Brightness in Radio Astronomy

General Terms

The brightness of celestial sources can be expressed in several different ways. The terms used by astronomers for these quantities include:

Special Terms

Radio astronomers use some terms and units for a couple of the above quantities that may be unfamiliar even to optical astronomers!

How Much is a Jansky?

Celestial sources of radio emission are much fainter than most human sources of radio waves, whether intentional (broadcast stations, cell phones) or otherwise (power lines, microprocessors, etc.). It is for this reason that radio astronomers seek observing sites far from population centers: to minimize potential interfering signals, just as optical astronomers seek to avoid "light pollution". To understand just how faint natural radio sources are, and what a jansky really measures, it is useful to make a quantitative comparison with more familiar "anthropogenic" radio signals.

FM radio broadcast stations in the United States typically have 100 kilowatts of effective radiated power (ERP), which includes gain factors from the transmitting antenna design (most radiation goes out horizontally but is equally distributed in azimuth, with a gain of perhaps 5 to 10 times that of an isotropic radiator, so the equivalent isotropic radiated power is only 10-20 kW). The range of such stations is usually about 50 miles = 80 km. The broadcast power will be reduced by some form of inverse-square law, even though it isn't isotropic. For simplicity, let's ignore any propagation effects and assume the arriving power density (APD) is given by an isotropic pattern modified by the gain, with the receiver in the direction of maximum gain. In this case,

APD = ERP / (4 π d2)

where d = the distance from transmitter to receiver. The bandwidth (BW) allocated to 1 FM station is 200 kHz. Let's assume the signal strength is uniform across this bandwidth. For the above parameters, the flux density at a receiver 80 km from the station -- near the edge of its effective range -- in the optimal-gain path will be:

Sν = APD / BW
     = ERP / (4 π d2 BW)
     = 105 W / [4 × 3.14 × (8 × 104 m)2 × (2 × 105 Hz)]
     = 6.2 × 10-12 W m-2 Hz-1
     = 6.2 × 1014 Jy

where 1 Jy = 10-26 W m-2 Hz-1 as noted above.

For comparison, most radio astronomy sources have signal strengths of a few Jy or less. The Sun, which is the brightest celestial source at most frequencies, has a flux density of about 106 - 108 Jy at 1 GHz, depending on whether there is surface activity (flares, etc.) or not. The brightest supernova remnant, Cassiopeia A, is about 3000 Jy at 1 GHz but a whopping 20,000 Jy at 100 MHz (the FM broadcast band), because it's a highly nonthermal (synchrotron) source -- as is Solar activity at these frequencies (Cas A is intrinsically much brighter than the Sun but appears fainter because it's a lot farther away). The faintest 1.4 GHz sources in recent large-scale radio surveys like the NRAO-VLA Sky Survey are a few milli-janskys. Newer, deeper surveys like the Evolutionary Map of the Universe project are targeting sources at the 50 μJy (50 micro-janskys) level, which is about 100 times fainter than the NVSS, or 60 million times fainter than Cas A. As you might surmise, such detections require that there is no significant interference from nearby radio broadcast stations!

It's also noteworthy that the brightness contrast between radio-frequency interference and radio astronomical sources is much greater than that between optical light pollution and most optical astronomical sources! Inner-city skies (when clear) can be up to 100 times (5 magnitudes) brighter than the darkest night skies far from any artificial light sources, reducing the number of visible stars from thousands to dozens. But as indicated above, a stray radio broadcast can easily be a million times brighter than the Sun at radio wavelengths, and a trillion times brighter than more "ordinary" radio sources! The contrast in the latter case is similar to that between the optical brightness of the Sun and the 3rd-magnitude stars that fill in many of the fainter parts of prominent constellations in the night sky.

How "Hot" is the Sky?

The Universe does not have a single physical temperature (if it did, then life could not exist, according to the laws of thermodynamics). Instead, it contains a mixture of hot and cold objects, running the gamut from a few kelvins to billions of kelvins. All things produce radiation of one sort or another over a range of frequencies, which can be characterized in flux, intensity, or brightness temperature terms.

At radio frequencies, the major types of radiation are:

The radio sky includes a wide variety of sources of all of the above types, whose relative contributions vary with direction, frequency, and time. Thus, just as the Universe lacks a uniform physical temperature, the sky lacks a uniform brightness temperature. But if discrete sources like stars, galaxies, and other objects of small angular extent are excluded, the general diffuse "background" has:

So how "hot" the sky appears varies, and at low frequencies, it has nothing to do with real temperature, except in special cases like the CMB. Below a few hundred MHz, the brightness temperature of the sky is very warm indeed, but above a GHz or so, where one can see the CMB, the sky is truly "cold" by human standards -- much colder than the ground in fact, or any person who happens to step in front of a radio telescope!

References

Steven Gibson | Radio Projects