Kappa mechanism

The Kappa - mechanism is a Pulsationsprozess that describes the changes in brightness of stars pulsating variables ( variable stars ). This mechanism can then enter into force when the opacity ( kappa ) increases in the stellar atmosphere with increasing temperature.

Basics

In general, there is a star in an equilibrium of forces. That is, the gravitational force, which attempts to contract the rating is balanced by radiation pressure generated by nuclear fusion within.

Deviations from this balance can cause the star pulsates. For example, the radius of the star is less than would correspond to the equilibrium state, the radiation pressure, and the star predominates expanded. Because of the inertia of this restoring force causes the star it expands to the equilibrium point addition; now dominates the gravity and the star shrinks again. The result is thus an oscillation, pulsating star. For most stars (such as the sun ), these pulsations are very small. The strength of the pulsation depends, therefore, on the type of the restoring force.

Kappa - mechanism

The kappa mechanism generates a restoring force that causes a star pulsates. Inside of a star is generated by nuclear fusion energy in the form of gamma radiation. This energy is, however, not directly emitted from the star: Because of the high density inside the star, the gamma radiation is scattered on their way to the surface of the star many times. This partial opacity of the stellar atmosphere is called opacity and often referred to by the Greek letter ( kappa). Inside a star, the opacity is, however, not constant. It depends on the pressure and the temperature, and also has a different value for each wavelength. Now takes the opacity with increasing temperature of the star's material, then can arise from pulsations. The kappa mechanism can then be described as follows:

• The material in a zone of the star atmosphere in which the opacity increases with increasing temperature, is compressed by external disturbances such as this layer moves toward the center of the star.
• The compression increase the pressure and temperature of this material.
• By increasing pressure and temperature the opacity increases.
• Due to the increased opacity of this layer now penetrates less radiation from the stellar interior to the exterior; they " jammed " underneath.
• This results in a layer below the large radiation pressure which results in that the layer now expands.
• The expanding layer is now cooler and the pressure drops, so the opacity is smaller again.
• Now the accumulated radiation can escape quickly.
• By the escape of radiation from the pressure below the layer decreases, whereby it is compressed toward the inside due to the star again stronger gravitational force and the cycle begins anew.

The process described above can be purely qualitatively well described by a steam engine in which the opacity corresponds to a valve.

Comments

The intensity changes, which are caused by the mechanism in kappa Cepheid, are not primarily due to a change in radius of the star, but, as described above, to a change of the pressure and the temperature inside of the star.

A prerequisite for the functioning of the kappa mechanism is an increase in opacity with the temperature. This dependence is usually found in Ionisationsschichten 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, ie the electrons are no longer bound to the atomic nuclei. How much now the atoms are ionized, that is, how many of the electrons are free to move depends on the temperature (which is especially true for helium). Helium has two electrons; In addition to the helium nuclei that have lost both electrons and He ions are present in the stellar atmosphere, ie helium atoms with only one electron.

Now the temperature rises, the number and the fully ionized helium sinks dominates. This also means that as the temperature increases the number of free electrons. The opacity will be significantly influenced by the number of free electrons, since the radiation is scattered at them and distracted. For the generation of pulsations in the layers of the stellar atmosphere are most favorable, in which the helium is ionized incomplete. There exists exactly the presumed function of the opacity of the temperature.

This layer is now somewhere below the stellar surface and the pulsations generated there then (but not the center ) also include the outlying parts of the star. If this layer is too close to the surface ( which is the case with hot stars ), there will be no strong pulsation as the outer layers are not sufficiently dense to pass the pulsation. Even in cool stars of the kappa mechanism no longer works because here, although the helium Ionisationsschicht is deeper in the star, but are formed near the surface convection and the energy can not be transported undisturbed by pure radiative processes to the outside.

The driven by the kappa mechanism radial pulsation occurs only in a narrowly defined temperature range ( Cepheid instability strip ). However, there is more instability regions where the δ Scuti and γ Doradus stars lie, which are also driven by the kappa mechanism. The difference lies substantially in the inner structure, such as the extension of the convection, and the type of the pulsation due to the star, which is used with the method of Asteroseismology to examine this structure. Kappa mechanism may cause not only radial, but especially the non- radial pulsations in these areas as equivalent to the vibrations of a water drop.

More instability regions at larger temperatures come about through Ionisationsschichten other elements. From astrophysical importance are the elements of the iron group, mainly iron itself, which form at somewhat higher temperatures and for stars that are on the main sequence are closer than the δ - Cepheids, a Pulsationsinstabilität. Stars whose pulsation are caused by these so-called iron opacity bump for example β Cepheids, SPB star ( slowly pulsating B stars ) and λ Eri - star. As in kappa mechanism by helium are excited, depending on the instability region here both radial and non-radial pulsations.