# How do you determine which star, between two, is more luminous?

For example, if star 1 is 4x bigger than star 2 but both are the exact same temperature how do you determine which is more luminous?

• Consider Stefan–Boltzmann law. But the problem as stated seems highly artificial. – Stan Liou Jul 16 '15 at 18:47
• It's a conceptual question I pulled from my astronomy text book. The link below states that in order to determine the luminosity of a star that is twice as large as the sun you would use the following equation: L = (2 R⊙)2(T⊙)4 = 4L⊙ (the Hertzsprung-Russell Diagram). How do I apply this to my question? astro.unl.edu/naap/hr/hr_background2.html – Jay Jul 16 '15 at 19:07
• Just use 4 times the radius instead of two times the radius. I can't understand your difficulty, star 1 is $4^2$ times as luminous. – ProfRob Jul 16 '15 at 20:31

## 1 Answer

One way to determine the luminosity of a star is to first determine its distance, d. Then one can use the formula, Luminosity = Flux * 4 * Pi * d$^2$. Flux is related to the apparent brightness that is measured with a telescope (and CCD or photometer). mag = -2.5 * Log(Flux) + c.

If the star is relatively nearby, one can use parallax to get the distance. If the star is in a binary system, one can solve for the distance from the period, orbital velocities and apparent size of the orbit. If you know the velocities throughout one orbit, then one knows how far it has physically traveled. Comparing this with the apparent size gives an approximate distance. However, since one usually does not know the inclination, this causes uncertainty. If it is an eclipsing binary, then you know that it is not very inclined and this works well. On the other hand, if it is eclipsing, one can usually determine the radii of the binary pair and then get distances from Stefan Boltzmann Law.

Another method for estimating luminosity is to locate the star in the HR Diagram (Luminosity vs Color). The color (difference between the magnitudes in two different filters) locates it horizontally, and stellar class locates it vertically in the diagram. One needs a spectrum of the star to determine the class.

And we have one more trick up our sleeves. If the star is a periodic variable such as a Cepheid or an RR Lyra, then there are relations between period of variability and luminosity.

• This is a highly confusing answer to what is an extremely simple question. – ProfRob Sep 15 '15 at 21:32