Forbidden line diagnostics of photoevaporative disc winds

Photoevaporation driven by high energy radiation from the central star plays an important role in the evolution of protoplanetary discs. Photoevaporative winds have been unambiguously detected through blue-shifted emission lines, but their detailed properties remain uncertain. Here we present a new empirical approach to make observational predictions of these thermal winds, seeking to fill the gap between theory and observations. We use a self-similar model of an isothermal wind to compute line profiles of several characteristic emission lines (the [Ne${\rm{\scriptsize II}}$] line at 12.81 $\mu$m, and optical forbidden lines such as [O${\rm{\scriptsize I}}$] 6300 $\mathring{A}$ and [S${\rm{\scriptsize II}}$] 4068/4076 $\mathring{A}$), studying how the lines are affected by parameters such as the gas temperature, disc inclinations, and density profile. Our model successfully reproduces blue-shifted lines with $v_{\rm peak} \lesssim 10$ km/s, which decrease with increasing disc inclination. The line widths increase with increasing disc inclinations and range from $\Delta v \sim 15-30$ km/s. The predicted blue-shifts are mostly sensitive to the gas sound speed. The observed [Ne${\rm{\scriptsize II}}$] line profiles are consistent with a thermal wind and point towards a relatively high sound speed, as expected for EUV photoevaporation. However, the observed [O${\rm{\scriptsize I}}$] line profiles require lower temperatures, as expected in X-ray photoevaporation, and show a wider scatter that is difficult to reconcile with a single wind model; it seems likely that these lines trace different components of a multi-phase wind. We also note that the spectral resolution of current observations remains an important limiting factor in these studies, and that higher resolution spectra are required if emission lines are to further our understanding of protoplanetary disc winds.