Download Lecture 1 - University of Cape Town

Lecture 10
• Today I plan to cover:
– A bit more about noise temperatures;
– Polarized radio signals;
– Radio spectroscopy.
NASSP Masters 5003F - Computational Astronomy - 2009
Typical noise temperatures
J D Kraus, “Radio Astronomy”
2nd ed., fig 8-6.(+ 7-25)
NASSP Masters 5003F - Computational Astronomy - 2009
Polarized EM waves – conventions:
y
x
Snapshot of a wave moving in the
positive z direction.
Left-hand circular polarization
according to IEEE convention.
(Physicists use the opposite
convention.)
z
Direction of rotation of
the field vector as seen
by an observer.
NASSP Masters 5003F - Computational Astronomy - 2009
Sources of polarized radio waves:
• Thermal? No
• Spectral line? No (unless in a strong B field)
• Synchrotron? YES.
– And this is the most common astrophysical emission
process.
• All jets emit synchrotron – and jets are everywhere.
Magnetic field B
Electron moving at
speed close to c
Linearly
polarized
emission.
NASSP Masters 5003F - Computational Astronomy - 2009
How to describe a state of polarization?
Stokes parameters I, Q, U and V.
I = total intensity.
Q = intensity of horizontal pol.
U = intensity of pol. at 45°
V = intensity of left circular pol.
V axis
U axis
Q axis
Therefore need 4
measurements to
completely define
the radiation.
Polarization fraction d:
Visualize with the “Poincaré sphere.” of radius I.
Q2  U 2  V 2
d
I
NASSP Masters 5003F - Computational Astronomy - 2009
Antenna response, and coherency matrices.
• The antenna response is different for
different incoming polarization states.
• This may be quantified by 4 ‘Stokes
effective areas’ AI, AQ, AU, AV.
• But it is more convenient to express both
the radiation and the antenna response as
coherency matrices:
1
S
2I
 I Q
U  iV

U  iV 
I  Q 
and
1
A
2 Ae
 AI  AQ
 A  iA
V
 U
AU  iAV 
AI  AQ 
• Then the power spectral density detected is
w = AeI×Tr(AS) (‘Tr’ = the ‘trace’ of the matrix, ie the sum of all diagonal terms.)
NASSP Masters 5003F - Computational Astronomy - 2009
Depolarization due to finite resolution
Arrows show the polarization direction.
Half-power contour
of the beam.
Nett
polarization
observed.
Waves from different areas of the source add incoherently. Result: some degree
of depolarization. In general, the finer the resolution, the higher the polarization fraction.
NASSP Masters 5003F - Computational Astronomy - 2009
Faraday rotation.
• Any linear polarized wave can be decomposed
into a sum of left and right circularly polarized
waves.
• In a magnetized plasma, the LH and RH
components travel at slightly different speeds.
• Result:
– The plane of polarization rotates.
– The amount of rotation θ is proportional to distance
travelled x the field strength x the number density of
electrons.
– θ is also proportional to λ2.
• Most due to Milky Way, but the Earth’s
ionosphere also contributes – in a time-variable
fashion. The ionosphere is a great nuisance and
radio astronomers would abolish it if they could.
NASSP Masters 5003F - Computational Astronomy - 2009
Faraday rotation
J D Kraus, “Radio Astronomy”
2nd ed., fig 5-4
The slope of the line is called
the rotation measure.
Why is there progressive depolarization with increase in wavelength?
NASSP Masters 5003F - Computational Astronomy - 2009
Faraday rotation - depolarization
Because the rotation measure is not uniform and may vary within the beam. Eg:
Half-power contour
of the beam.
NASSP Masters 5003F - Computational Astronomy - 2009
Radio spectroscopy
• The variation of flux with wavelength
contains a lot of information about the
source.
• We can pretty much divide sources into
– Broad-band emitters, eg
• Synchrotron emitters
• HII regions (ie ionized hydrogen)
• Thermal emitters
– Narrow-band emitters (or absorbers), eg
• HI (ie neutral hydrogen)
• Masers
• Neutral molecular clouds
NASSP Masters 5003F - Computational Astronomy - 2009
Broad-band emitters
• Most of these have spectra which, over
large ranges of wavelength, can be
described by a simple power law, ie

