New neighbours VI. Spectroscopy of DENIS nearby stars candidates

We present spectra of 36 nearby star candidates and 3 red giant candidates, identified in the DENIS database by Phan-Bao et al. (2003). 32 of the dwarf candidates are indeed nearby red dwarfs, with spectral types from M5.5 to M8.5. Out of 11 targets with low proper motion (mu < 0.1$ arc-sec/yr) but a Reduced Proper Motion above an inclusive threshold, 9 are red dwarfs. The 4 contaminants are all reddened F-K main sequence stars, and they could have been eliminated by checking for some well known high latitude molecular clouds. These stars might be of interest as probes of interstellar absorption. For the red dwarfs we derive spectral types and spectroscopic distances, using a new calibration of the PC3 spectral index to absolute magnitudes in the I, J, H and K photometric bands. We confirm 2 new members of the 12 pc volume (2 new M8.5), and one M7.5 NLTT object closer than 10pc. We also show that one quarter of the stars with photometric distances under 30 pc have too small a proper motion for inclusion in the NLTT catalog.