Source: http://www.setileague.org/askdr/jansky.htm (~2004)

Understanding the Jansky

Dear Dr. SETI: The Jansky (Jy) is defined as: . -26 . 2 1 10 Watts / Hz m Is the Hz term the frequency of reception, or the bandwidth of the received signal?

Argonaut Roy (via email)

The Doctor Responds:

Neither, Roy. It's the detector bandwidth of the receiver. But don't be discouraged; that was a really great question.

The key to understanding flux density is the "per Hertz" denominator in the definition of the Jansky. The Jansky is a unit of flux density used for natural continuum emissions. Since continuum sources are extremely broadband, it is difficult to exactly quantify their bandwidth. But we consider that they are broader than the detector bandwidth of the receiver being used to detect them, and assume that the received energy is more or less uniformly distributed across the receiver bandwidth. The detector will thus pick up more total power the wider its bandwidth is. First we measure total goo scooped up by the antenna (in Watts per square meter of collecting area). Then, if we divide that power reading by the bandwidth of the receiver, in Hertz, we get flux density in Watts per square meter per Hertz. Since a Watt per square meter per Hertz is one helluva lot of power, we divide it by 1026 to get a more realistic unit for measuring natural astrophysical phenomena. We call the resulting unit the Jansky, after the (accidental) father of radio astronomy.

So, to answer your question directly, we use receiver bandwidth when measuring flux density in Janskys. But remember that doing so only makes sense if the signal in question is spectrally BROAD, so that the recovered power can be assumed to be uniformly distributed across the receiver's detector bandwidth. While this is likely the case for continuum sources, it is decidedly not true for the kinds of narrow-band signals we look for in SETI (or, for that matter, any other signals likely to be generated by technology, as opposed to nature). That's why, although we characterize the sensitivity of radio telescopes in Janskys, the Jansky is not the appropriate unit of measure for the sensitivity of a SETI receiver. For those, we define sensitivity simply in Watts per square meter.

For what it's worth, the threshold sensitivity of the typical amateur SETI station (such as yours, Roy) is on the order of 10-23 Watts per square meter. This is about the sensitivity of the late Big Ear Radio Telescope at Ohio State University, back in 1977 when it detected the famous "Wow!" signal. We achieve that sensitivity through digital signal processing, which makes the instantaneous channel bandwidth ("bin width") exceedingly narrow, thus shutting out much of the broadband background noise. That trick only works if the signal we're trying to receive is ALSO very narrow. That trick also makes the Jansky a meaningless unit for the SETI enterprise (although if you use your SETI station to do continuum radio astronomy, then for that application you can talk Janskys).

1 of 2 ------Source: https://astronomy.stackexchange.com/questions/20704/how-are-people-converting-intensities-in-janskys-to-kelvin (~2018)

How are people converting intensities in Janskys to Kelvin?

Question: I'm reading some ALMA proposals and I am often seeing a conversion from Jy to Kelvin when, for example, people quote noise levels or source flux.

For example on their sensitivity calculator (https://almascience.nrao.edu/proposing/sensitivity-calculator) 1 mJy is equivalent to around 1 K when the angular resolution is 1". I can tell it somehow depends on the resolution because it won't give me a conversion unless I enter a resolution.

What's happening under the hood here? And why does their documentation treat sensitivities entered in Kelvin differently from when they're entered in Jy? Is this an interferometry thing?

Answer: This is, indeed, a result of how we measure things in radio astronomy. It's not just interferometry, but radio astronomy in general. The thing they're referring to is a concept called "brightness temperature". In the low frequency limit (valid for radio astronomy), we can use the Rayleigh-Jeans approximation, which gives us the expression 2 TB = Sν λ2 / (2 k θS ) where Sν is the flux density, λ is the wavelength, k is Boltzmann's constant, and θs is the size of the source (or the resolution in this case). As long as your source and wavelength are constant, brightness temperature and flux density can be interchanged.

The reason astronomers talk about temperatures instead of fluxes sometimes is twofold. First, a large number of objects examined by radio astronomers are not blackbodies. Therefore we cannot calculate their temperatures like we normally would. Instead, we calculate what their temperature would be if they were blackbodies. This at least gives us a value to compare them to other things.

Secondly, when discussing radio telescopes and antennae, we usually say that various parts of the antenna contribute different 'temperatures'. We can quantify system temperatures to help us understand noise.

------Source: http://physics.wku.edu/~gibson/radio/brightness.html (~2016)

Brightness in Radio Astronomy

(Open the source link to see the text.)

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