Cepheid variable

The Cepheids are a group of pulsating variables stars, in which, the fluctuations in the brightness of strictly periodic. They have special importance for astrophysics, because they serve as an indicator of the luminosity and thus the distances of stars. The Cepheids are giant stars and divide into several related groups.

The name derives from the star was in the Delta Cepheus, whose periodic variability was discovered in 1784

Typology and description

Cepheids pulsate with periods of 1-130 days and amplitudes of up to two size classes (mag ) in the visuals. Here, also the surface temperature and thus their spectral class between F and K varied with the spectral type at minimum with increasing period is reddish.

Classic or Delta Cepheids

The most important sub-class of pulsating variables star was named after the star δ Cephei in the constellation Cepheus, which has a period of about 5.37 days. During this time, changes its extension around 2.7 million kilometers.

These are stars with intermediate mass of about four to ten solar masses, who have drifted away in the Hertzsprung -Russell diagram from the main sequence and the instability strip crossing several times. The multiple crossing the instability strip is a sequence of helium flash in the core or in shells around the core of the star. On the extra energy the star react with an expansion in the range of red giants and in the subsequent contraction back is the instability strip run through again. You will reach a luminosity between the 1000 - to 10,000 times the sun and its spectral type is in the range of F6 to K2. It is supergiants of luminosity class Ia, Ib and II They belong to the disk population and occur in open clusters. The pulsation periods are in the classical Cepheids 2-45 days, with the upper end of which is to define just bad. For long-period Cepheids delta oscillations are not strictly periodic and there is a smooth transition to the group of yellow semi-regular variables. So yellow variables are counted in the Magellanic clouds with periods of up to 200 days, even to the classical Cepheids by some authors.

The periods of the classical Cepheids change with values ​​of up to 200 seconds per year. These changes are considered a sign of the evolution of stars, walking through the instability strip, been interpreted. However, the changes in the pulsation periods are often erratic and the development of models would be expected, a uniform change as for Polaris. Possibly even a Delta Cepheid has been observed when leaving the instability strip. V19 in M33 was a classical Cepheid with a period of 54.7 days and an amplitude of 1.1 like in B. The amplitude has dropped to less than 0.1 mag and the brightness by 0.5 may have increased. Because the star at the long end of the period distribution is close to the transition to the yellow semi- regular, but its nature is controversial. While evolutionary calculations can be expected that the number of Periodenab - and - rose should be identical, seem to show a reduction in their periods around 70 percent of the Cepheids. This behavior is interpreted as an indication of a weak wind rating, resulting in a weight loss of 10-7 solar masses per year.

The light curves of classical Cepheids show no exact repetition in its form. Due to the continuous observation with the Kepler space telescope could be shown that the light curve of V1154 Cygni fluctuations from cycle to cycle in the order of a few tenths of a percent contains. This noise could be due to a deviation from the axis of symmetry and are caused by local differences in the optical depth. Alternatively, this behavior could also be attributed to a possible interference of the oscillations of Cepheids by convection cells. Such convection cells have also been found in red supergiant Betelgeuse and as result there is also an irregular component in the light change.

Other well-known representative:

• Beta Doradus ( β Dor )
• Bezek ( η Aql )
• Mekbuda ( ζ Gem A)
• Polaris ( α UMi A)

Classical Cepheids are also referred to as Type I Cepheids. This term is used for all Cepheids with a metallicity of more than 0.5 percent of the number of atoms. Accordingly, metal-poor Cepheids are referred to as type II Cepheids. The absolute visual magnitude MV of classical Cepheids is from -1 to -6.

Bimodal Cepheids of type CEP (B )

Bimodal Cepheids vibrate simultaneously with two or more modes. These oscillations, which correspond to these modes have different frequencies. This is to vibrations of the

• Fundamental frequency and the first harmonic with a period ratio P0/P1 0.695 to 0.745
• The first and the second harmonic with a period ratio P1/P2 0.79 to 0.81
• The first and the third harmonic with a period ratio P1/P3 of about 0.67.

