Jansky

The jansky (symbol Jy) is a non-SI unit of spectral flux density,^[1] or spectral irradiance, equivalent to 10⁻²⁶ watts per square metre per hertz.

The flux density or monochromatic flux, $S$, of a source is the integral of the spectral radiance, $B$, over the source solid angle:

$S = \iint_{\mathrm{source}} B(\theta,\phi)\mathrm{d}\Omega$

The unit is named after pioneering US radio astronomer Karl Guthe Jansky, and is defined as:

$1 \ \mathrm{ Jy} = 10^{-26} \frac{ \mathrm{W} }{ \mathrm{m^2} \cdot \mathrm{Hz} }$ (SI) $= 10^{-23} \frac{\mathrm{erg}}{ \mathrm{s} \cdot \mathrm{cm^2} \cdot \mathrm{Hz} }$ (cgs)^[2]

Since the jansky is obtained by integrating over the whole source solid angle, it is most simply used to describe point sources; for example, the Third Cambridge Catalogue of Radio Sources (3C) reports results in Jy.

• For extended sources, the surface brightness is often described with units of Jy per solid angle; for example, Far Infra-Red (FIR) maps from the IRAS satellite are in MJy/sr.
• Although extended sources at all wavelengths can be reported with these units, for radio frequency maps, extended sources have traditionally been described in terms of a brightness temperature; for example the Haslam et al. 408 MHz all-sky continuum survey is reported in terms of a brightness temperature in K.

Unit conversions

Jansky units are not a standard SI Unit, so it may be necessary to convert the unit to Watts. However, other unit conversions are possible with respect to measuring this unit.

AB magnitude

The flux density in Jy can be converted to a magnitude basis, for suitable assumptions about the spectrum. For instance, converting an AB magnitude to a flux-density in microjanskys is straightforward:^[3]

$S_v \ [\mathrm{\mu Jy}] = 10^{6} \cdot 10^{23} \cdot 10^{-(\mathrm{AB}+48.6)/2.5} = 10^{(23.9-\mathrm{AB})/2.5}$

dBW/m²/Hz

The linear flux density in Jy can be converted to a decibel basis, suitable for use in fields of telecommunication and radio engineering.

1 Jansky is equal to -260 dBW/m²/Hz, or -230 dBm/m²/Hz.^[4]

$P_{dBW/m^2/Hz} = 10 \log_{10}(P_{Jy}) - 260$

$P_{dBm/m^2/Hz} = 10 \log_{10}(P_{Jy}) - 230$

Usage

The flux to which the jansky refers can be in any form of energy.

It was created for and is still most frequently used in reference to electromagnetic energy, especially in the context of radio astronomy.

The brightest astronomical radio sources have flux densities of the order of one to one hundred janskys. For example, the Third Cambridge Catalogue of Radio Sources lists some 300 to 400 radio sources in the Northern Hemisphere brighter than 9 Jy at 159 MHz. This range makes the jansky a suitable unit for radio astronomy.

Gravitational waves also carry energy, so their flux density can also be expressed in terms of janskys. Typical signals on Earth are expected to be 10²⁰ Jy or more.^[5] However, because of the poor coupling of gravitational waves to matter, such signals are difficult to detect.

When measuring broadband continuum emissions, where the energy is roughly evenly distributed across the detector bandwidth, the detected signal will increase in proportion to the bandwidth of the detector (as opposed to signals with bandwidth narrower than the detector bandpass). To calculate the flux density in janskys, the total power detected (in watts) is divided by the receiver collecting area (in square meters), and then divided by the detector bandwidth (in hertz). The flux density of astronomical sources is many orders of magnitude below 1 W/(m²·Hz), so the result is multiplied by 10²⁶ to get a more appropriate unit for natural astrophysical phenomena.^[6]

The millijansky, mJy, was sometimes referred to as a milli flux unit (m.f.u.) in the astronomical literature.^[7]

Orders of magnitude

Jansky (Jy)	Source
110,000,000	Radio-frequency interference from a GSM phone transmitting 0.5 W at 1800 MHz at a distance of 1 km (RSSI of -70 dBm)[8]
20,000,000	Disturbed Sun at 20 MHz (Karl Guthe Jansky's initial discovery, published in 1933)
4,000,000	Sun at 10 GHz
1,000,000	Milky Way at 20 MHz
10,000	1 Solar flux unit
2,000	Milky Way at 10 GHz
1,000	Quiet Sun at 20 MHz

Note: Unless noted, all values are as seen from the earth's surface.^[9]

References

1. http://science.jrank.org/pages/57879/jansky.html
2. Burke, Bernard F.; Graham-Smith, Francis (2009). An Introduction to Radio Astronomy (3rd ed.). Cambridge University Press. p. 9. ISBN 0-521-87808-X.
3. M. Fukugita; Shimasaku, K.; Ichikawa, T. (1995). "Galaxy Colors in Various Photometric Band Systems". PASP 107: 945–958. Bibcode:1995PASP..107..945F. doi:10.1086/133643.
4. http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt
5. B. S. Sathyaprakash; Schutz (2009-03-04). "Physics, Astrophysics and Cosmology with Gravitational Waves". Living Reviews in Relativity. Retrieved 2011-02-01.
6. Ask Dr. SETI (2004-12-04). "Research: Understanding the Jansky". Seti League. Retrieved 2007-06-13.
7. Ross, H.N. "Variable radio source structure on a scale of several minutes of arc". Bibcode:1975ApJ...200..790R. doi:10.1086/153851.
8. http://www.iucaf.org/SSS2010/presentations/day2/Clegg(Units).ppt
9. John Daniel Kraus. Radio Astronomy. ISBN 1882484002., table: radio spectrum of astronomical sources: http://astro.u-strasbg.fr/~koppen/10GHz/basics.html