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tokens: and planets with little Ly absorption but strong emission can be used to distinguish between these two classes of thermospheres. Based on the predicted strong absorption signals, WASP-80 b and GJ 3470 b are the most promising targets among our sample in the search for yet undetected escaping atmospheres. Appendix A: Calculation of the Ly<inline-formula specific-use="simple-math"><italic>α</italic></inline-formula> absorption signals Here, we describe the method used to calculate the Ly absorption in the simulated atmospheres. Although we use the term Ly absorption, we note that the actual physical process is scattering of photons out of our line of sight. Absorption of Ly with collisional de-excitation only occurs deep in the simulated atmospheres (see Fig. 6 ). We do not account for any emission or line transfer in the computation of the absorption signals, or for scattering of photons into our line of sight. We further assume a homogeneous brightness of the stellar disk in Ly emission. Fig. A.1 Computation of the transmission signals and images. The absorption is calculated by shooting rays through the planetary atmosphere. Density, temperature, and tangential velocity in each cell are taken into account. To compute the absorption signals we shoot rays through the spherical atmospheres (see Fig. A.1 ). The wavelength dependent transmission in a single ray with index is given by the product of the absorption in each cell: Here, is the neutral hydrogen density in cell with the cell width . is the standard Ly absorption cross-section with a Voigt-profile, shifted by the local tangential velocity of the gas. The Doppler width is given by the sum of the local thermal and turbulent widths (see Eq. ( 5 )); the latter is given by the speed of sound. Deuterium absorption is included with a deuterium fraction of according to measurements from Jupiter ( Lellouch et al. 2001 ). Fig. A.2 Simulated Ly transmission for low-potential planets. For each system we show the absorption in the Ly line from below the Roche lobe (solid line) and from unbound hydrogen (dashed, blue). Black dashed lines indicate the optical transit depth. Calculated transmission images are depicted next to each spectrum. The mass-loss rate decreases from top to bottom . Fig. A.3 Simulated Ly transmission spectra and images for high-potential planets plus WASP-80 b (same as Fig. A.2 ). With the exception of WASP-12 b (see text) and WASP-80 b, these planets produce small absorption signals. WASP-80 b produces the strongest absorption signal of all planets. The total transmission is given by: Here, is the number of rays and is half of the vertical resolution. In this equation, the first term accounts for the fraction of radiation that bypasses the simulated atmospheres (transmission equals one). In most of the systems this term is zero, because the simulated atmospheres cover the full stellar disk. The sum adds the transmission of each ray weighted with the fractional area that a ring