Kappa mechanism

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The kappa mechanism is a pulsation process that describes the changes in brightness of pulsation- variable stars ( variable stars ). This mechanism can come into effect when the opacity ( kappa ) in the stellar atmosphere increases with increasing temperature .

Basics

In general, there is an equilibrium of forces in a star. That is, the gravitational force that tries to contract the star is balanced by the radiation pressure created by the nuclear fusion inside.

Deviations from this equilibrium can cause the star to pulsate. For example, if the radius of the star is smaller than it would correspond to the equilibrium state, the radiation pressure predominates and the star expands. Because of the inertia, this pushing back force causes the star to expand beyond the equilibrium point; now gravity dominates and the star is shrinking again. So there is an oscillation , the star pulsates. In most stars (such as the sun ) these pulsations are very small. The strength of the pulsation therefore depends on the type of restoring force.

Kappa mechanism

The kappa mechanism creates a repulsive force that causes a star to pulsate. Energy in the form of gamma rays is generated inside a star by nuclear fusion . However, this energy is not radiated directly from the star: Due to the high density inside the star, the gamma radiation is scattered many times on its way to the surface of the star. This partial impermeability of the stellar atmosphere is called opacity and is often referred to with the Greek letter ( kappa ). Inside a star, however, the opacity is not constant. It depends on pressure and temperature and also has a different value for each wavelength . If the opacity increases as the temperature of the star material increases, pulsations can arise from it. The kappa mechanism can then be described as follows:

  • The material in a zone of the stellar atmosphere, in which the opacity increases with increasing temperature, is compressed by external disturbances, i.e. H. this layer moves towards the center of the star.
  • The compression increases the pressure and temperature of this material.
  • Increasing the pressure and temperature increases the opacity.
  • Due to the increased opacity of this layer, less radiation now penetrates from the star's interior to the outside; it "accumulates" underneath.
  • This creates a greater radiation pressure below the layer , which causes the layer to expand.
  • The expanding layer now becomes cooler and the pressure drops, which also reduces the opacity again.
  • The pent-up radiation can now escape quickly.
  • As the radiation escapes, the pressure below the layer decreases, which compresses it towards the interior of the star due to the now stronger gravitational force and the cycle begins again.

The process described above can be described in a purely qualitative manner using a steam engine in which the opacity corresponds to a valve.

Remarks

The changes in brightness that are triggered in Cepheids by the kappa mechanism are primarily not due to a change in the star's radius, but, as described above, to a change in the pressure and temperature inside the star.

The basic requirement for the functioning of the kappa mechanism is an increase in opacity with temperature. This dependence can mostly be found in the ionization layers of stars: the main components of most stars are hydrogen and helium . Because of the high temperatures inside the star, hydrogen and helium exist there as plasma , i.e. H. the electrons are no longer bound to the atomic nucleus . How strongly the atoms are ionized, i.e. H. how many of the electrons can move freely depends on the temperature (this is especially true for helium). Helium has two electrons; In addition to helium nuclei, who have lost both electrons are in the stellar atmosphere also He + - ions before, so helium atoms with only one electron.

If the temperature rises, their number falls and the fully ionized helium dominates. This also means that the number of free electrons increases with increasing temperature. The opacity is now significantly influenced by the number of free electrons, as the radiation is scattered and deflected on them. The layers in the stellar atmosphere in which the helium is incompletely ionized are the most favorable for the development of pulsations. There the presumed dependence of the opacity on the temperature prevails.

This layer will now lie somewhere below the star's surface and the pulsations generated there then also include the parts of the star that are outside (but not the center). If this layer is too close to the surface (which is the case with hot stars), there will be no strong pulsations, as the outer layers are not dense enough to transmit the pulsation. Even if the stars are too cool, the kappa mechanism no longer works because the helium ionization layer is deeper in the star, but convection processes form near the surface and the energy can no longer be transported to the outside without being disturbed by pure radiation processes.

The radial pulsation driven by the Kappa mechanism occurs only in a narrowly defined temperature range ( Cepheid instability stripes ). However, there are other regions of instability in which the δ-Scuti and γ-Doradus stars lie, which are also driven by the kappa mechanism. The difference lies essentially in the internal structure, such as the extent of the convection zones, and the type of pulsation of the stars, which is used with the method of asteroseismology to investigate this structure. In these areas, the Kappa mechanism can produce not only radial, but especially non-radial pulsations, equivalent to the vibrations of a drop of water.

Further regions of instability at higher temperatures result from ionization layers of other elements. Of astrophysical importance are the elements of the iron group, mainly iron itself, which form a pulsation instability at slightly higher temperatures and with stars that are closer to the main sequence than the δ-Cepheids. Stars whose pulsation is caused by this so-called iron opacity bump are, for example, β-Cepheids , SPB stars ( slowly pulsating B-stars ) and λ-Eri stars. As with the kappa mechanism by helium, both radial and non-radial pulsations are excited here, depending on the instability region.

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