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5. The spectral energy distributions

To obtain more information about the variations of the continuum light in the different episodes during the long time scale variations of HD 45677 we have constructed the spectral energy distribution (SED), from the UV to the infrared wavelength ranges, for several V magnitudes. An attempt was made to use as much simultaneous measured data as possible in these SEDs, but simultaneous blue and optical photometry and UV spectrophotometric data were available for a few dates only. Data measured at slightly different times, but at the same stellar brightness were therefore combined into one SED. The SEDs were corrected for interstellar and circumstellar extinction by comparing the observed fluxes to the theoretically observed flux (tex2html_wrap_inline3307) at earth in a photometric system:


equation698
In this formula tex2html_wrap_inline3309 is the flux emitted by the star per surface unit, tex2html_wrap_inline3311 is the stellar radius, d is the stellar distance, tex2html_wrap_inline3315 is the total extinction at a given wavelength (in magnitudes) and tex2html_wrap_inline3317 is the transmission function (normalized to unity) of the photometric filter. tex2html_wrap_inline3319 was taken from the Kurucz (1991) model for a B2 V star, assuming solar abundance. tex2html_wrap_inline3321 was obtained from the extinction laws by Steenman & Thé (1991), using the relation tex2html_wrap_inline3323 = tex2html_wrap_inline3325, with tex2html_wrap_inline3327 the ratio of total to selective extinction. A best value of this tex2html_wrap_inline3329, according to the tex2html_wrap_inline3331 test, was determined using a trial and error method. Since tex2html_wrap_inline3333 and d are not accurately known we fitted the parameter (tex2html_wrap_inline3337 to the observed fluxes for each value of tex2html_wrap_inline3339. The results of the fit procedure are listed in Table 4 (click here) and a typical resulting SED fit is shown in Fig. 11 (click here). In this figure we notice a very good fit to the theoretical Kurucz model in the ultraviolet and in the optical, with a large amount of excess radiation above photospheric levels in the infrared. The presence and appearance of this infrared excess once again indicates the existence of circumstellar dust around HD 45677.

From the SED, we also computed the scaled stellar luminosity using the following formula:


equation718
with tex2html_wrap_inline3341 the Kurucz model flux, fitted to the extinction-corrected SED. These scaled stellar luminosities are also listed in Table 4 (click here).

Again using Eq. (5), we also computed the total luminosity of the infrared excess of HD 45677 by taking tex2html_wrap_inline3343 from a tex2html_wrap_inline3345-spline fitted to the extinction-corrected SED of HD 45677 minus the corresponding Kurucz model flux. Beyond the last wavelength at which we have observational data, this model was extrapolated with a Planckian curve of 900 K, smoothly joined to the slope of the last spline curve. The resulting scaled luminosity of the infrared excess (tex2html_wrap_inline3347) turns out to be about 0.26 tex2html_wrap_inline3351 tex2html_wrap_inline3353, or about 28% of the stellar luminosity. When we also compute the fraction of the stellar luminosity absorbed by dust in the blue and ultraviolet (tex2html_wrap_inline3355) by taking the difference between the luminosities of the Kurucz model fitted to the extinction-corrected SED and a version of this model reddened with the parameters listed in Table 4 (click here), we typically obtain values like 82% of the stellar luminosity. The ratio tex2html_wrap_inline3357. The fact that tex2html_wrap_inline3359 suggests that either we are seeing a star/disk system at a small inclination angle, or that tex2html_wrap_inline3361 of the star's total extinction must be interstellar rather than circumstellar as tex2html_wrap_inline3363 is necessary to produce the re-radiated light as tex2html_wrap_inline3365. In view of the discussion in the previous sections, the first possibility seems more likely.


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