synchrotron radiation - some observational aspects · 2017. 4. 6. · (c)2013 van putten 4...
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Synchrotron radiation - some observational aspects
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Theory of synchrotron radiation (summary)
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Synchrotron radiation
B
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ea
2
1
e
a
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Synchrotron emission
1) Opening angle of emission cone ~ 2/gamma
2) Contraction of sweep time of the cone by 1-v~1/(2gamma^2)
3) Net result ~ (1-v)Delta t~1/gamma^3
t
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Synchrotron radiation power
is the pitch angle
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Emission spectrum
B
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ea
Total power emitted:
Derives from EM radiation integral
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Typical photon energies
Area=
Shape function F
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Spectrum from radiation and self-absorption
Transition frequency condition:
Above, medium is optically thin:
Below, medium is self-absorbed:
(Rayleigh-Jeans!)
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Brightness temperature
Black body temperature: temperature of a grey body emitting the observed intensity (at a given frequency)
One brightness temperature at all frequencies only for a genuine black body source
Emission spectrum of grey bodies is different: brightness temperature depends on choice of frequency bin
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At low frequencies, source is optically thick (to own synchrotron photons)
The spectrum satisfies Rayleigh-Jeans law – just like a black body spectrum
Assign effective temperature of e’s (typically with a power law distribution):
Rayleigh-Jeans regime
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Electron temperature
Dominant frequency of emission
Electron energy
EOS (relativistic fluid)
Electron temperature
(defines effective temperature)
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Electron temperature
From the observed dominant frequency:
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Brightness temperature Rayleigh-Jeans
Large optical depth
At thermal equilibrium
Full thermodynamic equilibrium
Brightness temperature
Rayleigh-Jeans at low frequencies
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~
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At low frequencies
Rayleigh-Jeans relativistic e’sLarge optical depth, self-absorbed (sum of BB-spectra,
one for each energy of the electron population)
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Typical synchrotron spectrum
p=2.4
Independent of p
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Observed radio spectra
Optically thin
Steepening (e.g. by cooling)
self-absorbed
Opacity increasing?
self-absorbed
opaque
self-absorbed?
Kellerman & Owen, 1998, in Galactic and Extragalactic radius astronomy, eds. Verschuur & Kellermann (Springer Verlag)
Optically thin
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How much energy is in e’s or B?
e-energy density to synchrotron power
e-energy density associated with a given radiation frequency range
B-energy density
(keeping L fixed)
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Total energy in particles and fields http://www.cv.nrao.edu/course/astr534/SynchrotronSrcs.html
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Minimum total pressure in particle and fields
Total pressure
Total pressure minimum
Equilibrium p
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Minimum pressure in particles and fields Total pressure
The minimum pressure is attained at approximate equipartition
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Minimum pressure (2nd derivation)
Consider p=2 as before
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Minimum pressure (2nd derivation)
Pressure in relativistic electron population
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Total pressure
Total pressure minimum
“Minimum near equipartition”
Minimum pressure (2nd derivation)
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Equipartition
Equipartition is natural if relaxation time is short
Here, equipartition argument leads to minimum energy
Useful to eliminate one parameter
e.g.http://www.cv.nrao.edu/course/astr534/SynchrotronSrcs.html
Thus,So, the “
So, the “4/3” relation between pressure of e’s and B holds at the minimum of the total pressure at given L or Tb.
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Equilibrium magnetic field strength
Total pressure
Total pressure minimum
Total pressure minimumEquilibrium value depends on R
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Results for moving blobs Transform by Doppler factor
Baryon number density, is zero in a leptonic jet
If electron-proton plasma, then
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Results for moving blobs
Energy densities
(cold)(relativistic)
Lorentz factor of blob
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Cyg A
(p=2.6)
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Cyg A
Equivalent to the luminosity of a galaxy, at the size R of a small galaxy!
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Cyg A
Indeed
Can show for each of the two lobes based on L:
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Questions
1. In true thermal equilibrium with a thermal source, the e’s assume a Maxwell energy distribution. Can their temperature be larger than the brightness temperature? [Hint: What is the role of synchrotron self-absorption?]
2. Based on the cooling time of a few million years, the lobes in Cyg A are “light bulbs” powered instantaneously by energy transport from jets emanating from the nucleus. The jets are hardly visible. What does this say about the efficiency of the jets as power carriers?
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