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The Physics Of Cepheid Variable Stars
The K-Mechanism
The Radius Of Cepheid Variables
Exercise-Determine The Radius Of Eta Aquilae

THE K-MECHANISM


It was Eddington who theorised what he called the 'valve mechanism', that is if a layer within the star became more opaque as it gets compressed it would hold back a larger amount of heat trying to get up to the surface. This would in effect make the star expand. However as the star expands, the layer becomes more transparent and heat would escape lowering the temperature and so allowing the star to fall back in to start another cycle.

The level of opacity of a layer must increase with compression, but Kramers law that governs opacity says that in most regions of stars, opacity actually decreases with compression.

Kramers Law:-

The opacity is both dependent on the stars density and temperature, but is more dependent on the temperature due to its power of 3.5. This is why the opacity usually increases upon compression, it takes special conditions to overcome the damping effect of most stellar layers which explains why pulsating stars are rare (around 1 in stars) in the universe.

The special conditions where Eddingtons 'valve mechanism' can operate were discovered some time later by a Russian astronomer S.Zhevakin. The region inside a star called the partial ionisation zone create more ionised particles when they are compressed rather than raise the temperature. When this happens, the density increases more than the temperature and so the opacity increases. This in term traps the heat and starts the stars expansion. Now during the expansion, the temperature does not drop by as much as what would be expected because the ions recombine with the electrons producing energy as they do so. The density also decreases which in turn lowers the opacity and so allows the star to contract and start the cycle again.

 

Diagram showing the opacity peak. The y-axis is the logarithm of the opacity, the x and z-axis the logarithms of the temperature and density respectively.

THE K-MECHANISM
ENTER A VALUE FOR THE TEMPERATURE AND DENSITY:

Temperature e.g. Sun's effective temperature=5800K

Density e.g. Sun's effective density=1.41

Opacity

 The graph below shows the changing of magnitude of a Cepheid and its temperature. Notice how the temperature (T) lags behind the magnitude (V).

Graph of Delta Cephei's various parameters over a period of time


 The Radius Of Cepheid Variables



 

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