Cepheids

The Cepheids [ t͡sefeˈiːdn̩ ] are a group of the pulsation- variable stars , in which the fluctuations in brightness are strictly periodic. They are of particular importance for astrophysics because they serve as an indicator for the luminosity and thus for the distances of stars. The Cepheids are giant stars and divide into several related groups.

It was named after the star Delta in Cepheus , whose periodic variability was discovered in 1784.

Typology and description

Cepheids pulsate with periods between 1 and 130 days and amplitudes of up to two size classes (mag) in the visual . At the same time, their surface temperature and thus their spectral class changes between F and K, with the spectral type becoming at a minimum reddish with increasing period.

Classical or Delta Cepheids

Light curve from the prototype of the classic Cepheid Delta Cephei. It shows the brightness in magnitudes against the pulsation phase.

The most important subclass of the pulsation-variable stars was named after the star δ Cephei in the constellation Cepheus , which has a period of approx. 5.37 days. During this time, its extension changes by around 2.7 million kilometers.

These are stars with an average mass of around four to ten solar masses that have moved away from the main sequence in the Hertzsprung-Russell diagram and cross the instability strip several times. The multiple crossing of the instability strip is a result of helium flashes in the core or in shells around the core of the stars. The stars react to the additional energy with an expansion in the area of the red giants and with the subsequent contraction back the instability strip is traversed again. They achieve a luminosity between 1000 and 10,000 times that of the sun and their spectral type is in the range from F6 to K2. They are supergiants of luminosity classes Ia, Ib and II. They belong to the disk population and occur in open star clusters . The pulsation periods of the classical Cepheids are between 2 and 45 days, whereby the upper end is difficult to define. In long-period Delta Cepheids, the vibrations are no longer strictly periodic and there is a smooth transition to the group of yellow semi-regular variables . For example, some authors still count yellow variables in the Magellanic Clouds with periods of up to 200 days among the classical Cepheids.

The periods of the classical Cepheids change with values of up to 200 seconds per year. These changes have been interpreted as a sign of the evolution of the stars, the wandering through the instability strip. However, the changes in the pulsation periods are often erratic and the development models would suggest a uniform change as with Polaris . A Delta Cepheid may even have been observed leaving the instability strip. V19 in M33 was a classic Cepheid with a period of 54.7 days and an amplitude of 1.1 mag in B. The amplitude fell to less than 0.1 mag and the brightness increased by 0.5 mag. Because the star at the long end of the period distribution is close to the transition to the yellow semi-regulars, its nature is controversial. While development calculations suggest that the number of period decreases and increases should be identical, a good 70 percent of the Cepheids seem to show a shortening of their periods. This behavior is interpreted as a sign of a weak stellar wind , which leads to a mass loss of 10 ⁻⁷ solar masses per year.

Even the light curves of the classical Cepheids do not show an exact repetition in their form. Continuous observation with the Kepler Space Telescope has shown that the light curve of V1154 Cygni contains fluctuations from cycle to cycle on the order of a few tenths of a percent. This noise could be the result of a deviation from axial symmetry and could be caused by local differences in the optical depth. Alternatively, this behavior could also be attributed to a possible disruption of the vibrations of the Cepheids by convection cells. Such convection cells have also been found in red supergiants such as Betelgeuse and there also lead to an irregular component in the light change.

Other well-known representatives:

Beta Doradus (β Dor)
Bezek (η Aql)
Mekbuda (ζ Gem A)

Classical Cepheids are also known as Type I Cepheids. This name is used for all Cepheids with a metallicity of more than 0.5 percent of the number of atoms. Accordingly, metal-poor Cepheids are called Type II Cepheids. The absolute visual brightness M _{V of} the classical Cepheids lies between −1 and −6.

Bimodal Cepheids of type CEP (B)

Bimodal Cepheids vibrate with two or more modes at the same time. These vibrations, which correspond to these modes, have different frequencies. These are vibrations of the

Fundamental frequency and the first harmonic with a period ratio P ₀ / P ₁ of 0.695 to 0.745
of the first and second harmonics with a period ratio P ₁ / P ₂ of 0.79 to 0.81
of the first and third harmonics with a period ratio P ₁ / P ₃ of approximately 0.67.

