Observing Solar-like Oscillations

We review techniques for measuring stellar oscillations in solartype stars. Despite great efforts, no unambiguous detections have been made. A new method, based on monitoring the equivalent widths of strong lines, shows promise but is yet to be confirmed. We also discuss several subtleties, such as the need to correct for CCD non-linearities and the importance of data weighting. 1. Why search for solar-like oscillations? Given the tiny amplitudes of oscillations in the Sun and the obvious problems in detecting similar oscillations in other stars, we should first ask whether the effort is justified. Oscillation frequencies give information about the sound speed in different parts of the stellar interior. They can be measured much more precisely than can any of the other fundamental parameters which have been discussed at this meeting. Accuracies of 10–10 have been achieved for “classical” multi-periodic pulsators stars such as δ Scuti stars, rapidly oscillating Ap (roAp) stars and β Cephei stars. These stars pulsate with amplitudes typically 1000 times greater than seen in the Sun, so why are we not satisfied with observing them? One reason is that the classical pulsating stars are only found in restricted areas of the HR diagram (the instability strips). Since oscillations in the Sun are thought to be excited by convective turbulence near the surface, all stars with an outer convective zone should undergo similar oscillations. This makes it possible, at least in principle, to perform seismic studies on all stars with spectral type later than about F5. 2 HANS KJELDSEN AND TIMOTHY R. BEDDING Figure 1. Evolution of oscillation frequencies in a 2.2M⊙ star, from model calculations by J. Christensen-Dalsgaard. Only modes with l = 0, 1, 2 and n ≤ 10 are shown. A second reason for studying solar-like oscillations is that the modes are easy to identify. There is little point in knowing the frequency of an oscillation mode unless you also know in which part of the star that mode is trapped. An oscillation mode is characterized by three integers: n (the radial order), l (the angular degree) and m (the azimuthal order). These specify the shape of the eigenfunction, which in turn determines the sensitivity of the oscillation frequency to the internal structure of the star. Figure 1 shows the oscillation frequencies of a non-rotating star (mass 2.2M⊙) as it evolves. At any instant during the star’s evolution, a vertical cross-section through this figure shows the frequencies of oscillation modes with l = 0, 1 and 2 (which are most easily observed in an unresolved star). However, in multi-periodic δ Scuti and β Cephei stars, only the lowest frequency modes are found to be excited to an observable level, presumably due to the details of the excitation process (the so-called κ mechanism). We are therefore forced to identify modes in the crowded lower region of the diagram. To further complicate matters, these stars tend to be rapid rotators, which causes a splitting of frequencies (analogous to Zeeman splitting). Finally, a given star is only observed to oscillate in a seemingly random subset of possible modes. Until reliable mode identification is achieved, it will be impossible to apply asteroseismology to these “classical” pulsating stars. In contrast, it is easy to identify the modes of solar-like oscillations. At least in the Sun, all modes in a broad frequency range are excited. In a star with no rotation or magnetic field, frequencies do not depend on m. Observing solar-like oscillations 3 Furthermore, these modes approximately satisfy an asymptotic relation, with modes of fixed l and differing n having regularly spaced frequencies separated by the so-called large separation, ∆ν. The resulting comb-like structure is clearly seen in the upper part of Figure 1 and allows modes to be identified directly from the oscillation spectrum. Measuring ∆ν provides an estimate of the stellar density. Moreover, the small differences between observed frequencies and those predicted by the asymptotic relation give crucial information about the sound speed deep inside the star. 2. Sensitivities of detection methods Velocity In the Sun, the strongest modes have velocity amplitudes of about 25 cm/s, which corresponds to a wavelength variation (δλ/λ) of less than 10, or 4.2μÅ at 5000 Å. Detecting such miniscule Doppler shifts in other stars is extremely difficult. Spectrographs cannot be made with absolute stabilities of 10, so one must simultaneously monitor the wavelength of a stable reference (e.g., a Na or K resonance cell, an I2 absorption cell or telluric absorption features). The noise levels at present are down to about 0.5m/s, which is a factor of two higher than the solar signal. Radius Given that solar periods are around 5 min, the change in radius is only about 12m or 17 microarcseconds. Astrometry of the solar limb using SoHO/MDI has recently revealed the oscillations (J. Kuhn et al., Proc. IAU Symp. 181, in press), but such observations will surely be impossible for other solar-like stars. Intensity The solar oscillations have been observed as variations in total intensity, with amplitudes of about 4 ppm (parts per million). Open clusters are a natural target for differential CCD photometry and the lowest noise level so far achieved is 5–7 ppm, from observations by Gilliland et al. (1993) of twelve stars in M67 using six telescopes (2.5m to 5m) during one week. This is an interesting noise level, less than a factor of two away from solar photometric amplitude. Ground-based photometric observations are severely hampered by atmospheric scintillation. Several space missions have been proposed, but only one has so far been launched: the EVRIS experiment, on board the Russian Mars96 probe, which ended in the Pacific Ocean. Temperature Since the change in radius during solar oscillations is insignificant, the intensity fluctuations observed in the Sun must result from local temperature changes in the atmosphere of about 6mK (δTeff/Teff ≈ 10). It has been suggested that these temperature changes can be measured by their effect on spectral absorption lines (Kjeldsen et al. 1995; 4 HANS KJELDSEN AND TIMOTHY R. BEDDING Bedding et al. 1996). For example, the Balmer lines in the Sun should show variations in equivalent width of about 6 ppm. As discussed below, the equivalent-width method has so far attained noise levels in other stars of 2–3 times the solar peak amplitude.