The goal of the proposed method is to analyse objects with pseudo-periodic light curves (i.e. approximately periodic signal) such as super giant, spotted, and semi-regular variable stars. The behaviour of these stars is difficult to describe, because it is not strictly periodic and there are different time-scales involved of different amplitudes. Even in Mira type stars, for example, very short time-scales are present (de Laverny et al. 1998). We want to determine the general time-scales causing the dispersion in the data. The method is more qualitative than quantitative at the present time although procedures are being developed to make it quantitative.
The photometric data of Hipparcos have two origins:
the Main mission and the Tycho mission. The latter used the star
mappers and gave two magnitudes and
, whereas the former
used the image dissector tube and produced
the so called
magnitude (van Leeuwen 1997).
The Hipparcos satellite provided around 13 000 000
measurements
of fluxes for 118 204 stars during a time interval of 3.3
years. A systematic search for variability and periodic stars
was carried out (cf. Eyer 1998) and the results were published (see
Grenon et
al. 1997 and van Leeuwen et al. 1997). On this occasion, the
variogram methodology was applied.
However, pseudo-periodic signals were published with only an
information of amplitude, and no information about time-scales.
Because time-scales of magnitude variations are also a
valuable information, a refined method was developed in order to
be able to describe pseudo-periodic signals.
The structure of the paper is now briefly described. We begin by reviewing the methods of statistical analysis of periodicity to be found in the literature. The variogram approach is introduced and closely analysed in Sect. 2. The third part contains some interesting results of our method on simulated data examples. The use of the variogram for spurious period discrimination is explained on a real case in Sect. 4. The variogram allows also to estimate the measurement noise, and is applied to the whole sample of Hipparcos stars. Finally, the robust variogram approach is applied to individual stars from Hipparcos photometry.
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