The values of P ₁ / P ₂ are the same in all observed astronomical systems, while the ratio between the fundamental oscillation and the first harmonic decreases sharply with increasing metallicity . There are also triple-mode Cepheids that pulsate either in the first three harmonics or in the fundamental and the first two harmonics.

The Blazhko effect is a slow, approximately periodic modulation of amplitude and phase that is observed in up to 50% of the RR Lyrae stars . 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 classic Cepheid V473 Lyrae and when analyzing the data from the OGLE and MACHO projects, around 20% of the Cepheids in the Magellanic Clouds show the characteristic Light curve modulation of the Blazhko effect.

In 9% of all CEPs-Cepheids in the Small Magellanic Cloud, secondary periods were found whose frequency differs only slightly from the fundamental. This cannot be caused by another radial pulsation and is interpreted as the presence of non-radial vibrations. There are also the 1O / X Cepheids, to which about 5 percent of all Cepheids in the Magellanic Clouds belong. These stars vibrate in the first harmonic and at least one second with a period ratio of 0.6 to 0.64. These additional vibrations are not compatible with the pulsation theory as radial vibrations. These Cepheids do not differ from the CEPS with the exception of the lack of short periods and a difficult-to-understand non-radial fashion.

DCEPS

This subtype shows a low amplitude of around 0.5 mag and symmetrical sinusoidal light curves . The periods are less than 7 days. About 50% of the s-Cepheids pulsate in the first harmonic , while the rest are fundamental pulsators . The most famous s-Cepheid is the polar star Alpha Ursae Minoris.

Unusual Cepheids

The "unusual Cepheids" (English. Anomalous Cepheids ) have short periods of two days to a few hours and belong to population II. In the Hertzsprung-Russell diagram, they are one magnitude above the horizontal branch on which the related RR Lyrae stars are located. Your prototype is BL Bootis . The unusual Cepheids have a massive core in which helium is burned and have a stellar mass between 1.3 and 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 binary star system merging into a blue straggler . The unusual Cepheids follow an independent period luminosity relationship.

Type II Cepheids

The term Type II Cepheids includes all radially pulsating variables with a large amplitude and a mass of about one solar mass . The traditional classification based on the light curves would differentiate between the BL Herculis stars, the W Virginis stars and the RV Tauri stars . The transition between the BL-Her stage and the W-Vir stage takes about 4 days and all Type II Cepheids with pulsation periods of more than 20 days are counted as RV Tauri stars. All three subspecies of the Type II Cepheids belong to the thick disk or halo population .

While the classical Cepheids are giants with masses between 4 and 10 solar masses, all types of Type II Cepheids are low-mass stars with a value around one solar mass . Development phases could be assigned to the various subtypes of type II Cepheids:

The BL Herculis stars cross the instability strip on their way from the horizontal branch to the asymptotic giant branch

The W Virginis stars are stars that loop from the asymptotic giant branch to higher temperatures and back again. These are caused by thermal pulses due to the explosive ignition of the helium flame

The RV Tauri stars, on the other hand, leave the asymptotic giant branch and transform into a white dwarf when they cool down

The Type II Cepheids also follow a period-luminosity relationship, but this is 1.5 may below that for classical Cepheids. There is a class of peculiar W-Virginis stars that show deviating light curves and are brighter than they should be according to the period-luminosity relationship. They are probably all double stars and the bright Cepheid kappa Pav seems to be one of the peculiar W-Virginis stars.

Occurrence in star catalogs

The General Catalog of Variable Stars currently lists around 800 stars with the abbreviations CEP or DCEP , which means that around 2% of all stars in this catalog belong to the Cepheid class. In addition, about 300 stars or 0.5% belong to type CW , which stands for type II Cepheids.

