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This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2M ⊙ < M < 55M ⊙ and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then a = 1. In summary, the relations for stars with different ranges of mass are, to a good approximation, as the following: [2] [4] [5]
Flux decreases with distance according to an inverse-square law, so the apparent magnitude of a star depends on both its absolute brightness and its distance (and any extinction). For example, a star at one distance will have the same apparent magnitude as a star four times as bright at twice that distance.
Early photometric measurements (made, for example, by using a light to project an artificial “star” into a telescope's field of view and adjusting it to match real stars in brightness) demonstrated that first magnitude stars are about 100 times brighter than sixth magnitude stars.
Luminosity distance D L is defined in terms of the relationship between the absolute magnitude M and apparent magnitude m of an astronomical object. = which gives: = + where D L is measured in parsecs.
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 ]
Prior to photographic methods to determine magnitude, the brightness of celestial objects was determined by visual photometric methods.This was simply achieved with the human eye by compared the brightness of an astronomical object with other nearby objects of known or fixed magnitude: especially regarding stars, planets and other planetary objects in the Solar System, variable stars [1] and ...
(The S 10 unit is defined as the surface brightness of a star whose V-magnitude is 10 and whose light is smeared over one square degree, or 27.78 mag arcsec −2.) The total sky brightness in zenith is therefore ~220 S 10 or 21.9 mag/arcsec² in the V-band. Note that the contributions from Airglow and Zodiacal light vary with the time of year ...
In an evolved star with a pure helium atmosphere, the electric field would have to lift a helium nucleus (an alpha particle), with nearly 4 times the mass of a proton, while the radiation pressure would act on 2 free electrons. Thus twice the usual Eddington luminosity would be needed to drive off an atmosphere of pure helium.