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29-604: The jansky (symbol Jy , plural janskys ) is a non- SI unit of spectral flux density , or spectral irradiance , used especially in radio astronomy . It is equivalent to 10 watts per square metre per hertz . The spectral flux density or monochromatic flux , S , of a source is the integral of the spectral radiance, B , over the source solid angle : S = ∬ source B ( θ , ϕ ) d Ω . {\displaystyle S=\iint \limits _{\text{source}}B(\theta ,\phi )\,\mathrm {d} \Omega .} The unit

58-755: A brightness temperature , useful in radio and microwave astronomy. Starting with Planck's law , we see B ν = 2 h ν 3 c 2 1 e h ν / k T − 1 . {\displaystyle B_{\nu }={\frac {2h\nu ^{3}}{c^{2}}}{\frac {1}{e^{h\nu /kT}-1}}.} This can be solved for temperature, giving T = h ν k ln ⁡ ( 1 + 2 h ν 3 B ν c 2 ) . {\displaystyle T={\frac {h\nu }{k\ln \left(1+{\frac {2h\nu ^{3}}{B_{\nu }c^{2}}}\right)}}.} In

87-1003: A decibel basis, suitable for use in fields of telecommunication and radio engineering. 1 jansky is equal to −260  dBW ·m·Hz, or −230  dBm ·m·Hz: P dBW ⋅ m − 2 ⋅ Hz − 1 = 10 log 10 ⁡ ( P Jy ) − 260 , P dBm ⋅ m − 2 ⋅ Hz − 1 = 10 log 10 ⁡ ( P Jy ) − 230. {\displaystyle {\begin{aligned}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{aligned}}} The spectral radiance in janskys per steradian can be converted to

116-432: A full radiometric description of the field of classical electromagnetic radiation of any kind, including thermal radiation and light . It is conceptually distinct from the descriptions in explicit terms of Maxwellian electromagnetic fields or of photon distribution. It refers to material physics as distinct from psychophysics . For the concept of specific intensity, the line of propagation of radiation lies in

145-526: A semi-transparent medium which varies continuously in its optical properties. The concept refers to an area, projected from the element of source area into a plane at right angles to the line of propagation, and to an element of solid angle subtended by the detector at the element of source area. The term brightness is also sometimes used for this concept. The SI system states that the word brightness should not be so used, but should instead refer only to psychophysics. The specific (radiative) intensity

174-511: A transparent medium with a non-unit non-uniform refractive index, the invariant quantity along a ray is the specific intensity divided by the square of the absolute refractive index. For the propagation of light in a semi-transparent medium, specific intensity is not invariant along a ray, because of absorption and emission. Nevertheless, the Stokes-Helmholtz reversion-reciprocity principle applies, because absorption and emission are

203-518: Is T b = B ν c 2 2 k ν 2 , {\displaystyle T_{b}={\frac {B_{\nu }c^{2}}{2k\nu ^{2}}},} which can be derived from the Rayleigh–Jeans law B ν = 2 ν 2 k T c 2 . {\displaystyle B_{\nu }={\frac {2\nu ^{2}kT}{c^{2}}}.} The flux to which

232-428: Is a quantity that describes the rate of radiative transfer of energy at P 1 , a point of space with coordinates x , at time t . It is a scalar-valued function of four variables, customarily written as I ( x , t ; r 1 , ν ) {\displaystyle I(\mathbf {x} ,t;\mathbf {r} _{1},\nu )} where: I  ( x , t  ; r 1 , ν )

261-665: Is defined to be such that a virtual source area, dA 1 , containing the point P 1 , is an apparent emitter of a small but finite amount of energy dE transported by radiation of frequencies ( ν , ν + dν ) in a small time duration d t , where d E = I ( x , t ; r 1 , ν ) cos ⁡ ( θ 1 ) d A 1 d Ω 1 d ν d t , {\displaystyle dE=I(\mathbf {x} ,t;\mathbf {r} _{1},\nu )\cos(\theta _{1})\,dA_{1}\,d\Omega _{1}\,d\nu \,dt\,,} and where θ 1

290-601: Is many orders of magnitude below 1 W·m·Hz, so the result is multiplied by 10 to get a more appropriate unit for natural astrophysical phenomena. The millijansky, mJy, was sometimes referred to as a milli-flux unit (mfu) in older astronomical literature. Note: Unless noted, all values are as seen from the Earth's surface. SI">SI The requested page title contains unsupported characters : ">". Return to Main Page . Spectral radiance Spectral radiance gives

319-542: Is named after pioneering US radio astronomer Karl Guthe Jansky and is defined as 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. Jansky units are not a standard SI unit, so it may be necessary to convert the measurements made in

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348-422: Is needed to emit a finite amount of light. For propagation of light in a vacuum, the definition of specific (radiative) intensity implicitly allows for the inverse square law of radiative propagation. The concept of specific (radiative) intensity of a source at the point P 1 presumes that the destination detector at the point P 2 has optical devices (telescopic lenses and so forth) that can resolve

