Editing Jansky (section)

== 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>