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Radio Astronomy Fundamentals

Learn the basics of radio astronomy, including noisy electromagnetic radiation, antenna design, types of electron acceleration, power spectrum analysis, source contribution measurement, antenna detection efficiency, polarization, and directionality of antennas.

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Radio Astronomy Fundamentals

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  1. Lecture 11 • (Was going to be • Time series • Fourier • Bayes • but I haven’t finished these. So instead:) • Radio astronomy fundamentals

  2. Radio Astronomy Fundamentals Noisy electro- magnetic radiation (transfers energy) Antenna (simple dipole example) Source (randomly accelerating electrons) Load resistance R • Types of electron acceleration: • Thermal (random jiggling) • Synchrotron (spiral) • Spectral line (resonant sloshing)

  3. Noise power spectrum • Analyse the signal into Fourier components. jth component is: • The Fourier coefficient Vj is in general complex-valued. Power in this component is: • Closely related to the ‘power spectrum’ we’ve already encountered in Fourier theory. Vj(t) = Vj exp(-iωjt) = Vj (cos[ωjt] + i sin[ωjt]) Pj = Vj*(t)Vj(t)/R = Vj *Vj/R (cos2[ωjt] + sin2[ωjt]) = Vj *Vj/R

  4. Averaging the power spectrum t = 1 t = 16 t = 4 t = 64

  5. Total noise power output by the antenna. • “Noise is noise”: signal from an astrophysical source is indistinguishable from contamination from • Background thermal radio noise. • Ditto from intervening atmosphere. • Noise generated in the receiver system. • Each of these makes a contribution to the total. Thus the total noise power is Ptotal = Psource + Pbackground + Patmosphere + Psystem

  6. On-and-off source comparison • The simplest way to determine the source contribution is to make 1 measurement pointing at the source, then a second pointing away from (but close to) the source, then subtract the two. • Scanning over the source is also popular. • Uncertainty in total power measurements is: • A low-pass filter with a time constant t is another way of ‘averaging’.

  7. Antenna detection efficiency • The source radiates at S W m-2 Hz-1. • The antenna has an effective area Ae in the direction of the source. (Eg for a dish antenna pointed to the source, this is close to the actual area of the dish.) • Thus the power per unit frequency interval picked up by the antenna is: • However, antennas are only sensitive to one polarisation... w = AeS watts per herz.

  8. Decomposition into polarised components The total power in the signal is the sum of the power in each polarization. An antenna can only pick up 1 polarization though.

  9. Dependence on source polarisation • If the source is unpolarized, the antenna will only pick up ½ the power, regardless of orientation. • If the source is 100% polarized, the antenna will pick up between 0 and 100% of the power, depending on orientation (and type of detector – eg is detector sensitive to linear polarization, or circular). • Obviously all values in between will be encountered. Thus measurement of source polarization is important.

  10. Directionality of antennas. A radio telescope often (not always) incorporates a mirror. These are supposed to be smooth mirrors? GMRT An optically ‘smooth’ surface Parkes Ok as long as the roughness is << λ.

  11. Directionality of antennas. Radio telescopes with a mirror can be analysed like any other reflecting telescope... Point Spread Function Focal plane Reflector

  12. A more usual treatment: It is often conceptually easier to imagine that the antenna is emitting radiation to the sky rather than absorbing it. Side lobe Beam width Side lobe Beam width ~λ/D, same as for any other reflector. Eg Parkes 64m dish at 21 cm, beam width ~ 15’.

  13. Going into a little more detail... • Essential quantities: • The distribution of brightness B(θ,φ) over the celestial sphere. (See next slide for definition of θ,φ.) The units of this are W m-2 Hz-1 sr-1 (watts per square metre per herz per steradian). • The effective area Ae of the antenna, in m2. (This is something which must be measured as part of the antenna calibration.) • The relative efficiency f(θ,φ) of the antenna, which is normalized such that it has a maximum of 1. (This shape must also be calibrated.) • The received power spectrum w (units: W Hz-1).

  14. Going into a little more detail... Pointing direction of the antenna – NOT the zenith. Kraus uses P where I have f. J D Kraus, “Radio Astronomy” 2nd ed., Fig 3-2.

  15. Going into a little more detail... • The general relation between these quantities is: Remember that the ½ only applies where B is unpolarized. • Further useful relations: • It can be shown that ΩA = λ2/Ae.

  16. Going into a little more detail... • Let’s consider two limiting cases: • B(θ,φ) = B (ie, uniform over the sky); • B(θ,φ) = Sδ(θ-0,φ-0) (ie, a point source of flux=S, located at beam centre). B(θ,φ)=Sδ B f f w = ½ AeS w = ½ λ2B ...the ½ still applies only for unpolarized B.

  17. Conversion of everything to temperatures. • Suppose our antenna is inside a cavity with the walls at temperature T (in kelvin). • It can be shown that the power per unit frequency picked up by the antenna is • Because of this linear relation between a white noise power spectrum and temperature, it is customary in radio astronomy to convert all power spectral densities to ‘temperatures’. Hence: w = kT watts per herz.

  18. System temperature • Tsource only says something about the real temperature of the source if • The source area is >>ΩA, and • The physical process producing the radio waves really is thermal. • Tatmosphere is a few kelvin at about 1 GHz. • Tbackground may be as much as 300 K if the antenna is seeing anything of the surroundings! Therefore avoid this. • Tsystem again says nothing about the real temperature of the receiver electronics. Rather it is a figure of merit – the lower the better. Ttotal = Tsource + Tbackground + Tatmosphere + Tsystem

  19. The more usual way to write the measurement uncertainty: • Thus the minimum detectable flux is • and the minimum detectable brightness: • Note: • Bmin not dependent on Ae. • Factors of 2 only for unpolarized case.

  20. A more realistic system: R M Price, “Radiometer Fundamentals”, Meth. Exp. Phys. 12B (1976), Fig 1, section 3.1.4. “Front end” “Back end”

  21. Jargon • The ‘antenna’: • the reflecting surface (ie the dish). • The ‘feed’: • usually a horn to focus the RF onto the detector. • The ‘front end’: • electronics near the Rx (shorthand for receiver). • The ‘back end’: • electronics near the data recorder. • The LO: • local oscillator. A 38 GHz feed horn. The corrugations are good for wide bandwidth. • RF: • Radio Frequency. • IF: • Intermediate Frequency.

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