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In astrophysics, the mass–luminosity relation is an equation giving the relationship between a star's mass and its luminosity, first noted by Jakob Karl Ernst Halm. [1] The relationship is represented by the equation: L L ⊙ = ( M M ⊙ ) a {\displaystyle {\frac {L}{L_{\odot }}}=\left({\frac {M}{M_{\odot }}}\right)^{a}} where L ⊙ and M ⊙ ...
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.
Luminosity is an absolute measure of radiated electromagnetic energy per unit time, and is synonymous with the radiant power emitted by a light-emitting object. [1] [2] In astronomy, luminosity is the total amount of electromagnetic energy emitted per unit of time by a star, galaxy, or other astronomical objects. [3] [4]
The minimum brightness is about magnitude +1.6 [14] when Mars is on the opposite site of the Sun from the Earth. Rotational variations can elevate or suppress the brightness of Mars by 5% and global dust storms can increase its luminosity by 25%. [14] [18]
The luminosity of the star, which can be measured from observations of the star's apparent brightness, [7] can then be written as: L = 4 π R s t a r 2 σ T s t a r 4 {\displaystyle L=4\pi R_{\rm {star}}^{2}\sigma T_{\rm {star}}^{4}} where the flux has been multiplied by the surface area of the star.
If atmospheric refraction is ignored, it can be shown from simple geometrical considerations (Schoenberg 1929, 173) that the path of a light ray at zenith angle through a radially symmetrical atmosphere of height above the Earth is given by = + + or alternatively, = (+) where is the radius of the Earth. The relative air mass is then
Brightness temperature or radiance temperature is a measure of the intensity of electromagnetic energy coming from a source. [1] In particular, it is the temperature at which a black body would have to be in order to duplicate the observed intensity of a grey body object at a frequency ν {\displaystyle \nu } . [ 2 ]
The luminosity thus obtained is known as the bolometric luminosity. Masses are often calculated from the dynamics of the virialized system or from gravitational lensing . Typical mass-to-light ratios for galaxies range from 2 to 10 ϒ ☉ while on the largest scales, the mass to light ratio of the observable universe is approximately 100 ϒ ...