The general applicability of self-similar solutions for thermal disc winds

TL;DR

This paper extends self-similar thermal wind models to include elevated bases and non-isothermal conditions, demonstrating their validity through hydrodynamic simulations and exploring implications for protoplanetary disc observations.

Contribution

It generalizes existing models of thermal disc winds to more realistic conditions, including elevation and temperature gradients, and validates these models with simulations.

Findings

Hydrodynamic simulations match self-similar models across various conditions.

Elevated wind bases significantly affect launch velocity and flow morphology.

Line profile widths depend on wind launch height and inclination.

Abstract

Thermal disc winds occur in many contexts and may be particularly important to the secular evolution and dispersal of protoplanetary discs heated by high energy radiation from their central star. In this paper we generalise previous models of self-similar thermal winds - which have self-consistent morphology and variation of flow variables - to the case of launch from an elevated base and to non-isothermal conditions. These solutions are well-reproduced by hydrodynamic simulations, in which, as in the case of isothermal winds launched from the mid-plane, we find winds launch at the maximum Mach number for which the streamline solutions extend to infinity without encountering a singularity. We explain this behaviour based on the fact that lower Mach number solutions do not fill the spatial domain. We also show that hydrodynamic simulations reflect the corresponding self-similar models across a range of conditions appropriate to photoevaporating protoplanetary discs, even when gravity, centrifugal forces, or changes in the density gradient mean the problem is not inherently scale free. Of all the parameters varied, the elevation of the wind base affected the launch velocity and flow morphology most strongly, with temperature gradients causing only minor differences. We explore how launching from an elevated base affects Ne II line profiles from winds, finding it increases (reduces) the full width at half maximum (FWHM) of the line at low (high) inclination to the line of sight compared with models launched from the disc mid-plane and thus weakens the dependence of the FWHM on inclination.