4 Physical parameters

Let us now constrain fundamental parameters of the star and its wind. The luminosity of AS314 may be estimated in different ways. Photometry of nearby stars with known MK spectral types shows that the interstellar extinction is distributed in this direction unevenly. For example, according to Neckel & Clare ([1980]) A_V reaches 3 mag at already 0.3-0.5 kpc from the Sun. However, their statistics is limited by 9 stars for a region of at least 10 square degrees around the star position. This region is projected on the cloud Lynds 410, which is the main source of interstellar extinction here. Lahulla & Hilton ([1992]) obtained UBV observations of about 100 stars in a $4\hbox{$^\circ$ }\times 4\hbox{$^\circ$ }$ region near Lynds 379 centered in 4 $\hbox{$^\circ$ }$ SW from the position of AS314. However, only a few stars from this survey are inside the boundaries of Lynds 410. Combining the results of these two papers for stars within Lynds 410, we found that in the $\sim 2.5\hbox{$^\circ$ }\times 2.5\hbox{$^\circ$ }$ region centered on AS314 A_V reaches $3.0\,\pm\,0.5$ mag at $2\,\pm\,1$ kpc, while no further extinction rise is seen until at least 6 kpc. This allows us to suggest that AS314 is located behind Lynds 410 with a lower limit of log $L_{\rm bol}/L_{\hbox{$\odot$ }} \ge 3.7$. We should note here that this luminosity estimate is very uncertaint, but it provides evidence that AS314 is not a classical Be star. The latter objects of a similar spectral type have luminosities at least 2 orders of magnitude smaller than the lower limit derived for AS314 (e.g., Zorec & Briot [1991]).

A luminosity calibration for B9-A2 supergiants by Rosendhal ([1974]) based on the strength of the Si II lines at 6347 and 6371 Å gives log $L_{\rm bol}/L_{\hbox{$\odot$ }} \ge 4.9$. A similar value, log $L_{\rm bol}/L_{\hbox{$\odot$ }} = 4.9\,\pm\,0.2$, follows from our spectroscopic estimate (Sect. 3.2). As a consequence the star is located close to the line of LBVs in the Hertzsprung-Russell diagram (Stothers & Chin [1994]). The bright H$\alpha$ line also suggests a high luminosity for the star as was pointed out by Talavera & Gómez de Castro ([1987]). Indeed, only those A-type supergiants with $M_V \le -8$ mag, such as HD160529 and HD168607, display so strong (EW $\ge 10$ Å) H$\alpha$ lines in emission (Fig. 6a).

As it is seen in Fig. 6b, the wings of the H$\delta$ line in AS314 are narrower than those of the Kurucz ([1994]) model atmospheres for $T_{\rm eff}= 9000$ K and log g = 1.5 and wider than those of HD160529 (log g = 0.55, Stahl et al. [1995]). These two values can be adopted as initial estimates for an upper and lower level of the surface gravity for AS314. Since the star displays small photometric and spectroscopic variations, these estimates seem to be reliable.

Our result for the spectral type determination, which comes mainly from the quantitative spectroscopy as the most reliable method, in combination with such a high luminosity lead to the MK type A0 Ia⁺ for AS314. de Jager & Nieuwenhuijzen ([1987]) give $T_{\rm eff}= 9100$ K for stars of such a spectral type. Thus, summarizing all the above estimates, we finally adopt the object's $M_V = -8.0 \,\pm\,0.5$ mag, which corresponds to log $L_{\rm bol}/L_{\hbox{$\odot$ }} = 5.2 \,\pm\,0.2$, $R_* = 160 \,\pm\,30 R_{\hbox{$\odot$ }}$, and implies $D \sim 10$ kpc. These $T_{\rm eff}$ and $L_{\rm bol}$ match the evolutionary track of a $20\;M_{\hbox{$\odot$ }}$ star (Schaller et al. [1992]) and imply log g = 1.3, which is located within the above limits.

