NASSP Masters 5003F - Computational Astronomy Lecture 10 Today I plan to cover: –A bit more about noise temperatures; –Polarized radio signals; –Radio spectroscopy.

NASSP Masters 5003F - Computational Astronomy Typical noise temperatures J D Kraus, “Radio Astronomy” 2 nd ed., fig 8-6.(+ 7-25)

NASSP Masters 5003F - Computational Astronomy Polarized EM waves – conventions: z x y Left-hand circular polarization according to IEEE convention. (Physicists use the opposite convention.) Direction of rotation of the field vector as seen by an observer. Snapshot of a wave moving in the positive z direction.

NASSP Masters 5003F - Computational Astronomy 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 How to describe a state of polarization? Visualize with the “Poincaré sphere.” of radius I. 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. Q axis U axis V axis Polarization fraction d: Therefore need 4 measurements to completely define the radiation.

NASSP Masters 5003F - Computational Astronomy Antenna response, and coherency matrices. The antenna response is different for different incoming polarization states. This may be quantified by 4 ‘Stokes effective areas’ A I, A Q, A U, A V. 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 = A e I×Tr(AS) (‘Tr’ = the ‘trace’ of the matrix, ie the sum of all diagonal terms.)

NASSP Masters 5003F - Computational Astronomy Depolarization due to finite resolution Half-power contour of the beam. Arrows show the pol- arization direction. 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. Nett polarization observed.

NASSP Masters 5003F - Computational Astronomy 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 λ 2. 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 Faraday rotation J D Kraus, “Radio Astronomy” 2 nd 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 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 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 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 index α = -2. Synchrotron sources have +ve α, averaging around HII regions exhibit a broken power law.

NASSP Masters 5003F - Computational Astronomy Broad-band emitters J D Kraus, “Radio Astronomy” 2 nd ed., fig 8-9(a) Note too that nearly all broad- band spectra are quite smooth.

NASSP Masters 5003F - Computational Astronomy 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. 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.) + -e

NASSP Masters 5003F - Computational Astronomy 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 λ 2. Effective temperature T eff = T(1-e - τ ). –Long λ - high τ - T eff ~ T – thus α = -2. –Short λ - low τ - T eff proportional to λ 2 - means flux density S is constant, or α = 0.

NASSP Masters 5003F - Computational Astronomy 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 ~ Effective temperature limited to < K by inverse Compton scattering. J D Kraus, “Radio Astronomy” 2 nd ed., fig PKS

NASSP Masters 5003F - Computational Astronomy Narrow-band spectra Molecular transitions: –Hundreds now known. –Interstellar chemistry. –Tracers of star-forming regions. –Doppler shift gives velocity information. Masers: –Eg OH, H 2 O, NH 3. –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 HIHI 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 H II – which is just a bare proton. The neutral atom has a very weak (lifetime ~ 10 7 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 HIHI 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 H I – 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 H I – we can see galaxies behind it at 21 cm, whereas visible light is strongly absorbed. Cosmic Doppler red shift z is given by

NASSP Masters 5003F - Computational Astronomy 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.)