6 Line profile morphology

6.1 General line profile morphology

A number of different line profiles are observed in our data set; at the resolution of our observations these are all seen to have counterparts in optical spectra (single & double peaked profiles and shell lines). Waters & Marlborough (1994) present high resolution and S/N spectra of the Br$\gamma$ transition of $\psi$ Per and 59 Cyg, and find the line profiles have no counterparts in the optical spectra; unfortunately our spectra are of insufficient resolution for us to search for such profiles, although we note that the broad, flat topped He I 2.058 $\mu$m features in BD+4 1002 & BD+29 4453 (Figs. 7 and 8) superficially resemble the Br$\gamma$ profile of 59 Cyg at the resolution of our spectra.

Of the sample of 66 isolated Be stars, 40 show Br$\gamma$ in emission and 3 show shell profiles. Of these stars BD+47 3985 clearly shows the effects of differing optical depths in the He I 2.058 $\mu$m and Br$\gamma$ lines, with He I 2.058 $\mu$m having a pronounced shell profile (indicating a large optical depth) while the central absorption in Br$\gamma$ does not extend below the level of the continuum.

Systematic changes in line profile with spectral type are only seen in Br$\gamma$, with the emission component seen superimposed on a photospheric absorption component in the spectra of late (B7-B9) stars. Given the late spectral type (and hence relatively low temperatures of these stars) this is unlikely to be a NLTE effect of the type identified by Murdoch et al. (1994). Rather it is likely to be due to a combination of the increasing strength of the photospheric feature and a reduction in the strength of emission due to the reasons outlined in Sect. 4.1. Additionally, the interplay of line source functions and opacities with stellar (and hence disc) temperature produces intrinsically narrower profiles for the cooler stars. For disc temperatures of 10 000 K and 6 000 K the line source function, S, throughout the disc is lower for the cooler disc than the hotter disc. However, close to the star (within $\sim$1 $R_{\ast}$) the disc opacity, $\kappa$, is also lower for the cooler disc than the hotter disc, while at larger radii the opacity of the cooler disc is larger than that of the hotter disc. Consequently the emission from the innermost part of the disc increases relative to the outer disc, and since the inner region is rapidly rotating (assuming a Keplerian disc) an increase in emission in the high velocity line wings is seen. However, for discs with temperatures lower than 6 000 K there is no such region where $\kappa_L / \kappa_H < S_L / S_H$ (where the suffixes L and H refer to lower and higher temperature discs respectively) ie the decrease in the source function with lower temperatures is always greater than the change in opacity throughout the entire disc. This means that in addition to a reduction in the source function, radiation finds it more difficult to escape from the rapidly rotating innermost regions of the disc, and so there is less emission in the high velocity wings of the IR lines, and so they appear narrower. Combined with the greater strength of the underlying photospheric feature in the cooler stars this means that narrow emission lines superimposed on strong photospheric absorption features are favoured, which is observed.

6.2 Line widths & projected rotational velocity

Several workers have investigated the relationships between line widths, equivalent widths and projected stellar rotational velocity (e.g. Dachs et al. 1986; Hanuschik 1989). They find evidence for a positive correlation between the projected stellar rotational velocity and the full width half maximum (FWHM) of the optical H I and Fe II lines. A further, weaker anti correlation was also found between the EW and FWHM of the lines. These relations are indicative of rotational broadening in the circumstellar material, where the lines with greater EW and smaller FWHM arise from disc regions with a greater radial extent (and hence lower rotational velocity).

We measured the FWHM of the Br$\gamma$and He I 2.058 $\mu$m profiles, and plotted these against the projected rotational velocities of the stars. (Figs. 5 and 6). A correlation between the FWHM of Br$\gamma$ and (weakly) He I 2.058 $\mu$m, and v sin i is observed, with a "conical'' distribution of points which is a characteristic of the plots of Hanuschik (1989). Best fits to the data give

$$FWHM({\rm Br}{\gamma})=0.759\ v \sin i+149~{\rm km~s}^{-1}$$ (2)

and

$$FWHM{\rm (He~I})=0.643\ v \sin i+247~{\rm km~s}^{-1}.$$ (3)

We note that with the exception of 2 stars in the Br$\gamma$ plot, all the points are found to lie above a line corresponding to $FWHM=v \sin i$.

No inverse correlation between EW and v sin i was found in either the Br$\gamma$ or He I data sets. This is likely to be due to the relatively large scatter observed in the EW datasets, given that the relationship is rather weak in the H$\alpha$ dataset of Hanuschik (1989).

6.3 V/R asymmetry

Many Be stars show asymmetric profiles, which exhibit a cyclic V(iolet)/R(ed) variability with periods ranging from 1-10 years, due to a one armed density wave in the circumstellar envelope (e.g. Okazaki 1991, 1997). We find that a total of 21 stars show double peaked profiles, with a subset of 5 showing asymmetric profiles.

One star, BD+58 2320, shows double peaked asymmetric line profiles in He I 2.058 $\mu$m and Br$\gamma$, but with opposite V/R ratios (Fig. 7). An interpretation of the line profiles based on differences in the radial velocities of the emitting regions is unlikely given that the H$\alpha$ line profiles show little evidence for large velocities over the regions of the disc responsible for optical and IR Hydrogen line emission. One possible explanation would be the presence of an inhomogeneous circumstellar environment, possibly as a result of discrete mass ejection events as envisaged for $\mu$ Cen (e.g. Hanuschik et al. 1993). This would suggest that rapid variability should be seen in the line profiles as the circumstellar material is circularised via viscous redistribution of angular momentum. Another possibility is that the difference in V/R ratio between lines arising at different radii (where He I emission forms at larger radii than Br$\gamma$) reflects the presence of a spiral density wave within the circumstellar disc. Such an explanation would suggest slow, correlated evolution of the V/R ratio for the two lines, and a possible systematic change in ratio through the various Hydrogen series as higher transitions probe regions closer to the star, and thus experience different disc densities. Time resolved observations are required to differentiate between these two possibilities.