Past Blog Tie-in:
• Stars, Part 1: Fundamental Properties
• Stars, Part 2: Spectral Classes and Spectral Types
As I said in the previous blog, Stars, Part 1: Fundamental Properties, if you know the radius and surface temperature of your star, you can use an equation based on Boltzmann's Law to calculate the Luminosity:
L = absolute luminosity of the star;
LSUN = absolute luminosity of the Sun;
R = absolute radius of the star;
RSUN = absolute radius of the Sun;
T = absolute temperature of the star;
TSUN = absolute temperature of the Sun
If all values are in solar units, the equation simplifies to:
Dividing the calculated luminosity by the measured luminosity returned the following statistics.
For solar-analog stars (Luminosity Class V), the numbers are quite good:
Standard Deviation: 6.59%
Which means that 64% of the calculated values fall in the range [86.92%, 102.41%].
For Luminosity Class I-IV stars, the numbers were less exciting:
Standard Deviation: 28.42%
So, 64% of the calculated values fall in the range [56.10%, 112.93%].
Over the entire data set, the statistics were as follows:
Standard Deviation: 21.43%
Which means that 64% of the calculated values fall in the range [68.07%, 110.93%].
So, while the Boltzmann equation isn't as accurate for the larger main-sequence and giant-plus stars, it is quite close. Outside the realm of solar-analog stars, I'd recommend basing your fictional star on an existing star which is close to the kind you want to use in your fictional system.