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Music of stars reveals their properties

How large and massive are the stars you see in the night sky? Although this might seem a simple question, conventional observational techniques, such as photometry and spectroscopy, cannot provide a direct answer to it. Fortunately, listening to the intriguing musical symphony of pulsating stars does. Using precise asteroseismic observations from the Kepler mission, a team of world scientists led by astronomers at the Max Planck Institute for Astrophysics (MPA) has characterized, for the first time, the properties of main-sequence field stars, determining their masses and radii in a completely model independent way.

Fig. 1: Artist's impression showing sound waves trapped in the interior of one star, with an orbiting planet in the foreground. Kepler has observed oscillations in more than 500 solar-type stars.
Credits: G. Perez Diaz, IAC (MultiMedia Service).

Fig. 2: Maximum frequency vs. effective temperature for the complete sample of stars, for which oscillations were detected. Evolutionary tracks for some stellar parameters are also plotted: at solar metallicity for 0.85 solar masses (dash-dotted line), 1.0 solar mass (solid line), and 1.15 solar masses (dashed line); and at sub-solar metallicity for 1.0 solar mass (dotted line). The Sun is marked with a dotted circle close to the bottom of the 1.0 solar mass track.

Fig. 3: This plot shows the effective temperature and a measure of the surface gravity (log g) for all targets, where log g was obtained from scaling relations. Stars with masses determined to be 1 solar mass ┬▒ 15% are plotted as red circles, while the rest of the stars with detected oscillations are plotted as grey diamonds (without error bars to reduce clutter). The spread is most likely due to differences in the chemical compositions of the stars. Stellar tracks and position of the Sun are the same as in Figure 2.

Our galaxy is comprised of stars of different sizes, ages, and chemical compositions. Current observational techniques can put some constraints on stellar properties, such as effective temperature, surface gravity and composition. However, in order to estimate masses and radii, these measurements need to be complemented with theoretical calculations of stellar evolution, where large uncertainties remain due to our limited understanding of the physical processes taking place in stellar interiors. This has implications in many fields of astrophysics, from characterizing simple stellar populations in galactic globular clusters to reconstructing the formation history of distant galaxies.

Fortunately, stars like the Sun are not static and provide us with additional information by means of their oscillations. Just like air flowing through a musical instrument, vigorous convective motions in the outer layers of stars excite acoustic waves that propagate through the stellar interior. Depending on the characteristics of its resonant cavity, the star will vibrate in different frequencies and overtones, periodically swelling and contracting as the pressure waves travel through its interior. Asteroseismology is the field of astrophysics occupied with the study of these (and other) types of stellar pulsation.

In principle, every star with a convective outer layer should present acoustic oscillations, often termed solar-like oscillations as they were first observed in the Sun. However, the brightness variations they produce are fairly small, and can be on the order of only a micro-magnitude. This level of precision is very challenging to obtain from ground observations, which led astronomers to look for possibilities of observing from space, where higher accuracy can be achieved.

The Kepler mission has been the most successful example of asteroseismic observations. As the illustration in Figure 1 shows, one of the main aims of this satellite is to detect extrasolar planets by the ”transit method“. As the planet on its orbit moves between the parent star and the observer it will lead to a small dimming of the star. The detected spectra of oscillations need to be carefully analysed to distinguish between an external cause such as a planet and intrinsic oscillations of the star itself. Staring at the same field in the sky for the entire mission, Kepler continuously and simultaneously monitors the brightness of more than 100,000 stars in our galaxy.

One of the many important achievements of the Kepler mission is the detection of oscillations in more than 500 stars in the so called main-sequence phase. In this longest evolutionary phase in a star's lifetime, stellar energy is produced by fusion of hydrogen - their main constituent - into helium.

Using a measure of the stellar surface temperature (known as effective temperature), we can compare in Figure 2 the seismic observations — measured with an unprecedented level of precision - with theoretical predictions. Interestingly enough, it turns out that a large fraction of the seismic observations lie in the region where evolutionary tracks for stars with masses close to one solar mass are located. Is it possible to pinpoint the masses and radii of these stars?

Asteroseismology provides the answer by what is known as the ”direct method“ for mass and radius determination. The two global asteroseismic quantities, the large frequency separation and the frequency of maximum oscillation power, are tightly correlated over a wide range of values. Moreover, they are correlated with the accurately known solar parameters, such as the surface temperature, through scaling relations. As the oscillations depend on the characteristics of the resonant cavity (i.e. the size of the star), we can directly determine the mass and radius of a star using the global seismic parameters coupled with the effective temperature.

Figure 3 shows more than 70 targets with a mass determined to be close to solar among the large ensemble of stars with oscillations detected. For a few of these stars, accurate metallicities (i.e. the abundance of elements heavier than hydrogen and helium) have been measured from spectroscopy, and the agreement with evolutionary calculations is exquisite. The data therefore suggests that we have successfully identified, for the first time, an evolutionary sequence of field stars with masses very close to one solar mass.

These findings have several interesting implications for astrophysics. We can now perform differential analysis on stars with similar masses but in different evolutionary stages, following their development throughout the main-sequence phase. It also demonstrates the capability of asteroseismology to characterize stellar populations in a certain region of the sky.

Seismic observations coupled with effective temperature estimates allow the determination of masses and radii to a very high level of precision for stars in different evolutionary phases. This opens the exciting possibility of deriving stellar ages to a precision exceeding that possible by other techniques adopted in stellar population studies, such as isochrones or chromospheric activity dating. Combining these results with parameters obtained from stellar colours, such as metallicities, and angular diameter (and thus distances when comparing this with radii) could offer a complete picture of the stellar population in the Kepler field.

The possibilities are many, and the potential of asteroseismology to constrain theoretical models, unveil underlying physical processes, and discover the dynamical history of our galaxy is finally being exploited.

V. Silva Aguirre, L. Casagrande, R. Sch├Ânrich, A. Weiss


V. Silva Aguirre, W. J. Chaplin, J. Ballot, S. Basu, T. R. Bedding, et al., "Constructing a One-solar-mass Evolutionary Sequence Using Asteroseismic Data from Kepler", 2011, The Astrophysical Journal, 740, L2 linkPfeilExtern.gif

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