Period-Luminosity Relationship of Type I Cepheids - Need Better Formula

[Desmos]

This is related to a HW post I made over in the HW forum. I am stuck trying to find a more detailed formula for the Period-luminosity relationship of Type I Cepheids.

Wikipedias description doesn't seem to match with the book (or include any mention of type I or type II), and frankly the graphical approach in my book isn't cutting it for me. Is there a better formula/relationship out there.

It seems I might be able to get a decent estimate by taking making my own linear/log function from the graph, but when I do so the answer varies quite a bit depending on which values for the points on the graph I estimate.

 

[chemisttree]

Read Wiki more carefully.

Cepheid variables are divided into at least two subclasses: Population I or classical Cepheids, and Population II or W Virginis Cepheids. The former are young massive stars, whereas the latter are older fainter stars.[13] Population I and II Cepheids follow different period-luminosity relationships. The luminosity of Population II Cepheids is, on average, less than classical Cepheids by about 1.5 magnitudes (but still brighter than RR Lyrae stars).

Also from the Wiki article,

M_v = -2.81 log₁₀(P) - 1.43( +/- 1)

where:

M_v = absolute magnitude (Population 1 Cepheids)
P = period in days

http://en.wikipedia.org/wiki/Cepheid_variable

 

[Desmos]

I went ahead and used that as well. However the book makes a distinction between type and population. O well, thanks though.