Brightness temperature and antenna temperature

At radio frequencies the power coming out of a resistor is proportional to its temperature, so it’s natural to describe any noise power as “the temperature a resistor would need to be to produce this much.” Radio astronomy uses that everywhere. Your receiver has a noise temperature, the sky has a temperature, the ground has a temperature, and a spectral line has a temperature.

Brightness temperature (T_B) belongs to the sky. It’s the temperature a black body would need to have to look as bright as that patch of sky at that frequency. Galactic hydrogen in the plane reaches tens of kelvin, and around 100 K in the brightest directions.

Antenna temperature (T_A) belongs to your setup. It’s the extra noise your receiver sees when the antenna points at the source, and it depends on how the source compares with your beam.

Extended sources: beam filling

If the emission is bigger than your beam, the antenna temperature is roughly the brightness temperature times the beam efficiency, and it does not depend on antenna size. A 17 dBi horn and a 4 m dish pointed at the same bright stretch of Galactic HI see similar line strengths. The dish sees a smaller patch in more detail; it does not see a stronger line. This is the reason a horn works for a first detection, and it’s why LAB-010 qualifies the “aperture drives sensitivity” rule of thumb.

Point sources: aperture is everything

For a source much smaller than the beam, what matters is the effective area A_e. A 1.8 m dish at 55% efficiency has about 1.40 m² of effective area. A source of 1 jansky gives it:

1.40 × 10⁻²⁶ / (2 × 1.381 × 10⁻²³) = 0.51 mK

Half a millikelvin, against a system temperature of 100 K or more. That’s why small stations stick to the hydrogen line and a few of the brightest continuum sources, and why every factor in antenna gain counts once you go after anything compact.

Calibrating your own axis

Most first spectra are in arbitrary units. A rough scale comes from pointing the antenna at the ground (close to 290 K) and at cold sky away from the plane (a few tens of kelvin including your own spillover), and treating the difference as a known temperature step. LAB-012 describes this, and the radiometer equation tells you how long a given line temperature takes to show.