The GAPS programme at TNG. XLIV. Projected rotational velocities of 273 exoplanet-host stars observed with HARPS-N

Context. The leading spectrographs used for exoplanets' search and characterization offer online data reduction softwares (DRS) that yield, as an ancillary result, the full-width at half-maximum (FWHM) of the cross-correlation function (CCF) that is used to estimate the radial velocity of the host star. The FWHM also contains information on the stellar projected rotational velocity v_eq sin i_★, if appropriately calibrated.
Aims: We wanted to establish a simple relationship to derive the v_eq sin i_★ directly from the FWHM computed by the HARPS-N DRS in the case of slow-rotating solar-like stars. This may also help to recover the stellar inclination i_★, which in turn affects the exoplanets' parameters.
Methods: We selected stars with an inclination of the spin axis compatible with 90 deg by looking at exoplanetary transiting systems with known small sky-projected obliquity: for these calibrators, we can presume that v_eq sin i_★ is equal to stellar equatorial velocity v_eq. We derived their rotational periods from photometric and spectroscopic time series and their radii from the spectral energy distribution (SED) fitting. This allowed us to recover their v_eq, which could be compared to the FWHM values of the CCFs obtained both with G2 and K5 spectral-type masks.
Results: We obtained an empirical relation for each mask: this can be used to derive v_eq sin i_★ directly from FWHM values for slow rotators (FWHM < 20 km s⁻¹). We applied our relations to 273 exoplanet-host stars observed with HARPS-N, obtaining homogeneous v_eqsin i_★ measurements. When possible, we compared our results with the literature ones to confirm the reliability of our work. We were also able to recover or constrain i_★ for 12 objects with no prior v_eq sin i_★ estimation.
Conclusions: We provide two simple empirical relations to directly convert the HARPS-N FWHM obtained with the G2 and K5 mask to a v_eq sin i_★ value. We tested our results on a statistically significant sample, and we found a good agreement with literature values found with more sophisticated methods for stars with log ɡ > 3.5. We also tried our relation on HARPS and SOPHIE data, and we conclude that it can be used as it is also on FWHM derived by HARPS DRS with the G2 and K5 mask, and it may be adapted to the SOPHIE data as long as the spectra are taken in high-resolution mode.

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