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Classical Cepheid variable

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Hertzsprung–Russell diagram showing the location of several types of variable stars superimposed on a display of the different luminosity classes.

Classical Cepheids are a type of Cepheid variable star. They are young, population I variable stars that exhibit regular radial pulsations with periods of a few days to a few weeks and visual amplitudes ranging from a few tenths of a magnitude up to about 2 magnitudes. Classical Cepheids are also known as Population I Cepheids, Type I Cepheids, and Delta Cepheid variables.

There exists a well-defined relationship between a classical Cepheid variable's luminosity and pulsation period,[1][2] securing Cepheids as viable standard candles for establishing the galactic and extragalactic distance scales.[3][4][5][6] Hubble Space Telescope (HST) observations of classical Cepheid variables have enabled firmer constraints on Hubble's law, which describes the expansion rate of the observable Universe.[3][4][6][7][8] Classical Cepheids have also been used to clarify many characteristics of our galaxy, such as the local spiral arm structure and the Sun's distance from the galactic plane.[5]

Around 800 classical Cepheids are known in the Milky Way galaxy, out of an expected total of over 6,000. Several thousand more are known in the Magellanic Clouds, with more discovered in other galaxies;[9] the Hubble Space Telescope has identified some in NGC 4603, which is 100 million light years distant.[10]

Properties

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The evolutionary track of 5 M☉ star crossing the instability strip during a helium burning blue loop

Classical Cepheid variables are 4–20 times more massive than the Sun,[11] and around 1,000 to 50,000 (over 200,000 for the unusual V810 Centauri) times more luminous.[12] Spectroscopically they are bright giants or low luminosity supergiants of spectral class F6 – K2. The temperature and spectral type vary as they pulsate. Their radii are a few tens to a few hundred times that of the sun. More luminous Cepheids are cooler and larger and have longer periods. Along with the temperature changes their radii also change during each pulsation (e.g. by ~25% for the longer-period l Car), resulting in brightness variations up to two magnitudes. The brightness changes are more pronounced at shorter wavelengths.[13]

Cepheid variables may pulsate in a fundamental mode, the first overtone, or rarely a mixed mode. Pulsations in an overtone higher than first are rare but interesting.[2] The majority of classical Cepheids are thought to be fundamental mode pulsators, although it is not easy to distinguish the mode from the shape of the light curve. Stars pulsating in an overtone are more luminous and larger than a fundamental mode pulsator with the same period.[14]

When an intermediate mass star (IMS) first evolves away from the main sequence, it crosses the instability strip very rapidly while the hydrogen shell is still burning. When the helium core ignites in an IMS, it may execute a blue loop and crosses the instability strip again, once while evolving to high temperatures and again evolving back towards the asymptotic giant branch. Stars more massive than about 8–12 M☉ start core helium burning before reaching the red-giant branch and become red supergiants, but may still execute a blue loop through the instability strip. The duration and even existence of blue loops is very sensitive to the mass, metallicity, and helium abundance of the star. In some cases, stars may cross the instability strip for a fourth and fifth time when helium shell burning starts.[citation needed] The rate of change of the period of a Cepheid variable, along with chemical abundances detectable in the spectrum, can be used to deduce which crossing a particular star is making.[15]

Classical Cepheid variables were B type main-sequence stars earlier than about B7, possibly late O stars, before they ran out of hydrogen in their cores. More massive and hotter stars develop into more luminous Cepheids with longer periods, although it is expected that young stars within our own galaxy, at near solar metallicity, will generally lose sufficient mass by the time they first reach the instability strip that they will have periods of 50 days or less. Above a certain mass, 20–50 M☉ depending on metallicity, red supergiants will evolve back to blue supergiants rather than execute a blue loop, but they will do so as unstable yellow hypergiants rather than regularly pulsating Cepheid variables. Very massive stars never cool sufficiently to reach the instability strip and do not ever become Cepheids. At low metallicity, for example in the Magellanic Clouds, stars can retain more mass and become more luminous Cepheids with longer periods.[12]

Light curves

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Delta Cephei lightcurve
Phase-folded UBVRI light curves of Delta Cephei, prototype of the classical Cepheids, showing magnitude versus pulsation phase[16]

A Cepheid light curve is typically asymmetric with a rapid rise to maximum light followed by a slower fall to minimum (e.g. Delta Cephei). This is due to the phase difference between the radius and temperature variations and is considered characteristic of a fundamental mode pulsator, the most common type of type I Cepheid. In some cases the smooth pseudo-sinusoidal light curve shows a "bump", a brief slowing of the decline or even a small rise in brightness, thought to be due to a resonance between the fundamental and second overtone. The bump is most commonly seen on the descending branch for stars with periods around 6 days (e.g. Eta Aquilae). As the period increases, the location of the bump moves closer to the maximum and may cause a double maximum, or become indistinguishable from the primary maximum, for stars having periods around 10 days (e.g. Zeta Geminorum). At longer periods the bump can be seen on the ascending branch of the light curve (e.g. X Cygni),[17] but for period longer than 20 days the resonance disappears.

