Ionization fraction as a function of selected line intensity ratios for dense gas. The range of observed line ratios is shown in blue and the validity range is in purple. We show the analytical function as a black solid line showing relation between f_e (y-axis) and intensity ratios (x-axis) of CN/N₂H⁺(top panel), N(CN)/N(N₂H⁺)(second panel), ¹³CO/HCO⁺(third panel), and C¹⁸O/HCO⁺(bottom panel). The analytical functions (Eq. 2), its 3−σ variance (grey shaded area) and the validity ranges are taken from Bron et al. (2021).