic gamma radiation, World
scientific publishing✓ Heitler W., 1954, Quantum theory of radiation, International Series of
Monographs on Physics, Oxford: Clarendon✓ Blumenthal G.R. & Gould R.J., 1970, Reviews of Modern Physics
3
Contents
✓ Introduction
✓ I. Emission of charged particles
✓ II. Cyclo-Synchrotron radiation
✓ III. Compton scattering
✓ IV. Bremsstrahlung radiation
4
Introduction
5
Introduction ●○
Non black-body radiation
✓Black-Body radiation is simple ideal limit✓ independent of internal processes, geometry...✓ Simple law
✓No black body radiation if:✓ Optically thin media
✓ <= finite source size and finite interaction cross sections✓ => absorption/emission/reflection features
✓Matter not at thermal equilibrium✓ <= low density, high energy plasmas
✓Then, radiation properties depend on✓ The particle distributions ✓ The microphysics: what processes?
6
Introduction ●●
Radiation processes
✓Lines (bound-bound):✓ Atomic, molecular transitions (radio to X-rays)✓ Nuclear transitions (γ-rays)
✓Edges (bound-free):✓ ionization/recombination
✓Nuclear reactions, decay and annihilations:✓ bosons, pions... ✓ electron-positron, photon-photon
✓Collective processes✓ Faraday rotation, Cherenkov radiation...
✓Free-free radiation of charged particles in vacuum:✓ Cyclo-synchrotron radiation✓ Compton scattering✓ (Bremsstrahlung radiation)
7
I. Radiation of relativistic particles
8
Emission of relativistic particles ●○○○
Emission from non-relativistic particles✓Electro-magnetic field created by charges in motion:
✓ Charged particles in uniform motion do not emit light✓ Only charged, accelerated particles can emit light
✓ Liénard-Wiechert potentials (1898): (A,Φ) => E-B✓ Power:✓ Spectrum:
✓Emission of low-energy particles:
✓ Total power:
✓ Dipolar field perpendicular to acceleration:
✓ Polarization depends on the direction:✓ Is also the emission in the particle rest frame...
@Pe
@⌦=
q2a2
4⇡csin2 ✓
Pe =2q2a2
3c
9
~E / ~n⇥ (~n⇥ ~a)
P / ~E2
P⌫ /���FFT( ~E)
���2
a
θ
Emission of relativistic particles ●●○○
Change of frame✓Relativistic particles:
✓ Velocity✓ Lorentz factor✓ Energy✓Momentum
✓Let’s consider a particle✓ moving at velocity β as seen in the observer frame K in the parallel direction✓ emitting radiation in its rest frame K’
✓Total emitted power: ✓ Is a Lorentz invariant:✓ Acceleration is not:✓ Emission of relativistic particles strongly enhanced: ✓ High energy sources are amongst the most luminous sources...
a0k = �3aka0? = �2a?
10
� = v/c� = 1/(1� �2)1/2
E = �mc2 Ek = (� � 1)mc2
p = (�2 � 1)1/2 = ��
Pe = P 0e =
2q2a02
3c
Pe =2q2
3c�4
⇣�2a2k + a2?
⌘
Emission of relativistic particles ●●●○
Relativistic beaming✓Angles: an example
✓ Emitting body moving at velocity v✓ Photon emitted perpendicular to motion in the
body frame✓ Photon
✓ must fly at c in all frames✓ observed with parallel velocity v✓ observed with perpendicular velocity c/γ✓ observed with an angle
✓Angular distribution of emission:
✓ beaming✓ enhancement
11
c
body frame
(c2�
v2)1
/2=
c/�
✓
c
vobserver frame
sin ✓ = 1/�
@Pr
@⌦=
1
�4(1� � cos ✓)4
@P 0e
@⌦0
Emission of relativistic particles ●●●●
Relativistic beaming
✓The dipolar emission of charge particles:✓ The angular distribution depends on the
(a,v) angle
✓ Beaming is still present and
a v
av
a
v=0
12
✓ ⇡ 1/�
para
llel a
ccel
erat
ion
perpendicular acceleration
Cyclo-Synchrotron radiation
- Emitted power- Spectrum- Radiation from many particles- Polarization- Self-absorption
13
Cyclo-synchrotron radiation ●○○○○○○○○○○○○○○
Synchrotron in astrophysics
✓Applications to astrophysical sources started in the mid 20th
✓Most observations in radio but also at all wavelengths
14Galactic center
SNR
Radio galaxies
jupiter
PWN
⌫B =qB
2⇡mc
Cyclo-synchrotron radiation ●●○○○○○○○○○○○○○
Cyclo-synchrotron radiation
hν
✓Radiation from particles gyrating the magnetic field lines
✓Relativistic gyrofrequency
✓Assumptions:✓ Classical limit:
✓ Otherwise: quantization of energies, Larmor radii...✓ Observable cyclotron scattering features in accreting neutron stars...
