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4 Results and discussion

We find well pronounced and rather symmetric wine-bottle structures in the profiles of HR 335, 1660, 2749, 2825, 3237, 8773, and pronouncedly asymmetric wine-bottle inflexions in the profiles of HR 1622 and 6118. The average vsini for these eight stars is 124 km s-1 which is well below the sample average of $\rm 236~km\,s^{-1}$. This clearly indicates that wine-bottle structures are associated with Be stars with low inclination as shown by Hummel (1994) and Hanuschik et al. (1996). This effect can be clearly seen in Fig. 9 where we have plotted the ${I_{\rm p}}/{I_{\rm c}}$ ratio versus the equivalent width and marked the eight stars on it.

  \begin{figure}
\par\includegraphics[width=6.6cm,clip]{h2226f9.eps} \end{figure} Figure 9: A plot of the ${I_{\rm p}}/{I_{\rm c}}$ ratio versus the equivalent width, W

From its definition, the magnitude of the equivalent width is expected to increase with an increasing ${I_{\rm p}}/{I_{\rm c}}$ ratio. This behaviour is clearly noticed in the above figure. Furthermore, however, the wine-bottle type stars plotted here, tend to lie above the general scatter, indicating that they have smaller equivalent widths (magnitude-wise) than expected from their ${I_{\rm p}}/{I_{\rm c}}$ ratio. Since the equivalent width depends on the width of the line, the reduction in the former probably indicates that the emission lines are narrower in these cases. Or, in other words, these particular stars have low $vs{\rm in}i$values.

It may be pointed out that in twelve of the stars viz. HR 264, 496, 1087, 1789, 1858, 1910, 2356, 3858, 5440, 5778, 5941 and 7106, the line profiles appear to be broader than the 25 Å coverage of the spectrum. Therefore in Fig. 9, the equivalent widths of these stars may be marginally underestimated. However, this will not affect the above conclusions, because this underestimation, if corrected, will only enhance the separation between the wine bottle stars and the rest.

A comprehensive review of the mechanisms which broaden the line profiles has been given by Hanuschik et al. (1996). The principal amongst them are the thermal broadening, the kinematical broadening, the shear broadening (Horne & Marsh 1986) and the non-coherent scattering broadening (NSB) (Avrett & Hummer 1965; Hummel & Dachs 1992; Hummel 1994). As shown there, the amount of broadening due to each of these mechanisms depends largely on the inclination of the rotation axis of the star. For symmetrical profiles, and for most ranges of inclination (except for almost pole-on or low inclination stars), kinematic broadening is the largest and most important contributor to the profile width. The kinematic broadening occurs because of the supposedly Keplerian motion of the gas in the disc. Since the projected Keplerian velocity in the disc ( ${v_{\rm k}}{\rm sin}i$) is expected to increase with the stellar rotational velocity $(v{\rm sin}i)$, the observed widths of the line should also increase with the stellar $v{\rm sin}i$ values. Although simple, this scenario still gives a useful qualitative picture. In Figs. 10 and 11 we have plotted the observed fullwidths (E') and the halfwidths (l) of the profiles versus $v{\rm sin}i$.

  \begin{figure}
\par\includegraphics[width=6.6cm,clip]{h2226f10.eps} \end{figure} Figure 10: A plot of the observed full widths of the lines E ${^{\prime }}$ versus $v{\rm sin}i$


  \begin{figure}
\par\includegraphics[width=6.6cm,clip]{h2226f11.eps} \end{figure} Figure 11: A plot of the observed half widths (l) versus $v{\rm sin}i$

In these figures we have excluded the twelve stars mentioned in the above paragraph, which show profiles broader than 25 Å, since E' and l cannot be accurately determined for these profiles. A good correlation is seen in both the figures as found earlier too (Andrillat & Fehrenbach 1982; Dachs et al. 1986). This result tends to indicate that kinematics is the dominant factor in broadening the widths of the observed emission line profiles.

It, however, does not mean that the contribution of NSB and other mechanisms to the line widths is always negligible. NSB, in particular, is equally important in the case of low inclination or near pole-on stars as pointed out by Hanuschik (1996). In such cases, since NSB and kinematic broadening are of the same order (Hanuschik 1996), the convolution of the two is not expected to lead to a final width much different than that caused by each mechanism separately. Thus the effects of NSB broadening may be lost in the scatter of the points in Figs. 10 and 11.

Regarding the shape of the profiles, Hummel (1994) has shown how emission lines of symmetric shape, ranging from the wine-bottle structure type to the shell profiles, can be satisfactorily explained by the NSB mechanism. His model calculations show how the peak separation of the V and R components and also the equivalent width should relate to the changes in the inclination (or $v{\rm sin}i$) of the circumstellar disc. From our data we have selected nineteen sources for which the line profiles are symmetric or nearly symmetric with respect to the V and R components. These sources are HR 496, 1087, 1165, 1508, 1789, 1858, 1934, 1956, 2284, 2356, 2492, 2845, 3858, 3946, 4787, 5193, 5440, 6510 and 6712. In Fig. 12 we have plotted the peak separation $\Delta v$ versus vsini.

  \begin{figure}
\par\includegraphics[width=6.6cm,clip]{h2226f12.eps} \end{figure} Figure 12: A plot of $v{\rm sin}i$ versus the observed peak separation between the V and R components, $\Delta v$, for those stars that showed symmetrical profiles

Here, barring three stars, viz. HR 1789, 1934 and 5440, the remaining stars do show $\Delta v$ increasing with $v{\rm sin}i$ as expected qualitatively from the model calculations of Hummel (1994). If the above three stars are excluded, the correlation coefficient for the rest of the data comes out to be 0.72 which is rather good. A common feature in the excluded stars (HR 1789, 1934, and 5440) is that their central absorption features, on the average, are more pronounced than those of the majority of other stars of Fig. 12. It seems that for such kind of profiles the model may need some additional ingredient, but this can be verified with a larger body of data.

The equivalent width W versus $\Delta v$ plot for the sample of these nineteen stars is shown in Fig. 13.

  \begin{figure}
\par\includegraphics[width=6.6cm,clip]{h2226f13.eps} \end{figure} Figure 13: A plot of the observed equivalent widths versus peak separation between the V and R components for those stars that showed symmetrical profiles

Although there is only a weak correlation (correlation coefficient 0.2), a trend of W (in magnitude) decreasing with $v{\rm sin}i$ is indicated which is qualitatively consistent with the model. The scatter in Figs. 12 and 13, may be attributed to an intrinsic variation in the rotational velocities of the stars, whereas the model calculations have been made for a specific rotational velocity. In general, therefore, it is concluded that the results of Figs. 12 and 13 are consistent with the work of Hummel (1994).

Acknowledgements

The authors wish to thank D.B. Pancholi for his able assistance on the telescope floor during some of the observational runs. We thank the referee for his valuable suggestions. The work was supported by the Department of Space, Government of India.


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