1. NASSP Masters 5003F - Computational Astronomy - 2009 Lecture 9 – Radio Astronomy Fundamentals Source (randomly accelerating electrons) Noisy electro- magnetic radiation (transfers energy) Antenna (simple dipole example) Load resistance R Types of electron acceleration: Thermal (random jiggling) Synchrotron (spiral) Spectral line (resonant sloshing)

2. NASSP Masters 5003F - Computational Astronomy - 2009 Noise power spectrum Analyse the signal into Fourier components. jth component is: The Fourier coefficient V j is in general complex-valued. Power in this component is: Closely related to the ‘power spectrum’ we’ve already encountered in Fourier theory. V j (t) = V j exp(-i ω j t) = V j (cos[ω j t] + i sin[ω j t]) P j = V j *(t)V j (t)/R = V j *V j /R (cos 2 [ω j t] + sin 2 [ω j t]) = V j *V j /R

3. NASSP Masters 5003F - Computational Astronomy - 2009 Averaging the power spectrum t = 1t = 16 t = 64t = 4

4. NASSP Masters 5003F - Computational Astronomy - 2009 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 P total = P source + P background + P atmosphere + P system

5. NASSP Masters 5003F - Computational Astronomy - 2009 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: –Note the Poisson-like character: σ P is proportional to P. A low-pass filter with a time constant t is another way of ‘averaging’.

6. NASSP Masters 5003F - Computational Astronomy - 2009 Antenna detection efficiency The source radiates at S W m -2 Hz -1. The antenna has an effective area A e 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 = A e S watts per herz.

7. NASSP Masters 5003F - Computational Astronomy - 2009 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.

8. NASSP Masters 5003F - Computational Astronomy - 2009 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.

9. NASSP Masters 5003F - Computational Astronomy - 2009 Directionality of antennas. A radio telescope often (not always) incorporates a mirror. Parkes GMRT Ok as long as the roughness is << λ. An optically ‘smooth’ surface These are supposed to be smooth mirrors?

10. NASSP Masters 5003F - Computational Astronomy - 2009 Directionality of antennas. Reflector Focal plane Point Spread Function Radio telescopes with a mirror can be analysed like any other reflecting telescope...

11. NASSP Masters 5003F - Computational Astronomy - 2009 A more usual treatment: Beam width Side lobe It is often conceptually easier to imagine that the antenna is emitting radiation to the sky rather than absorbing it. Beam width ~ λ /D, same as for any other reflector. Eg Parkes 64m dish at 21 cm, beam width ~ 15’.

12. NASSP Masters 5003F - Computational Astronomy - 2009 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 A e of the antenna, in m 2. (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 ).

13. NASSP Masters 5003F - Computational Astronomy - 2009 Going into a little more detail... J D Kraus, “Radio Astronomy” 2 nd ed., Fig 3-2. Pointing direction of the antenna – NOT the zenith. Kraus uses P where I have f.

14. NASSP Masters 5003F - Computational Astronomy - 2009 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 Ω A = λ 2 /A e.

15. NASSP Masters 5003F - Computational Astronomy - 2009 Going into a little more detail... Let’s consider two limiting cases: –B( θ, φ ) = B (ie, uniform over the sky); –B( θ, φ ) = S δ ( θ-0, φ-0 ) (ie, a point source of flux=S, located at beam centre). f f B B( θ,φ )=S δ w = ½ λ 2 B w = ½ A e S...the ½ still applies only for unpolarized B.

16. NASSP Masters 5003F - Computational Astronomy - 2009 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.

17. NASSP Masters 5003F - Computational Astronomy - 2009 System temperature T source only says something about the real temperature of the source if –The source area is >> Ω A, and –The physical process producing the radio waves really is thermal. T atmosphere is a few kelvin at about 1 GHz. T background may be as much as 300 K if the antenna is seeing anything of the surroundings! Therefore avoid this. T system again says nothing about the real temperature of the receiver electronics. Rather it is a figure of merit – the lower the better. T total = T source + T background + T atmosphere + T system

18. NASSP Masters 5003F - Computational Astronomy - 2009 The more usual way to write the measurement uncertainty: Thus the minimum detectable flux is and the minimum detectable brightness: Note: 1.B min not dependent on A e. 2.Factors of 2 only for unpolarized case.

19. NASSP Masters 5003F - Computational Astronomy - 2009 A more realistic system: R M Price, “Radiometer Fundamentals”, Meth. Exp. Phys. 12B (1976), Fig 1, section 3.1.4. “Back end” “Front end”

20. NASSP Masters 5003F - Computational Astronomy - 2009 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.

21. NASSP Masters 5003F - Computational Astronomy - 2009 Flux calibration The bandwidth and gain of the radiometer tend not to be very stable. There are several methods of calibration. Eg: 1.Switching between the feed and a ‘load’ at a temperature similar to the antenna temperature. But, this can be < 20 K... 2.Periodic injection of a few % of noise into the feed. Noise sources can be made much more stable than noise detectors. Still good to look occasionally at an astronomical source of known, stable flux. Should also be unresolved (compact). –Difficult conditions to meet all together! Compact sources tend to vary with time.