6 Statistics

6.1 General characteristics

The lines are very broad, with mean FWHM of $204\pm12\ {\rm km\ s}^{-1}$ for Pa ${\rm\beta }$ and $207\pm26\ {\rm km\ s}^{-1}$ for Br ${\rm\gamma }$. Line peaks are, generally, slightly blueshifted and very rarely redshifted. The blueshift is, in most cases, very slight, only seldom exceeding $60\ {\rm km\ s}^{-1}$ for Pa ${\rm\beta }$ and $90\ {\rm km\ s}^{-1}$ for Br ${\rm\gamma }$. In fact, most lines have their peaks located within $20\ {\rm km\ s}^{-1}$ of the rest velocity.

Typical parameters for each type of line profiles and comparison between them are discussed in the following sections.

Figure 3: Top panel: distribution of the Full Width at Half Maximum for Pa ${\rm\beta }$ type I (solid line) and type  IV R (dotted line) profiles. Bottom panel: same as top panel for Br ${\rm\gamma }$

   
6.2 The type I and type IV R line profiles

Type I lines are broad, with FWHM ranging between 100 and $300\ {\rm km\ s}^{-1}$ (Fig. 3), and slightly blueshifted but seldom redshifted (Fig. 4).

Figure 4: Top panel: distribution of the line peak velocity for Pa ${\rm\beta }$ type I (solid line) and type IV R (dotted line) profiles. Bottom panel: same as top panel for Br ${\rm\gamma }$

The Pa ${\rm\beta }$type I lines are nearly symmetric, with Afs mostly falling between 1 and 1.2 (Fig. 5).

Figure 5: Top panel: distribution of the asymmetry factor, Af, for Pa ${\rm\beta }$ type I (solid line) and type  IV R (dotted line) profiles. Bottom panel: same as top panel for Br ${\rm\gamma }$

The Br ${\rm\gamma }$type I line profiles are slightly more asymmetric, with Afs concentrated more between 1.4 and 1.8 (Fig. 5), as well as towards a value of 3.

The distributions of the maximum velocities observed in the blue and red wings of type I profiles, are shown in Fig. 6 as solid lines.

Figure 6: Distribution of the maximum velocities seen in the line wings. Top panel: data for Pa ${\rm\beta }$ type I (solid lines) and type  IV R (dotted lines) profiles; Bottom panel: same as top panel for Br ${\rm\gamma }$

The average maximum velocities observed are $282\ {\rm km\ s}^{-1}$ and $240\ {\rm km\ s}^{-1}$ respectively for the blue and red wings of the Pa ${\rm\beta }$ profiles. The equivalent values for the Br ${\rm\gamma }$ profiles are, respectively $305\ {\rm km\ s}^{-1}$ (blue wing) and $208\ {\rm km\ s}^{-1}$ (red wing). Hence, while Pa ${\rm\beta }$ type I profiles tend to be symmetric, Br ${\rm\gamma }$ profiles tend to show less extended red wings (by about $100\ {\rm km\ s}^{-1}$).

Type IV R line profiles correspond to inverse P Cygni (IPC) profiles and therefore are characterized by the presence of a redshifted absorption feature. Typical velocities for these are between $50\ {\rm km\ s}^{-1}$ and $300\ {\rm km\ s}^{-1}$, while their EWs can be as low as $2.5\ {\rm km\ s}^{-1}$ for DS Tau's Pa ${\rm\beta }$ profile and as large as $30.8\ {\rm km\ s}^{-1}$ for YY Ori's Pa ${\rm\beta }$ profile.

For an easier comparison between the observed properties of type IV R and of type I line profiles (which constitute the majority of the profiles), the distributions of the various observed parameters for IPC profiles are plotted with those corresponding to type I profiles in Figs. 4 to 6.

The observational characteristics of IPC profiles are similar to those of type I profiles except for factors related to the redshifted absorption, most notably apparent in the Af and the maximum velocity observed for the red wing of the profile, as can be clearly seen in Figs. 5 and 6. For IPC Pa ${\rm\beta }$ lines, the median Af is 1.67 (cf. median Af =1.16 for type I Pa ${\rm\beta }$ profiles). For Br ${\rm\gamma }$ IPC lines, only one (in five) has a value for Af in the interval 0 to 5 (see Fig. 5). Of the remaining IPC profiles, three have negative values for Af (due to the larger equivalent width of the absorption than that of the emission redward of the rest velocity) and one has an Af of around 5.8. Also, the red wing in IPC profiles extends to less than $200\ {\rm km\ s}^{-1}$ for about 60% of the lines. In contrast, type I profiles have red wings extending to such low velocities for less than 35% of the lines.

The line widths of IPC and type I profiles, as measured by the FWHM, are not significantly different. However, the former tend to be narrower than the latter, with a larger percentage of stars of the former type occupying the 150 to $200\ {\rm km\ s}^{-1}$ bin in Fig. 3. Also, the distributions of the line peak velocity for IPC and type I profiles are similar, with a significant percentage of profiles peaking just blueward of the system's rest velocity (see Fig. 4). However, one should note that unlike the distribution for type I Br ${\rm\gamma }$ profiles, more than half of the Br ${\rm\gamma }$ IPC profiles have their line peaks occurring between about $60\ {\rm km\ s}^{-1}$ and $100\ {\rm km\ s}^{-1}$ (Fig. 4). Finally, the distributions of the maximum velocity observed at the blue wing of both IPC and type I profiles are similar, with that for Br ${\rm\gamma }$ IPC profiles slightly shifted to higher velocities (Fig. 6).

   
6.3 The type II and type III line profiles

The number of emission lines classified as either type II or type III is small. For emission lines of these classes, histograms of the various line parameters were therefore not computed. The emission lines with these types of profiles have characteristics similar to those displayed by type I profiles. Differences arise due to the presence of the blueshifted absorption feature in CW Tau (type II B) and due to the presence of the redshifted absorption feature in the remaining stars (types II R and III R). These absorptions change mainly the asymmetry factors, which become larger for types II R and III R and smaller for type II B relatively to Afs in type I profiles. In conclusion, all types of observed line profiles have broadly similar characteristics. Most of the differences in their properties, as indicated by the various measured parameters, seem to result from the presence of absorption features (e.g. blueshifted in CW Tau and redshifted in IPC profiles) superimposed on the common emission. The blue wing of all line profiles (the least affected by absorption features) have similar characteristics (width, maximum observed velocity) independently of the type of line profile. This seems to point to a common origin of the emission observed in the various types of profiles.