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Astron. Astrophys. 326, 620-628 (1997)

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5. Analysis of the continuum flux distribution

All of the low-resolution spectra of [FORMULA]  Cet were obtained in a trailed mode and therefore cannot be calibrated in absolute units. For the same reason, the observational material cannot be used to investigate the UV light curves during the pulsation cycle. We therefore analysed the phase-averaged observations. For this purpose, we constructed the mean energy flux distribution by co-adding all of the low-resolution images for a given camera. We first filtered short and long wavelength images by a five-point filter with least-squares weights and fitted them, in the sense of the minimum least-square deviations, to SWP 29811 and LWP 9636 images, respectively. As one can see from Table 2, there are 8 low-resolution SWP images symmetrically distributed over pulsating phases. In particular, 3 images (SWP 29807, 29808 and 29811) were taken at [FORMULA], whereas another 3 images (SWP 29809, 29813 and 29814) at [FORMULA]. The remaining two observations were obtained at [FORMULA] (SWP 29810) and [FORMULA] (SWP 29812), respectively. We therefore calculated the mean spectrum, assuming the same weights for all the low-resolution SWP images. In the case of the low-resolution LWP images taken at [FORMULA] = 0.1901, 0.4960, 0.5565 and 0.8625, we first derived the mean spectrum from observations at [FORMULA] = 0.4960 and 0.5565, and then calculated the arithmetic mean spectrum for this camera. These observational data are supplemented by the ground-based observations from 3300 Å  to 6050 Å  made by Schild et al. (1971). Thus the analysed energy flux distribution of [FORMULA]  Cet contains UV and visual observations in the form of three pieces of the spectrum corresponding to wavelength regions 1200 - 1950 Å, 1900 - 3200 Å  and 3300 - 6050 Å, respectively.

Next, the observed flux distribution was dereddened by means of the mean extinction curve given by Savage & Mathis (1979). As the first approach, we adopted the extinction curve corresponding to E( [FORMULA] ) = 1.7 E( [FORMULA] ) = [FORMULA]. The last equality corresponds to E( [FORMULA] ) = [FORMULA] shown in Table 1. Having dereddened flux distribution, we searched for the best fit of the theoretical flux to the observed one, in the least-squares sense, by adjusting log [FORMULA] and log g. During this procedure, we also introduced two additional parameters to make an agreement in the continuum levels of the three regions of the spectrum mentioned above. Theoretical fluxes were interpolated from the published Kurucz (1979a, b ) grid of models with a solar abundance of elements. According to Buser & Kurucz (1992), the Kurucz (1979a, b ) grid of models for O to G stars together with the new models for F- to K-stars (Kurucz 1991) provide an extensive, quasi-homogeneous grid of low-resolution theoretical flux spectra for a significant range of stellar parameters, covering most of the observed HR diagram. We found the best fit solution for log [FORMULA] = 4.354 and log g = 3.63, but an almost equally good fit (in the sense of the least-squares deviations) exists for a sequence of models shown in Fig. 1. The results are most sensitive to the adopted value of E( [FORMULA] ), cf. Fig. 1, where solutions corresponding to E( [FORMULA] ) = [FORMULA] and [FORMULA] are also plotted. An increase in E( [FORMULA] ) from [FORMULA] to [FORMULA] results in [FORMULA] log [FORMULA] = 0.02 and [FORMULA] log g = 0.15, which can be regarded as error boxes for these photospheric parameters derived from the observed slope of the continuum. The best fit solution with E( [FORMULA] ) = [FORMULA] is displayed in Fig. 3.

[FIGURE] Fig. 3. The best fit of the predicted flux of radiation (continuous line) to IUE and visual observations of [FORMULA]  Cet (points).

Similar analysis was made for the high-resolution images of [FORMULA]  Cet. Also in this case, only relative energy flux distributions can be studied, but now due to the small aperture used, with the exception of the LWP 6341 image. The carefully reprocessed images were pre-filtered by a 121-point running mean filter reducing the spectral resolution to about 5 Å, comparable with the low-resolution IUE observations. These spectra (cf. Table 2) were obtained with a time step of about 30 min and are well distributed over the pulsating phase. The mean spectrum was therefore calculated with the same weights for all images. No important discrepancy was found between the two sets of data for the continuum flux distribution, although using high-resolution images and assuming E( [FORMULA] ) = [FORMULA] the best fit solution exists for slightly different parameters of log [FORMULA] = 4.378 and log g = 3.67. These values however are within the error boxes ( [FORMULA] log [FORMULA] and [FORMULA] log [FORMULA] ) estimated from the analysis of the low-resolution spectra of [FORMULA]  Cet.

Now, we examined how well the phase-averaged energy flux distribution represents the steady state model. For this purpose, theoretical fluxes generated for a nonadiabatic model of [FORMULA]  Cet (cf. Sect. 2.2) at pulsating phases [FORMULA]   (n =0,...,9) were used to construct the mean flux (in logarithmic scale) and compared with the flux distribution corresponding to the steady-state model. We found the differences less than 0.0006 dex. in the considered wavelength region.

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© European Southern Observatory (ESO) 1997

Online publication: October 15, 1997