You may have noticed that in the last two posts talking about data calibration that the data is measured in temperature units. This is one of the (many) weird things about (radio) astronomy – the use of temperature to measure the response of the telescope to a source. I call this use of temperature for measurement weird because most radio sources are non-thermal (their measured radiation is not the result of random thermal motions of particles). Like most unusual things in astronomy, this is mostly a result of historical use, but there is reasoning behind the use of temperature units.

You may have encountered the Planck black body curve before. If not, a picture of the curve is below. The Planck curve simply describes the intensity of a radiating source of a given temperature at different wavelengths (or frequencies). At the long wavelengths of the radio regime, this curve can be approximated as a simple relation between the intensity, wavelength and temperature of a source ( $I \propto \frac{T_b}{\lambda^2}$), which is known as the Rayleigh-Jeans law. Thus, it is simple to relate the measured intensity of a source to a temperature at radio wavelengths.

Now, I mentioned that most radio sources are non-thermal. However, for a given intensity and frequency/wavelength, it is still possible to use the Rayleigh-Jeans law to calculate a temperature as though the source were a thermal radiator. Radio astronomers refer to this as a “brightness temperature”. It doesn’t relate to the actual temperature of a source (as measured by random thermal motions of particles), but it is a convenient way to describe the intensity of a source. Historically, this use of brightness temperature developed because of an assumption that all sources would be thermal sources.

One of the reasons the temperature measurement is useful is because it is a good way to characterize noise. If you are worried about spill-over radiation from the ground into your radio dish, you are concerned with black body radiation at 300 K (room temperature). The noise of a receivers is also characterized in temperature. Original receivers were dominated by thermal noise as they were often at or near room temperature. Now, receivers are cooled to decrease the noise but they are still characterized in a temperature. (For example, ALFA has a system noise temperature of 30 K.) Thus, if you want to know how strong a signal you need to be measurable above the noise of the receiver, it is useful to know the signal in the same units as the noise – temperature.