Sérsic Profile
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Sérsic Profile
The Sérsic profile (or Sérsic model or Sérsic's law) is a mathematical function that describes how the Radiance#Intensity, intensity I of a galaxy varies with distance R from its center. It is a generalization of de Vaucouleurs' law. José Luis Sérsic first published his law in 1963. Definition The Sérsic profile has the form \ln I(R) = \ln I_ - k R^ , or I(R) = I_0 \exp, where I_ is the surface brightness, intensity at R = 0. The parameter n, called the "Sérsic index," controls the degree of curvature of the profile (see figure). The smaller the value of n, the less centrally concentrated the profile is and the shallower (steeper) the logarithmic slope at small (large) radii is. The equation for describing this is: \frac = -(k/n)\ R^ . Today, it is more common to write this function in terms of the half-light radius, Re, and the intensity at that radius, Ie, such that : I(R)=I_e \exp\left\, where b_n is approximately 2n-1/3 for n>8. b_n can also be approximated t ...
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Radiance
In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiation, and to quantify emission of neutrinos and other particles. The SI unit of radiance is the watt per steradian per square metre (). It is a ''directional'' quantity: the radiance of a surface depends on the direction from which it is being observed. The related quantity spectral radiance is the radiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. Historically, radiance was called "intensity" and spectral radiance was called "specific intensity". Many fields still use this nomenclature. It is especially dominant in heat transfer, astrophysics and astronomy. "Intensity" has many other meanings in physics, with the most common being power per unit ...
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