Stellar oscillations appear all across the Hertzsprung-Russell diagram. Recent theoretical studies support their existence also in the atmosphere of M dwarfs. These studies predict for them short periodicities ranging from 20 min to 3 h. Our Cool Tiny Beats (CTB) programme aims at finding these oscillations for the very first time.With this goal, CTB explores the short time domain of M dwarfs using radial velocity data from the High Accuracy Radial velocity Planet Searcher (HARPS)-European Southern Observatory and HARPS-N high-precision spectrographs. Here we present the results for the two most long-term stable targets observed to date with CTB, GJ 588 and GJ 699 (i.e. Barnard's star). In the first part of this work we detail the correction of several instrumental effects. These corrections are especially relevant when searching for subnight signals. Results show no significant signals in the range whereM dwarfs pulsations were predicted. However, we estimate that stellar pulsations with amplitudes larger than ~0.5ms-1 can be detected with a 90 per cent completeness with our observations. This result, along with the excess of power regions detected in the periodograms, opens the possibility of non-resolved very low amplitude pulsation signals. Next generation more precise instrumentation would be required to detect such oscillations. However, the possibility of detecting pulsating M-dwarf stars with larger amplitudes is feasible due to the short size of the analysed sample. This motivates the need for completeness of the CTB survey. © 2017 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society

We acknowledge funding from AYA2014-30147-C03-01 by MINECO/Spain. This study is based on observations made with the 3.6-m ESO Telescope at la Silla under programme ID 191.C-0505. We acknowledge Stefan Dreizler, Enrico Gerlach, Sandra Jeffers, James Jenkins, Christofer Marvin, Julien Morin, Aviv Ofir, Ansgar Reiners and Ulf Seemann for their participation in the preparation of this programme proposal and their support and useful discus- sions. The authors thank the referee T. B¨ohm for his suggestions that helped improved this paper