✓ B uniform at the Larmor scale (parallel and perp)✓ ! no strong B curvature (pulsars and rapidly rotating neutron stars)✓ ! no small scale turbulence (at the Larmor scale)✓ ! no large losses (tcool >> 1/νB,r)
✓Emission/Absorption15
⌫B,r =1
�
qB
2⇡mc
h⌫B << mc2 B < Bc = 12⇥ 1012 G
Cyclo-synchrotron radiation ●●●○○○○○○○○○○○○
Emitted Power and cooling time
✓Circular motion:
✓Emission of an accelerated particle: ✓ Power goes as p2
✓ Power goes as B2
✓ Isotropic distribution of pitch angles:
✓Cooling time:
✓ ISM (B=1µG): tcool>tuniverse as far as γ<103
✓ AGN jets (B=10µG, γ=104): tcool = 107yr (=travel time!)
✓Maximal loss limit
16
a = a? =⌫B2⇡�
v?
P =2q2
3c3�4a2? = 2c�TUBp
2?
P =4
3c�TUBp
2
tcool
=�mc2
Pe⇡ 25yr
B2�
�2B <2q
r20 VLA, 6cmCentaurus A
30 000 lyr
tcool
>> 1/⌫B,r
Cyclo-synchrotron radiation ●●●●○○○○○○○○○○○
Emission Spectrum
✓ Sinus modulation of the electric field at νB:
✓ Spectrum = one cyclotron line at νB= νB,r
a
obser
ver
Very low energy particles:
17
Cyclo-synchrotron radiation ●●●●●○○○○○○○○○○
✓ Moderate beaming
✓ Asymmetrical modulation of the electric field at νB,r:
✓ Spectrum = many harmonic lines at kνB,r=kνB/γ
Emission Spectrum
obser
ver
Mid-relativistic particles:
18
�t ⇡ 1/(⌫B,r�3)
⌫c =3
2�2⌫B sin↵
Cyclo-synchrotron radiation ●●●●●●○○○○○○○○○
✓ Strong beaming: δθ=1/γ
✓ Pulsed modulation of the electric field at νB:
✓ Spectrum = continuum up to
Emission Spectrum
obser
ver
Ultra-relativistic particles:
19
γ γ2γ γ2
@
2P
@(⌫/⌫B)@⌦= 4�T cUB�
2?⌫
2
⌫
2B
1X
n=1
n
2 (cos ✓ � �k)2
(1� �k cos ✓)2J
2n(x)
x
2+ J
02n (x)
��
⌫
⌫B(1� �k cos ✓)�
n
�
�
Cyclo-synchrotron radiation ●●●●●●●○○○○○○○○
Emission Spectrum
✓Exact spectrum depends on:✓ the particle energy✓ the pitch angle α:✓ the observation angle θ
with respect to B
✓Line broadening results from integration over:✓ Observation direction✓ Particle pitch angle✓ Particle energy
cos↵ = �k/�
x = (⌫/⌫B)�? sin ✓
20
Cyclo-synchrotron radiation ●●●●●●●●○○○○○○○
✓High energy plasmas have a continuous spectrum:
✓Peaks at the critical frequency:
✓Most of the emission is at νc* ✓ AGN (B=10µG, γ=104): 10cm
✓ Crab nebula (B=0.1mG, γ=107): 10 keV
✓Highest possible energy of photons:
Spectrum of Relativistic Particles@P
@(⌫/⌫B)= 12
p3�T cUBG
✓⌫
2⌫⇤c
◆
G(x) = x
2
K4/3(x)K1/3(x)�
3x
5
⇣K
24/3(x)�K
21/3(x)
⌘�
⌫⇤c =3
2⌫B�
2 / B�2
h⌫ = 3mec2/↵f ⇡ 70MeV
21
�2B <2q
r20
Cyclo-synchrotron radiation ●●●●●●●●●○○○○○○
Spectrum of many particles
✓Emission integrated over the particle distribution:
✓Thermal distribution:✓ Same as for a single particle for the mean energy..
