Rafael Garrido

Asteroseismology, that is, the use of the frequency content of a time series caused by variations in brightness or radial velocity of a stellar object, is based on the hypothesis that such a series is harmonic and therefore can be described by a sum of sines and cosines. If this were not the case (e.g., the oscillations of an ellipsoid of revolution) it cannot be guaranteed that the Discrete Fourier transform is the least squares approximation to the time series. This report studies the effect of extending the Fourier kernel to a particular quaternion and exploring the impact when it is applied to the best time series that we have (GOLF/SoHO) from the closest star, our Sun. The results are consistent with a notable improvement in the signal-to-noise ratio in the low frequency range. This opens the possibility of detecting the elusive g modes of the Sun in future works.

Stellar pulsation is a common phenomenon and is sustained because of coherent driving mechanisms. When pulsations are driven by heat or convective mechanisms, it is usual to observe combination frequencies in the power spectra of the stellar light-curves. These combination frequencies are not solutions of the perturbed stellar structure equations. In dense power spectra from a light-curve of a given multiperiodic pulsating star, they can compromise the mode identification in asteroseismic analyses, and hence they must be treated as spurious frequencies and removed. In this paper, a method based on fitting the set of frequencies that best describes a general non-linear model, like the Volterra series, is presented. The method allows these frequencies to be extracted from the power spectrum, thereby improving the frequency analysis and enabling hidden frequencies to emerge from what was initially considered as noise. Moreover, the method yields frequencies with uncertainties several orders of magnitude smaller than the Rayleigh dispersion, which is sometimes used as if it were an error when identifying combination frequencies. Furthermore, it is compatible with the classical counting cycles method, the so-called O-C method, which is valid only for mono-periodic stars. The method creates the possibility of characterizing the non-linear behaviour of a given pulsating star by studying in detail the complex generalized transfer functions on which the model is based.

A multisite photometric campaign for the β Cephei and eclipsing variable 16 Lacertae is reported. 749 h of high-quality differential photoelectric Strömgren, Johnson and Geneva time series photometry were obtained with 10 telescopes during 185 nights. After removing the pulsation contribution, an attempt was made to solve the resulting eclipse light curve by means of the computer program ebop. Although a unique solution was not obtained, the range of solutions could be constrained by comparing computed positions of the secondary component in the Hertzsprung–Russell diagram with evolutionary tracks. For three high-amplitude pulsation modes, the uvy and the Geneva UBG amplitude ratios are derived and compared with the theoretical ones for spherical-harmonic degrees ℓ ≤ 4. The highest degree, ℓ = 4, is shown to be incompatible with the observations. One mode is found to be radial, one is ℓ = 1, while in the remaining case ℓ = 2 or 3. The present multisite observations are combined with the archival photometry in order to investigate the long-term variation of the amplitudes and phases of the three high-amplitude pulsation modes. The radial mode shows a non-sinusoidal variation on a time-scale of 73 yr. The ℓ = 1 mode is a triplet with unequal frequency spacing, giving rise to two beat-periods, 720.7 d and 29.1 yr. The amplitude and phase of the ℓ = 2 or 3 mode vary on time-scales of 380.5 d and 43 yr. The light variation of 2 And, one of the comparison stars, is discussed in the appendix.

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Using ultra-precise data from space instrumentation we found that the underlying functions of stellar light curves from some AF pul- sating stars are non-analytic, and consequently their Fourier expansion is not guaranteed. This result demonstrates that periodograms do not provide a mathematically consistent estimator of the frequency content for this kind of variable stars. More importantly, this constitutes the first counterexample against the current paradigm which considers that any physical process is described by a contin- uous (band-limited) function that is infinitely differentiable.

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics