A correlation between stellar brightness variations and the gravitational acceleration at a star's surface has been observed that allows this acceleration to be measured with a precision of better than 25%. See Letter p.427
“Twinkle, twinkle little star, how I wonder what you are.” Given the wording of this old nursery rhyme, it is highly satisfying that Bastien et al.1 (page 427 of this issue) find that a star's twinkle may hold the key to determining its properties. The authors used data from NASA's Kepler space mission to show that accurate measurements of variations in a star's light reveal information about the acceleration of gravity at the star's surface. This result is significant for the characterization of stars, and in particular for the determination of radii of stars hosting planetary systems.
Essentially all knowledge about distant stars derives from observation of the light emitted by their outer layers. Therefore, the properties of these layers are central to the study of stars. These properties have conventionally been obtained from analysis of stellar spectra, but the gravitational acceleration (g) has proved notoriously difficult to nail down, and the resulting uncertainty about this quantity has substantial effects on the measurement of other properties, such as temperature and chemical composition.
Analyses of variations in stellar brightness caused by stellar oscillations (asteroseismology), particularly those based on the spectacular data from the Kepler mission2, provide precise determinations of g but require extensive observations and complex analysis, which are available for only a limited number of stars. However, stellar oscillations are not the only factor that contributes to variations in brightness. Bastien and colleagues show that g is also reflected in these variations.
One of the properties of a star's brightness variations measured by Bastien et al. is the total range of the variations. This includes variations on timescales of days that may have a number of causes, such as the rotation of large starspots across the disc of the star. In addition to this total range, the authors characterize the variations in terms of what they call 'flicker' — variations that occur on timescales shorter than eight hours (Fig. 1). In the Kepler data, they identify a substantial fraction of Sun-like stars that have a low range, defining what they dub 'flicker floor' (see Fig. 3 in the paper). Bastien et al. find that, for a subset of these flicker-floor stars whose precise values of g are known from asteroseismology2, there is a close correlation between flicker and g, with the amplitude of the flicker increasing with decreasing g. For other stars on the flicker floor, this correlation provides a means of determining g with a precision of better than 25% — between two and three times better than the precision obtained from conventional observations.
As Bastien et al. note, the general dependence of brightness variations on stellar properties can be described in terms of stellar evolution. Young stars tend to have stronger magnetic activity, with many starspots, and hence display a large total range of variations. With increasing age, this activity diminishes and the stars settle on the flicker floor. As the stars grow older their radii increase, leading to a lower g and a higher flicker.
Bastien and colleagues demonstrate how flicker can be used to measure g, but do not provide a detailed analysis of the physical nature of the flicker. The stars for which the investigation was carried out have outer convection zones, in which energy is transported to the surface through the motion of gas. In the Sun, this transport is visible in granulation — a time-varying pattern of small-scale brighter and dimmer regions on the solar surface that reflects hot, rising and cooler, sinking gas pockets. Granulation also leads to minute variations in the total solar brightness.
The authors' study indicates that stellar granulation is a contributor to flicker. Indeed, the spatial scale and other properties of granulation depend on g (ref. 3), with lower g resulting in a larger scale and thus probably causing larger brightness variations on timescales relevant to flicker, in agreement with the correlation that the authors found. Further support for the relationship between granulation and flicker comes from other Kepler observations and modelling of red-giant stars4. Brightness variations caused by granulation are expected in all the stars considered by the authors, hence defining a lower limit to the variations — the flicker floor. A better physical understanding of the origin of flicker might allow the observed brightness variations to be used to probe the dynamics of the outermost stellar layers. The resulting improved stellar modelling could, in turn, improve the accuracy with which g can be determined.
The very small amplitude of flicker makes it essentially unobservable using ground-based telescopes, owing to the effect of Earth's atmosphere. However, the ability to measure flicker with Kepler observations will be valuable in the continuing analysis of Kepler data on exoplanets, which are detected through the slight dimming of a star's light as a planet transits, or passes in front of it. An accurate determination of g from flicker greatly aids the analysis of spectroscopic observations used to infer the chemical composition of planet-hosting stars, and so advances our understanding of planet formation5. Furthermore, planetary transit observations provide a measurement of only planetary radius relative to stellar radius, and uncertain information about stellar radii hampers the characterization of the planets. With knowledge of g from flicker, as well as of the surface temperature and composition of the star, fits of stellar models to these quantities can be used to obtain a more precise value of the stellar radius, and hence of the planetary radius.
Beyond Kepler, the authors' technique will be valuable for NASA's planned Transiting Exoplanet Survey Satellite (TESS), which is slated for launch in 2017. TESS will carry out an all-sky survey for extrasolar planetary systems by monitoring at least half a million stars, and will require efficient methods to characterize the target stars. The same applies to the European Space Agency's Planetary Transits and Oscillations of Stars (PLATO) exoplanet mission, should it be selected for launch in 2022–24.
Therefore, Bastien and colleagues' analysis holds great promise for measuring stellar properties and understanding the complex dynamics of the outermost layers of stars. Studying the twinkling of stars does indeed help us to understand what they are.