Nonthermal Radiation
The simplicity and universality of thermal radiation result from the requirement of
equilibrium between the radiation and matter.
Only one variable, T, determines the Planck spectrum.
Many radiation processes in astrophysics produce a continuum spectrum in
nonequilibrium environments, e.g., when the gas is not sufficiently opaque.
Example: nonequilibrium recombination continua (more on recombination later).
Example 2: the radiation of charged particles moving in a magnetic field synchrotron radiation.
Synchrotron radiation (relativistic cyclotron radiation)
Δθ
r
The radiation comes off normal to the electron trajectory, and in a
narrow beam for relativistic electron speeds.
Characteristic Frequencies
Force balance for motion perpendicular to the local B-field gives:
r r
r
v
eB v
ev × B
= ⊥
(recall, FB =
)
r
mec
c
v
eB⊥
⇒ νm ≈
≈
2πr 2πm e c
2
The last equation gives the “cyclotron” frequency for nonrelativistic
electrons. The full relativistic expression (“synchrotron frequency”) is,
€
2


eB⊥
Ee
νm =
.

2
2πm e c  me c 
Note that both expressions are linear in B. We expect radiation at this
frequency and its harmonics, but where does the continuum come from?
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Distribution of electron energies
Note that νm ~ Ee2, so a distribution of electron energies implies a continuum
of frequencies.
In most realistic situations we do not expect an equilibrium Maxwell
distribution of electron energies, but rather a nonequilibrium power-law
distribution:
N(Ee) dEe = C (Ee)-γ dEe.
What is the form of the emitted spectrum with this distribution?
The power radiated per electron is (we won’t derive):
 E e 2
P = B⊥ 
.
2
 mec 
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And the intensity of the radiation is:
1 l
∞
Iν =
∫ 0 dr ∫ 0 P(E e )δ (ν − ν m )Cn(E e )E e−γ dE e ,
4π
where the first integral is taken over the emitting line of sight.
Note that,
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γ +1
2
Iν ∝ B⊥ ν
− ( γ −1)
2
.
Log(Fν (W m-2 Hz-1))
-22
γ ≈ 1.6
-23
-24
-25
γ ≈ 3.0
-26
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-27
-28
8
10
Log(ν (Hz))
Crab nebula
12
14
16
18
Astrophysical Sources of Nonthermal Radiation
- Planetary magnetospheres
- Solar Corona
- Supernova remnants
- Pulsars
- Active galactic nuclei and jets