More Details about Radio Astronomy

Radio Telescopes

Such an instrument consists of an antenna to intercept the radio waves and convert them into an electronic signal, the receiver to amplify and filter the signals, and a computer to deal with any subsequent processing and recording, as well as the control or the telescope.

For antennas we use parabolic mirrors which concentrate the radio waves onto a dipole in the focus. The oscillating field of the electromagnetic wave induces in the dipole an alternating voltage which is boosted by a low-noise preamplifier and is fed to the receiver. As with an optical telescope, the mirror has two functions: to capture as much energy from the wave, and to concentrate the sensitivity to a suitably small region in the sky. A mirror of diametre D has an effective area A_eff = π (D/2)² and captures of an object with flux F within a bandwidth B a power of

P = B F A_eff / 2 The factor of 2 comes in because a dipole registers only electric fields which are oriented parallel to its length. Due to the wave nature of the radiation this mirror has a finite angular resolution. In the radio region this is described by the width of the antenne beam (HPBW = Half-Power Beam Width). For a uniformly illuminated circular mirror one obtains HPBW = 58.8° λ/D One may also define an important parameter, the antenna's effective solid angle, in which it is sensitive, and relate it to the HPBW: Ω_A = λ²/ A_eff ≈ 1.27 (HPBW/58.8°)²

Radiation Quantities

The emission from celestial bodies consists only in a more or less broad-band noise, whose strength may vary with time. The function of a telescope is to measure the strength of this unmodulated signal. The receiver electronics - in particular the preamplifier - also produces broad-band noise due to thermal motions of the conduction electrons and noise produced in active devices (transistors). It is common and useful to characterize the power received by the telescope in terms of the temperature whose thermal noise gives the same strength. The latter amounts to kTB at a band width B. This gives the definition of antenna temperature as k T_ant B = P Every (celestial) body of temperature T emits thermal radiation, whose intensity (specific intensity, surface brightness, ...) is given by a blackbody law (Planck function) I = B(f,T) = (2hf³/ c²) / (exp(hf/kT) – 1) ≈ 2kT (f/c)²
= (2760 T)/λ² with the unit W/m²/Hz/steradian. This is the power that passes along a line-of sight through 1 m² of a detector's area in a bandwidth of 1 Hz and into a cone of 1 unit solid angle (steradian). The solid angle is measured as the surface on a sphere with radius 1 which intercepted by the cone; the entire sphere having the solid angle 4 π. This quite complicated definition takes account of the fact that the brightness of e.g. a wall does not change when viewed from a greater distance. This quantity is often confused with the flux which diminishes with distance.

At the temperatures encountered in sky objects and in the radio region one has hf/kT « 1 and thus one can approximate the Planck function by the Rayleigh-Jeans approximation. If we also use the sensible unit 1 Jy (Jansky) = 10^-26 W/m² for the flux, one gets the simple numerical expression with temperature in Kelvin and wavelength in Meters.

We note that the intensity is directly proportional to temperature, which shows the usefulness of the habit to think in terms of temperatures.

The intensity is the power which the body radiates into a unit solid angle, and which we receive from it pre unit solid angle. If the object, as seen from us, fills the solid angle of Ω the radiative flux (flux, flux density; in principle, one should also use a frequency index to indicate that it is specified for a bandwidth of 1 Hz - like the intensity I)

F = I Ω which depends on distance. For a point source (Ω < Ω_A), which is not resolved by the telescope, the captured power with a band width B is P = B F A_eff / 2 = B I Ω A_eff Thus the antenna temperature is the true source temperature but reduced by the filling factor Ω/Ω_A: T_ant = T Ω/Ω_A and depends on the distance.

On the other hand, from an extended source, whose emission fills completely the antenna beam, one measures only the part which is captured by the antenna beam:

P = B I Ω_A A_eff / 2 Therefore the antenna temperature is equal to the true temperature of the object. T_ant = P/(2kB) = T This property is used during a flux calibration: The antenna temperature of the ground or the wall of a large building is about 290 K.

System Parameters

For the interpretation of the data one needs to know several parameters of the antenna and receiver system:

System temperature: this is a measure of the internal noise level of the receiver system, and hence of its sensitivity. It is measured by comparison of the signals from a known source (e.g. the flux calibrator) and from the 'empty' sky: p(source)/p(sky) = (T_source + T_sys) / (T_sky + T_sys) For a first approximation it often suffices to neglect the sky contribution: T_sys ≈ T_source / (p(source)/p(sky)-1) However, the thermal radiation of the sky is important, especially at higher frequencies. For a more accurate determination one needs to measure and interprete the sky profile.
Half-Power Beam Width (HPBW): describes the angular resolution of the antenne. It can be measured by a drft scan of e.g. the Sun.
Effective area of the antenna can be derived from the measured HPBW using: A_eff = (π/4) * (58.8° λ/HBPW)²

Observational Methods

The principal issue on radio astronomy is noise. Signals from celestial sources are nothing but wide-band unmodulated noise, which often is only slightly above the noise produced by the receiver electronics. The aim of measurements is it to determine the level of one noisy signal in comparison with another. Because of the steady inherent fluctuations of the signal level one averages (or integrates) the signals over a time span as long as possible, since the residual error of the average over n samples of a pure noise signal increases with √n , and hence the relative error decreases like 1/√n . On top of that there may be short- and long-term changes of the receiver properties such as gain and noise figure, caused by changes in temperature and supply voltage, changes in the earth atmosphere by solar irradiation, weather, passing clouds, or small-scale temperature inhomogeneities. The more accurate one wants to measure and the weaker is the source, the various influences become more important.

There are several methods to separate the signal of interest from the varying hackground:

For sources that are not too weak, one can use the drift scan: The antenns is held fixed at the position where the source will be in a few minutes time. As the apparent movement of the sky lets the source travel across antenna beam, one registers first an increase of the signal, then a decrease. The maximum yields the strength of the source, the lower portions before and after give the sky background. This method also provides infomation about the width and shape of the antenna beam.
In the On/Off-method one observes the source for some time, then the sky nearby. As every time the source is observed the signal will be slightly higher, carrying out this procedure many times will permit to measure this difference with sufficient accuracy.
If the wanted signal level is comparable with the amplitude of statistical fluctations of the measurement, a continuous comparison with a constant reference signal is required: This can be a load resistor held at constant temperature which is switched to to receiver input (Dicke switching), a constant-level noise source, or the sky next to the object (beam switching). The measurements are carried out by alternating between the source and the reference signal, from which the difference is derived.
Spectral observations show 'left' and 'right' of the emission feature any continuum radiation or noise. Since this of no interest for the interpretation of the line emission, it is considered as an underlying background, the 'baseline'. As a receiver may normally show a frequency dependence across the passband, one determines the accurate run of the baseline by matching a suitable function to the parts which are devoid of emission features. To measure the line components this baseline is subtracted from the raw spectrum.