tokens: optimize the chances of finding new systems with gas. 4.1 Flux predictions for atoms When making predictions for C i , C ii and O i masses, the conversion to fluxes is more complicated than with CO where the excitation is dominated by the CMB (see Section 3.5.2 ). Since these lines are at shorter wavelengths, the dust radiation field can become dominant (see Fig. B1 ). While the dust radiation field seen by the gas is not easy to assess, especially as most of our targets are unresolved, it is well known for β Pic. Thus, we use the same radiation field as found in Matrà et al. (in preparation) for that system. For other targets, we fit each SED individually and use the ratio of the dust fluxes at 158, 610 and 63 μm to those of β Pic to scale up or down the β Pic radiation field and so get predictions for the fluxes of each individual system for C ii , C i and O i (see Appendix B ). Note that we also take account of the optical thickness of each line in our flux calculations using the method described in Section 3.5.6 . 4.2 C <sc>ii</sc> model predictions and results We start off by comparing our C ii model predictions to Herschel observations. In Fig. 7 , we plot our predictions of C ii mass as a function of distance to the star. To do so, we use our analytical model using equation ( 11 ) to get the total carbon mass and equation ( 15 ) to get the ionization fraction and then compute . The predicted C ii masses are shown as red points in Fig. 7 . We keep the same style as the CO plot (Fig. 4 ), i.e. systems with gas detected are labelled with their names. If in addition, they have C ii detected, the label is blue (not black). NLTE detection thresholds are computed using the same code as described to compute CO population levels in NLTE (see Appendix B for details). We overplot the detection limits at 5σ in 1 h in both LTE (thin lines) and NLTE (thick lines) for Herschel /PACS (in red) where we assumed the typical sensitivity reached for non-detections (Riviere-Marichalar et al. 2014 ), for SPICA/SAFARI (in orange) and for a future far-IR mission (such as FIRS) with a 10 m aperture (in green) where the sensitivities are taken from the SPICA and FIR surveyor documentation. 4 The assumed sensitivities are summarized in Table 3 . We compute the electron density as a function of the C ii mass (using equation 14 ) with our model to compute the NLTE lines. Figure 7. C ii mass (in M ⊕ ) as a function of distance to Earth ( d ). Planetary systems with gas detections are labelled with their names. If C ii is detected, the label is in blue (black otherwise). The C ii mass lower limits worked out from observations are shown as green arrows, and for β Pic we show the mass derived from Herschel observations using Kral et al. ( 2016 ) as a green point. The red points are predictions from our model. The red downward arrows show systems that are in the blue hatched area on Fig. 1 , which cannot keep CO trapped on solid bodies. The purple points show predictions
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