The values ​​of P1/P2 are observed in all astronomical systems the same, while the ratio between the fundamental and the first harmonic decreases strongly with increasing metallicity. There are also triple-mode Cepheids that pulsate either in the first three harmonics or the fundamental frequency and the first two harmonics.

Blazhko the effect is a slow, nearly periodic modulation of the amplitude and the phase, which is seen in up to 50% of the RR Lyrae. The period of the Blazhko effect can take values ​​from a few days up to 2500 days. In recent years, a similar modulation of the light curve with a period of 1200 days has been found in the classical Cepheid V473 Lyrae and in analyzing the data of the OGLE and the MACHO project show about 20 % of the Cepheids in the Magellanic Clouds, the characteristic light curve modulation of the Blazhko effect.

In 9% of all CEPs Cepheids in the Small Magellanic Cloud secondary periods have been found whose frequency differs only slightly from the fundamental. This can not be caused by a further radial pulsation and is interpreted as presence of non- radial vibrations. There is also the 1O/X-Cepheiden to which approximately 5 percent of all Cepheids belong to the Magellanic Clouds. These stars oscillate in the first harmonic and at least one second period with a ratio of 0.6 to 0.64. These additional vibrations are not compatible as radial oscillations with pulsation. These Cepheids are no different from the CEPS except for the absence short periods and just a difficult to understand non-radial fashion.

DECPS

This subtype shows a low amplitude of like the 0.5 and symmetric sinusoidal light curves. Periods are less than 7 days. Approximately 50 % of the s- Cepheids pulsate in the first harmonic, while the rest are Grundschwingungspulsatoren. The bekannste s- Cepheid is Polaris Alpha Ursae Minoris.

Unusual Cepheids

The " unusual Cepheids " ( engl. anomalous Cepheids ) have short periods of two days to a few hours and are members of population II. In the Hertzsprung -Russell diagram they are a magnitude above the horizontal branch, on which the related RR Lyrae stars are located. Their prototype is BL Boo. The unusual Cepheids have a solid core, is burned in the helium and have a stellar mass from 1.3 to 2.1 solar masses. The metallicity, the proportion of elements heavier than helium in its atmosphere, is two orders of magnitude below the value of the sun. These Cepheids are very rare and their origin is unclear. It is often described as the result of a merger of a binary system to a blue straggler. The unusual Cepehiden follow an independent period luminosity relation.

Type II Cepheids

The notion of type II Cepheids summarizes all radially - pulsating variable with a large amplitude and a mass of about one solar mass. The traditional classification based on the light curves would differ between the BL Herculis stars, the W Virginis stars and RV Tauri stars. The transition between the BL- production stage and the W Vir - stage occurs approximately at 4 days and all type II Cepheids with pulsation periods of more than 20 days are attributed to the RV Tauri stars. All three subtypes of type II Cepheids belong to the thick disk or halo population.

While the classical Cepheids are giants with masses 4-10 solar masses, all kinds of type II Cepheid stars are low mass with a value of around one solar mass. The various subtypes of type II Cepheids could be assigned to phases of development:

• The BL Herculis stars cross the instability strip on their way from the horizontal branch to the Asymptotic Giant
• The W Virginis stars are stars that loops from the asymptotic giant branch to higher temperatures and perform back again. These are caused by thermal pulses due to the explosive ignition of helium burning
• The contrast RV Tauri stars leave the Asymptotic Giant Branch and transform by cooling off in a white dwarf

The type II Cepheids follow a period-luminosity relationship, but 1.5 is like below those for classical Cepheids. There is a class of pekuliären W Virginis stars, which show different light curves and are brighter than they should be according to the period-luminosity relationship. You are probably all double stars and the bright Cepheid kappa Pav seems to be among the pekuliären W Virginis stars.