Physics of the pulsation process

The basis for the pulsation of the Cepheids is the kappa mechanism , which is based on a change in opacity with increasing temperature. The cycle comes about when due to a disturbance the matter in a certain layer of the star's interior is compressed. This leads to an increase in density and temperature in the layer. This increases the opacity, which is why a smaller proportion of the radiation generated by core processes inside is passed on into the outer atmosphere, which falls inwards due to the lack of radiation pressure. In the layer controlling the pulsation, on the other hand, the dammed up radiation leads to an increase in temperature and expansion, whereby the opacity decreases and the stored energy is released. The additional energy now again leads to an expansion of the visible outer atmosphere, which expands beyond equilibrium. The energy released by the pulsating layer results in compression and the cycle begins again. In the case of the Cepheids, the layer controlling the vibrations lies in the zone with the transition from single to double ionized helium. However, not all of the yellow giants lying in the instability strip between the Cepheids are pulsation-variable stars like these. They only show a low amplitude of less than 0.03 mag in their light curves and radial velocity measurements only show changes with low amplitudes of a few tens of meters per second instead of up to 100 kilometers per second in the case of the classic Cepheids. The cause of 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 distances . As bright giant stars they can be observed up to a distance of a few megaparsecs , with the Hubble space telescope up to about 20 megaparsecs, so also in neighboring galaxies.

This makes use of the fact that the luminosity of a Cepheid (expressed as absolute brightness ) is closely related to its pulsation period ( ). A period-luminosity relationship for the classical Cepheids is: ${\ displaystyle M}$ ${\ displaystyle P / \ mathrm {days}}$

{\ displaystyle M = -2 {,} 81 \ cdot \ log (P / \ mathrm {days}) -1 {,} 43 \ ,.}

With it it is possible to infer its absolute brightness from the observation of the light change of a Cepheid. An additional dependence of the period-luminosity relationship on metallicity is the subject of scientific discussions. The connection between the pulsation period and the mean luminosity was discovered by the American astronomer Henrietta Swan Leavitt in 1912 while observing stars with variable brightness in the Small Magellanic Cloud .

The conversion between the measurable apparent brightness and the absolute brightness can then be done using the distance equation ${\ displaystyle m}$ ${\ displaystyle M}$

{\ displaystyle D = 10 ^ {(m-M + 5) / 5}}

determine its distance (in parsecs) after the extinction has been corrected with the aid of the essence function . Investigations of large numbers of Cepheids in the Magellanic Clouds as part of the OGLE project show a deviation from the linear period-luminosity relationship. According to this, long-period Cepheids are somewhat weaker than the PL relationship suggests. ${\ displaystyle D}$

The following procedures are used to calibrate the period-luminosity relationship:

Distance determination by direct parallax measurement
Baade-Wesselink technology
When a Cepheid is in a star cluster with the help of the main sequence fitting
Direct distance measurement with the help of light echoes at RS Pup
Comparison with theoretical period-luminosity relationship

The accuracy of distance measurement in cosmological distances by Cepheids is limited by the blending effect . This is a superposition of several stars due to the limited resolution when observing Cepheids in other galaxies. The measured light from the place of the Cepheid is in many cases the sum of the light of several stars, whereby the Cepheid appears brighter than it is as a single star. These superimpositions can only be recognized to a limited extent on the basis of the amplitude and the change in color of the light change, since these changes can also be the result of different metallicity . Therefore, the distance to extragalactic Cepheids must be corrected based on the resolution of the observation instrument using empirical formulas.

Impostor

Cepheids Impostors (German "Cepheiden- imposter ") are pulsationsveränderliche stars whose light curve resembles that of a Cepheid. However, if the photometric measurements are subjected to a Fourier analysis or the star is observed spectrographically, then differences to the real Cepheids become apparent. Examples are HD 18391 and V810 Cen.

The Impostor are the result of a development in an interacting binary star system with a mass exchange between the components. This allows one of the stars to pass through the instability strip and start pulsing like single stars as Cepheids. Since the impostors have a different mass and chemical composition during the phase of variability, they do not follow the period-luminosity relationship. According to simulation calculations, about 5 percent of all Cepheids are in reality Impostor. A distance to a single Cepheid on the basis of a noisy light curve should therefore not be used as the only criterion for determining the distance. The Impostor belong to the group of Binary Evolution Pulsators, which can also be misinterpreted as RR Lyrae stars .

Lack of mass problem

Cepheids are preferred objects for checking calculated star models, as their masses in binary stars can be determined empirically through pulsation studies and with the help of the Baade-Wesselink technique . From such observations, Cepheid masses have been derived which are systematically 20% lower than the result of simulation calculations. This deviation is known as the missing mass problem .

