Continuum Processes (in High-Energy Astrophysics) 3rd X-ray Astronomy school Wallops Island May 12-16 May

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Continuum Processes (in High-Energy
Astrophysics)3rd X-ray Astronomy schoolWallops
Island May 12-16 May

• Ilana HARRUS (USRA/NASA/GSFC)

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Bremsstrahlung
What is Bremsstrahlung? (and why this bizarre
name of braking radiation?) Historically noted
in the context of the study of electron/ion
interactions. Radiation of EM waves because of
the acceleration of the electron in the EM field
of the nucleus. And when a particle is
accelerated it radiates .
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Bremsstrahlung
Important because for relativistic particles,
this can be the dominant mode of energy loss.
Whenever there is hot ionized gas in the
Universe, there will be Bremsstrahlung emission.
Provide information on both the medium and the
particles (electrons) doing the radiation. The
complete treatment should be based on QED gt in
every reference book, the computations are made
classically and modified (Gaunt factors) to
take into account quantum effects.
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Bremsstrahlung (non relativistic)
Use the dipole approximation (fine for
electron/nucleus bremsstrahlung)---
v
-e
b
R
Ze
Electron moves mainly in straight line-- Dv
Ze2/me ?(b2v2t2)-3/2 bdt 2Ze2/mbv Electric
field E(t) Ze3sinq/mec2R(b2v2t2)
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Bremsstrahlung (for one NR electron)
(using Fourier transform)
E(w) Ze3sinq/mec2R p/bv e-bw/v Energy per
unit area and frequency is
dW/dAdw cE(w)2 So that integrated on all
solid angles dW(b)/dw 8/3p
(Z2e6/me2c3) (1/bv)2 e-2bw/v
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Bremsstrahlung
For a distribution of electrons in a medium with
ion density ni. Electron density ne and same
velocity v. Emission per unit time, volume,
frequency dW/dVdtdw neni2pv ??bmin
dW(b)/dw bdb Approximation
contributions up to bmax This implies (after
integration on b) dW/dVdtdw
(16e6/3me2vc3) neniZ2 ln(bmax /bmin)
with bmin h/mv and bmax v/w
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Bremsstrahlung
If QED used, the result is dW/dVdtdw
(16pe6/33/2me2vc3) neniZ2 gff(v,w)
Karzas Latter, 1961, ApJS, 6, 167
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Bremsstrahlung
Now for electrons with a Maxwell-Boltzmann
velocity distribution. The probability dP that a
particle has a velocity within d3v is
dP ? e-E/kT d3v ? v2e(-mv2/2kT)dv Integration
limits 1/2 mv2 gtgt hn (Photon discreteness
effect) and using dw2pdn dW/dVdtdn
(32pe6/3mec3) (2p/3kTme)1/2 neniZ2 e(-hn/kT)
ltgffgt 6.8 10-38 T-1/2neniZ2 e(-hn/kT)
ltgffgt erg s-1 cm-3 Hz-1 ltgffgt is the velocity
average Gaunt factor
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Bremsstrahlung
Approximate analytic formulae for ltgffgt
From Rybicki Lightman Fig 5.2 (corrected) --
originally from Novikov and Thorne (1973)
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Bremsstrahlung
u hn/kT g2 Ry Z2/kT 1.58x105 Z2/T
Numerical values of ltgffgt.
From Rybicki Lightman Fig 5.3 -- originally
from Karzas Latter (1961)
When integrated over frequency dW/dVdt
(32pe6/3hmec3) (2pkT/3me)1/2 neniZ2 ltgBgt
1.4x10-27 T1/2neniZ2 ltgBgt erg s-1 cm-3
(14.4x10-10T)
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Cyclotron/Synchrotron Radiation
Radiation emitted by charge moving in a magnetic
field.
First discussed by Schott (1912). Revived after
1945 in connection with problems on radiation
from electron accelerators, Very important in
astrophysics Galactic radio emission (radiation
from the halo and the disk), radio emission from
the shell of supernova remnants, X-ray
synchrotron from PWN in SNRs
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Cyclotron/Synchrotron Radiation
As with Bremsstrahlung, complete (rigorous)
derivation is quite tricky. First for a
non-relativist electron frequency of gyration in
the magnetic field is wL eB/mc 2.8 B1G MHz
(Larmor) Frequency of radiation wL
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Synchrotron Radiation
Angular distribution of radiation (acceleration ?
velocity). Rybicki Lightman
Because of relativistic effects beaming and
Dq1/g Gyration frequency wB wL/g Observer
sees radiations for duration Dtltltlt T 2p/wB This
means that the spectrum includes higher harmonics
of wB. Maximum is at a characteristic frequency
which is wc 1/Dt g2eB? /mc
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Synchrotron Radiation
Total emitted radiation is P 2e4B?2/3m2c3 b2g2
2/3 r02 c g2 B?2 when ggtgt1 Or P ? g2 c
sT UB sin2q (UB is the magnetic energy density)
P1.6x10-15 g2 B2 sin2q erg s-1
Life time of particle of energy t ? E/P 20/gB2
yr Example of Crab-- Life time of X-ray producing
electron is about 20 years. P ? 1/m2
synchrotron is negligible for massive particles.
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Synchrotron Radiation
The computation of the spectral distribution of
the total radiation from one UR electron
(computation done in both polarization directions
-- parallel and perpendicular to the direction of
the magnetic field). P?(w) (?3e3/4pmc2) B sinq
F(x)G(x) xw/wc P?(w) (?3e3/4pmc2) B sinq
F(x)-G(x) Where F(x)x?8x K 5/3(y)dy G(x)x
K 5/3(x) and K modified Bessel function and wc
3/2g2 wLsinq Total emitted power per
frequency P(w)(?3e3/2pmc2) B sinq F(w/ wc)
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0.29

