  We present new radial velocity measurements of the ultra-cool dwarf VB 10,
which was recently announced to host a giant planet detected with astrometry.
The new observations were obtained using optical spectrographs(MIKE/Magellan
and ESPaDOnS/CHFT) and cover a 63% of the reported period of 270 days. We apply
Least-squares periodograms to identify the most significant signals and
evaluate their corresponding False Alarm Probabilities. We show that this
method is the proper generalization to astrometric data because (1) it
mitigates the coupling of the orbital parameters with the parallax and proper
motion, and (2) it permits a direct generalization to include non-linear
Keplerian parameters in a combined fit to astrometry and radial velocity data.
In fact, our analysis of the astrometry alone uncovers the reported 270 d
period and an even stronger signal at 50 days. We estimate the uncertainties in
the parameters using a Markov Chain Monte Carlo approach. The nominal precision
of the new Doppler measurements is about 150 s$^{-1}$ while their standard
deviation is 250 ms$^{-1}$. However, the best fit solutions still have RMS of
200 ms$^{-1}$ indicating that the excess in variability is due to uncontrolled
systematic errors rather than the candidate companions detected in the
astrometry. Although the new data alone cannot rule-out the presence of a
candidate, when combined with published radial velocity measurements, the False
Alarm Probabilities of the best solutions grow to unacceptable levels strongly
suggesting that the observed astrometric wobble is not due to an unseen
companion.
