SIMBAD references

The reliable determination of rotation-activity correlations (RACs) depends on precise measurements of the following stellar parameters: T_eff, parallax, radius, metallicity, and rotational speed v sin i. In this paper, our goal is to focus on the determination of these parameters for a sample of K and M dwarfs. In a future paper (Paper II), we will combine our rotational data with activity data in order to construct RACs. Here, we report on a determination of effective temperatures based on the (R-I)_ C_ color from the calibrations of Mann et al. and Kenyon & Hartmann for four samples of late-K, dM2, dM3, and dM4 stars. We also determine stellar parameters (T_eff, log(g), and [M/H]) using the principal component analysis-based inversion technique for a sample of 105 late-K dwarfs. We compile all effective temperatures from the literature for this sample. We determine empirical radius-[M/H] correlations in our stellar samples. This allows us to propose new effective temperatures, stellar radii, and metallicities for a large sample of 612 late-K and M dwarfs. Our mean radii agree well with those of Boyajian et al. We analyze HARPS and SOPHIE spectra of 105 late-K dwarfs, and we have detected v sin i in 92 stars. In combination with our previous v sin i measurements in M and K dwarfs, we now derive P/sin i measures for a sample of 418 K and M dwarfs. We investigate the distributions of P/sin i, and we show that they are different from one spectral subtype to another at a 99.9% confidence level.