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The relationship is represented by the equation: = where L ⊙ and M ⊙ are the luminosity and mass of the Sun and 1 < a < 6. [2] The value a = 3.5 is commonly used for main-sequence stars. [ 3 ] This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2 M ⊙ < M < 55 M ⊙ and does not apply to red giants ...
Mass-to-light ratios in application can be used to gain insight into the dark matter content and dust extinction in a galaxy. [4] Historically, rotation curves for spiral galaxies have been used to study galaxies, but mass-to-light ratios prove more accurate as a method of measuring mass. [5]
This latter form of the relation is known as the baryonic Tully–Fisher relation (BTFR), and states that baryonic mass is proportional to velocity to the power of roughly 3.5–4. [ 8 ] The TFR can be used to estimate the distance to spiral galaxies by allowing the luminosity of a galaxy to be derived from its directly measurable line width.
A preliminary description of the three areas of this diagram was made in 2003 by Eric F. Bell et al. from the COMBO-17 survey [1] that clarified the bimodal distribution of red and blue galaxies as seen in the analysis of Sloan Digital Sky Survey data [2] and even in de Vaucouleurs's 1961 analyses of galaxy morphology. [3]
The best-fit value of n correlates with galaxy size and luminosity, such that bigger and brighter galaxies tend to be fit with larger n. [ 5 ] [ 6 ] Setting n = 4 gives the de Vaucouleurs profile : I ( R ) ∝ e − b R 1 / 4 {\displaystyle I(R)\propto e^{-bR^{1/4}}} which is a rough approximation of ordinary elliptical galaxies .
Therefore, the stellar luminosity function is used to derive a mass function (a present-day mass function, PDMF) by applying mass–luminosity relation. [2] The luminosity function requires accurate determination of distances, and the most straightforward way is by measuring stellar parallax within 20 parsecs from the earth.
The choice of using 50% was arbitrary, but proved to be useful in further works by R. A. Fish in 1963, [147] where he established a luminosity concentration law that relates the brightnesses of elliptical galaxies and their respective R e, and by José Luis Sérsic in 1968 [148] that defined a mass-radius relation in galaxies. [139]
According to Brada and Milgrom, [7]. The acceleration constant of the modified dynamics (), a 0, appears in various predicted regularities pertinent to galaxies.For example, it features as an upper cutoff to the mean surface density (or mean surface brightness translated with M/L) of galaxies, as observed and formulated in the Freeman law for disks, and of the Fish law for ellipticals.