Since the sun has an abs mag of 4.83 (per Wikipedia) and a luminosity of 1 sun (by definition), then can it be said that a star with an abs mag of 2.415 (which is 10x brighter) has a luminosity of 10 suns?
Is this true…
A) Always?
B) As a general rule of thumb, but there are exceptions?
C) Never, unless by coincidence
D) Only true (or generally true) for Main Sequence stars?
It’s been a while since I’ve thought about magnitudes with any regularity, but I believe the answer is somewhere between (B) and ©. When astronomers usually say “absolute magnitude”, they usually mean “absolute visual magnitude”, which depends on how much light the star is emitting in the visual band. However, “luminosity” without any further specification usually refers to the star’s total energy output, including in the infrared & ultraviolet parts of the spectrum. So in principle, a star could have the same visual magnitude as the sun but have a lot more luminosity (if, say, it emitted the same amount of visible light but a lot more infrared.)
Now, if you’re talking about the bolometric magnitude and the bolometric luminosity, then your logic is correct: in both cases, you’re accounting for all the radiant energy of the star. Similarly, if you talk about the visual magnitude and the visual luminosity, you’re restricting both figures to deal with the visible light energy only, and then your logic follows.
Finally, since most stars radiate with essentially a black-body spectrum, two stars with the same surface temperature will emit the same amount of light per surface area at all wavelengths. In this special case, the larger star will emit proportionally more light at all wavelengths, meaning that the ratio between the stars’ bolometric luminosities will be the same as the ratio of their visible luminosities, and so the differences between their bolometric magnitudes and their visible magnitudes will be equal.
And in fact, the solar luminosity is a relatively commonly-used unit in astrophysics.