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What numerical value does the pulsation constant $Q$ take in the formula that Eddington derived for variable stars: $$P\sqrt{\rho} = Q,$$ where $\rho$ — average star density, $P$ — period?

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  • $\begingroup$ What do you get when you enter typical values for density and period? $\endgroup$ Jan 19, 2022 at 21:16
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    $\begingroup$ Your question is unclear. For what specific case of values are you interested, or are you interested in a physical interpretation? $\endgroup$ Jan 20, 2022 at 0:00
  • $\begingroup$ @GrapefruitIsAwesome the question seems clear enough to me at least, but I've added some words to make it even clearer. It's going to be some number in units of s kg^1/2 m^-3/2 for example, but what is that number? $\endgroup$
    – uhoh
    Jan 20, 2022 at 11:10
  • $\begingroup$ I agree with @GrapefruitIsAwesome. What is asked beyond plugging in values into that equation? $\endgroup$ Jan 20, 2022 at 11:25
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    $\begingroup$ @Александр Иванов you question would become more interesting if you can expand it with a bit background to your question. Especially expand it on the level you expect an answer to be, and include the question's background with your prior knowledge. As it stands now, an answer could vary between typing two numbers from a pocket calculator up to writing a whole essay or even book on the matter. $\endgroup$ Jan 20, 2022 at 13:18

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This is an attempt to answer the question as to the value of the Eddington pulsation constant as it relates to Cepheid variables. The constant, $Q$, is defined as: $$Q = P\sqrt{\rho} = P\sqrt{\frac{\bar{\rho}_\odot}{\bar{\rho}}}$$

where $P$ is the pulsation period and $\rho$ is the star density. Pulsation period is typically specified in days and the density is relative to the sun's mean density, $\bar{\rho}_\odot$. (see eqn. 11 in Asteroseismology)

As this constant really isn't constant, only approximately, this answer will be more of a survey with references for additional details.

Period (days) Reference Notes
0.03 - 0.04 Handler Over the whole HR diagram for the radial fundamental mode
0.033 Handler For the sun
0.0329 Joshi $\delta$ Scuti stars
0.033 $\pm$ 0.002 Abdel-Sabour YZ Boo
0.037 Watson \beta Cephei stars
0.03 < $Q$ < 0.08 Scuflaire Theoretical calculations
0.179 Percy 89 (V441) Herculis

There are probably a bunch more that could be added. Some additional interesting reading related can be found in The Secret Lives of Cephids.

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