6 Projected rotational velocities $v \sin i$

Projected rotational velocities have been measured using the telluric lines for determining the instrumental profile of the spectrograph and assuming a solar-like center-to-limb variation. We derived $v\,\sin i$ values in the range from 8kms^-1 to 26kms^-1 (Table 1). Figure3 shows the $v\,\sin i$ distribution of the brown dwarfs in comparison with that of T Tauri stars listed in Table2. Both distributions peak at a $v\,\sin i$ of 17 to 21kms^-1, indicating that there is no crucial difference between the rotational velocities of the studied brown dwarfs and T Tauri stars.

Based on $v\,\sin i$ and the radius of the object an upper limit of the rotational period can be derived:

$$P_{\rm max}[\mbox{d}]= 50.6145 \frac{R [{R}_{\odot}]}{(v \sin i) [\mbox{km}\,\mbox{s}^{-1}]}\cdot$$ (1)

The radii of the objects are estimated from bolometric luminosities and effective temperatures given by Comerón et al. (2000). The approximate upper limits for the rotational periods are between one and three days (Table1).

Figure 3: Histogram of $v\,\sin i$ for brown dwarfs (hashed) and T Tauri stars in ChaI. For details see Sect.6.