Background

 

Short overview (click on links to go there):

RR Lyrae stars and the Blazhko effect

Past and present observational studies of the Blazhko effect

Explanations for the Blazhko effect in RR Lyrae stars

New developments in line profile analysis

New Approaches to solve the old Blazhko puzzle in RR Lyrae stars

References


 

 

Figure 1: This time lapse movie of bright globular cluster M3 was taken over a single night. Most of the variable stars visible above are RR Lyrae stars, stars that can quickly double their brightness while becoming noticeably bluer. Furthermore, these stars vary their light in a distinctive pattern that allows unique identification. Lastly, since RR Lyrae stars all have the same intrinsic brightness, identifying them and measuring how dim they appear tells how far they are, since faintness means farness. These distances, in turn, help calibrate the scale of the entire universe (picture credit and copyright: Hartman & Stanek).

 

RR Lyrae stars have been studied for over a century now, and play an important role in astrophysics. These pulsating variables have periods of 0.2-1.1 day, and show brightness variations of the order of a magnitude. They serve as standard candles to fix the cosmological distance scale, and as mainly Population II stars they are witnesses of the evolution of the universe. Until not so long ago, these stars were considered to be prototypes of radially pulsating stars.

Depending on their light curves and pulsation characteristics RR Lyrae stars are divided into different subclasses (Figure 2, Bailey classification). The RRab stars, with high-amplitude non-sinusoidal light curves, pulsate in the fundamental radial mode. RRc light curves have smaller amplitudes and are rather simusoidal. They pulsate in the radial first overtone. The RRd stars pulsate in both radial modes simultaneously.

 

Figure 2: Bailey classification of RR Lyrae stars.

 

The most intriguing subclass of RR Lyrae stars consists of stars showing the Blazhko effect, the phenomenon of amplitude or phase modulation. These stars have light curves that are modulated on timescales of typically tens to hundreds of days (Figure 3). Blazhko (1907) was the first to report this phenomenon in RW Dra.

The estimated incidence rate of Blazhko variables among the galactic RRab stars (fundamental mode pulsators) is about 20-30 % (Szeidl 1988; Moskalik & Poretti 2002). For the RRc Blazhko stars (first overtone pulsators) this rate is less than 5 %. In the LMC the incidence rate for RRab stars is only half as large, which is probably a metallicity effect.

 

Figure 2: Illustration of the lightcurve changes over the Blazhko cycle (created by D. Welch based on MACHO project data, Alcock et al. 2000).

 

 

The Blazhko effect has been the frequent subject of photographic and photometric studies (e.g., Szeidl & Kollath 2000). Traditionally, the phenomenon was studied by means of O-C analysis. Therefore the observations were in general strongly biased towards the ascending branch and maximum phase of the primary light curve, a sampling pernicious for the Fourier analysis recently used to describe the changes in the light curve throughout the Blazhko cycle. Rigorous frequency analyses of photometric data covering complete light curves were carried out for northern field Blazhko stars by e.g., Borkowski (1980), Kovacs (1995), Smith et al. (2003), just to mention a few. For RR Lyr, the brightest Blazhko star, important spectroscopic studies were performed by Struve & Blaauw (1948) and Preston et al. (1965).


For a long time the presence of the Blazhko effect in RRc stars was an open question: because of the small changes in the height of maximum of their light curves it was more difficult to detect. The controversy was resolved by the systematic studies of accurate CCD data of globular clusters and the large variable star data bases resulting from microlensing surveys (e.g., MACHO, OGLE). These studies have cast a new light upon the study of RR Lyrae variability (Moskalik & Poretti 2003; Alcock et al. 2000, 2003), and have yielded important statistics on the phenomenology of the Blazhko effect.

The frequency spectra of light and radial velocity curves of RR Lyrae Blazhko stars exhibit either a doublet structure or an equally-spaced triplet structure around the main pulsation frequency and its harmonics, with a small frequency separation corresponding to the Blazhko frequency. The observed period ratios are 0.95-1.05, which excludes the possibility of another radial mode being excited.

 

 

The present data sample indicates that there could be a continuous transition between the variables showing an equidistant triplet and those displaying only a close doublet, suggesting that both features are the result of the same phenomenon. A large majority of the Blazhko stars have a larger modulation peak at the higher (rather than the lower) frequency side of the main pulsation component.

Another interesting fact is the absence of the Blazhko effect among the longperiod RRab stars (Smith 1981). Blazhko stars at their greatest light amplitude fall approximately on the curve of amplitude versus period as
defined by stars with regular light curves. This indicates that the Blazhko effect tends to reduce the maximum light level.

Period changes are a common feature in RR Lyrae stars, and also occur in Blazhko stars (Smith 1995; Szeidl & Kollath 2000; LaCluyzé et al. 2002). The observed period variability is too fast to be of evolutionary nature.
In some stars the Blazhko effect ceased. Some well-studied field Blazhko stars are reported to display, besides their Blazhko cycles, also very long periods of the order of years. RR Lyrae, for example, shows a cycle of about
4 years, at the end of which the strength of the modulation suddenly decreases, and a phase shift of about 10 days occurs in the Blazhko cycle. This phenomenon is still unexplained, though it has been used as an argument for the magnetic models.

 

The most plausible hypotheses to explain the phenomenon focus on two types of models, both involving nonradial pulsation components: the resonance models and the magnetic models.

 

For some general information on stellar pulsations (radial/nonradial) and asteroseismology, a link will be added here soon.

 

 

Figure 3: Schematic overview of the plausible models for the Blazhko effect.

