Classical Cepheids (also known as delta Cephei stars, type I Cepheids or population I Cepheids) are among the most famous and most important variable stars. They are relatively young, massive, radially pulsating stars with well-defined relationships between absolute magnitude and period, making them important distance indicators. Classical Cepheids may oscillate in the fundamental, first, or second overtone modes. So far, OGLE has yielded catalogs of 3375 (Soszyński et al. 2008), 4630 (Soszyński et al. 2010), 32 (Soszyński et al. 2011), and 20 (Pietrukowicz et al. 2013) classical Cepheids in the Large Magellanic Cloud, Small Magellanic Cloud, towards the Galactic center, and in the Galactic disk, respectively.
Fundamental-mode Cepheids have periods ranging from about 1 to over 200 days, but typical periods are a few days. Their light curves are usually asymmetric with a rapid rise to maximum light and a slower decline. In most classical Cepheids the light curve shapes are correlated with the oscillation periods, which is called the Hertzsprung progression. Cepheids with periods in the range 6-20 days show a secondary bump along both the light and the velocity curves, probably caused by a 2:1 resonance between the fundamental mode and the second overtone. The bump appears on the descending branch of the light curves of Cepheids with periods of about 6 days and for longer periods it progresses backward in phase. Around periods of 10 days, the bump passes through maximum light, then moves down in the ascending branch and disappears for periods longer than 20 days. Cepheids with the longest periods (>100 days) usually have small-amplitude nearly sinusoidal light curves. Below we present 14 light curves of typical fundamental-mode classical Cepheids in the Large Magellanic Cloud. The light curves are arranged according to their periods. Hover the cursor over the images to get the information about the designation and coordinates of each star.
The last two light curves were obtained with the OGLE Shallow Survey (Ulaczyk et al. 2012), because these Cepheids are too bright for the regular OGLE survey.
Some fundamental-mode Cepheids, usually with periods in the range 6-12 days, have light curves which do not fit this pattern. Their amplitudes are much smaller than for typical Cepheids in this range of periods and the secondary bumps are invisible or barely visible. Here are four examples of such objects from the Large Magellanic Cloud:
Cepheids pulsating in the first overtone generally show smaller light amplitudes and more symmetric light curves than fundamental-mode pulsators. The maximum pulsation period of the overtone Cepheids depends on the metallicity of the stellar environment in which they appear: in the Small Magellanic Cloud it is 4.5 days, in the Large Magellanic Cloud it is nearly 6 days, while in the Milky Way the longest-period overtone Cepheid has a period of 7.6 days (Baranowski et al. 2009). The lower limit for the first-overtone Cepheid periods can be adopted for any value, because there is no natural boundary between overtone Cepheids and delta Scuti stars - both types of stars smoothly pass one into another. In the OGLE catalogs we have adopted a period of 0.24 days as the lower limit for first overtone Cepheids. Here are some example light curves of the first-overtone Cepheids detected in the Galactic bulge and Large Magellanic Cloud:
Cepheids pulsating solely in the second overtone are very rare objects. Almost all known stars of this type have been detected through the OGLE observations. Second-overtone Cepheids are much more common in the metal-poor environments - in the Small Magellanic Cloud we identified 83 such objects, while in the Large Magellanic Cloud only 14. Second-overtone oscillations produce nearly sinusoidal light curves with small amplitudes (below 0.1 mag).
Some classical Cepheids pulsate simultaneously in two or even three modes. Their light curves collected over a longer timespan and phased with one of the pulsation periods are scattered, because the secondary periodicity is superimposed on the primary one. Using Fourier techniques it is possible to separate both light curves, like in this double-mode Cepheid oscillating in the fundamental and first-overtone modes:
The most numerous group of double-mode Cepheids in the Magellanic Clouds have the first and second overtones excited. In the Galaxy such stars are much less common. This is an example identified by OGLE toward the Galactic center:
Triple-mode Cepheids are very rare. In the OGLE catalogs there are only 10 such objects. In this example all three modes are separated from each other:
Cepheids in eclipsing binary systems
Cepheids that are components of eclipsing binary systems are unique objects, because they allow us to directly measure the masses of pulsating stars and independently calibrate them as distance indicators. The longstanding problem related to the theory of classical Cepheids was the discrepancy between mass estimates obtained from pulsational and stellar evolution models. The star whose light curve is plotted below - OGLE-LMC-CEP-0227 - provided the first determination of the dynamical mass of a classical Cepheid to an unprecedented 1% accuracy (Pietrzyński et al. 2010). This measurement solved the mass discrepancy problem. The left panel shows the original light curve folded with the pulsation period, the other two panels show the separated pulsational and eclipsing light curves.
In the OGLE databases we discovered several classical Cepheids which are members of binary systems. One of them - OGLE-LMC-CEP-1718 - is of particular interest, because it is an eclipsing binary system consisting of two first-overtone Cepheids. Below we separated all the components of its light curve - two Cepheids and the eclipsing light curve with the 1.13-year orbital period. Due to an eccentric orbit, only one eclipse per period is visible in this system.