✓Power-law distribution:✓ Integrated emission:
✓ Power-law spectrum with ✓ slope:✓ minimal energy:✓ maximal energy:
22
j⌫ =
ZP⌫(⌫, �)f(�)d�
f(�) / �2e��/✓
f(�) / ��s
↵ =s� 1
2
j⌫ /RG(3⌫/2⌫B�2)��s
d�
/ ⌫
�(s�1)/2Rx
(s�3)/2G(x)dx
/ ⌫
�↵
G(x)
j(ν)
⌫min / B�2min
⌫max
/ B�2
max
Cyclo-synchrotron radiation ●●●●●●●●●●○○○○○
The Crab Nebula
✓Pulsar wind nebula✓ Outflow of high energy electrons✓Magnetized medium (0.1 mG)
✓Synchrotron emission from radio to γ-rays
✓Broken power-law distribution✓ Two slopes: s1, s2
✓ Two breaks: γ1, γ223
γ1
γ2
s1
s2
Cyclo-synchrotron radiation ●●●●●●●●●●●○○○○
Polarization
✓One single particle produces a coherent EM fluctuation✓ Intrinsically polarized: elliptically✓ Depends on p, α and θ
✓Turbulent magnetic field: no net polarization
✓Ordered magnetic field:✓ Ensemble of particles with random pitch angles => partially linearly
polarized✓ Polarization angle perpendicular to observed B:✓ High polarization degree:
✓ depends on frequency and particle energy✓ averaged over all frequencies: Π=75% !✓ In average over PL distribution of particles: Π=(s+1)/(s+7/3)
⇧(⌫, p) =P? � Pk
P? + Pk
P? >> Pk
24
Cyclo-synchrotron radiation ●●●●●●●●●●●●○○○
Polarization
✓Such high polarization is characteristic of synchrotron radiation
✓Measure of the direction gives the direction of B
M87 - OPTICAL POLARIZATION
ARC
SEC
ARC SEC-10 -11 -12 -13 -14 -15
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
M87 - RADIO POLARIZATION
ARC
SEC
ARC SEC-10 -11 -12 -13 -14 -15
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
Figure 5
I A
B1
B2
LOP-1
HOP-3HOP-2
HOP-1
M87 - OPTICAL POLARIZATION
ARC
SEC
ARC SEC-10 -11 -12 -13 -14 -15
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
M87 - RADIO POLARIZATION
ARC
SEC
ARC SEC-10 -11 -12 -13 -14 -15
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
Figure 5
I A
B1
B2
LOP-1
HOP-3HOP-2
HOP-1
25
Crab nebula
M87
↵⌫(p, ⌫) =c2
2h⌫31
p�[�pj⌫ ]
�+h⌫/mc2
�
⇡ 1
2m⌫21
p�@� (�pj⌫)
j⌫ = n@P
@⌫@⌦
Cyclo-synchrotron radiation ●●●●●●●●●●●●●○○
Synchrotron self-absorption
✓ Absorption decreases with frequency✓ high energy photons are weakly absorbed✓ low energy photons are highly absorbed
True absorption
Stimulated emission (negative absorption)
hν
Spontaneous emission
hν
True absorption Stimulated emission(negative absorption)
hν
hν
26
emission coefficient: absorption coefficient:
Cyclo-synchrotron radiation ●●●●●●●●●●●●●●○
Synchrotron self-absorption
✓Radiation transfer:✓ Equation for specific intensity Iν:✓ Solution for a uniform layer of thickness L:
✓ τν=ανL is the optical depth at energy hν✓When τν<<1: thin spectrum✓When τν>>1: thick spectrum✓ transition for:
✓The transition energy increases with optical depth, i.e. with:✓ Physical thickness of the layer✓ Density of the medium
27
@I⌫dl
= j⌫ � ↵⌫I⌫
I⌫ =j⌫↵⌫
(1� e�↵⌫L)
⌧⌫ = ↵⌫L ⇡ 1
Cyclo-synchrotron radiation ●●●●●●●●●●●●●●●
Self-absorbed Spectra
✓Thermal distribution ✓ Power-law distribution
