Editing Cepheid variable (section)

== Pulsation model ==
[[File:Polaris time-lapse illustrating Cepheid type variability.gif|thumb|Time lapse of the Cepheid type variable star Polaris illustrating the visual appearance of its cycle of brightness changes.]]
{{See also|Kappa–mechanism}}
The accepted explanation for the pulsation of Cepheids is called the Eddington valve,<ref name=":0">{{cite journal|bibcode=1984S&T....68..519S|title=Eddington's Valve and Cepheid Pulsations|journal=[[Sky and Telescope]]|volume=68|pages=519|last1=Smith|first1=D. H.|year=1984}}</ref><ref name=":1">{{cite book |doi=10.1888/0333750888/4130 |chapter=American Association of Variable Star Observers |title=The Encyclopedia of Astronomy and Astrophysics |year=2001 |isbn=0-333-75088-8 }}</ref> or "[[κ-mechanism]]", where the Greek letter κ (kappa) is the usual symbol for the gas opacity.

[[Helium]] is the gas thought to be most active in the process. Doubly [[ionization|ionized]] helium (helium whose atoms are missing both electrons) is more opaque than singly ionized helium. As helium is heated, its temperature rises until it reaches the point at which double ionisation spontaneously occurs and is sustained throughout the layer in much the same way a fluorescent tube 'strikes'. At the dimmest part of a Cepheid's cycle, this ionized gas in the outer layers of the star is relatively opaque, and so is heated by the star's radiation, and due to the increasing temperature, begins to expand. As it expands, it cools, but remains ionised until another threshold is reached at which point double ionization cannot be sustained and the layer becomes singly ionized hence more transparent, which allows radiation to escape. The expansion then stops, and reverses due to the star's gravitational attraction. The star's states are held to be either expanding or contracting by the [[hysteresis]]<ref>{{Cite journal |last1=Auvergne |first1=M. |last2=Baglin |first2=A. |last3=Morel |first3=P. -J. |date=1981-12-01 |title=On the existence of hysteresis effects in pulsating stars |url=https://ui.adsabs.harvard.edu/abs/1981A&A...104...47A |journal=Astronomy and Astrophysics |volume=104 |issue=1 |pages=47–56 |bibcode=1981A&A...104...47A |issn=0004-6361}}</ref> generated by the doubly ionized helium and indefinitely flip-flops between the two states reversing every time the upper or lower threshold is crossed. This process is rather analogous to the [[relaxation oscillator]] found in electronics.{{Citation needed|date=September 2024}}

In 1879, [[August Ritter (civil engineer)|August Ritter]] (1826–1908) demonstrated that the adiabatic radial pulsation period for a homogeneous sphere is related to its [[surface gravity]] and radius through the relation:

<math display="block"> T = k \,\sqrt \frac R g </math>

where k is a proportionality constant. Now, since the surface gravity is related to the sphere mass and radius through the relation:

<math display="block"> g = k' \frac M {R^2} = k' \frac {RM} {R^3}  = k' R\rho</math>

one finally obtains:

<math display="block"> T \sqrt \rho = Q </math>

where ''Q'' is a constant, called the pulsation constant.<ref name="SalarisCassisi2005">{{cite book|author1=Maurizio Salaris|author2=Santi Cassisi|title=Evolution of Stars and Stellar Populations|url=https://books.google.com/books?id=r1dNzr8viRYC|date=13 December 2005|publisher=[[John Wiley & Sons]]|isbn=978-0-470-09222-4|page=180}}</ref>