Precise radial velocities of Proxima Centauri - Strong constraints on a substellar companion

We present differential radial velocity measurements of Proxima Centauri co llected over 4 years with the ESO CES with a mean precision of 54 ms(-1). W e find no evidence of a periodic signal that could corroborate the existenc e of a substellar companion. We put upper limits (97% confidence) to the co mpanion mass ranging from 1.1 to 22 M-Jup at orbital periods of 0.75 to 300 0 d, i.e. separations 0.008-2 AU from Prox Cen. Our mass limits concur with limits found by precise astrometry (Benedict et al. 1998a and priv. comm.) which strongly constrain the period range 50-600 d to 1.1-0.22 M-Jup. Comb ining both results we exclude a brown dwarf or supermassive planet at separ ations 0.008-0.69 AU from Prox Cen. We also find that, at the level of our precision, the RV data are not affected by stellar activity.