Raylei
gh-Je
ans
thick
thin
28Tends to BB radiation in the thick part Does not tend to BB radiation in the thick part
thin
thic
kF⌫/⌫5/2
F ⌫/⌫2
Compton Scattering
29
- Thomson/Klein-Nishina regimes- Spectrum, angular distribution- Particle cooling- Multiple scattering
Compton scattering ●○○○○○○○○○○○
In the particle rest frame✓Scattering of light by free electrons
✓Result described by 6 quantities
✓4 Conservation laws:✓ Energy✓Momentum
✓1 symmetry
✓One quantity is left undetermined, e.g. the scattering angle θ
✓Direction/energy relation
✓Photon loose energy in the particle rest frame
✓Two regimes:✓ The Thomson regime (hν0<mc2): coherent scattering: hν=hν0
✓ The Klein-Nishina regime (hν0>mc2): incoherent scattering: hν<hν0 30
hν0
hν
γ
θ
h⌫0 +mc2 = h⌫ + �mc2
h⌫0c
~n0 =h⌫
c~n+mc~p
h⇥
h⇥0=
1
1 +
h�0mec2
(1� cos �)
hν0hν γ hν0hνh⌫0
1 + 2h⌫0/mc2 h⌫ h⌫0
backward scattering (θ=π) forward scattering (θ=0)
Compton scattering ●●○○○○○○○○○○
Thomson scattering✓Scattering of linearly polarized waves:
✓ Harmonic motion of the particle✓ Emission of light in all directions
✓Scattering of unpolarized waves:✓ Average of linearly polarized waves with random directions
✓ Scattered power:
✓ Thomson cross section:
✓ Total cross section:
✓ Partially polarized:
✓Spectrum: a line at the incident frequency 31
hν0
hν
γ
θ
@P
@⌦=
@�
@⌦F
@�
@⌦=
3
8⇡�T
1 + cos
2 ✓
2
�T = 6.65⇥ 10�25cm2
⇧ =
1� cos
2 ✓
1 + cos
2 ✓
� = �T3
4
1 + !0
!30
✓2!0(1 + !0)
1 + 2!0� ln (1 + 2!0)
◆+
ln (1 + 2!0)
2!0� 1 + 3!0
(1 + 2!0)2
�
Compton scattering ●●●○○○○○○○○○
Klein Nishina scattering ✓Requires quantum mechanics but still
analytical formulae
32
� ⇡ �T !0=
1
Thomson Regime
Klein-Nishina Regime
h⌫=
mc2
Total cross section:
Ang
ular
dis
tribu
tion:
Spec
trum
Differential cross sections:
hν0/mc2
10-5
10-1
1
10
102
103
d�
d⌦= �T
3
16⇡
✓h⌫
h⌫0
◆2 ✓h⌫0h⌫
+h⌫
h⌫0� sin2 ✓
◆
⌫ = 2�0⌫0
Compton scattering ●●●●○○○○○○○○
In the source frame✓ In the particle frame: one incident parameter (hν0)
✓ In the source frame: new dependance on✓ The particle energy✓ The collision angle
✓Photon can now gain/loose energy
✓An example:✓ Head-on collision:
✓ Cold photon hν0 and relativistic electron γ0>>1✓ Photon energy in the particle frame:
✓ Thomson backward scattering:✓ Emitted photon energy in the electron frame:✓ Photon energy in the source frame:
✓ In the end:✓ Compton up-scattering
✓Often: isotropy assumption and average over angles33
⌫00 = 2�0⌫0
⌫0 = ⌫00
⌫ = 4�20⌫0
h⌫00 << mc2
Compton scattering ●●●●●○○○○○○○
In the source frame
✓For isotropic distributions:
✓The Thomson limit:
✓The scattered spectrum:
✓Average energy of scattered photons
✓ Down scattering:
✓ Up-scattering:✓ Amplification factor:
✓Scattering by relativistic plasmas produces high energy radiation
✓Particle cooling:
34
�0h⌫0 << mc2
(�0 � 1)mc2 < h⌫0
(�0 � 1)mc2 > h⌫0
A =< h⌫ >
h⌫0⇡ �2
@Ep
@t=
4
3c�T p
2Uph
Compton scattering ●●●●●●○○○○○○
Blazar Spectra
✓E > TeV! Comptonization?
