Detecting planets around very cool dwarfs at near infrared wavelengths with the radial velocity technique

Context. Radial velocity monitoring of very cool dwarfs such as late M- and hot L-dwarfs has become a promising tool to search for rocky planets as well as to follow-up planetary candidates around dwarfs found by transit surveys. These stars are faint at optical wavelengths, as their spectral flux distribution peaks at near-infrared (NIR) wavelengths. For this reason, it is desirable to measure the radial velocities in this wavelength regime. However, in the NIR there are only very few medium- and high-resolution spectrographs available which are mounted at large telescopes. In the near future, high-resolution spectrographs for the NIR will be built, which will allow us to search for rocky planets around cool M-dwarfs and L-dwarfs from radial velocities monitoring. Methods. Stellar atmosphere synthetic models for an M- and an L-dwarf with temperatures of 2200 K and 1800 K, respectively, and a theoretical spectrum of the Earth's transmission in the spectral range from 0.9 to 2.5 \mum are used. We simulate a series of Doppler-shifted spectra observed with different resolving powers and signal-to-noise ratios, and for different rotational broadenings of the dwarf. For different combinations of the input parameters we recover the radial velocity by means of cross-correlation with a high signal-to-noise ratio template and determine the associate uncertainties. Results. The highest precision in radial velocity measurements for the cool M-dwarf is found in the Y band around 1.0 \mum, while for the L-dwarf it is determined in the J band around 1.25 \mum. We note that synthetic models may lack of some faint absorption features or underestimate their abundances. Conversely, some instrumental/calibration aspects that are not taken into account in our estimations would rise the uncertainties.