# Presentation: 912178

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

- Ilana HARRUS (USRA/NASA/GSFC)

## 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 .

**Notes:**
First observed when high energy electron were stopped in a thick target. 
Also known as free-free emission in the language of atomic physics in the sense that the radiation corresponds to transitions between unbound states in the field of the nucleus. 
Explain the concept. With the particle centered/ cdeltaT. 

## 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 ===> in every reference book, the computations are made “classically” and  modified (“Gaunt” factors) to take into account quantum effects.

**Notes:**
Radio emission from compact regions of ionized hydrogen at temperatures T~10,000 K, 
diffuse X-ray emission of hot-intergalatic gas in clusters of galaxies (10^8), or 
emission from X-ray binaries (10^7). 
Add a word about why electrons. 

## Bremsstrahlung (non relativistic)

- Use the dipole approximation (fine for electron/nucleus bremsstrahlung)---

- -e

- Ze

- v

- b

- Electron moves mainly in straight line--     		v = Ze2/me (b2+v2t2)-3/2 bdt = 2Ze2/mbv
- Electric field: E(t) =Ze3sin/mec2R(b2+v2t2)

- R

**Notes:**
Put things in perspective; Electron rest mass is 511 keV-- 
In X-ray regimes (0.1-10 keV) electrons are up to ten’s of KeV but still small... 

## Bremsstrahlung (for one NR electron)

-             (using Fourier transform)
-               E() =Ze3sin/mec2R /bv e-b/v
- Energy per unit area and frequency is:
-                   dW/dAd = c|E()|2
-  So that integrated on all solid angles:
-          dW(b)/d 8/3 (Z2e6/me2c3) (1/bv)2 e-2b/v

**Notes:**
Note that one can approximate the e function with a step function when wb/v is large the exponetial goes to zero. 

## 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/dVdtd = neni2v bmin dW(b)/dbdb
-           Approximation: contributions up to bmax
- 	This implies (after integration on b)
-        dW/dVdtd =  (16e6/3me2vc3) neniZ2 ln(bmax /bmin)
-             with   bmin ~ h/mv    and    bmax~ v/

**Notes:**
Note the dimension of the equation. 
Also bmin== quantum effects means == Deltaxdeltap~h deltax=b, deltap=mv  or 
OR staigh  line approximation not valid: deltav~v
bmin-=4Ze^2/pimv^2
And use the larger of both... 

## Bremsstrahlung

- If QED used, the result is:
-      dW/dVdtd =  (16e6/33/2me2vc3) neniZ2 gff(v,)

- Karzas & Latter, 1961, ApJS, 6, 167

## 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 >> hPhoton discreteness effect) and using d=2d
- dW/dVdtd =
-     (32e6/3mec3) (2/3kTme)1/2 neniZ2 e(-h/kT) <gff> ==
-     6.8 10-38 T-1/2neniZ2 e(-h/kT) <gff> erg s-1 cm-3 Hz-1
- <gff> is the velocity average Gaunt factor

**Notes:**
Don’t be fooled by the evil empire: d3v is the vectord3v.. 
Limit because otherwise no photon created. 

## Bremsstrahlung

- From Rybicki & Lightman Fig 5.2 (corrected) -- originally from Novikov and Thorne (1973)

- Approximate analytic formulae for <gff>

**Notes:**
Note that at hnu/kt <<1 G only depends on the log of frequency-- (small variation). 
X-ray == g(nu, T) = sqrt(3)/pi ln(kt/hnu)

## Bremsstrahlung

- From Rybicki & Lightman Fig 5.3 -- originally from Karzas & Latter (1961)

-  u =h/kT ;
- 2 = Ry Z2/kT
-     =1.58x105 Z2/T

- Numerical values of <gff>.

- When integrated over frequency:
- dW/dVdt = (32e6/3hmec3) (2kT/3me)1/2 neniZ2 <gB>   == 1.4x10-27 T1/2neniZ2 <gB> erg s-1 cm-3

- (1+4.4x10-10T)

**Notes:**
Gff for u >>1are not important (the spectrum cuts off for these values). 
Gff is around 1 for u ~ 1 and in the range of 1 to 5 for 0.0001<u<1. 
Gff is one is a good approximation. 
For non-thermal bremm== use whatever distributions of velocity and integrate the previous equations... 

## Cyclotron/Synchrotron Radiation

- 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...

- Radiation emitted by charge moving in a magnetic field.

**Notes:**
If you read the early literature (Ginzburg Syrovatskii) -- The magnetobremsstrahlung was not widely accepted by astronomers until 1958 (in Paris) -- in contrast of the meeting in Manchester in 1955 where people where still arguing about it. 

## 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 L =eB/mc
- = 2.8 B1G MHz (Larmor)
- Frequency of radiation == L

**Notes:**
Write the vector v in term of B// and Bperpendicular. 
Dp/dt=e/c vXB  (p=gamma mv) == omegab=omegalarmor/gamma. 
Cyclotron radiation is dipole in nature-- for a circular motion, equivalent to 2 perpendicular 
Linear oscillators (or a rigid dipole Perpendicular to the magnetic field.). 

