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Asteroseismic techniques

One of the most powerful tool in asteroseismology is the asteroseismic inversion technique which allows to estimate the physical properties of the stars, by solving integral equations expressed in terms of the experimental data. Inversion techniques are well known and applied with success to several branches of the physics, from geophysics to the radiation theory. Applications to the helioseismic data have been studied extensively and inversion methods and techniques have been reviewed and mutually compared by several authors, leading to extraordinary results about the global properties of the Sun. In the stellar context, asteroseismic inversions have been applied with success only to white dwarfs, but today there is a lot of expectation for obtaining striking results also for the case of the solar-type stars.

For these reasons, M. P. Di Mauro has dedicated part of 2004 to work in collaboration with J. Christensen-Dalsgaard of the University of Aarhus at the project to realize the first inversion of observed oscillation frequencies of a solar-type star, by extending the helioseismic techniques to the case of the stars. The difficulties rise from the fact that for the solar-type stars, due to the low amplitude of oscillations, the sets of data include only few observed frequencies of low harmonic degree. In addition, it should be considered that the global parameters of a star, such as mass, radius, luminosity and chemical composition are known within some errors, so that the structure of a model cannot be well constrained and hence might be very different from the observed star. Preliminary results, obtained for Procyon A, by inverting a set of 45 observed frequencies by Martic et al. A&A 418, 295 (2004), have been presented at the conference SOHO14/GONG 2004. From the inversion results, M.P. Di Mauro concluded that present observations of oscillation frequencies of Procyon A seem to indicate that this star is in main-sequence phase with a mass of about $(1.47-1.52)  M_{\odot}$. It is obvious that conclusions need to be accurately discussed on the light of the variations within the errors of the observed global parameters. Further studies are still in progress.

Figure 1.16: The relative isothermal squared sound-speed differences between Procyon A and a stellar model as obtained by inversion of Martic et al. (2004) data. The model used here is characterized by $M/M_{\odot}=1.47$, $Age=1.78$ (Gyr), $L/L_{\odot}=6.88$, $T_{\rm eff}= 6501 (\mathrm{K})$, $ R/R_{\odot}=2.07$, $Z=0.016$.

Another important property of the oscillation spectra is that a sharp variation localized at certain acoustic depth in the structure of a pulsating star produces a distinctive quasi-periodic signal in the frequencies of oscillation. The characteristics of such signal are related to the location and thermodynamic properties of the layer where the sharp variation occurs. Sources of sharp variations are the borders of convection zones and regions of rapid variation in the first adiabatic exponent $\Gamma_1$, such as the one that occurs in the region of second ionization of helium.

Several attempts have been tried in order to isolate the generated oscillatory components directly from the frequencies of oscillations or from linear combination of them (large separations, second differences, etc). The common approach consists in removing a smooth component from the frequencies and to fit the residual signal to a theoretical expression, which is related to the properties of the sharp feature. This method can be applied, for example, to determine the properties of the base of the convective envelope (Monteiro, Christensen-Dalsgaard and Thompson 2000; Ballot, Turck-Chièze and García 2004) and in particular to put limits on the extension of the convective overshoot (Monteiro, Christensen-Dalsgaard and Thompson 2002), or to investigate the border of the convective core (Mazumdar and Antia 2001; Nghiem et al. 2004). But in particular, this peculiar property of the oscillation frequencies can be used to infer the helium abundance in the stellar envelope, by studying the variation of the first adiabatic exponent $\Gamma_1$ in the region of second ionization of helium. Unfortunately, one of the main problem in the application of such an approach rises from the fact that signals coming from different sharp features in the interior of the star might overlap generating a complex behaviour.

At the moment, M. P. Di Mauro, A. Miglio of the University of Liege (Belgium), J. Christensen-Dalsgaard of the University of Aarhus (Denmark) and L. Mantegazza of the Astronomical Observatory of Brera-Merate are working on a new technique based on the Principal Component Analysis (Golyandina et al. 2001; Ghil et al. 2002) in order to isolate all the different oscillatory components directly from the oscillation frequencies. Studies are still in progress.

Preliminary results of a photometric multisite campaign on the $\delta$ Scuti-type Pre-Main-Sequence star IP Per, performed for about 40 nights with nine telescopes, have been also presented (). These data confirm the multiperiodic nature of this star and permit to determine at least 9 pulsational frequencies. A preliminary nonradial theoretical analysis seems to show that the star pulsates in a mixture of l=0, 1, 2 modes.

next up previous contents index
Next: Chemical Peculiar stars of Up: Stellar oscillations and asteroseismology Previous: Solar-type stars   Contents   Index
Innocenza Busa' 2005-11-14