377-405: Is the angle between the line of propagation r and the normal P 1 N 1 to dA 1 ; the effective destination of dE is a finite small area dA 2 , containing the point P 2 , that defines a finite small solid angle d Ω 1 about P 1 in the direction of r . The cosine accounts for the projection of the source area dA 1 into a plane at right angles to

406-440: Is unsuitable for the description of a collimated beam, while spectral flux density is suitable for that purpose. Specific (radiative) intensity is built on the idea of a pencil of rays of light . In an optically isotropic medium, the rays are normals to the wavefronts , but in an optically anisotropic crystalline medium, they are in general at angles to those normals. That is to say, in an optically anisotropic crystal,

435-499: The above expression for the collected energy dE , one finds dE = I  ( x , t  ; r 1 , ν ) cos θ 1 dA 1 cos θ 2 dA 2 dν dt / r : when the emitting and detecting areas and angles dA 1 and dA 2 , θ 1 and θ 2 , are held constant, the collected energy dE is inversely proportional to the square of the distance r between them, with invariant I  ( x , t  ; r 1 , ν ) . This may be expressed also by

464-404: The details of the source area dA 1 . Then the specific radiative intensity of the source is independent of the distance from source to detector; it is a property of the source alone. This is because it is defined per unit solid angle, the definition of which refers to the area d A 2 of the detecting surface. This may be understood by looking at the diagram. The factor cos θ 1 has

493-420: 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

522-491: The effect of converting the effective emitting area d A 1 into a virtual projected area cos θ 1 dA 1 = r d Ω 2 at right angles to the vector r from source to detector. The solid angle d Ω 1 also has the effect of converting the detecting area d A 2 into a virtual projected area cos θ 2 dA 2 = r d Ω 1 at right angles to the vector r , so that d Ω 1 = cos θ 2 dA 2 / r . Substituting this for d Ω 1 in

551-426: The energy does not in general propagate at right angles to the wavefronts. The specific (radiative) intensity is a radiometric concept. Related to it is the intensity in terms of the photon distribution function, which uses the metaphor of a particle of light that traces the path of a ray. The idea common to the photon and the radiometric concepts is that the energy travels along rays. Another way to describe

580-412: The geometrical aspects of the Stokes-Helmholtz reversion-reciprocity principle. For the present purposes, the light from a star can be treated as a practically collimated beam , but apart from this, a collimated beam is rarely if ever found in nature, though artificially produced beams can be very nearly collimated. For some purposes the rays of the sun can be considered as practically collimated, because

609-435: 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 Jy or more. 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

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638-548: 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

667-413: The line of propagation indicated by r . The use of the differential notation for areas dA i indicates they are very small compared to r , the square of the magnitude of vector r , and thus the solid angles d Ω i are also small. There is no radiation that is attributed to P 1 itself as its source, because P 1 is a geometrical point with no magnitude. A finite area

696-526: The low-frequency, high-temperature regime, when h ν ≪ k T {\displaystyle h\nu \ll kT} , we can use the asymptotic expression : T ∼ h ν k ( B ν c 2 2 h ν 3 + 1 2 ) . {\displaystyle T\sim {\frac {h\nu }{k}}\left({\frac {B_{\nu }c^{2}}{2h\nu ^{3}}}+{\frac {1}{2}}\right).} A less accurate form

725-424: The same for both senses of a given direction at a point in a stationary medium. The term étendue is used to focus attention specifically on the geometrical aspects. The reciprocal character of étendue is indicated in the article about it. Étendue is defined as a second differential. In the notation of the present article, the second differential of the étendue, d G , of the pencil of light which "connects"

754-413: The statement that I  ( x , t  ; r 1 , ν ) is invariant with respect to the length r of r  ; that is to say, provided the optical devices have adequate resolution, and that the transmitting medium is perfectly transparent, as for example a vacuum, then the specific intensity of the source is unaffected by the length r of the ray r . For the propagation of light in

783-412: The sun subtends an angle of only 32′ of arc. The specific (radiative) intensity is suitable for the description of an uncollimated radiative field. The integrals of specific (radiative) intensity with respect to solid angle, used for the definition of spectral flux density , are singular for exactly collimated beams, or may be viewed as Dirac delta functions . Therefore, the specific (radiative) intensity

812-738: The two surface elements dA 1 and dA 2 is defined as d 2 G = d A 1 cos ⁡ ( θ 1 ) d Ω 1 = d A 1 d A 2 cos ⁡ ( θ 1 ) cos ⁡ ( θ 2 ) r 2 = d A 2 cos ⁡ ( θ 2 ) d Ω 2 . {\displaystyle d^{2}G=dA_{1}\cos(\theta _{1})\,d\Omega _{1}={\frac {dA_{1}\,dA_{2}\cos(\theta _{1})\cos(\theta _{2})}{r^{2}}}=dA_{2}\cos(\theta _{2})\,d\Omega _{2}.} This can help understand

841-938: The unit to the SI equivalent in terms of watts per square metre per hertz (W·m·Hz). 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: S v   [ μ Jy ] = 10 6 ⋅ 10 23 ⋅ 10 − AB + 48.6 2.5 = 10 23.9 − AB 2.5 . {\displaystyle 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}}.} The linear flux density in janskys can be converted to

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