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 Aeff = π (D/2)2
and captures of an object with flux F within a bandwidth B
a power of
P = B F Aeff / 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:
ΩA = λ2/ Aeff ≈ 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 Tant 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 < ΩA),
which is not resolved by the telescope, the captured power with a band width B is
P = B F Aeff / 2 = B I Ω Aeff
Thus the antenna temperature is the true source temperature but reduced by the
filling factor Ω/ΩA:
Tant = T Ω/ΩA
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 ΩA Aeff / 2
Therefore the antenna temperature is equal to the true temperature of the object.
Tant = 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) = (Tsource + Tsys) / (Tsky + Tsys)
For a first approximation it often suffices to neglect the sky contribution:
Tsys ≈ Tsource / (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:
Aeff = (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.