One way to solve the problem is to assume that stars of medium mass will lose mass before or during the Cepheid phase. A mass loss rate of around 10 ⁻⁷ solar masses per year would reflect the average period changes in classical Cepheids well. But the Cepheids are too hot to allow a dust-driven stellar wind like the AGB stars and the pulsations are not strong enough for such a high rate of mass loss. A search for remnants of such ejected matter around Cepheids in the form of a circumstellar nebula - with one possible exception of the prototype δ Cephei - did not reveal any signs of a massive loss of mass.

Theoretical studies show that a pulsation-controlled mass loss in combination with convective overshoot during the main sequence phase could solve the problem of missing mass. The concept of convective overshooting describes the fact that with convective energy transport, matter travels a further distance at an equilibrium point due to the motion impulse and therefore the mixing is stronger than under simplified assumptions. Taking convection into account when simulating the evolution of stars is problematic, however, since there is no general physical theory for calculating convection that describes the processes on all scales.

literature

Gerhard Mühlbauer: Cepheids: Milestones in the Universe. (PDF) In: Stars and Space - Astronomy in School. No. 10, 2003.
Database Of Galactic Classical Cepheids David Dunlap Observatory

Web links

Commons : Cepheids - Collection of images, videos and audio files

ESO: Pulsating Star Mystery Solved - November 24, 2010

Individual evidence

^ Scott G. Engle, Edward F. Guinan: X-ray, UV and Optical Observations of Classical Cepheids: New Insights into Cepheid Evolution, and the Heating and Dynamics of Their Atmospheres . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1206.4282 .
^ DG Turner, LN Berdnikov: On the crossing mode of the long-period Cepheid SV Vulpeculae . In: Astronomy & Astrophysics . tape 423 , 2004, p. 335-340 .
↑ LM Macri, DD Sasselov, KZ Stanek: A Cepheid is No More: Hubble's Variable 19 in M33 . In: The Astrophysical Journal . tape 550 , 2001, pp. L159-L162 .
↑ Hilding R. Neilson: Pulsation and Mass Loss Across the HR Diagram: From OB stars to Cepheids to Red Supergiants . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1309.4115v1 .
↑ A. Derekas , Gy. M. Szabo , L. Berdnikov, R. Szabo, R. Smolec, LL Kiss, L. Szabados, M. Chadid , NR Evans, K. Kinemuchi, JM Nemec, SE Seader, JC Smith, P. Tenenbaum: Period and light curve fluctuations of the Kepler Cepheid V1154 Cyg . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1207.2907v1 .
↑ Hilding R. Neilson, Richard Ignace: Convection, granulation and period jitter in classical Cepheids . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1402.0874v1 .
^ C. Chiosi: The evolution of the Cepheid stars . In: Confrontation between stellar pulsation and evolution; Proceedings of the Conference . tape 550 . Bologna, Italy 1990, p. 158-192 .
↑ P. Moskalik: Multi-Periodic Oscillations in Cepheids and RR Lyrae-Type Stars . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1208.4246 .
↑ WA Dziembowski: Puzzling Frequencies in First Overtone Cepheids . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1212.0993 .
↑ DG Turner, VV Kovtyukh, RE Luck, LN Berdnikov: The pulsation mode and distance of the Cepheid FF Aquilae . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1306.1228v1 .
^ G. Fiorentino, M. Monelli: Anomalous Cepheids in the Large Magellanic Cloud: Insight on their origin and connection with the star formation history . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1202.2752 .
↑ V. Ripepi, M. Marconi, MI Moretti, G. Clementini, MR. L. Cioni, R. de Grijs, JP Emerson, MAT Groenewegen, VD Ivanov, JM Oliveira: The VMC Survey. VIII. First results for Anomalous Cepheids . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1310.5967v1 .
↑ Noriyuki Matsunaga, Michael W. Feast, Igor Soszynski: Period-luminosity relations of type II Cepheids in the Magellanic Clouds . In: Astrophysics. Solar and Stellar Astrophysics . 2010, arxiv : 1012.0098 .
↑ Noriyuki Matsunaga et al. a .: Cepheids and other short-period variables near the Galactic Center . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1211.0151 .
↑ Variability types General Catalog of Variable Stars, Sternberg Astronomical Institute, Moscow, Russia. Retrieved February 2, 2019 .
^ R. Kippenhahn, A. Weigert: Stellar Structure and Evolution (Astronomy and Astrophysics Library) . Springer Verlag, Mannheim 1994, ISBN 3-540-50211-4 .
^ Byeong-Cheol Lee, Inwoo Han, Myeong-Gu Park, Kang-Min Kim, David E. Mkrtichian: Detection of the 128 day radial velocity variations in the supergiant alpha Persei . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1205.3840 .
^ MW Feast, RM Catchpole: The Cepheid period-luminosity zero-point from HIPPARCOS trigonometrical parallaxes . In: Monthly Notices of the Royal Astronomical Society . tape 286 , February 1, 1997, p. L1-L5 , bibcode : 1997MNRAS.286L ... 1F .
↑ Alejandro García-Varela, Beatriz Sabogal, María Ramírez-Tannus: A Study on the Universality and Linearity of the Leavitt Law in the LMC and SMC Galaxies . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1303.0809v1 .
↑ Chow-Choong Ngeow, Hilding Neilson, Nicolas Nardetto, Massimo Marengo: Essence Function for Galactic Cepheids: Application to the Projection Factors . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1209.4701v1 .
↑ Joy M. Chavez, Lucas M. Macri, Anne Pellerin: Blending of Cepheids in M33 . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1208.1048 .
^ David G. Turner et al .: The Cepheid Impostor HD 18391 and its Anonymous Parent Cluster . In: Astrophysics. Solar and Stellar Astrophysics . 2009, arxiv : 0907.2904v1 .
↑ P. Karczmarek et al .: The occurrence of Binary Evolution Pulsators in the classical instability strip of RR Lyrae and Cepheid variables . In: Astrophysics. Solar and Stellar Astrophysics . 2016, arxiv : 1612.00465v2 .
^ Emese Plachy: Cepheid investigations in the era of space photometric missions . In: Astrophysics. Solar and Stellar Astrophysics . 2017, arxiv : 1705.01919v1 .
↑ Hilding R. Neilson, Norbert Langer, Scott G. Engle, Ed Guinan, Robert Izzard: Classical Cepheids Require Enhanced Mass Loss . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1210.6042 .
↑ M. Marengo et al. a .: An Infrared Nebula Associated with Δ Cephei: Evidence of Mass Loss? In: The Astrophysical Journal . tape 725 , 2010, p. 2392 , doi : 10.1088 / 0004-637X / 725/2/2392 .
↑ Hilding R. Neilson, Matteo Cantiello, Norbert Langer: The Cepheid mass discrepancy and pulsation-driven mass loss . In: Astrophysics. Solar and Stellar Astrophysics . 2011, arxiv : 1104.1638 .