A minority of classical Cepheids show nearly symmetric sinusoidal light curves. These are referred to as s-Cepheids, usually have lower amplitudes, and commonly have short periods. The majority of these are thought to be first overtone (e.g. X Sagittarii), or higher, pulsators, although some unusual stars apparently pulsating in the fundamental mode also show this shape of light curve (e.g. S Vulpeculae). Stars pulsating in the first overtone are expected to only occur with short periods in our galaxy, although they may have somewhat longer periods at lower metallicity, for example in the Magellanic Clouds. Higher overtone pulsators and Cepheids pulsating in two overtones at the same time are also more common in the Magellanic Clouds, and they usually have low amplitude somewhat irregular light curves.[2][18]

Discovery

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Historical light curves of W Sagittarii and Eta Aquilae

On September 10, 1784 Edward Pigott detected the variability of Eta Aquilae, the first known representative of the class of classical Cepheid variables. However, the namesake for classical Cepheids is the star Delta Cephei, discovered to be variable by John Goodricke a month later.[19] Delta Cephei is also of particular importance as a calibrator for the period-luminosity relation since its distance is among the most precisely established for a Cepheid, thanks in part to its membership in a star cluster[20][21] and the availability of precise Hubble Space Telescope and Hipparcos parallaxes.[22]

Period-luminosity relation

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Main article: Period-luminosity relation
The two Period-Luminosity Characteristics of Classic and Type II Cepheids

A classical Cepheid's luminosity is directly related to its period of variation. The longer the pulsation period, the more luminous the star. The period-luminosity relation for classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt in an investigation of thousands of variable stars in the Magellanic Clouds.[23] She published it in 1912[24] with further evidence. Once the period-luminosity relation is calibrated, the luminosity of a given Cepheid whose period is known can be established. Their distance is then found from their apparent brightness. The period-luminosity relation has been calibrated by many astronomers throughout the twentieth century, beginning with Hertzsprung.[25] Calibrating the period-luminosity relation has been problematic; however, a firm Galactic calibration was established by Benedict et al. 2007 using precise HST parallaxes for 10 nearby classical Cepheids.[26] Also, in 2008, ESO astronomers estimated with a precision within 1% the distance to the Cepheid RS Puppis, using light echos from a nebula in which it is embedded.[27] However, that latter finding has been actively debated in the literature.[28]

The following experimental correlations between a Population I Cepheid's period P and its mean absolute magnitude Mv was established from Hubble Space Telescope trigonometric parallaxes for 10 nearby Cepheids:

[26]

with P measured in days.

The following relations can also be used to calculate the distance d to classical Cepheids:

[26]

or

[29]

I and V represent near infrared and visual apparent mean magnitudes, respectively. The distance d is in parsecs.

Small amplitude Cepheids

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Classical Cepheid variables with visual amplitudes below 0.5 magnitudes, almost symmetrical sinusoidal light curves, and short periods, have been defined as a separate group called small amplitude Cepheids. They receive the acronym DCEPS in the GCVS. Periods are generally less than 7 days, although the exact cutoff is still debated.[30] The term s-Cepheid is used for short period small amplitude Cepheids with sinusoidal light curves that are considered to be first overtone pulsators. They are found near the red edge of the instability strip. Some authors use s-Cepheid as a synonym for the small amplitude DECPS stars, while others prefer to restrict it only to first overtone stars.[31][32]

Small amplitude Cepheids (DCEPS) include Polaris and FF Aquilae, although both may be pulsating in the fundamental mode. Confirmed first overtone pulsators include BG Crucis and BP Circini.[33][34]

Uncertainties in Cepheid determined distances

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Chief among the uncertainties tied to the Cepheid distance scale are: the nature of the period-luminosity relation in various passbands, the impact of metallicity on both the zero-point and slope of those relations, and the effects of photometric contamination (blending) and a changing (typically unknown) extinction law on classical Cepheid distances. All these topics are actively debated in the literature.[4][7][12][35][36][37][38][39][40][41][42][43]

These unresolved matters have resulted in cited values for the Hubble constant ranging between 60 km/s/Mpc and 80 km/s/Mpc.[3][4][6][7][8] Resolving this discrepancy is one of the foremost problems in astronomy since the cosmological parameters of the Universe may be constrained by supplying a precise value of the Hubble constant.[6][8]

