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Lecture 10

Lecture 10. Today I plan to cover: A bit more about noise temperatures; Polarized radio signals; Radio spectroscopy. Typical noise temperatures. J D Kraus, “Radio Astronomy” 2 nd ed., fig 8-6.(+ 7-25). Polarized EM waves – conventions:. y. Left-hand circular polarization

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Lecture 10

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  1. Lecture 10 • Today I plan to cover: • A bit more about noise temperatures; • Polarized radio signals; • Radio spectroscopy.

  2. Typical noise temperatures J D Kraus, “Radio Astronomy” 2nd ed., fig 8-6.(+ 7-25)

  3. Polarized EM waves – conventions: y Left-hand circular polarization according to IEEE convention. (Physicists use the opposite convention.) x Snapshot of a wave moving in the positive z direction. Direction of rotation of the field vector as seen by an observer. z

  4. 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.

  5. How to describe a state of polarization? Stokes parametersI, 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 Therefore need 4 measurements to completely define the radiation. Q axis Polarization fraction d: Visualize with the “Poincaré sphere.” of radius I.

  6. 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: • Then the power spectral density detected is and w = AeI×Tr(AS) (‘Tr’ = the ‘trace’ of the matrix, ie the sum of all diagonal terms.)

  7. Depolarization due to finite resolution Half-power contour of the beam. Arrows show the pol- arization direction. 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.

  8. 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 θis 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.

  9. 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?

  10. Faraday rotation - depolarization Because the rotation measure is not uniform and may vary within the beam. Eg: Half-power contour of the beam.

  11. 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

  12. Broad-band emitters • Most of these have spectra which, over large ranges of wavelength, can be described by a simple power law, ie • For thermal sources, the Rayleigh-Jeans approximation to the black-body radiation law gives a spectral indexα = -2. • Synchrotron sources have +ve α, averaging around +0.8. • HII regions exhibit a broken power law.

  13. Broad-band emitters J D Kraus, “Radio Astronomy” 2nd ed., fig 8-9(a) Note too that nearly all broad- band spectra are quite smooth.

  14. HII regions + -e • 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. • 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.)

  15. Optical depth • Whenever you have a combination of radio waves and plasma, optical depthτ 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.

  16. Some more about synchrotron • Already covered the basics in slide 4. • Also subject to optical depth effects: • 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. J D Kraus, “Radio Astronomy” 2nd ed., fig 10-10 PKS 1934-63

  17. 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.

  18. 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.

  19. 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.

  20. 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 shiftz is given by

  21. 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.)

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