[1] Scott G. Engle, Edward F. Guinan: X-ray, UV and Optical Observations of Classical Cepheids: New Insights into Cepheid Evolution, and the Heating and Dynamics of Their Atmospheres . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1206.4282 .

[2] DG Turner, LN Berdnikov: On the crossing mode of the long-period Cepheid SV Vulpeculae . In: Astronomy & Astrophysics . tape 423 , 2004, p. 335-340 .

[3] LM Macri, DD Sasselov, KZ Stanek: A Cepheid is No More: Hubble's Variable 19 in M33 . In: The Astrophysical Journal . tape 550 , 2001, pp. L159-L162 .

[4] Hilding R. Neilson: Pulsation and Mass Loss Across the HR Diagram: From OB stars to Cepheids to Red Supergiants . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1309.4115v1 .

[5] A. Derekas , Gy. M. Szabo , L. Berdnikov, R. Szabo, R. Smolec, LL Kiss, L. Szabados, M. Chadid , NR Evans, K. Kinemuchi, JM Nemec, SE Seader, JC Smith, P. Tenenbaum: Period and light curve fluctuations of the Kepler Cepheid V1154 Cyg . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1207.2907v1 .

[6] Hilding R. Neilson, Richard Ignace: Convection, granulation and period jitter in classical Cepheids . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1402.0874v1 .

[7] C. Chiosi: The evolution of the Cepheid stars . In: Confrontation between stellar pulsation and evolution; Proceedings of the Conference . tape 550 . Bologna, Italy 1990, p. 158-192 .