S 
• For thermal sources, the Rayleigh-Jeans
approximation to the black-body radiation
law gives a spectral index α = -2.
• Synchrotron sources have +ve α,
averaging around +0.8.
• HII regions exhibit a broken power law.
NASSP Masters 5003F - Computational Astronomy - 2009
Broad-band emitters
J D Kraus, “Radio Astronomy”
2nd ed., fig 8-9(a)
Note too that nearly all broadband spectra are quite smooth.
NASSP Masters 5003F - Computational Astronomy - 2009
HII regions
• The gas here is ionized and hot (10,000 K is
typical) – usually as a result of intense irradiation
from a massive young star.
• The radiation comes from electrons accelerated
(diverted) as they come close to a positive ion.
+
-e
• This radiation mechanism is called free-free,
because the electron being accelerated is not
bound to an atom either before its encounter or
after. But it is basically a thermal process.
• Otherwise known as bremsstrahlung (braking
radiation.)
NASSP Masters 5003F - Computational Astronomy - 2009
Optical depth
• Whenever you have a combination of
radio waves and plasma, optical depth τ
plays a role.
– High τ = opaque – behaves like a solid body.
– Low τ = transparent.
• τ for a plasma is proportional to λ2.
• Effective temperature Teff = T(1-e-τ).
– Long λ - high τ - Teff ~ T – thus α = -2.
– Short λ - low τ - Teff proportional to λ2 - means
flux density S is constant, or α = 0.
NASSP Masters 5003F - Computational Astronomy - 2009
Some more about synchrotron
• Already covered the
basics in slide 4.
• Also subject to optical
depth effects:
J D Kraus, “Radio Astronomy”
2nd ed., fig 10-10
PKS 1934-63
– At low frequencies,
opacity is high, the
radiation is strongly
self-absorbed:
• α ~ -2.5.
• Effective temperature
limited to < 1012 K by
inverse Compton
scattering.
NASSP Masters 5003F - Computational Astronomy - 2009
Narrow-band spectra
• Molecular transitions:
– Hundreds now known.
– Interstellar chemistry.
– Tracers of star-forming regions.
– Doppler shift gives velocity information.
• Masers:
– Eg OH, H2O, NH3.
– Like a laser – a molecular energy transition
which happens more readily if another photon
of the same frequency happens to be passing
 radiation is amplified, coherent.
– Spatially localized, time-variable.
• Recombination lines.
NASSP Masters 5003F - Computational Astronomy - 2009
HI
• The I indicates the degree of ionization. I
means none – just the neutral atom.
Hydrogen has only 1 electron so the
highest it can go is HII – which is just a
bare proton.
• The neutral atom has a very weak (lifetime
~ 107 years!) transition between 2 closely
spaced energy levels, giving a photon of
wavelength 21 cm (1420 MHz).
• But because there is so much hydrogen,
the line is readily visible.
NASSP Masters 5003F - Computational Astronomy - 2009
•
•
•
•
HI
Because the transition is so weak, and
also because of Doppler broadening,
hydrogen is practically always optically
thin (ie completely transparent).
Thus the intensity of the radiation is
directly proportional to the number of
atoms.
Concept of column density in atoms per
square cm.
Hydrogen will be seen in emission if it is
warmer than the background, in
absorption otherwise.
NASSP Masters 5003F - Computational Astronomy - 2009
HI – Doppler information
• Hubble relation between distance and
recession velocity allows distance of far
galaxies to be estimated.
– Hence: 3D information about the large-scale
structure of the universe.
• Our Milky Way is transparent to HI – we
can see galaxies behind it at 21 cm,
whereas visible light is strongly absorbed.
• Cosmic Doppler red shift z is given by
obs  true
1 v c
v
z

 1  for v  c
2
true
c
1  v c 
NASSP Masters 5003F - Computational Astronomy - 2009
HI – Doppler information
• Within galaxies:
– Doppler broadening tells about the distribution of
velocities within a cloud of hydrogen.
– the Doppler shift of the HI line maps the rotation curve
of the galaxy, eg:
NGC 2403
Credit: F Walter et al (2008).
(Courtesy Erwin de Blok.)
NASSP Masters 5003F - Computational Astronomy - 2009