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

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.

Dust entrainment in photoevaporative winds: Densities and imaging

“…Dust entrainment in photoevaporative extreme-ultraviolet-(EUV-) driven winds has first been investigated by Owen et al (2011), later by Hutchison et al (2016a,b), and very recently by Hutchison & Clarke (2021) and , building on the semi-analytical modelling of Clarke & Alexander (2016) (which has recently been generalised by Sellek et al 2021). All studies found an entrainment of dust grains of several µm in size.…”

The importance of X-ray frequency in driving photoevaporative winds

“…Since we do not solve the hydrodynamics, we cannot determine the velocities 𝑣 for our simulations. However, we can assume that they are initially subsonic (Clarke & Alexander 2016;Sellek et al 2021) at the base of the wind and so the poloidal kinetic energy term 𝑣 2 𝑝 /2 is small compared to the thermal term 𝑃/𝜌, while the azimuthal kinetic energy term 𝑣 2 𝜙 /2 ∼ Φ 2 . Thus, we define the Bernoulli surface as the location where…”

“…Photoevaporative winds are thermally launched: they occur when the upper layers of a disc become heated by high energy ★ E-mail: ads79@cam.ac.uk radiation from either the central star (internal photoevaporation) or a massive neighbour (external photoevaporation) and the resulting pressure gradients drive material off of the disc. Broadly speaking, this is expected to happen for radii 𝑟 𝐺 𝑀 * 𝑐 2 𝑆 (for stellar mass 𝑀 * and sound speed in the wind 𝑐 𝑆 ) where the available thermal energy is enough to overcome the gravitational potential of the star (Shu et al 1993;Hollenbach et al 1994;Font et al 2004;Alexander et al 2014;Clarke & Alexander 2016;Sellek et al 2021). Equivalently, one can invert this to say that at a radius 𝑅, material must be heated above the escape temperature 𝑇 esc ∼ 𝐺 𝑀 * 𝜇𝑚 𝐻 2𝑘 𝐵 𝑅 (Owen et al 2012).…”

Anatomy of Photoevaporation Base: Linking the Property of the Launched Wind to Irradiation Flux

“…Self-similar disk wind models explain that the power-law index of the base density profile limits an allowable range of v 2 in order for the streamline to reach infinity (Clarke & Alexander 2016;Sellek et al 2021). Self-similar thermal winds are known to generally take the maximum of the allowed M 2 at the base, otherwise, the whole R-z plane cannot be filled with the self-similar winds (Sellek et al 2021). In this way, the large-scale profiles of the disk winds also matter in determining the base property.…”

“…One needs information on flow geometry to compute adiabatic cooling without performing hydrodynamic simulations. For disk photoevaporation, recent analytical models of thermally driven winds (Clarke & Alexander 2016;Sellek et al 2021) may be available for that purpose. Analytic modeling of c 2 (or flow structure) is a next step in future work.…”