Jansky

Jansky units are not a standard SI unit, so it may be necessary to convert the measurements made in the unit to the SI equivalent in terms of watts per square metre per hertz (W·m⁻²·Hz⁻¹). However, other unit conversions are possible with respect to measuring this unit.

The flux density in janskys 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:{{cite journal | first1=M. |last1=Fukugita | title=Galaxy Colors in Various Photometric Band Systems | journal=Publications of the Astronomical Society of the Pacific | date=1995 | volume=107 | pages=945–958 | doi=10.1086/133643 | last2=Shimasaku | first2=K. | last3=Ichikawa | first3=T. |bibcode = 1995PASP..107..945F | doi-access=free }}

$$S\_v~[\backslash mathrm\{\backslash mu\}\backslash text\{Jy\}]\; =\; 10^\{6\}\; \backslash cdot\; 10^\{23\}\; \backslash cdot\; 10^\{-\backslash tfrac\{\backslash text\{AB\}\; +\; 48.6\}\{2.5\}\}\; =\; 10^\backslash tfrac\{23.9\; -\; \backslash text\{AB\}\}\{2.5\}.$$

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

1 jansky is equal to −260 dBW·m⁻²·Hz⁻¹, or −230 dBm·m⁻²·Hz⁻¹:{{cite web |url=http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt |title=Units and Calculations |last1=Davis |first1=Mike |format=PPT |date=June 2002 |website=iucaf.org |access-date=2025-03-12 |url-status=live |archive-url=https://web.archive.org/web/20160303223821/http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt |archive-date=2016-03-03 }}

$$\backslash begin\{align\}$$

P_{\text{dBW}\cdot\text{m}^{-2} \cdot \text{Hz}^{-1}} &= 10 \log_{10}\left(P_\text{Jy}\right) - 260, \\

P_{\text{dBm}\cdot\text{m}^{-2} \cdot \text{Hz}^{-1}} &= 10 \log_{10}\left(P_\text{Jy}\right) - 230.

\end{align}

The spectral radiance in janskys per steradian can be converted to a brightness temperature, useful in radio and microwave astronomy.

Starting with Planck's law, we see

$$B\_\{\backslash nu\}\; =\; \backslash frac\{2h\backslash nu^3\}\{c^2\}\backslash frac\{1\}\{e^\{h\backslash nu/kT\}-1\}.$$

This can be solved for temperature, giving

$$T\; =\; \backslash frac\{h\backslash nu\}\{k\backslash ln\backslash left\; (1+\backslash frac\{2h\backslash nu^3\}\{B\_\backslash nu\; c^2\}\backslash right\; )\}.$$

In the low-frequency, high-temperature regime, when $h\backslash nu\; \backslash ll\; kT$, we can use the asymptotic expression:

$$T\backslash sim\; \backslash frac\{h\backslash nu\}k\backslash left(\backslash frac\{B\_\backslash nu\; c^2\}\{2h\backslash nu^3\}+\backslash frac\; 12\backslash right).$$

A less accurate form is

$$T\_b\; =\; \backslash frac\{B\_\{\backslash nu\}c^2\}\{2k\backslash nu^2\},$$

which can be derived from the Rayleigh–Jeans law

$$B\_\{\backslash nu\}\; =\; \backslash frac\{2\backslash nu^2\; kT\}\{c^2\}.$$

The flux to which the jansky refers can be in any form of radiant 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 1–100 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.{{cite journal |first1= B. S. |last1=Sathyaprakash |first2=Bernard F. |last2 = Schutz | title = Physics, Astrophysics and Cosmology with Gravitational Waves |journal=Living Reviews in Relativity |date=2009-03-04 |volume=12 |issue=1 |page=2 |doi=10.12942/lrr-2009-2 |doi-access=free |pmid=28163611 |pmc=5255530 |arxiv=0903.0338 |bibcode=2009LRR....12....2S }} 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·m⁻²·Hz⁻¹, so the result is multiplied by 10²⁶ to get a more appropriate unit for natural astrophysical phenomena.

{{cite web

| author= Ask SETI

| publisher = SETI League

| title = Research: Understanding the Jansky

| url=http://www.setileague.org/askdr/jansky.htm

| date=2004-12-04

| access-date = 2007-06-13

}}

The millijansky, mJy, was sometimes referred to as a milli-flux unit (mfu) in older astronomical literature.

{{cite journal

| last=Ross |first=H.N.

| title= Variable radio source structure on a scale of several minutes of arc

| journal=The Astrophysical Journal

| year=1975

| volume=200

| page=790

| bibcode=1975ApJ...200..790R|doi = 10.1086/153851 |doi-access=free

}}

Note: Unless noted, all values are as seen from the Earth's surface.{{cite book | first=John Daniel | last=Kraus | title=Radio Astronomy | year=1986 | publisher=Cygnus-Quasar Books | isbn=1882484002 | at=Table: Radio spectrum of astronomical sources | url=http://astro.u-strasbg.fr/~koppen/10GHz/basics.html | access-date=2013-08-24 | archive-url=https://web.archive.org/web/20130516042600/http://astro.u-strasbg.fr/~koppen/10GHz/basics.html | archive-date=2013-05-16 | url-status=dead }}

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Category:Radio astronomy

Category:Units of measurement

Category:Non-SI metric units

Category:Units of measurement in astronomy