A list of the more common uses of the term “temperature”, and their interrelationships
The Radex manual gives a nice, concise description of these terms
Kinetic Temperature
The “normal” temperature, that appears in the ideal gas law. The average translational kinetic energy of particles.
Excitation Temperature
A property of a pair of energy levels, equal to the temperature of a system in thermodynamic equilibrium that would produce the same population ratio.Defined by the following equation
The excitation temperature is equal to the kinetic temperature in the limit of thermodynamic equilibrium.
Brightness Temperature
A property of a body radiating at a specific intensity. Equal to the temperature of an ideal blackbody that would emit at the same intensity.
Equal to the Rayleigh Jeans temperature at long wavelengths.
Rayleigh-Jeans Temperature
A property of an object radiating at a given specific intensity. Equal to the temperature of a Rayleigh-Jeans emitter that would emit at the same intensity
Converges to the brightness temperature at long wavelengths.
Radiation Temperature
Synonymous with the Rayleigh Jeans temperature.
Antenna Temperature
The power received by an antenna, expressed as a temperature
or, expressed in terms of source flux,
Here, \eta_A is the efficiency of the antenna (the fraction of radiation detected by the telescope), and A is the telescope area.
Main Beam Temperature
The antenna temperature, corrected for the telescope efficiency
The main beam temperature and (Rayleigh Jeans) radiation temperature are equal when a source is resolved (i.e. it fills the telescope beam). Otherwise,