We present a sample of 32 stars of spectral types G and K and luminosity classes I–V, with moderate activity levels, covering four orders of magnitude of surface gravity and a representative range of effective temperature. For each star we obtained high signal-to-noise ratio (S/N) spectra from the Telescopio Internacional de Guanajuato Robótico-Espectroscópico (TIGRE–HEROS) with a spectral resolving power of $R\approx 20\, 000$ and measured the Ca ii K line widths of interest, W0 and W1. The main physical parameters are determined by means of iSpec synthesis and Gaia EDR3 parallaxes. Mass estimates are based on matching to evolution models. Using this stellar sample, which is highly uniform in terms of spectral quality and assessment, we derive the best-fitting relation between emission-line width and gravity g, including a notable dependence on effective temperature Teff, of the form $W_1 \propto g^{-0.229} T_{\rm eff}^{+2.41}$. This result confirms the physical interpretation of the Wilson–Bappu effect as a line saturation and photon redistribution effect in the chromospheric Ca ii column density, under the assumption of hydrostatic equilibrium at the bottom of the chromosphere. While the column density (and hence W1) increases towards lower gravities, the observed temperature dependence is then understood as a simple ionization effect: in cooler stars, Ca ii densities decrease in favour of Ca i.
We present a detailed analysis of five bright spectroscopic binary systems (HD 18665, HD 27131, HD 171852, HD 215550, and HD 217427) that have orbital periods of P ≲ 500 days. We determined the complete set of orbital parameters using the toolkit RadVel by analyzing the observed radial velocity curves.To study the properties of the five systems, we also analyzed the intermediate resolution spectra (R ≈ 20,000) observed with the TIGRE telescope and determined the stellar parameters of the primary stars using the toolkit iSpec. With Gaia Early Data Release 3 parallaxes, a correction for interstellar extinction using the 3D dust map, and bolometric corrections, we placed the stars in the Hertzsprung-Russell diagram and compared the positions with stellar evolution tracks calculated with the Eggleton code to determine the masses and ages of the primary stars. They have all evolved to the giant phase. Finally, we were able to determine the masses of the secondary stars and to estimate the orbital inclinations i of the binary systems.
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