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Synchrotron Radiation
Hypothesis Energy spectrum of the electrons
between energy E1 and E2 can be approximated by a
power-law -- N(E)KE-r dE (isotropic,
homegeneous). Number of e- per unit volume,
between E and EdE (in arbitrary direction of
motion)
Intensity of radiation in a homogeneous magnetic
field I(n,k)(?3/r1) G(3r-1/12) G(3r19/12)
e3/mc2 (3e/2pm3c5)(r-1)/2 K B sinq(r1)/2
n-(r-1)/2
Average on all directions of magnetic field (for
astrophysical applications). L is the dimension
of the radiating region I(n) a(r) e3/mc2
(3e/4pm3c5)(r-1)/2 B(r1)/2 K L n-(r-1)/2 erg
cm-2 s-1 ster-1 Hz-1 where a(r) 2(r-1)/2
?(3/p)G(3r-1/12) G(3r19/12) G(r5/4)/8(r1)
G(r7/4)
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Synchrotron Radiation
If the energy distribution of the electrons is a
power distribution
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Synchrotron Radiation
Estimating the two boundaries energies E1 and E2
of electrons radiating between n1 and n2.
E1(n) mc2 4pmcn1/3eBy1(r) 1/2 250
n1/By1(r) 1/2 eV E2(n) mc2 4pmcn2/3eBy2(r)
1/2 250 n2/By2(r) 1/2 eV
y1(r) and y2(r) are tabulated (or you can
compute them yourself..).
If interval n2/ n1 ltlt y1(r)/y2(r) or if rlt1.5
this is only rough estimate

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Synchrotron Radiation
Expected polarization (P?(w) - P?(w))/(P?(w)
P?(w)) (r1)/(r 7/3) can be very high
(more than 70).
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Synchrotron Self-Absorption
A photon interacts with a charged particle in a
magnetic field and is absorbed (energy
transferred to the charge particle). This occurs
below a cut-off frequency The main result is
For a power-law, the optically thick spectrum is
proportional to B-1/2v5/2 independent of the
spectral index. gt break frequency
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Compton/Inv Compton Scattering
For low energy photons (hn ltlt mc2), scattering is
classical Thomson scattering (EiEs sT 8p/3
r02)
Eshns
q
Eihni
Pe, E
More general EsEi (1Ei(1-cosq)/mc2)-1 or
ls-lilc(1-cosq)
(lc h/mc) This means that Es is always
smaller than Ei Even more general
(Klein-Nishina) ds/d? 1/2 r02
y2(y1/y -sin2q) with yEs/Ei
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Compton/Inv Compton Scattering
If electron kinetic energy is large enough,
energy transferred from electron to the photon
Inverse Compton One can use previous formula
(valid in the rest frame of the electron) and
then Lorentz transform. So EifoeEilabg(1-bcos
q) then Eifoe becomes Esfoe and
EslabEsfoeg(1bcosq') This means that Eslab ?
Eilab g2 The boost can be enormous!
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Inverse Compton Scattering
Inverse Compton Scattering
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Compton/Inv Compton Scattering
The total power emitted Pcompt 4/3
sTcg2b2Uph1-f(g,Eilab) 4/3 sTcg2b2Uph And Uph
is the initial photon energy density We had
Psync ? g2 c sT UB In fact Psync/Pcompt UB
/Uph Synchrotron inverse Compton off virtual
photons in the magnetic field. Both
synchrotron and IC are very powerful tools gt
direct access to magnetic and photon energy
density.
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Not covered

• Thermal bremsstrahlung absorption (energy
  absorbed by free moving electrons)
• Black body radiation
• Transition radiation (often not mentioned)

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Books and references

• Rybicki Lightman "Radiative processes in
  Astrophysics"
• Longair "High Energy Astrophysics"
• Shu "Physics of Astrophysics"
• Tucker "Radiation processes in Astrophysics"
• Jackson "Classical Electrodynamics"
• Pacholczyk "Radio Astrophysics"
• Ginzburg Syrovatskii "Cosmic Magnetobremmstrahlu
  ng" 1965 Ann. Rev. Astr. Ap. 3, 297
• Ginzburg Tsytovitch "Transition radiation"