Greetings.

I can't find any place where an organization specifically states what is taken as a Cepheid variable's apparent magnitude to estimate its distance. That is to say, what value of the Cepheid's light curve is taken to determine the distance modulus, m - M, where of course M is estimated from its period: the maximum, the minimum, or an average.

I suppose in a rigorous computation we'd first construct the mean curve with error bars such as that shown for alf Ori on page 3 of the AAVSO 5-Star Analysis Tutorial to check that we cannot draw a straight line through the 95% error bars, etc., but my question what do we take as 'm' in the distance modulus? The brightest average perhaps? .. say 0.68 magnitude? [I'm ignoring that Betelgeuse is not Cepheid.]

In an introductory lab, we can just eyeball what we think would be its apparent magnitude, but again, is that the "mean" of the overall max to min values (.. ignoring obvious outliers), or just the maximum of the high points (.. again ignoring obvious outliers), or getting a little fancy and using the max of the "mean curve" with imagined 95% error bars and just trust our gut feeling (and eyeballs) to guess .. more specifically, letting the mind's eye do the work.

Thanks for your comments.

df

Apparently this question was a show-stopper. How about just a guess which value of apparent magnitude to use in determining the distance modulus? Anyone? You don't even have to be an expert ... it would be interesting just how many folks are using something other which has been acknowledged by IAU.

I'm not sure but I guess you should use (max mag + min mag) / 2. Where max and min mag is an average magnitud at the top and bottom points of the lightcurve.

I have no particular expertise re this question, but here goes:

1) I'll restate your question to clarify what I think I am answering: "What absolute magnitude measure is used in the Cepheid Period-Luminosity (P-L) Relationship?" Is it the maximum of the lightcurve, the minimum, average of the two, the integrated mean, etc.

2) at one level, perhaps it doesn't matter. Use the measure of your choice to make the P-L graph, then "read out" the same measure from the period of the star whose distance you are trying to determine. This could be erroneous depending on how the shape of the LC changes with period.

3) some googling leads me to https://arxiv.org/pdf/astro-ph/0012376.pdf ("Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant ") by Freedman et. al. which forms a P-L relationship for stars in the LMC using HST observations. I don't have time to read this paper, but drilling down on this and its references will probably yield the answer. A superficial browse leaves me thinking they are using "mean" magnitude, but I don't know if that is avg of min and max, or an integrated mean.

If you determine the answer, please report back!

Gary Billings

VStar's Leavitt Law Calculator plugin allows you to select the series to use from a loaded dataset (e.g. del Cep). It computes the apparent mean magnitude from all loaded observations for the selected series. I too have wondered about the most appropriate approach. The plugin allows the period (from VSX by default) and default computed mean apparent magnitude to be changed.

See:

References I've used:

I'd like to extend the plugin to other variable types like Type II Cepheids and RR Lyr at some point.

David

I found some lecture notes: http://www.astro.sunysb.edu/metchev/PHY515/cepheidpl.html

It is said there, that mean apparent magnitude was used.

Leavitt's original works should be accessible through NASA ADS.

Best wishes,

Tõnis