[8] P. Moskalik: Multi-Periodic Oscillations in Cepheids and RR Lyrae-Type Stars . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1208.4246 .

[9] WA Dziembowski: Puzzling Frequencies in First Overtone Cepheids . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1212.0993 .

[10] DG Turner, VV Kovtyukh, RE Luck, LN Berdnikov: The pulsation mode and distance of the Cepheid FF Aquilae . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1306.1228v1 .

[11] G. Fiorentino, M. Monelli: Anomalous Cepheids in the Large Magellanic Cloud: Insight on their origin and connection with the star formation history . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1202.2752 .

[12] V. Ripepi, M. Marconi, MI Moretti, G. Clementini, MR. L. Cioni, R. de Grijs, JP Emerson, MAT Groenewegen, VD Ivanov, JM Oliveira: The VMC Survey. VIII. First results for Anomalous Cepheids . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1310.5967v1 .

[13] Noriyuki Matsunaga, Michael W. Feast, Igor Soszynski: Period-luminosity relations of type II Cepheids in the Magellanic Clouds . In: Astrophysics. Solar and Stellar Astrophysics . 2010, arxiv : 1012.0098 .

[14] Noriyuki Matsunaga et al. a .: Cepheids and other short-period variables near the Galactic Center . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1211.0151 .

[GCVS1-15] Variability types General Catalog of Variable Stars, Sternberg Astronomical Institute, Moscow, Russia. Retrieved February 2, 2019 .

[16] R. Kippenhahn, A. Weigert: Stellar Structure and Evolution (Astronomy and Astrophysics Library) . Springer Verlag, Mannheim 1994, ISBN 3-540-50211-4 .

[17] Byeong-Cheol Lee, Inwoo Han, Myeong-Gu Park, Kang-Min Kim, David E. Mkrtichian: Detection of the 128 day radial velocity variations in the supergiant alpha Persei . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1205.3840 .

[18] MW Feast, RM Catchpole: The Cepheid period-luminosity zero-point from HIPPARCOS trigonometrical parallaxes . In: Monthly Notices of the Royal Astronomical Society . tape 286 , February 1, 1997, p. L1-L5 , bibcode : 1997MNRAS.286L ... 1F .

[19] Alejandro García-Varela, Beatriz Sabogal, María Ramírez-Tannus: A Study on the Universality and Linearity of the Leavitt Law in the LMC and SMC Galaxies . In: Astrophysics. Solar and Stellar Astrophysics . 2013, arxiv : 1303.0809v1 .

[20] Chow-Choong Ngeow, Hilding Neilson, Nicolas Nardetto, Massimo Marengo: Essence Function for Galactic Cepheids: Application to the Projection Factors . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1209.4701v1 .

[21] Joy M. Chavez, Lucas M. Macri, Anne Pellerin: Blending of Cepheids in M33 . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1208.1048 .

[22] David G. Turner et al .: The Cepheid Impostor HD 18391 and its Anonymous Parent Cluster . In: Astrophysics. Solar and Stellar Astrophysics . 2009, arxiv : 0907.2904v1 .

[23] P. Karczmarek et al .: The occurrence of Binary Evolution Pulsators in the classical instability strip of RR Lyrae and Cepheid variables . In: Astrophysics. Solar and Stellar Astrophysics . 2016, arxiv : 1612.00465v2 .

[24] Emese Plachy: Cepheid investigations in the era of space photometric missions . In: Astrophysics. Solar and Stellar Astrophysics . 2017, arxiv : 1705.01919v1 .

[25] Hilding R. Neilson, Norbert Langer, Scott G. Engle, Ed Guinan, Robert Izzard: Classical Cepheids Require Enhanced Mass Loss . In: Astrophysics. Solar and Stellar Astrophysics . 2012, arxiv : 1210.6042 .

[26] M. Marengo et al. a .: An Infrared Nebula Associated with Δ Cephei: Evidence of Mass Loss? In: The Astrophysical Journal . tape 725 , 2010, p. 2392 , doi : 10.1088 / 0004-637X / 725/2/2392 .

[27] Hilding R. Neilson, Matteo Cantiello, Norbert Langer: The Cepheid mass discrepancy and pulsation-driven mass loss . In: Astrophysics. Solar and Stellar Astrophysics . 2011, arxiv : 1104.1638 .