Examples

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Several classical Cepheids have variations that can be recorded with night-by-night, trained naked eye observation, including the prototype Delta Cephei in the far north, Zeta Geminorum and Eta Aquilae ideal for observation around the tropics (near the ecliptic and thus zodiac) and in the far south Beta Doradus. The closest class member is the North Star (Polaris) whose distance is debated and whose present variability is approximately 0.05 of a magnitude.[6]

Designation (name) Constellation Discovery Maximum Apparent magnitude (mV)[44] Minimum Apparent magnitude (mV)[44] Period (days)[44] Spectral class Comment
η Aql Aquila Edward Pigott, 1784 3m.48 4m.39 07.17664 F6 Ibv  
FF Aql Aquila Charles Morse Huffer, 1927 5m.18 5m.68 04.47 F5Ia-F8Ia  
TT Aql Aquila 6m.46 7m.7 13.7546 F6-G5  
U Aql Aquila 6m.08 6m.86 07.02393 F5I-II-G1  
T Ant Antlia 5m.00 5m.82 05.898 G5 possibly has unseen companion. Previously thought to be a type II Cepheid[45]
RT Aur Auriga 5m.00 5m.82 03.73 F8Ibv  
l Car Carina   3m.28 4m.18 35.53584 G5 Iab/Ib  
δ Cep Cepheus John Goodricke, 1784 3m.48 4m.37 05.36634 F5Ib-G2Ib double star, visible in binoculars
AX Cir Circinus   5m.65 6m.09 05.273268 F2-G2II spectroscopic binary with 5 M☉ B6 companion
BP Cir Circinus   7m.31 7m.71 02.39810 F2/3II-F6 spectroscopic binary with 4.7 M☉ B6 companion
BG Cru Crux   5m.34 5m.58 03.3428 F5Ib-G0p  
R Cru Crux   6m.40 7m.23 05.82575 F7Ib/II  
S Cru Crux   6m.22 6m.92 04.68997 F6-G1Ib-II  
T Cru Crux   6m.32 6m.83 06.73331 F6-G2Ib  
X Cyg Cygnus   5m.85 6m.91 16.38633 G8Ib[46]  
SU Cyg Cygnus   6m.44 7m.22 03.84555 F2-G0I-II[47]  
β Dor Dorado   3m.46 4m.08 09.8426 F4-G4Ia-II  
ζ Gem Gemini Julius Schmidt, 1825 3m.62 4m.18 10.15073 F7Ib to G3Ib  
V473 Lyr Lyra   5m.99 6m.35 01.49078 F6Ib-II  
R Mus Musca   5m.93 6m.73 07.51 F7Ib-G2  
S Mus Musca   5m.89 6m.49 09.66007 F6Ib-G0  
S Nor Norma   6m.12 6m.77 09.75411 F8-G0Ib brightest member of open cluster NGC 6087
QZ Nor Norma   8m.71 9m.03 03.786008 F6I member of open cluster NGC 6067
V340 Nor Norma   8m.26 8m.60 11.2888 G0Ib member of open cluster NGC 6067
V378 Nor Norma   6m.21 6m.23 03.5850 G8Ib  
BF Oph Ophiuchus   6m.93 7m.71 04.06775 F8-K2[48]  
RS Pup Puppis   6m.52 7m.67 41.3876 F8Iab  
S Sge Sagitta John Ellard Gore, 1885 5m.24 6m.04 08.382086[49] F6Ib-G5Ib  
U Sgr Sagittarius (in M25)   6m.28 7m.15 06.74523 G1Ib[50]  
W Sgr Sagittarius   4m.29 5m.14 07.59503 F4-G2Ib Optical double with γ2 Sgr
X Sgr Sagittarius   4m.20 4m.90 07.01283 F5-G2II
V636 Sco Scorpius   6m.40 6m.92 06.79671 F7/8Ib/II-G5  
R TrA Triangulum Australe   6m.4 6m.9 03.389 F7Ib/II[50]  
S TrA Triangulum Australe   6m.1 6m.8 06.323 F6II-G2  
α UMi (Polaris) Ursa Minor Ejnar Hertzsprung, 1911 1m.86 2m.13 03.9696 F8Ib or F8II  
AH Vel Vela   5m.5 5m.89 04.227171 F7Ib-II  
S Vul Vulpecula   8m.69 9m.42 68.464 G0-K2(M1)  
T Vul Vulpecula   5m.41 6m.09 04.435462 F5Ib-G0Ib  
U Vul Vulpecula   6m.73 7m.54 07.990676 F6Iab-G2  
SV Vul Vulpecula   6m.72 7m.79 44.993 F7Iab-K0Iab  
SU Cas Cassiopeia   5m.88 6m.30 01.9 F5II  

See also

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References

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