Contour maps of the reduced χ² of the He(2³S) absorption for (a) HAT-P-32 b, (b) WASP-69 b, (c) GJ 1214 b, and (d) WASP-76 b (with different scales of temperature and Ṁ). Dotted curves represent the best fits; the large symbols denote the constrained ranges for a confidence level of 95% (see Sect. 3.5). In panels a and b, the upward triangles represent the limits imposed by including blue and red components (see text). The downward triangles in panel a are the T–Ṁ obtained when assuming null radial velocities of the gas inside the ionisation front (IF) region and in panel b when not including the turbulence broadening. The yellow upward triangles in panel c correspond to the T–Ṁ range obtained when the fast solar wind is considered. The red symbols in panel d correspond to the flux density reduced by a factor of four and those in white for the nominal upper limit. Overplotted are also the curves and symbols for several H/He ratios (e.g. labelled ‘90’ for a H/He of 90/10, ‘98’ for H/He = 98/2). The black dots represent the T–Ṁ grid of the simulations. The minima shown are those obtained from the solutions of the hydrodynamic and non-LTE models for a physically meaningful range of the parameter space.