SummaryWe present spectral diagnostics for the fluxes of emission lines, in the spectral range 3600-4400 Å, during the cooling phase of stellar flares on dMe stars. Using these diagnostics, electron temperatures have been computed for flares on AD Leonis, Proxima Centauri and UV Ceti. This preliminary model assumes a single flare loop containing a homogeneous, stationary optically-thin flare plasma.

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.