Observation and modelling of main-sequence star chromospheres - XVII. Rotation of dM4 stars

Using two different spectrographs, High Accuracy Radial velocity Planet Searcher (European Southern Observatory) and SOPHIE (Observatoire de Haute Provence), we have measured v sin i for a sample of 23 dM4 stars. These are the first measurements of v sin i for most of the stars studied here. We measured v sin i to a precision of 0.3 km s(-1) and a detection limit of about 0.5-1 km s(-1). All our targets have similar (R - I)(C) colour. This is an advantage and facilitates the determination of the narrowest cross-correlation profiles for v sin i similar to 0. In our sample, we detected rotation for 21 stars (12 dM4e stars and nine dM4 stars) and we did not detect rotation in a further two stars. This result shows that there are many dM4 fast rotators (of the order of 5 d), and many more than in the case of dM1 stars. We determined radii and effective temperatures for all our target stars. The effective temperatures were derived using the (R - I)(C) colour and empirical far-red colour-effective temperature correlations. We derived the radii from the standard formulae relating M-bol, bolometric correction (BC) and T-eff. We find that the distribution of P/sin i (the projected rotation period) is bimodal with a maximum for slow rotators around 14 d and for fast rotators around 6 d, similar to dM1 stars. The rotation period appears to decrease with decreasing radius, both among dM4 and dM4e stars. The same finding was obtained in our previous study of dM1 stars.