The Chaotic Music of Variable Stars

Space-based observations of RR Lyrae variable stars, once considered the paragon of simplicity, are revealing turmoil in their daily vibrations.

RR Lyrae
The prototype of RR Lyrae variable stars is of course RR Lyrae itself, discovered by Williamina Fleming in 1901.
ESO Online Digitized Sky Survey
Lyra plays high overhead on summer evenings, and a star at the constellation’s border keeps time. This star, RR Lyrae, brightens and fades every half day by a full magnitude, producing a slow beat mimicked by others across the sky.

These stars used to be considered the paragon of simplicity. Having run out of hydrogen in its core some time ago, they’re frantically fusing helium to stave off gravity’s inevitable inward pull. The star heats, expands, then cools and contracts: a regular radial vibration.

But RR Lyrae stars are not as simple as they once seemed. Recent space missions have provided the near-continuous observations needed to show that these variables are actually pulsing in complex, unpredictable ways.

Not-So-Simple Variables

Blazhko period
About half of all RR Lyrae stars cycle their beats, with the brightness and timing of their pulse's peak evolving over a period of weeks. The movie uses ground-based data, but space-based observations show this so-called Blazhko effect, already not well understood, is not as simple as previously thought.
The Blazhko Project (http://www.univie.ac.at/tops/blazhko/RRLyrae2004.html)
Sergey Blazhko, a Russian astronomer, noticed a long time ago that these stars might not be as simple as they seem. In 1907 he observed the peak of RW Draconis’s half-day pulsation cycle over a period of weeks. RR Lyrae itself has a so-called “Blazhko period” of 41 days. Yet even though astronomers could predict the Blazhko effect, the mechanism behind it defied explanation.

Decades of ground-based observations from amateurs and professionals alike, including dedicated surveys such as the Konkoly Blazhko Survey, have already reaped countless measurements of RR Lyrae stars. But viewing stars that complete a pulsation every 12 or so hours from the ground has its disadvantages — half the pulsations happen during the day. Monitoring a star continuously for a full Blazhko period would be impossible without relying on many different kinds of telescopes spread across the globe. And even with a global network, a station would basically see the same section of the cycle every night, making independent verification problematic.

The launch of high-precision, star-watching spacecraft opened the prospect of near-continuous observations. Elisabeth Guggenberger (University of Vienna, Austria) was one of the astronomers who leaped to take advantage of CoRoT and Kepler data. The two spacecraft have been on the hunt for exoplanets, but they’ve obtained wonderfully precise data on hundreds of variable stars in the process.

Variable stars in M3
Most of the variable stars in this movie of the globular cluster Messier 3 are RR Lyrae stars.
Joel Hartman & Krzysztof Stanek (Harvard / CfA)
Presenting her results at a recent Harvard-Smithsonian Center for Astrophysics seminar, Guggenberger focused on two RR Lyrae stars: CoRoT 105288363 (observed for 145 days, or four complete Blazhko periods) and V445 Lyr (588 days, eight complete Blazhko periods). What she found was that both stars have not one, but two Blazhko periods — that is, the stars vary in a periodic way on three different timescales.

And that’s not all. Periodic variation can’t explain additional irregularities. In fact, she writes in a set of conference proceedings, “Of eight observed Blazhko cycles in V445 Lyr, not one resembles another.”

The observed complexity demands an explanation. Some theorists have proposed turbulent, small-scale magnetic fields or shock waves reverberating within the star to explain the irregularities. But only one model so far has offered an explanation using hard numbers.

“These results are very new and not many experts have had time to develop new models,” says Robert Szabo (Konkoly Observatory, Hungary), who coauthored that study. “I think it is fair to say that my group has gotten the farthest so far.”

In his team’s model, overtones — similar to the higher-order frequencies that lend a plucked guitar string its distinctive sound — accompany the star’s fundamental vibrations. (Guitars' overtones are generally pleasing to the ear, but the overtones in RR Lyrae stars would be quite dissonant if put to music; their overtones do not have integer frequency ratios.) Interactions with higher-frequency overtones destabilize the vibrations. Though the individual pulses might appear quite regular, the cycles of beats are rendered unpredictable.

Szabo’s result provides a good explanation for some of the irregularities observed in RR Lyrae stars, time will tell if it can explain the full range of observed behavior.

The Future of Variable Stars

As astronomers continue to struggle with understanding stars’ inner structures, will space-based observations eclipse amateur contributions? Hardly. Spacecraft’s short lifetimes can’t accommodate the evolution that transforms stars over decades or centuries: Kepler and COROT are both retired, for example, with only a faint chance of Kepler’s reinstatement. (Canada’s MOST satellite is still functioning but aging, now more than 10 years old.) The collective lifetime of scores of amateurs, on the other hand, is quite a bit longer.

Also, while spacecraft provide continuous, high-precision brightness measurements — a feat simply not possible from the ground — they might only observe a given star every half-hour. Though amateurs’ brightness measurements might not beat a satellite’s precision, they can better pinpoint the moment a pulsating star peaks in brightness.

5 thoughts on “The Chaotic Music of Variable Stars

  1. Robert L. Oldershaw

    The same discrete self-similar modeling that worked of RR Lyrae variable stars and excited He atoms also is successful with:

    SX Phoenicis variables,
    Delta Scuti variables, and
    ZZ Ceti variables,

    as can be seen and studied at: http://arxiv.org/a/oldershaw_r_1

  2. Alzie

    The light curve is reminiscent of relaxation oscillators in electroncs.
    They produce eerily similar saw tooth waveforms.

    These oscillators rely on the charge and discharge of capacitors
    with trigger type devices.
    They are non resonant,
    ie. they have no high quality resonance associated with them
    to control the oscillation frequency.
    They are notoriously sensitive to external effects
    such as supply voltage and loading.

    They can easily be nudged into fully chaotic random periodicities.

    Eg. I can see these stars being very sensitive to
    irregularities in fuel supply and
    external gravitational influences.

    Its pretty cool that there are these analogs all throughout physics, biology, etc.

  3. Bruce

    Thanks for that Alzie. I thought the light curve looked familiar. Examples of similarity across vastly differing scales and environments are common. I.e., a spiral galaxy looking like a tropical cyclone which in turn looks like soapy water going down a sink drain. But this doesn’t imply a causal link between these phenomena, just that similar mathematical functions can be applicable in widely differing settings.

  4. Mike W. Herberich

    I would imagine that our friend Robert Oldershaw would want to contribute a word or two as to scalability phenomena, from drain to galaxy … or even from subatomic to super-galactic, universal. The simple association "electronic" or "electric" should actually support that. We all know that capacitive as well as resistive effects are all over the place wherever there happens to be an electron on the run. But, then again, I trust that the researchers occupied with this article’s findings must have thought of such associations long before us.

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