I'm currently working on an assignment related to Cepheid Variable stars, and I feel like I've basically gotten all the relevant concepts down pat. However, in the course of my work, I've discovered that there are two separate ways to calculate absolute magnitude - one related to distance and apparent magnitude (which is for stellar objects in general)...
M = m - 5((logD) - 1)
...and the other related to the period of the star (which is unique to Cepheids - this equation, specifically, to classical ones):
M = -2.43 * ((logP)-1) - (4.05)
When I calculated the M values separately according to these two methods, it turned out that the M calculated from apparent magnitude were incorrect, whereas those calculated from the Cepheid period were always correct (according to the SIMBAD database). Just to make 100% sure that my first method was right, I checked with some non-Cepheid stars, and the results were perfect, so it's only the Cepheids that are being problematic.
So why is it that you can't use the "classic" formula for Cepheids? My current theory is that it has to do with the fact that the light curve is asymmetrical so the "average" apparent magnitude number is actually not representative of the real curve, but I'd like to make sure that this is actually the case!
EDIT: In response to a request for my working, I’ll use my data on Eta Aquilae as an example:
Method 1: Distance is 423.73 parsecs. Maximum m is 3.5 and min m is 4.3, avg. is 3.9. We thus plug into the formula: M = 3.9 - 5((log427.73) - 1). M = -4.24, which, according to SIMBAD, is wrong. Using the similar parallax equation provides the same result.
Method 2: Period is 7.18 days. Plugging in gives: M = -2.43 * ((log7.18)-1) - (4.05). M = -3.68, which, according to SIMBAD, is correct.
Hope that helps!