We present a precise kinematic study of very young brown dwarfs (BDs) in the ChaI cloud based on radial velocities (RVs) measured with UVES / VLT. This is compared to the kinematics of T Tauri stars (TTS) in the same field, based on both own measurements and on RVs from the literature. More UVES spectra were taken compared with a former paper (Joergens & Guenther 2001), and the reduction of the spectra was improved, while studying the literature for RVs of T Tauri stars in ChaI led to a cleaned and enlarged sample of T Tauri stars. The result is an improved empirical RV distribution of BDs as well as of TTS in ChaI. We found that nine BDs/VLMSs (M6-M8) in ChaI have a RV dispersion of 0.9 km/s measured in terms of a standard deviation. This is consistent with the dispersion measured earlier in terms of fwhm of 2.1 km/s. The studied sample of 25 TTS (G2-M5) has a dispersion of 1.3 km/s (standard deviation). The RV dispersion of the BDs is consistent within the errors with that of TTS, which is in line with the finding of no mass dependence in some theoretical models of the ejection-scenario for the formation of brown dwarfs. In contrast to current N-body simulations, we did not find a high-velocity tail for the BDs RVs. We found hints suggesting different kinematics for binaries compared to predominantly single objects in ChaI. The global RV dispersion for ChaI members (1.24 km/s) is significantly lower than for Taurus members (2.0 km/s), despite higher stellar density in ChaI showing that a fundamental increase in velocity dispersion with stellar density of the star-forming region is not established observationally. The RVs of BDs observed in ChaI are less dispersed than predicted by existing models for the ejection-scenario.

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