 

The resonance models:


The resonance models are based on a (nonlinear) resonance between the radial fundamental mode and a nonradial mode. In these models the dipole (l =1) modes have the highest probability to be nonlinearly excited (Cox 1993; Van Hoolst et al. 1998). Nowakowski & Dziembowski (2001) predict significant amplitude and phase modulation in the case of excitation of a rotationally split m = 1 pair. The modulation period is determined by the rotation rate (currently unknown) and the Brunt-Väisälä frequency in the deepest part of the radiative interior. Peterson (1996) measured the line-widths via cross-correlation for 27 RR Lyrae stars and obtained an upper limit for v sin i of 10 km/s.


The magnetic models:


The magnetic models, like the simple oblique pulsator model for roAp stars (Kurtz 1982), suppose that Blazhko stars have a magnetic field inclined to the stellar rotation axis (Cousens 1983; Shibahashi & Takata 1995). The main radial mode is deformed by the magnetic field to have an additional quadrupole component (l = 2), for which the symmetry axis coincides with the magnetic axis. Due to the star's rotation our view of the pulsation components changes, causing the observed amplitude modulation. Shibahashi \& Takata (1995) predict a quintuplet structure in the frequency spectrum, but also show that the quintuplet looks almost like a triplet for certain geometrical configurations. Depending on which of the side components we then observe, the Blazhko period is supposed to be equal to the rotation period or half of the rotation period.
According to the latest model, a magnetic field of about 1 kG is needed in this model for the amplitude modulation to be observable. Whereas Babcock (1958) and Romanov et al. (1994) reported a variable magnetic field in RR Lyr with a strength up to 1.5 kG, Preston (1967) and Chadid et al. (2001, 2004) contradict these measurements.

In both the magnetic (Shibahashi 2000) and the resonance models (Nowakowski & Dziembowski 2001) the pulsation amplitudes are considered to be constant. The observed modulation of the light curve is a consequence of rotation. The degree of modulation is aspect-dependent in both models. Each of the models predicts modulation components of equal amplitudes, in sharp contrast to the large majority of the frequency patterns observed. The question of why RRc Blazhko stars have significantly lower incidence rates has not yet been addressed in the magnetic model. The resonance model does predict a lower probability for first overtone pulsators to show amplitude modulation, although still not in the degree observed. Deviations from strict amplitude/phase modulations (see e.g., Szeidl 1988; Smith et al. 2002) need to be explained by future modelling. The different incidence rates in different populations (LMC and Galactic Bulge), probably related to metallicity (Moskalik & Poretti 2002; Alcock et al. 2003), have yet to be taken into account. Finally, convective turbulence may play a role in driving/quenching the Blazhko effect.

We can conclude that the basic physical understanding of the Blazhko phenomenon is still missing, and the viable models need fine-tuning. As both models for explaining the Blazhko effect are based on the presence of nonradial components, their detection and identification is of utmost importance for understanding the mechanism behind the amplitude modulation.

 

Up to now most observational studies of Blazhko stars were based on photometric data. High-resolution line profiles offer much better diagnostics to find and identify nonradial oscillation components in pulsating stars. A few years ago the first line profile study aiming at an identification of the nonradial mode(s) was carried out by Kolenberg et al. (2003). It was based on a set of 669 high-resolution (R=40000) spectra of RR Lyr, obtained
with the spectrograph ELODIE attached to the 1.93-m telescope at the Observatoire de Haute-Provence in France (Chadid et al. 1999). A detailed study of the variations of the FeII line profile at 4923.921 Angström, led to a clear detection of nonradial pulsation components in the star. By means of an adapted version of the moment method (Balona 1986; Aerts 1996; Kolenberg 2002), the detected nonradial modes were identified as nonaxisymmetric (with respect to the rotation axis) modes of degree l < 4 (see below). The incomplete coverage of the data over the Blazhko cycle hampered a more precise identification. As this kind of analysis is a first essential step towards a decisive confrontation between the theoretical models and the observations, more spectroscopic data, additional data, better spread over the Blazhko cycle, and similar data sets of additional (Blazhko) RR Lyrae stars are highly desired.

 

Figure 4: What is the geometry of the pulsation modes responsible for the modulation we observe? That is the question we want to solve. For that we need to develop a suitable 'magnifying glass', a technique that can lift out the concerned modes.

 

The Blazhko Project is a large international collaboration, set up to join efforts in obtaining a better understanding of the Blazhko phenomenon in RR Lyrae stars. The project was founded in Vienna and started its activities in the autumn of 2003.

Methodology:

The starting point for improving the modelling is an extensive data of a limited sample of field RR Lyr Blazhko and non-Blazhko stars: a few RRab Blazhko stars, in the northern and in the southern hemisphere, and also one RRc Blazhko target. Important is the inclusion of a few well-selected non-modulated RR Lyrae stars in the target list, of which similar data are being gained, to be compared with the Blazhko stars.

The required data set consists of high-resolution R > 40000, high-S/N (>100) spectroscopic data evenly spread over the Blazhko cycle for the target stars. A few very detailed snapshots (S/N > 200) are being (and will be) obtained with telescopes of the 8-m class, and will help to distinguish between different nonradial modes (see Section 5.1.1). Simulation studies reveal how much high-resolution data are minimally needed to be able to disentangle the modes, and what would be their optimal time spread. Additional radial velocities over a longer time base can be obtained with smaller telescopes, and provide essential information to interpret the line profile variations. Finally, photometric data gathered over a time base of at least a year, are needed to ensure the required frequency resolution. For the interpretation of the data we will use the available spectroscopic identification methods (described below), as well as combined techniques presently being developed (see Zima et al. 2004).

 

References

General list of references, not only the ones referred to in the text.

This list will be updated and extended soon!

Click here for the NASA ADS Astronomy/Planetary Query Form .

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