Classical Cepheid variable stars are supergiants with periods in the range of 1–5 days. The light curve amplitude is typically between 0.5 and 2 magnitudes in the V band, and the velocity amplitude due to the pulsation is in the range of 30–60 km s−1.
Different to RR Lyrae, which can be found at all Galactic latitudes, Cepheids are strongly asso- ciated with the Galactic plane. More than 800 Cepheids are known in the Milky Way, and a few 1000 have been found in the two nearest galaxies, the Magellanic Clouds.
Cepheids show a close relationship between period and luminosity, which was found by Henrietta S. Leavitt in 1912 (Leavitt and Pickering 1912). This relation has given Cepheids a unique role in establishing the distances of near galaxies and hence the distance scale of the Universe, the “distance ladder”.
Cepheid Types and Light Curve Properties
Among Cepheids, two types can be distinguished: Classical Cepheids (or type I Cepheids) are comparatively young stars of ages ∼108 yr with masses of 2− 3 M
. They show a strong con-
centration towards the Galactic plane and have low space velocities. Their ages can be estimated from star clusters. Within period-luminosity diagrams, they occupy a narrow strip.
Type II Cepheids are fainter than type I Cepheids of comparable period. From globular clusters, as well as from being present in the Galactic halo, their age can be estimated as being up to 15× 109 yr. This implies that they must be less massive than type I Cepheids. Type II Cepheids can also be distinguished from type I Cepheids by the shape of their light curves. Most type I Cepheids, of which δ Cephei is a prototype, have asymmetric light curves, showing a steep rise to their maximum and a slower decline. Type II Cepheids, in contrast, show almost sinusoidal light curves.
Fig. 2.14 shows the light curves of the type I Cepheid SU Cygni in different photometric bands. As also for the RR Lyrae stars, the amplitude decreases as one goes from the ultraviolet to the
infrared. Some Cepheids of short periods have nearly sinusiodal light curves with amplitudes of only 0.5 mag.
0.0 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6
U
B
V
R
II
J
K
mag
D
Phase
Figure 2.14 Amplitude and phase variation of a typical Galactic Cepheid as a function of increasing wavelength. Note for increasing wavelength the monotonic drop in amplitude, the progression toward more symmetric light variation, and the phase shift of maximum toward later phases. The wavelength increases from top (ultraviolet, blue, and visual) to bottom (red and near-infrared out to K=2.2 µm). Taken from Madore and Freedman (1991).
Cepheids as Standard Candles
The relation between period and luminosity of a Cepheid comes directly from the Stefan-Boltzmann law (Catelan and Smith 2015). When expressed in bolometric magnitude units,
Mbol =−5 log(R) − 10 log(Teff) + const. (2.69)
Combining this with the pulsation equation Equ. (2.37), one gets
logP + 0.5 log(M) + 0.3Mbol+ 3 log Teff+ const = log Q, (2.70)
where M is the stellar mass. From this, at a constant effective temperature, the period should increase with increasing luminosity.
The period-luminosity relation was first found empirically by Leavitt and Pickering (1912), and then calibrated by Shapley (1918).
Fig. 2.15 shows near-infrared period-luminosity relations for type I and type II Cepheids in the Large Magellanic Cloud. For type I and type II, both the offset and the slope differ.
log
K
s-0.5 0.0 0.5 1.0 1.5 12
type I fundamental type I
first overtone type II 14 16 18
Figure 2.15Near-infrared period-luminosity relations for Cepheids of type I and II in the Large Magellanic Cloud. Among type I, both fundamental and first overtone Cepheids are indicted. Adapted from Matsunga et al. (2009).
The Evolution of Cepheids
Cepheids of type I are stars who are more massive than the Sun, having evolved from main sequence stars of 2–20 M . Such a star starts pulsating as a Cepheid when it crosses the instability
Like for other types of variables within the instability strip, κ and γ mechanisms within the H and He partial ionized zones are the most important drivers for pulsation. The variability of Cepheids of type I is caused by pulsations, being mainly driven by κ and γ mechanisms. The zone where He goes from singly to doubly ionized is mostly important to the driving of the pulsation. As the lifetimes of such massive stars like Cepheids of type I are short, they are relatively young stars with ages in the range of 107 years for the brightest and most massive ones, to a few 108 for the faintest and less massive ones. For this reason, Cepheids of type I are found in systems that have experienced recent star formation. Thus, within the Milky Way, Cepheids belong to the young disk population.
In contrast, Cepheids of type II are old, evolved stars with low masses of about 0.5–0.6 M . They
have evolved away from the main sequence, up to the giant branch, down the horizontal branch, back up the AGB, but are experiencing He flashes as He burning briefly switches on. This shifts the star to higher temperature and over the instability strip (Catelan and Smith 2015).