Activity index as a function of ξ values: the GESiDR5 results are represented with grey circles, and the triangles represent the values we find with our new method. The black triangles are the stars in the sample, and the coloured triangles represent the Gaia benchmark stars: red for α Cen A, green for 18 Sco, blue for τ Cet, and magenta for β Hyi. The dot-dashed line is the trend observed for the GES values.