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A star like Deneb, for example, has a luminosity around 200,000 L ⊙, a spectral type of A2, and an effective temperature around 8,500 K, meaning it has a radius around 203 R ☉ (1.41 × 10 11 m). For comparison, the red supergiant Betelgeuse has a luminosity around 100,000 L ⊙ , a spectral type of M2, and a temperature around 3,500 K ...
A difference of 5 magnitudes between the absolute magnitudes of two objects corresponds to a ratio of 100 in their luminosities, and a difference of n magnitudes in absolute magnitude corresponds to a luminosity ratio of 100 n/5. For example, a star of absolute magnitude M V = 3.0 would be 100 times as luminous as a star of absolute magnitude M ...
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 2M ⊙ < M < 55M ⊙ and does not apply to red giants or white dwarfs. As a star approaches the Eddington luminosity then a = 1.
Note that the brighter the star, the smaller the magnitude: Bright "first magnitude" stars are "1st-class" stars, while stars barely visible to the naked eye are "sixth magnitude" or "6th-class". The system was a simple delineation of stellar brightness into six distinct groups but made no allowance for the variations in brightness within a group.
For example, a magnitude 2.0 star is 2.512 times as bright as a magnitude 3.0 star, 6.31 times as magnitude 4.0, and 100 times magnitude 7.0. The brightest astronomical objects have negative apparent magnitudes: for example, Venus at −4.2 or Sirius at −1.46.
The equation of hydrostatic equilibrium may need to be modified by adding a radial acceleration term if the radius of the star is changing very quickly, for example if the star is radially pulsating. [9] Also, if the nuclear burning is not stable, or the star's core is rapidly collapsing, an entropy term must be added to the energy equation. [10]
The Eddington limit is not a strict limit on the luminosity of a stellar object. The limit does not consider several potentially important factors, and super-Eddington objects have been observed that do not seem to have the predicted high mass-loss rate. Other factors that might affect the maximum luminosity of a star include: Porosity.
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 ...