Kappa mechanism
The kappa opacity mechanism (κ-mechanism) is the driving mechanism behind the changes in luminosity of many types of pulsating variable stars. The term Eddington valve has been used for this mechanism, but this is increasingly obsolete.[1]
Here, the Greek letter kappa (κ) is used to indicate the radiative opacity at any particular depth of the stellar atmosphere. In a normal star, an increase in compression of the atmosphere causes an increase in temperature and density; this produces a decrease in the opacity of the atmosphere, allowing energy to escape more rapidly. The result is an equilibrium condition where temperature and pressure are maintained in a balance. However, in cases where the opacity increases with temperature, the atmosphere becomes unstable against pulsations.[2] If a layer of a stellar atmosphere moves inward, it becomes denser and more opaque, causing heat flow to be checked. In return, this heat increase causes a build-up of pressure that pushes the layer back out again. The result is a cyclic process as the layer repeatedly moves inward and then is forced back out again.[3]
Stellar non-adiabatic pulsation resulting from the κ-mechanism occurs in regions where hydrogen and helium are partly ionized, or where there are negative hydrogen ions. An example of such a zone is in RR Lyrae variables where the partial second ionization of helium occurs.[2] Hydrogen ionization is most likely the cause of pulsation activity in Mira variables, rapidly oscillating Ap stars (roAp) and ZZ Ceti variables. In Beta Cephei variables, stellar pulsations occur at a depth where the temperature reaches approximately 200,000 K and there is an abundance of iron. The increase in the opacity of iron at this depth is known as the Z bump, where Z is the astronomical symbol for "metals" – elements other than hydrogen and helium.[4]
References
[edit]- ↑ Tao, Louis; Spiegel, Edward; Umurhan, O. Matt (1998). "Stellar Oscillations". APS Division of Fluid Dynamics Meeting Abstracts: LC.10. Bibcode:1998APS..DFD..LC10T.
- 1 2 Maeder, André (2009). Physics, formation and evolution of rotating stars. Astronomy and astrophysics library. Springer. p. 373. ISBN 978-3-540-76948-4.
- ↑ de Boer, Klaas Sjoerds; Seggewiss, Wilhelm (2008). Stars and stellar evolution. L'Editeur: EDP Sciences. p. 172. ISBN 978-2-7598-0356-9.
- ↑ LeBlanc, Francis (2010). An Introduction to Stellar Astrophysics. John Wiley and Sons. p. 196. ISBN 978-0-470-69957-7.
Further reading
[edit]- Radial Stellar Pulsations. Princeton lesson on radial pulsation, with kappa and epsilon mechanisms.
- Pulsating Stars: Stars that Breathe. Presentation of Swinburne University of Technology, 2010.
- Cox, John P. (1963). "On Second Helium Ionization as a Cause of Pulsational Instability in Stars". The Astrophysical Journal. 138: 487. Bibcode:1963ApJ...138..487C. doi:10.1086/147661.
- Stein, R. F.; Cameron, A. G. W. (1966). Stellar evolution. Bibcode:1966stev.conf.....S.
- John P. Cox (1980). Theory of Stellar Pulsation. Princeton University Press. ISBN 978-0-691-08253-0.
- Andre Maeder (19 December 2008). Physics, Formation and Evolution of Rotating Stars. Springer Science & Business Media. ISBN 978-3-540-76949-1. In Fig. 15.8 at p. 399 there is a schematic representation of the variations of V magnitude, radial velocity, radius with respect to the minimum radius and effective temperature of a classical Cepheid (δ Ceph) over one period.