✓Model = Synchrotron Self-Compton (SSC) + Doppler boosting✓ Seed photons = synchrotron photons✓ The same particle emit though synchrotron and scatter these photons
✓Here: ✓ A=108 => γ=104
✓ hν0 = 0.1 keV => KN regime✓ Synchrotron peaks at Bγ2, Compton amplifies with A=γ2 => B! 35
optical X-RaysUV !-Rays
Compton scattering ●●●●●●●○○○○○
Single scattering by many electrons✓Emission integrated over the particle
distribution
✓Thermal distribution:✓ Same as for a single particle for the
mean energy..
✓Power-law distribution:✓ Power-law spectrum with
✓ slope:✓ minimal energy: hν0 γ2min
✓ maximal energy: hν0 γ2max
✓Scattered photons distributions should also be integrated over the source seed photons
36
f(�) / �2e��/✓
f(�) / ��s
↵ =s� 1
2
Compton scattering ●●●●●●●●○○○○
Multiple Scattering
✓Photons can undergo successive scattering events
✓Medium of finite size L: Thomson optical depth:
✓Competition scattering/escape:✓ τ (or τ2) = Mean number of scattering before escape ✓ τ<1: single scattering✓ τ>1: multiple scattering
✓y parameter = <photon energy change> before escape✓ y= <Energy change per scattering> * <scattering number> ✓ For mono-energetic particles: y = τγ2
✓ For thermal distributions: y = 4τθ(1+4θ)
37
⌧T = ne�TL
Compton scattering ●●●●●●●●●○○○
The SZ effect
✓Typical distortion whose amplitude gives: y ≈ τθ ≈ 10-4
✓Bremsstrahlung gives T
✓=> density...
38
kBTph=2.7 KkBTe=1-10 keV ("e=kBTe/mec2≈10-2, p≈#≈0.1)
!=Ne"TL ≈ 10-2
Compton up-scatteringCold photons
Hot electrons
Compton scattering ●●●●●●●●●●○○
Compton orders
hν0/mc2=10-7
γ0=10 A =100
bumpy spectrum
cutoff at the particle energy
τ => spectrum hardness
A A AA
39
Compton scattering ●●●●●●●●●●●○
Compton regimesSub-relativistic particles: hν0/mc2 < p < 1
Thomson regime hν0#0<< mc2
Inefficient scattering: A = 1
Ultra-relativistic particles: #0>> 1KN regime: hν0#0>mc2
Efficient scattering: A >> 1
w0=10-4, p0=1 (w0 g0 < 1)A = 2
Power-law spectrum- cutoff at the particle energy- Slope = ln(τ)/ln(A)
one-bump spectrum= single scattering !
