# Why can't you calculate the absolute magnitude of cepheid variables from apparent magnitude?

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!

Thank you!

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!

• Can you give more detail so that your calculation can be debugged? – my2cts May 29 '18 at 20:26
• And what are you defining as "the" absolute magnitude of a Cepheid variable? – Rob Jeffries May 29 '18 at 20:42
• The first method is generic for any source of light but it doesn't consider any obstruction, modification on the way, while the second one is an instrinsic property of Cepheid variables. All in all the first method should be accompanied by corrections from other things like dust on the way, lensing, etc... Try observing if the discrepancy is systematic or random, if it is random it is very likely some correction as said, if not you might need to check for a deeper reason (which I don't know) – ohneVal May 29 '18 at 20:58
• @RobJeffries In the lab I give my students I mean the arithmetic mean of the maximum and minimum. It seems that H.S. Leavitt used the "mean magnitude" when she first reported on the period-luminosity relationship for these stars, but I'm not sure if she did a proper average over the cycle or something as simple as I give my students. – dmckee --- ex-moderator kitten May 30 '18 at 1:54

You can do this if you know the distance.

And that is important because it is how you calibrate the period-luminosity relationship in the first place.

But the main point here is that we use Cepheid variable stars to measure distance (as one step on the distance ladder), meaning that we don't know that distance. By using

1. Groups of Cepheid variables that all have about the same distance (in the original measurement these are stars in the Magelenic clouds) to learn that longer periods are associated with brighter stars (and to fit a mathematical relationship between period and magnitude).

2. The small number of Cepheid variables close enough to range by direct parallax to calibrate the observation into absolute rather than apparent magnitude.

we make these stars into a ruler, and use them to measure the distance to nearby galaxies.

• I understand the bit about using the period-magnitude relationship to measure distance, but therein I seem to run into the opposite problem - AKA, the correct magnitude and period for some reason give me the wrong distance. – Corrigendum May 30 '18 at 15:53
• Follow-up question: how does one determine the distance without knowing the period-magnitude relationship? – Corrigendum May 30 '18 at 16:13
• "Follow-up question: how does one determine the distance without knowing the period-magnitude relationship?" Like it says in the post "by direct parallax". – dmckee --- ex-moderator kitten May 30 '18 at 21:41
• Okay, fair enough. That's what I thought, and that's what's worked thus far. The problem still stands, however, that even though the distance is right and the apparent magnitude should be right and the formula is definitely right, the absolute magnitude provided is wrong, and no one seems to be able to answer why this is the case. – Corrigendum May 31 '18 at 15:27
• What do you expect us to say about the data in front of you? Ask the person who set the assignment. – dmckee --- ex-moderator kitten May 31 '18 at 16:24