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The star's luminosity can be estimated by comparison of the spectrum of a nearby star. The distance is then determined via the following inverse square law: = where is the apparent brightness and is the luminosity. Using the Sun as a reference we can write
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 ...
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 ]
Delta Cephei is also of particular importance as a calibrator of the Cepheid period-luminosity relation since its distance is among the most precisely established for a Cepheid, partly because it is a member of a star cluster [52] [53] and the availability of precise parallaxes observed by the Hubble, Hipparcos, and Gaia space telescopes. [54]
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.
A classical Cepheid's luminosity is directly related to its period of variation. The longer the pulsation period, the more luminous the star. The period-luminosity relation for classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt in an investigation of thousands of variable stars in the Magellanic Clouds. [23]
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]
Intrinsic variables, whose luminosity actually changes periodically; for example, because the star swells and shrinks. Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.