=> AGN/Blazars=> X-ray binaries 40
Relativistic particles: #0>>1 Thomson regime: hν0#0<< 1
Efficient scattering: A >> 1
Compton scattering ●●●●●●●●●●●●
X-ray binaries
✓Soft states:✓Multi-color black body at 1 keV from the accretion disk✓ Non-thermal comptonization in a hot corona (τ=1)
✓Hard states:✓ Soft photons from the accretion disk or synchrotron✓ Inefficient thermal Comptonization in a hot corona (100 keV, τ=0.01)
✓What heating acceleration mechanism?41
Zdziarsky 2003
Bremsstrahlung radiation
42
Bremsstrahlung ●○○○
Bremsstrahlung
✓Radiation of charged particles accelerated by the Coulomb field of other charges
✓Astrophysical sources:✓ Some modes of hot accretion disks✓ Hot gas of intra-cluster medium (1-10
keV)✓ ...
43
~v
Bremsstrahlung ●●○○
Easy bremsstrahlung
✓ Assumptions:✓ Classical physics✓ Sub-relativistic particles✓ Far collision (small deviation, no recombination)✓ Small energy change (Δv << v i.e. hν<<mv2/2)
✓Single event✓ No p+/p+, e-/e-, e+/e+ Bremsstrahlung ✓ p+/e, iZ+/e Bremsstrahlung✓ Approximation: static heavy iZ+
✓Approximated motion: ✓ Typical collision time: τ ≈ 2b/v✓ Typical velocity change: Δv ≈ τ a ≈ τ F/m ≈ τ Z e2/(mb2) ≈ 2Ze2/(mvb)✓ τ and Δv characterize the motion = enough to compute the spectrum
44
� << 1
2b
b
~v
Ze
h⌫
Bremsstrahlung ●●●○
Easy bremsstrahlung✓Spectrum:
✓Fourier transform:
✓One single particle produces a flat spectrum:
✓Many particles with a range of impact parameters:✓ with bmin from the small angle approximation✓ with bmax from ντ<1
✓ Produce a flat spectrum that cuts at the electron energy✓ Total losses:
45
@P
@⌫/
���FFT ( ~E)���2/ |FFT (~a)|2
TF [~̇v] =
Z +1
�1~̇v(t)e�2i⇡⌫tdt ⇡
⇢0 if ⌫⌧ >> 1�~v if ⌫⌧ << 1
⌫
@E@⌫
1/⌧1 1/⌧2
b1
b2 < b1
@P
@V @⌫= ninev
Z bmax
bmin
@E@⌫
2⇡bdb =32⇡e6
3m2c3vnineg↵(v, ⌫)
@E@⌫
(v, b) ⇡⇢
0 if ⌫⌧ >> 116e6Z2
3c3m2v2b2 if ⌫⌧ << 1
@P@V @⌫
h⌫mv2/2Pcool
/ ni
ne
Z2v
1/v
✓Emission integrated over the particle distribution
✓Power-law distributions produce power-law spectra
✓Thermal distributions:✓ Emission coefficient: ✓ Total losses:
✓Relativistic and quantum correction can be added to give more general spectra
✓ In media of finite size: bremsstrahlung self-absorption at low energy✓ c.f. synchrotron
j⌫ / nineZ2T�1/2e�h⌫/kBT
Pcool
/ ni
ne
Z2T 1/2
Bremsstrahlung ●●●●
Emission from many electrons
46
h⌫
j⌫
kBT1 kBT2
T2 > T1
Summary✓Particle cooling:
✓ Synchrotron: P ∝ σT p2 UB
✓ Compton in the Thomson regime: P ∝ σT p2 Uph
✓ Bremsstrahlung: P ∝ σT αf p Ui (with Ui= ni mec2)✓Photons:
✓ Synchrotron: ✓ Thin spectrum of 1 particle peaks at νc ∝ γ2 B✓ Thin spectrum of a power-law distribution is a power-law✓ Absorption => Thick spectrum at low frequency
✓ Compton✓ Amplification factor in the Thomson regime: A = γ2
✓ Mildly relativistic particles: power-law spectrum✓ Comptonization by a relativistic power-law distribution is a PL spectrum
✓ Bremsstrahlung✓ Flat spectrum✓ up to the particle energy
47