Talk:Mass–luminosity relation

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A fact from Mass–luminosity relation appeared on Wikipedia's Main Page in the Did you know column on 27 August 2009 (check views). The text of the entry was as follows:

Did you know... that the mass-luminosity relation, first derived by Arthur Eddington in 1924, helps astronomers find the distances to binary star systems?

A record of the entry may be seen at Wikipedia:Recent additions/2009/August.

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Expert needed

Is it M or M cubed? The first section says L is proportional to M for the limiting case, but the rest of the article says M cubed. Either change this (if you know it), or explain what was really meant. Długosz (talk) 23:39, 27 August 2009 (UTC)[reply]

For normal stars, its M cubed. But according to one source, for massive stars, it becomes proportional to M. I was not sure how much to include about that, because usually its M cubed. (or a = 3.5). Danski14^(talk) 01:15, 28 August 2009 (UTC)[reply]

The mass-luminosity relation isn't a pure power relation because the tangent line to the graphed curve of main sequence stars, plotted as log luminosity versus log mass, does not always go through (0,0).

Accordingly, the model [ L = b M^a ] is better than the model [ L = M^a ], though sometimes b may be equal to one.

You should get a mass-luminosity composite function that is piecewise continuous. I'll see if I can make one from a graph of log luminosity versus log mass for (main sequence) eclipsing binary stars.

If M<=0.6224 then L = 0.3815 M^2.5185

If M>0.6224 and M<=1 then L = M^4.551

If M>1 and M<=3.1623 then L = M^4.351

If M>3.1623 and M<=16 then L = 2.7563 M^3.4704

The data I have stop at about M=16, so I can't go higher than this until I get data for the upper main sequence. Here's a guess, though.

If M>16 then L = 42.321 M^2.4853

Jenab6 (talk) 01:51, 1 June 2010 (UTC)[reply]

Age and Metallicity?

There's also the question of the star's age, because most stars increase in luminosity as they grow older. These equations don't appear to include age as a variable. Do they represent mean luminosity? Peak luminosity? Luminosity at zero-age main sequence ignition? Metallicity also impacts luminosity -- are these equations for Solar metallicity? How do they change at other metallicities? 2601:441:5000:ADF0:35DA:C87E:75C2:A251 (talk) 00:21, 27 July 2023 (UTC)[reply]