Assume a star with a surface temperature of 28000K and a radius of 5.16x109 m. L

Question

Assume a star with a surface temperature of 28000K and a radius of 5.16x109 m. Let this star be located at a distance of 123 pc from Earth. Determine the following: a) Absolute bolometric magnitude b) Apparent bolometric magnitude I know that the bolometric magnitude is the magnitude integrated over all possible wavelengths, but I'm not sure how to apply that.
Assume a star with a surface temperature of 28000K and a radius of 5.16x109 m. Let this star be located at a distance of 123 pc from Earth. Determine the following: a) Absolute bolometric magnitude b) Apparent bolometric magnitude I know that the bolometric magnitude is the magnitude integrated over all possible wavelengths, but I'm not sure how to apply that.

Explanation / Answer

b)
The apperant bolometric magnitude is calculated as follows:
m = - 2.72 - 2.5 · log(L/d^2)
Where L is the luminosity given by
L = 4(pi)R^2(sigma)T^4

R is the radius of the star = 5.16*10^9 m
sigma is the Stefan-Boltzmann constant 5.67 × 10-8 W·m-2·K-4
T is the absolute temperature of the star

L = 1.16547839419318272*10^31

m = - 2.72 - 2.5 · log(1.16547839419318272*10^31/(123*3.0857*10^16)^2)
m = 12.51

a) The absolute magnitude is M = m - 5 (log D - 1) D is the distance of the star in parsec M = 12.51 - (log123 - 1) M = 11.42

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