Mass-Luminosity Relation

Written by User 1

Last Updated: January 17, 2011, 10:41 pm (UTC)
Originally created on January 17, 2011

Like humans, all stars are unique. Some may be very similar but on the whole, they are all different. Unlike humans however, knowing just one property of the star says a lot about everything else.

With the majority, if not all stars, the more massive it is, the bigger it will end up being. It will also shine brighter but at the cost of a shorter lifespan.

The luminosity (actual brightness) of a star is dependent on two main factors: its age and its mass.

Stars generally begin dimly and steadily brighten as they pass through their main sequence. Towards the end of main sequence, if it has enough mass, the star swells up often changing color before dying out.

Although the age of a star will change, for the most part, its mass will remain almost the same. There are exceptions as in the case of the supermassive Wolf-Rayet stars which may lose 50% of their mass during their lifespan. For other main-sequence stars however, knowing the mass is knowing the luminosity.

L = M ^ 3.5

Which can be re-arranged to:

M = L ^ (1 / 3.5)

L : luminosity (in solar luminosities)
M : mass of star (in solar masses)

Note that this will only work for a star in the middle of their time through main sequence as the sun currently is.

Sirius is a main sequence star which happens to be the brightest star in our night sky. It has a luminosity of 25.4 times that of the sun. Using the second relation gives a mass that is 2.52 times that of the sun. Using more precise methods, scientists have determined that the actual mass is 2.02 times that of the sun.

Alpha Centauri is probably the best known star system in the night sky due to it being the one closest to the sun. Alpha Centauri A, the brightest of the three stars (the others being a Cen B and Proxima Cen) is 1.519 times as luminous as the sun. Using the second relation again, its mass is found to be 1.127 times that of the sun, a much closer approximation to the actual value of 1.100.

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