RR Lyrae stars
RR Lyrae variables are old, low-mass, radially pulsating stars with periods in the range between 0.2 and 1 day. They are a numerous class of variable stars that populate galactic halos, thick disks and globular clusters. In the H-R diagram, RR Lyrae stars can be found in the narrow region where the horizontal branch intersects the pulsational instability strip. Their relatively small range of absolute mean magnitudes (because they lie on the horizontal branch) makes them important distance indicators in both our own Galaxy and those nearby. RR Lyrae stars are also excellent tracers of the chemical and dynamical properties of the oldest observable population of stars, so they give us insight into the earliest history of galaxies. Taking into account the pulsation modes, RR Lyrae stars can be divided into fundamental-mode (commonly referred to as RRab stars, sometimes called RR0 stars), first-overtone (RRc or RR1 stars) and double-mode (RRd or RR01 stars) pulsators. The existence of second-overtone pulsators among RR Lyrae variables (RRe or RR2 stars) is a matter of controversy.
So far, the OGLE project has published catalogs containing in total over 65,000 RR Lyrae stars: 24,906 objects in the Large Magellanic Cloud (Soszyński et al. 2009), 2475 in the Small Magellanic Cloud (Soszyński et al. 2010), and 38,257 in the Galactic bulge (Soszyński et al. 2011, 2014). This huge collection will soon be extended by variables discovered in the course of the ongoing fourth phase of the OGLE project.
Fundamental-mode pulsators (RRab stars)
In 1902 Solon Bailey divided RR Lyrae stars into three groups - RRa, RRb, and RRc - based upon the amplitude and skewness of the light curves. It was then noticed that RRa and RRb stars pulsate in the same (fundamental) mode, and they were merged to one, RRab, type. The pulsation periods of the fundamental-mode RR Lyrae stars range from about 0.3 to 1.0 days (Population II pulsators with longer periods are classified as type II Cepheids), but the vast majority of them have periods longer than 0.45 days. The distribution of periods correlates with the metallicity of RR Lyrae stars, namely more metal-poor variables have on average longer pulsation periods.
Fundamental-mode RR Lyrae stars have asymmetric light curves with a steep rising branch and a slow decrease of brightness after the maximum. Bumps on the light curves are very common, but the detailed morphology of the light curves depends on the chemical composition of the stars. This feature is used for metallicity measurements based on the photometric observations of RR Lyrae variables (see for example Jurcsik & Kovacs 1996 for V-band and Smolec 2005 for I-band light curves). The amplitudes of the photometric variations are strongly correlated with the periods. The shortest-period RRab variables usually have the largest amplitudes: up to 1.5 mag in the V band, and up to 1 mag in the I band. The amplitudes become typically smaller when we move to the RRab stars with longer periods. Below we show several typical light curves of RRab stars detected by the OGLE project in the Galactic bulge. The photometry was obtained in the Cousins I bandpass. Move the mouse pointer over the image to see the designation and J2000 equatorial coordinates of the star.
The RR Lyrae variables above show stable or nearly stable light curves. However, a significant number of RRab stars (up to 50% according to Jurcsik et al. 2009) exhibit long-term modulations of the amplitudes and phases of their light curves. This phenomenon was discovered by Sergey Blazhko in 1907 and the origin of this effect remains a mystery to the present day. The Blazhko modulation of light curves may be strictly periodic (with periods ranging from days to years), multi-periodic, or irregular. Below we show four RRab stars with conspicuous Blazhko effects. To display the amplitude changes, left panels present unfolded light curves collected over two years - 2012 and 2013. Right panels show the same light curves folded with the pulsation periods.
This animation illustrates how the phase and amplitude of the light curve changes over the course of one Blazhko cycle, which in this case lasts 155 days.
First-overtone pulsators (RRc stars)
RR Lyrae variables that pulsate in the first-overtone mode have periods from about 0.2 days to slightly more than 0.5 days. These stars have much more symmetric light curves and smaller amplitudes than RRab pulsators. In some cases the light curves of RRc stars are nearly sinusoidal, which severely hampers their identification, especially when poorer-quality photometry is available. Usually, RRc stars exhibit a small secondary bump located on the ascending branch.