## Synchrotron Radiation 

- Because of relativistic effects: beaming  and~1/
- Gyration frequency B = L/
- Observer sees radiations for duration t<<< T =2/B
- This means that the spectrum includes higher harmonics of B.
- Maximum is at a characteristic frequency which is:
-             c ~ 1/t ~ 2eB /mc

- Angular distribution of radiation (acceleration  velocity).
- Rybicki & Lightman

**Notes:**
Gyration frequency B = L/
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## Synchrotron Radiation

- Total emitted radiation is:
- P= 2e4B2/3m2c3 2 = 2/3 r02 c 2 B2  when >>1
- Or         P  2 c T UB sin2(UB is the magnetic energy density)
-              P~1.6x10-15 2 B2 sin2  erg s-1

- Life time of particle of energy  /P ~ 20/B2 yr
- Example of Crab-- Life time of X-ray producing electron is about 20 years.
- P  m2 : synchrotron is negligible for massive particles.

**Notes:**
Tell them to keep that formula in mind. 

## 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() = (3e3/4mc2) B sin [F(x)+G(x)] ; x=/c
- P() =(3e3/4mc2) B sin [F(x)-G(x)]
- Where F(x)==x∫∞x K 5/3(y)dy ; G(x)==x K 5/3(x) and K modified Bessel function
- and  c = 3/22 Lsin
- 	     Total emitted power per frequency:
- 		P()=(3e3/2mc2) B sin F(c)

**Notes:**
Send them to read the article by Ginzburg. Be careful about the H and B 

## 0.29

**Notes:**
Mentioned that you have lifted this graph from Dan’s talk. 

## Synchrotron Radiation

- Hypothesis:  Energy spectrum of the electrons between energy E1 and E2 can be approximated by a power-law  --
-     N(E)=KE dE  (isotropic, homegeneous).
- Number of e- per unit volume, between E and E+dE (in arbitrary direction of motion)

- Intensity of radiation in a homogeneous magnetic field:
- I(,k)=(3/+1) (3-1/12) (3+19/12) e3/mc2 (3e/2m3c5)(-1)/2     K [B sin(+1)/2 -(-1)/2

- Average on all directions of magnetic field (for astrophysical applications).  L is the dimension of the radiating region
- I()= a() e3/mc2 (3e/4m3c5)(-1)/2  B(+1)/2  K L -(-1)/2 erg cm-2 s-1 ster-1 Hz-1
- where
- a() = 2(-1)/2 (3/(3-1/12) (3+19/12) (+5/4)/[8(+1) (+7/4)]

**Notes:**

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## Synchrotron Radiation

- If the energy distribution of the electrons is a power  distribution

## Synchrotron Radiation

-  y1( and y2() are tabulated (or you can compute them yourself..).

- Estimating the two boundaries energies E1 and E2 of electrons radiating between 1 and 2.

- E1() ≤ mc2 [4mc/3eBy1(] 1/2 = 250 [/By1(] 1/2 eV
- E2() ≤ mc2 [4mc/3eBy2(] 1/2 = 250 [/By2(] 1/2 eV

- If interval 2/ 1 << y1(/y2( or if <1.5 this is only rough estimate

## Synchrotron Radiation

- Expected polarization:
- (P() - P())/(P() + P())  ==  (+1)/(+ 7/3)
- can be very high (more than 70%).

## 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.
- ====> break frequency

## Compton/Inv Compton Scattering 

- Es=hs

- For low energy photons (h << mc2), scattering is classical Thomson scattering (Ei=Es; T = 8/3 r02)

- More general:    Es=Ei (1+Ei(1-cos)/mc2)-1   or
-                             s-i=c(1-cos)   (c =h/mc)
-   This means that Es is always smaller than Ei
- Even more general: (Klein-Nishina)
-                d/d = 1/2 r02 y2(y+1/y -sin2) with y=Es/Ei

- Pe, E

- Ei=hi

- 

**Notes:**


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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 : Eifoe=Eilab(1-cos) then Eifoe becomes Esfoe and Eslab=Esfoe(1+cos')
- This means that Eslab  Eilab 2
-         The boost can be enormous!

**Notes:**



## Inverse Compton Scattering

## Compton/Inv Compton Scattering 

- The total power emitted:
-  Pcompt = 4/3 Tc22Uph[1-f(,Eilab)] ~ 4/3 Tc22Uph
- And Uph is the initial photon energy density
- We had Psync  2 c T 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 ===> direct access to magnetic and photon energy density.

**Notes:**


Effect of repeated Compton scatterings in a finite, thermal medium. 

## Not covered

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

## 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 Magnetobremmstrahlung" 1965 Ann. Rev. Astr. Ap. 3, 297
- Ginzburg & Tsytovitch "Transition radiation"