Figure 5: Spectral line variations in different spectra of AS314. The 1997 spectrum is shown by a solid line, the 1998 spectrum by a long-dashed line, the 1999 spectrum by a short-dashed line

In order to determine the temperature of the dusty envelope we model the overall observed SED with the DUSTY code (Ivezic et al. [1999]), which solves the radiation transfer problem in spherical dusty envelopes. In the model we used the optical properties of amorphous carbon (Hanner [1988]), which is expected to form around evolved luminous stars (Bjorkman [1998]). The density distribution was assumed to be proportional to the inversed square distance from the star. A good fit to the observed SED was obtained for a dust temperature of 100 K at the inner envelope boundary and the overall optical depth of the envelope of 0.03. The corresponding distance of the hottest grains from the star was found to be 0.2 pc. The calculated SED virtually passes through the observed data points and is, therefore, not displayed in Fig. 2. However, the lack of the IR data (such as information about the spectral properties in the $10\; \mu$m region) does not allow us to constrain the envelope model better. The dust temperature is close to that derived for the galactic LBVs HR Car (170 K), AG Car and WRA 751 (130 K, de Winter et al. [1992]). The lower temperature found for AS314 suggests that an event (perhaps, an outburst), which might have led to the dust formation occurred earlier than in the other quoted LBVs.

The first three lines of the Balmer series in AS314 have PCyg-type profiles, which may be interpreted as a consequence of spherical mass loss, while their broad wings suggest a noticeable amount of electron scattering in the stellar wind. Comparison of the object's H$\alpha$ line profile with those of other LBVs with similar $T_{\rm eff}$ shows that both red wing and the absorption component are narrower in AS314 (see Fig. 6a). This implies a smaller terminal velocity ($v_\infty$) and a smaller electron scattering optical depth ( $\tau_{\rm e}$) for AS314. Since $v_\infty$ for HD160529 is about 90 kms^-1(Sterken et al. [1991]), this value may be suggested as an upper level of $v_\infty$ for AS314.

The relationship between the wind momentum and luminosity for supergiants (Kudritzki [1998]) being applied to the parameters of AS314, as derived above, gives an estimate of the mass loss rate, $\dot{M} \sim 10^{-5}$ $M_{\hbox{$\odot$ }} \;{\rm yr}^{-1}$. In order to constrain the parameters of the object's stellar wind we tried to model its Balmer line profiles under assumptions of spherical geometry and $\beta$-velocity law using a radiation transfer Sobolev code by Pogodin ([1986]). Electron scattering was treated in a simplified way as described in Castor et al. ([1970]), which is reasonable given a small expected $\tau_{\rm e}$.

Figure 6: a) Comparison of the H$\alpha$ profiles of AS314 and of two LBV candidates. The profiles of AS314 are shown by solid lines with no additional symbols (the 1997 spectrum), with circles (1998), or with crosses (1999). The profile of HD160529 (Stahl et al. [1995]) is shown by a long-dashed line, while that of HD168607 (Chentsov & Luud [1989]) by a short-dashed line. b) H$\delta$ line profiles of AS314 (solid line), HD160529 (solid line with dots), and that of the Kurucz ([1994]) model atmosphere for $T_{\rm eff}= 9000$ K, log g=1.5 (dashed line). Extrema of all the line profiles are shifted to the zero velocity. The velocity is given in kms-1, while the intensity is normalized to continuum

The best fit parameters are as follows: $\dot{M} =$ $2\ 10^{-5}\; M_{\hbox{$\odot$ }}$yr^-1, $\beta = 1.3$, $v_\infty = 75$ kms^-1, w₀ = 0.02 (wind velocity at the photospheric level in units of $v_\infty$), and $\tau_{\rm e} = 0.4$. The agreement of the calculated and observed profiles is not perfect (see Fig. 7) and reflects the simplifications adopted (spherical symmetry, the electron scattering treatment) as well as difficulties of using the Sobolev method for small velocity gradients. Nevertheless, the derived wind parameters are in reasonable agreement with those of the other hypergiants quoted here.