Physics of Pulsationsprozesses

Basis for the pulsation of the Cepheid kappa mechanism based on a change in the opacity with increasing temperature. The cycle is concluded when due to a malfunction, the matter is compressed in a particular layer of the stellar interior. This leads to an increase in the density and temperature of the layer. Thus, the opacity is increased, and therefore the heat generated by the core processes in the interior of the radiation to a lesser extent into the external atmosphere is passed falling inwardly due to the lack of radiation pressure. In which the pulsation controlling layer the accumulated radiation causes a temperature increase and expansion, thereby decreasing the opacity and the stored energy is released. The extra energy back now leads to an expansion of the visible outer atmosphere, the hinausexpandiert about the balance. The freed from the vibrant energy leads to a compression layer and the cycle begins again. For the Cepheids, the vibrations controlling layer is located in the zone with the transition from simple to doubly ionized helium. However, not all yellow giant, which lie in the instability strip between the Cepheids, pulsationsveränderliche star like this. They only show a small amplitude of less than 0.03 may in their light curves and radial velocity measurements show only small changes with amplitudes of some 10 meters per second instead of up to 100 kilometers per second at the classical Cepheids. The reason for the different behavior of these stable stars in the instability strip is not known.

Distance measurement

Delta Cephei stars are used as standard candles for measuring distance. As bright giant stars are up to a distance of a few megaparsecs to observe with the Hubble Space Telescope up to about 20 megaparsecs, ie, even in neighboring galaxies.

This exploits that the luminosity of a Cepheid (expressed as absolute brightness) is in fixed connection with its pulsation period (). A period-luminosity relation for the classical Cepheids is:

With it, it is possible from the observation of light variation of a Cepheid to close to its absolute brightness. An additional function of the period-luminosity relation for the metallicity is the subject of scientific debate. The relationship between the pulsation period and the average luminosity was discovered by the astronomer Henrietta Swan U.S. Leavitt 1912 in the observation brightness of variable stars in the Small Magellanic Cloud.

The conversion between the measurable apparent brightness and the absolute brightness can then use the distance equation

Its distance ( in parsecs ) determine, after the extinction was corrected using the entity function. Studies of large numbers of Cepheids in the Magellanic Clouds as part of the OGLE project show a deviation from the linear period-luminosity relationship. Thus, long-period Cepheids are somewhat fainter than can be expected, the PL relationship.

For calibration of the period-luminosity relation, the following methods are used:

• Distance determination by direct parallax
• Baade - Wesselink technique
• If a Cepheid is located in a cluster using the main sequence fittings
• Direct distance measurement using light echoes in RS Pup
• Comparison with theoretical period-luminosity relationship

The accuracy of the distance measurement at cosmological distances by Cepheid is limited by the blending effect. It is a superposition of several stars due to the limited resolving power for the observation of Cepheids in other galaxies. The measured light from the place of Cepheids is in many cases the sum of the light of several stars, whereby the Cepheid appear brighter than it is a single star. These overlays are only partially be seen from the amplitude and the change in color of the light change, as these changes may be the result of a different metallicity. Therefore, the distance to extragalactic Cepheids must be corrected for the resolution of the observation instrument based on empirical formulas.

Problem of the missing mass

Cepheids are a prime target for verification of computed stellar models, since their masses can be determined empirically in double stars, by Pulsationsstudien and Baade - Wesselink using the technique. From such observations Cepheidenmassen have been derived which are systematically 20 % lower than the result of simulation calculations. This deviation is referred to as the problem of the missing mass (English missing mass problem).

One way to solve the problem is to accept a loss in mass of intermediate-mass stars before or while they go through the Cepheid phase. A mass loss rate to the 10-7 solar masses per year would well represent the average period changes in classical Cepheids. But Cepheids are too hot to allow a dust- driven stellar wind as the AGB stars and the pulsations are not strong enough for such a high mass loss rate. A search for the remains of those ejected in the explosion to Cepheids in the form of a circumstellar nebula has - provided, however, no evidence of a massive mass loss - with the possible exception of the prototype δ Cephei.

Theoretical studies show that a pulsationsgesteuerter mass loss in combination with convective overshooting during the main sequence phase could solve the problem of the missing mass. The term of the convective overshoot describes the fact that, for convective energy transport material at a point of equilibrium due to the movement or pulse travels a longer distance and therefore the mixing is higher than under simplified assumptions. Considering the convection in the simulation of the development of stars is problematic, however, since there are no general physical theory to calculate the convection, which describes the operations at all scales.