The variability and rotation of ultra cool dwarfs (UCDs) provide important information on the atmospheres and evolution of these very low mass stars and brown dwarfs. As part of an ongoing program to investigate this, the projected rotation velocities, vsini, derived from high resolution VLT/UVES spectroscopy via cross correlation are presented for 16 field UCDs (M9V-L7.5V). This doubles the number of L dwarfs for which vsin i has been measured. All targets are found to have vsin i between 10 and 40km/s confirming that L dwarfs are rapid rotators. Radial velocities have also been measured to a precision of 1-2km/s. From the random distribution of the rotation axes, i, and theoretically predicted radii, one-sided confidence intervals are placed on the rotation periods of individual objects. These are compared with published period data obtained from photometric monitoring programs. From this, the period of 31h for the L0.5 dwarf 2M0746+2000
published by Gelino et al. (2002, Ph.D. Thesis, New Mexico State University) may be ruled out as the rotation period. The period of 11.2±0.8h for the L1.5 dwarf 2M1145+2317
obtained by Bailer-Jones & Mundt (2001A&A...367..218B
) is consistent with the present vsin i results so is plausibly the true rotation period. The inclination of the rotation axis is constrained to be i=62°-90° with an expectation value of 76°. Alternatively the data set a lower limit on the radius of 0.1R☉
, which is within the range of radii predicted by models for brown dwarfs older than 0.5Gyr. Similarly, the period of 2.7±0.1h detected by the same authors for 2M1334+1940
is also confirmed as the likely rotation period; the inclination is i=27°-44°(<i≥34°). Where no variability or period was detected by the monitoring programs the likely reason is low contrast modulating surface features. However, in three cases variability but no period was detected, even though the likely rotation period range inferred from vsin i lies within the timescale to which the monitoring was sensitive. This reinforces the ``masking hypothesis'' of Bailer-Jones & Mundt (2001A&A...367..218B
), the idea that the evolution of photospheric features on timescales shorter than the rotation period obscure the regular modulation of the light curve. As has been previously discussed, a likely candidate for such features is inhomogeneous dust clouds.