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In 1856, Norman Robert Pogson formalized the system by defining a first magnitude star as a star that is 100 times as bright as a sixth-magnitude star, thereby establishing the logarithmic scale still in use today. This implies that a star of magnitude m is about 2.512 times as bright as a star of magnitude m + 1.
Blue and white supergiants are high luminosity stars somewhat cooler than the most luminous main sequence stars. 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).
The apparent magnitude of stars in the same cluster is equivalent to their absolute magnitude and so this early diagram was effectively a plot of luminosity against temperature. The same type of diagram is still used today as a means of showing the stars in clusters without having to initially know their distance and luminosity. [ 4 ]
Magnitude values do not have a unit. The scale is logarithmic and defined such that a magnitude 1 star is exactly 100 times brighter than a magnitude 6 star. Thus each step of one magnitude is times brighter than the magnitude 1 higher. The brighter an object appears, the lower the value of its magnitude, with the brightest objects reaching ...
L ★ is the star's luminosity (bolometric luminosity) in watts; L 0 is the zero point luminosity 3.0128 × 10 28 W; M bol is the bolometric magnitude of the star; The new IAU absolute magnitude scale permanently disconnects the scale from the variable Sun.
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.
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 object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance. Another way to express the luminosity distance is through the flux-luminosity relationship, = where F is flux (W·m −2), and L is luminosity (W). From this the luminosity distance (in meters ...