The importance of X-ray frequency in driving photoevaporative winds

Photoevaporative winds are a promising mechanism for dispersing protoplanetary discs, but so far theoretical models have been unable to agree on the relative roles that the X-ray, Extreme Ultraviolet or Far Ultraviolet play in driving the winds. This has been attributed to a variety of methodological differences between studies, including their approach to radiative transfer and thermal balance, the choice of irradiating spectrum employed, and the processes available to cool the gas. We use the \textsc{mocassin} radiative transfer code to simulate wind heating for a variety of spectra on a static density grid taken from simulations of an EUV-driven wind. We explore the impact of choosing a single representative X-ray frequency on their ability to drive a wind by measuring the maximum heated column as a function of photon energy. We demonstrate that for reasonable luminosities and spectra, the most effective energies are at a few $100~\mathrm{eV}$, firmly in the softer regions of the X-ray spectrum, while X-rays with energies $\sim1000~\mathrm{eV}$ interact too weakly with disc gas to provide sufficient heating to drive a wind. We develop a simple model to explain these findings. We argue that further increases in the cooling above our models - for example due to molecular rovibrational lines - may further restrict the heating to the softer energies but are unlikely to prevent X-ray heated winds from launching entirely; increasing the X-ray luminosity has the opposite effect. The various results of photoevaporative wind models should therefore be understood in terms of the choice of irradiating spectrum.Comment: 20 pages, 11 figures; This article has been accepted for publication in MNRAS Published by Oxford University Press on behalf of the Royal Astronomical Society after minor revision