Note that the latter light curve is significantly scattered. This is because this RRc star changed its pulsation period over the time span of the OGLE observations. Such a feature is very common among first-overtone RR Lyrae stars, especially those with periods longer than 0.35 days. Two other examples of RRc stars with significant period changes are shown below. The presented photometry was collected over only three years. The light curves are folded with "the best" constant periods.
The Blazhko effect is also observed in some RRc stars, but it is a much less common phenomenon than in RRab stars. Less than 10% of first-overtone RR Lyrae stars exhibit Blazhko modulation. This is an example of a Blazhko RRc star from the Galactic bulge:
Double-mode pulsators (RRd stars)
Some RR Lyrae stars may have two simultaneously excited pulsation modes: the fundamental and the first overtone. Such stars are often called RRd stars. The relative number of RRd stars among the whole population of RR Lyrae variables strongly depends on the metallicity of the stellar environment. In the relatively metal-rich Galactic bulge only 0.5% of RR Lyrae stars are double-mode pulsators, while in the metal-poor Small Magellanic Cloud as many as 10% of RR Lyrae variables are of RRd type. In most RRd stars the ratios of the two pulsation periods have a very small range - from 0.74 to 0.75. Only in the Galactic bulge did the OGLE project discover double-mode RR Lyrae stars with exceptionally small period ratios, down to 0.726.
In the vast majority of RRd stars the first-overtone component has larger amplitude than the fundamental mode. After separation of the modes, the first-overtone light curve usually has a similar shape and amplitude as in the single-mode RRc stars, while the fundamental-mode component clearly differs from the RRab light curves - it has small amplitude and nearly sinusoidal shape. Two RRd stars from the Galactic bulge are presented below. The left panels display original photometry folded with the first-overtone periods, the middle and right panels show separated first-overtone and fundamental-mode components, respectively.
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OGLE discovered the first double-mode RR Lyrae stars exhibiting the Blazhko effect (Soszyński et al. 2014). It is interesting that all known Blazhko RRd stars have slightly different period ratios than other (non-Blazhko) RRd stars (Jurcsik et al. 2014, Smolec et al. 2015). In the example below, the modulation of amplitude is well visible in the unfolded light curve (upper panel). Two lower panels show the same light curve divided into the first-overtone and fundamental-mode components. The Blazhko effect causes the large scatter of the data points in the phased light curves. Note that this is a rare case of an RRd star where fundamental-mode has larger amplitude than the first-overtone.
Mode-switching RR Lyrae stars
During their evolution, RR Lyrae stars should change the pulsation modes, although the detection of such changes is extremely unlikely as we observe stars in "human" timescales. Fortunately, OGLE monitors the brightness of such a large number of pulsating stars that we were able to discover several RR Lyrae stars that underwent a mode-switching (Soszyński et al. 2014). Two light curves presented below belong to the same RR Lyrae star in the Galactic bulge. The left panel shows the data points collected in the years 2001-2005 when our object was a double-mode RR Lyrae star (the light curve is folded with the fundamental-mode period), while the right panel displays observations obtained in 2010-2014 when the star became a typical single-mode RRab variable. OGLE survey for the first time provided an opportunity to directly observe the phenomenon of the mode switching in RR Lyrae stars. Note that the fundamental-mode period slightly changed during the process.
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Pseudo-RR Lyrae stars (Binary Evolution Pulsators)
Pulsating stars which are components of eclipsing binary systems are of particular interest, because they give us an opportunity to directly measure their masses and sizes. Unfortunately, to date no RR Lyrae star which is a member of an eclipsing binary system has been discovered, so masses of RR Lyrae stars are known only from models. In the OGLE databases we found a few candidates for RR Lyrae stars in eclipsing binary systems. The light curve of one of these objects - OGLE-BLG-RRLYR-02792 - is shown below. 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.
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OGLE-BLG-RRLYR-02792 was spectroscopically studied by Pietrzyński et al. (2012), who precisely determined the mass of the pulsating component. Surprisingly, it turned out that the mass of the pulsator is very small - only 0.26 of the Solar mass - completely at odds with the theoretical predictions for RR Lyrae stars. This object is probably the first representative of a new class of pulsating stars - Binary Evolution Pulsators - objects which mimic RR Lyrae stars, but have completely different internal structure and evolution history. The evolution of these stars is governed by the mass exchanges between two components of the binary system. It is estimated that about 0.2% of objects classified as RR Lyrae stars are actually Binary Evolution Pulsators.
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