Editing Jansky

{{Short description|Unit of spectral flux density}}
{{other uses}}
{{use dmy dates |date=July 2020}}
{{Infobox unit
| name = jansky
| image = 
| caption = 
| standard = non-SI [[Metric system|metric]] unit
| quantity = [[spectral flux density]]
| symbol = Jy
| namedafter = [[Karl Guthe Jansky]]
| extralabel = 
| extradata = 
| units1 = SI units
| inunits1 = {{val|e=-26|u=W⋅m<sup>−2</sup>⋅Hz<sup>−1</sup>}}
| units2 = CGS units
| inunits2 = {{val|e=-23|u=erg⋅s<sup>−1</sup>⋅cm<sup>−2</sup>⋅Hz<sup>−1</sup>}}
}}
The '''jansky''' (symbol '''Jy''', plural ''janskys'') is a non-[[SI]] unit of [[spectral flux density]],<ref>{{cite web|url=https://www.iau.org/publications/proceedings_rules/units/|title=International Astronomical Union &#124; IAU|website=www.iau.org}}</ref> or [[spectral irradiance]], used especially in [[radio astronomy]]. It is equivalent to 10<sup>&minus;26</sup> [[watt]]s per [[square metre]] per [[hertz]].

The ''spectral flux density'' or ''monochromatic flux'', {{mvar|S}}, of a source is the integral of the spectral radiance, {{mvar|B}}, over the source [[solid angle]]:
<math display="block">S = \iint\limits_\text{source} B(\theta,\phi) \,\mathrm{d}\Omega.</math>

The unit is named after pioneering US radio astronomer [[Karl Guthe Jansky]] and is defined as
{{unbulleted list | style = padding-left: 1.5em;
| 1 = <math>1~\mathrm{Jy} = 10^{-26}~\mathrm{W}{\cdot}\mathrm{m^{-2}}{\cdot}\mathrm{Hz^{-1}}</math> ([[SI]])<ref>{{cite book |last1=Burke |first1=Bernard F. |last2=Graham-Smith |first2=Francis | title=An Introduction to Radio Astronomy | page=9 | edition=3rd | date=2009 | publisher=[[Cambridge University Press]] | isbn=978-0-521-87808-1 }}</ref>
| 2 = <math>1~\mathrm{Jy} = 10^{-23}~\mathrm{erg}{\cdot}\mathrm{s^{-1}}{\cdot}\mathrm{cm^{-2}}{\cdot}\mathrm{Hz^{-1}}</math> ([[centimetre–gram–second system of units|CGS]]).
}}
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 janskys.
* For extended sources, the surface brightness is often described with units of janskys per solid angle; for example, far-infrared (FIR) maps from the [[IRAS]] satellite are in megajanskys per [[steradian]] (MJy⋅sr<sup>−1</sup>).
* 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&nbsp;MHz all-sky continuum survey is reported in terms of a brightness temperature in [[kelvin]].<ref>{{Cite journal|last=Haslam|first=C. G. T.|date=1985-03-01|title=The 408 MHz all-sky continuum survey|url=http://adsabs.harvard.edu/abs/1985BICDS..28...49H|journal=Bulletin d'Information du Centre de Donnees Stellaires|volume=28|pages=49|bibcode=1985BICDS..28...49H|issn=1169-8837}}</ref>

== Unit conversions ==
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<sup>−2</sup>·Hz<sup>−1</sup>). However, other unit conversions are possible with respect to measuring this unit.

=== AB magnitude ===
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:<ref name="fuk95">{{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 }}</ref>
<math display="block">S_v~[\mathrm{\mu}\text{Jy}] = 10^{6} \cdot 10^{23} \cdot 10^{-\tfrac{\text{AB} + 48.6}{2.5}} = 10^\tfrac{23.9 - \text{AB}}{2.5}.</math>

=== dBW·m<sup>−2</sup>·Hz<sup>−1</sup> ===

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&nbsp;[[Decibel watt|dBW]]·m<sup>−2</sup>·Hz<sup>−1</sup>, or −230&nbsp;[[dBm]]·m<sup>−2</sup>·Hz<sup>−1</sup>:<ref>{{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 }}</ref>
<math display="block">\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}</math>

=== Temperature units ===

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
<math display="block">B_{\nu} = \frac{2h\nu^3}{c^2}\frac{1}{e^{h\nu/kT}-1}.</math>
This can be solved for temperature, giving
<math display="block">T = \frac{h\nu}{k\ln\left (1+\frac{2h\nu^3}{B_\nu c^2}\right )}.</math>
In the low-frequency, high-temperature regime, when <math>h\nu \ll kT</math>, we can use the [[asymptotic expression]]:
<math display="block">T\sim \frac{h\nu}k\left(\frac{B_\nu c^2}{2h\nu^3}+\frac 12\right).</math>

A less accurate form is
<math display="block">T_b = \frac{B_{\nu}c^2}{2k\nu^2},</math>
which can be derived from the [[Rayleigh–Jeans law]]
<math display="block">B_{\nu} = \frac{2\nu^2 kT}{c^2}.</math>

== Usage ==
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 source]]s 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&nbsp;Jy at 159&nbsp;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 10<sup>20</sup>&nbsp;Jy or more.<ref>{{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 }}</ref>  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 (signal processing)|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&nbsp;W·m<sup>−2</sup>·Hz<sup>−1</sup>, so the result is multiplied by 10<sup>26</sup> to get a more appropriate unit for natural astrophysical phenomena.<ref>
{{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
}}</ref>

The millijansky, mJy, was sometimes referred to as a milli-flux unit (mfu) in older astronomical literature.<ref name=Ross75>
{{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
}}</ref>

== Orders of magnitude ==

{| class="wikitable"
|-
! Value (Jy)
! Source
|-
|align="right"| {{val|110000000}}
| [[Radio-frequency interference]] from a [[GSM]] telephone transmitting 0.5&nbsp;W at {{val|1.8|u=GHz|fmt=gaps}} at a distance of 1&nbsp;km ([[RSSI]] of −70&nbsp;[[dBm]])<ref>{{cite web|url=http://www.iucaf.org/SSS2010/presentations/day2/Clegg(Units).ppt |title=Data |publisher=iucaf.org |access-date=2019-11-14}}</ref>
|-
|align="right"| {{val|20000000}}
| [[Sunspots|Disturbed Sun]] at 20&nbsp;MHz ([[Karl Guthe Jansky]]'s initial discovery, published in 1933)
|-
|align="right"| {{val|4000000}}
| Sun at 10&nbsp;GHz
|-
|align="right"| {{val|1600000}}
| Sun at [[Hydrogen line|1.4&nbsp;GHz]]
|-
|align="right"| {{val|1000000}}
| [[Milky Way]] at 20&nbsp;MHz
|-
|align="right"| {{val|10000}}
| 1 [[solar flux unit]]
|-
|align="right"| {{val|2000|fmt=gaps}}
| [[Milky Way]] at 10&nbsp;GHz
|-
|align="right"| {{val|1000|fmt=gaps}}
| [[Sunspots|Quiet Sun]] at 20&nbsp;MHz
|}

Note: Unless noted, all values are as seen from the Earth's surface.<ref>{{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 }}</ref>

== References ==
{{reflist}}

{{Clear}}
{{Radio-astronomy}}

[[Category:Radio astronomy]]
[[Category:Units of measurement]]
[[Category:Non-SI metric units]]
[[Category:Units of measurement in astronomy]]