  The detection of planets around very low-mass stars with the radial velocity
method is hampered by the fact that these stars are very faint at optical
wavelengths where the most high-precision spectrometers operate. We investigate
the precision that can be achieved in radial velocity measurements of low mass
stars in the near infrared (nIR) Y-, J-, and H-bands, and we compare it to the
precision achievable in the optical. For early-M stars, radial velocity
measurements in the nIR offer no or only marginal advantage in comparison to
optical measurements. Although they emit more flux in the nIR, the richness of
spectral features in the optical outweighs the flux difference. We find that
nIR measurement can be as precise than optical measurements in stars of
spectral type ~M4, and from there the nIR gains in precision towards cooler
objects. We studied potential calibration strategies in the nIR finding that a
stable spectrograph with a ThAr calibration can offer enough wavelength
stability for m/s precision. Furthermore, we simulate the wavelength-dependent
influence of activity (cool spots) on radial velocity measurements from optical
to nIR wavelengths. Our spot simulations reveal that the radial velocity jitter
does not decrease as dramatically towards longer wavelengths as often thought.
The jitter strongly depends on the details of the spots, i.e., on spot
temperature and the spectral appearance of the spot. Forthcoming nIR
spectrographs will allow the search for planets with a particular advantage in
mid- and late-M stars. Activity will remain an issue, but simultaneous
observations at optical and nIR wavelengths can provide strong constraints on
spot properties in active stars.
