Classical Cepheid variable
Classical Cepheids are a type of
There exists a well-defined
Around 800 classical Cepheids are known in the
Properties
Classical Cepheid variables are 4–20 times more massive than the Sun,
Cepheid variables may pulsate in a
When an
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
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
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
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
with P measured in days.
The following relations can also be used to calculate the distance d to classical Cepheids:
or
I and V represent near infrared and visual apparent mean magnitudes, respectively. The distance d is in parsecs.
Small amplitude Cepheids
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
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
Examples
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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