On the functional form of the metallicity-giant planet correlation,

Astronomy and Astrophysics, Volume 551, pp. A112 (2013)

*The aim of this work was to use a multi-approach technique to derive the most accurate values possible of the physical parameters of the δ Sct star HD174966, which was observed with the CoRoT satellite. In addition, we searched for a periodic pattern in the frequency spectra with the goal of using it to determine the mean density of the star. First, we extracted the frequency content from the CoRoT light curve. Then, we derived the physical parameters of HD174966 and carried out a mode identification from the spectroscopic and photometric observations. We used this information to look for the models fulfilling all the conditions and discussed the inaccuracies of the method because of the rotation effects. In a final step, we searched for patterns in the frequency set using a Fourier transform, discussed its origin, and studied the possibility of using the periodicity to obtain information about the physical parameters of the star. A total of 185 peaks were obtained from the Fourier analysis of the CoRoT light curve, all of which were reliable pulsating frequencies. From the spectroscopic observations, 18 oscillation modes were detected and identified, and the inclination angle (62.5*^{°+7.5}_{-17.5}) and the rotational velocity of the star (142 km s^{-1}) were estimated. From the multi-colour photometric observations, only three frequencies were detected that correspond to the main ones in the CoRoT light curve. We looked for periodicities within the 185 frequencies and found a quasiperiodic pattern Δν ~ 64 µHz. Using the inclination angle, the rotational velocity, and an Echelle diagram (showing a double comb outside the asymptotic regime), we concluded that the periodicity corresponds to a large separation structure. The quasiperiodic pattern allowed us to discriminate models from a grid. As a result, the value of the mean density is achieved with a 6% uncertainty. So, the Δν pattern could be used as a new observable for A-F type stars.

**Figure 1 | Fourier transform of various subsets selected by amplitude.** The blue, green, red, and cyan lines correspond to the FT calculated from the subset including the first 30, 60, 112, and 168 (all the peaks except the close ones) highest amplitude frequencies, respectively. The peaks corresponding to the large separation (64 µHz) and its sub-multiples are labeled.

Astronomers’ interest in δ Scuti stars – which present variable luminosities as a consequence of radial and non-radial pulsations of its surface – has surged in recent years since it was shown that, using an appropriate observational technique, it is possible to detect excitation modes which were previously undetectable. As data from CoRoT and Kepler satellites became available, astronomers can now analyze δ Scuti stars’ frequency spectra and search for regular patterns in these frequencies.

The star HD174966 was sampled every 32s by CoRoT for a total of 27,2 days, yielding a Rayleigh frequency resolution of 0,037 d^{-1} and a frequency sampling of 0,0018 d^{-1}. The data was analyzed by two different methods with excellent agreement, resulting in a total of 185 frequency peaks. The team also used spectroscopic data of this star, obtained with the HARPS spectrograph, covering a baseline of 53 days, and new multi-colour photometric observations taken with the 0.9m telescope at Observatorio de Sierra Nevada, during two runs of 29 and 7 nights.

The spectroscopic data allowed the team to estimate several physical parameters of HD174966, including its mass, radius, metallicity and effective temperature. The data were then used in the identification (determination of the radial order, n, and spherical degree, l, of a vibrational mode) of a total of 18 frequency modes, 14 of which also have a photometric counterpart in the CoRoT set. The best fitting theoretical models were then determined and only 21 models out of 500.000 were found fulfilling all the restraints.

In order to search for periodicities, a Fourier analysis was employed (Fig. 1) and a pattern with a periodicity of 64 µHz was found. Several arguments demonstrate that this periodicity is associated with the large separation structure and therefore, can be used as an observable quantity for δ Scuti stars.

This quantity, in turn, is an additional new observable for this type of pulsators that allows the determination of the star’s physical parameters with uncertainties considerably lower than those obtained with other methods. This is especially true for the mean density, which was determined with an uncertainty of 6%, never before reached for any non-binary δ Scuti star. Furthermore, this method has the advantage of not requiring any assumptions regarding the rotation of the star. For all this, this method presents the potential of becoming a major source of precise information for δ Scuti stars.

The project was lead by the CAUP member Antonio García Hernández who calculated the Fourier transform to determine the frequency pattern, computed the grid of models and carried out the mode identification of the multi-colour photometric frequencies. In addition, he used the observational results to discriminate the models and reach the final conclusion.