Timescales diagnostics for saving viscous and MHD-driven dusty discs from external photoevaporation

TL;DR

This study models the co-evolution of gas and dust in protoplanetary discs that are viscously driven, MHD-wind driven, or a hybrid, under external FUV irradiation. Using 1D radial simulations with a hybrid $\alpha$-prescription ($\alpha_{\mathrm{tot}}=\alpha_{\mathrm{SS}}+\alpha_{\mathrm{DW}}$, $\psi_{\mathrm{DW}}=\alpha_{\mathrm{DW}}/\alpha_{\mathrm{SS}}$) and FRIEDv2-based photoevaporation, the authors track gas and dust radii, lifetimes, and dust loss due to winds. They find that disc fate is controlled by outward spreading versus erosion; MHD-wind discs erode less but do not enjoy longer lifetimes in most regimes, and dust lifetimes are dominated by inward drift and wind entrainment, with high-$G_0$ environments washing out differences between transport modes. The results underscore the potential importance of disc substructures for retaining solids and enabling planet formation in irradiated environments, and they motivate incorporating substructures and chemistry in future, more detailed models.

Abstract

The evolution of protoplanetary discs is a function of their internal processes and of their environment. It is unclear if angular momentum is mainly removed viscously or by magnetic winds, or by a combination of the two. While external photoevaporation is expected to influence disc evolution and dispersal, there are observational limitations towards highly irradiated discs. The interplay between these ingredients and their effect on the gas and dust distributions are poorly understood. We investigate the evolution of both the gaseous and solid components of viscous, MHD-wind or hybrid discs, in combination with external FUV-driven mass loss. We test which combinations of parameters protect discs from external irradiation, allowing the solid component to live long enough to allow planet formation to succeed. We run a suite of 1D simulations of smooth discs with varying initial sizes, levels of viscous and MHD-wind stresses modeled via an $α$ parametrisation, and strengths of the external FUV environment. We track disc radii, various lifetime diagnostics, and the amount of dust removed by the photoevaporative wind, as a function of the underlying parameters. The biggest role in determining the fate of discs is played by a combination of its ability to spread radially outwards and the strength of FUV-driven erosion. While MHD wind-driven discs experience less FUV erosion due to the lack of spread, they do not live for longer compared to viscously evolving discs, especially at low-to-moderate FUV fluxes, while higher fluxes yield disc lifetimes that are insensitive to the disc's angular momentum transport mechanism. For the solid component, the biggest role is played by a combination of inward drift and removal by FUV winds. This points to the importance of other physical ingredients, such as disc substructures, even in highly-irradiated disc regions, in order to retain solids.

Figures (12)

• Figure 1: The mass accretion rates, photoevaporative mass loss rates and MHD-wind-driven mass loss rates for discs of different initial sizes and with different values of $\psi_\mathrm{DW}$, namely $\psi_\mathrm{DW}=0$ (purely viscous disc, dotted lines), $\psi_\mathrm{DW}=1$ (hybrid disc, dashed lines), and $\psi_\mathrm{DW}\gg1$ (purely MHD-wind disc, continuous lines). For explanatory purposes we consider here high irradiation, $1000\,G_0$, and low-to-moderate total $\alpha_\mathrm{tot} = 10^{-4} - 10^{-3}$. The purple vertical dashed lines represent the gas disc lifetime diagnostic $t_{\mathrm{dep},\mathrm{gas}}$ (cfr. subsect. \ref{['subsec:Diagnostics']})
• Figure 2: The mass-accretion rate vs. the mass-loss rate in the wind (either the photoevaporative wind alone -- blue dots --, or combined with the MHD wind -- red dots), obtained from mock observations at random times, selected randomly from a uniform distribution in the interval $[0\,\mathrm{My},31.6\,\mathrm{My}]$. Each panel shows the outcome of these experiments for different fixed underlying $\psi_\mathrm{DW} = \alpha_\mathrm{DW}/\alpha_\mathrm{SS}$, while the initial disc sizes, total $\alpha_\mathrm{tot}$, and (finite) FUV fluxes are drawn randomly (values from Table \ref{['tbl:parameters']}).
• Figure 3: Typical evolution of representative dust and gas quantities for either fully MHD-driven discs (continuous lines) or fully viscous discs (dashed lines), subjected to external photoevaporation, as a function of initial disc size ${R_\mathrm{c}}$ (different columns). Top row: dust radii $R_{90\%,\mathrm{d}}$ enclosing 90% of the dust mass, and $R_{90\%,{}^{12}\mathrm{CO}}$, the radius which encloses 90% of the ${{}^{12}\mathrm{CO}}$ emission, calculated following 2023ApJ...954...41T. Upward triangles label the cases where the dust radii initially expand, while circles indicate those that do not, due to external irradiation. Middle row: time evolution of the total dust mass, mass accreted onto the star, and mass lost to wind. The vertical red lines denote the times when the dust mass reaches fraction of the initial mass (set to 1/1000). Bottom row: time evolution of the gas mass. Similarly to the dust, the vertical purple lines denote the times when the gas mass reaches 1/1000 of the initial mass. The underlying total $\alpha_\mathrm{tot}=10^{-3}$ and the FUV flux is set to $1000\,G_0$.
• Figure 4: Fraction of dust mass lost to wind as a function of the initial disc size ${R_\mathrm{c}}$, for different $\psi_\mathrm{DW}=\alpha_\mathrm{DW}/\alpha_\mathrm{SS}$ and $\alpha_\mathrm{tot}=\alpha_\mathrm{DW} + \alpha_\mathrm{SS}$.
• Figure 5: Disc diagnostics as a function of $\psi_\mathrm{DW} = \alpha_\mathrm{DW}/\alpha_\mathrm{SS}$ for different total $\alpha_\mathrm{tot} = \alpha_\mathrm{DW} + \alpha_\mathrm{SS}$ (different colours and line styles, see legends in the last column), and for different FUV fluxes over different rows (see label above each row). In all cases, the disc's initial size ${R_\mathrm{c}} = 100\,\mathrm{AU}$. Upward pointing arrows at $t=31.6\,\mathrm{My}$ show that the data points represent lower bounds. Left column: $t_{\mathrm{dep},\mathrm{dust}}$, the time when the total dust mass drops below 1/1000 of the initial dust mass. Second column: $t_{\mathrm{dep},\mathrm{gas}}$, the time when the gas mass drops below 1/1000 of the initial gas mass. Third column: $t_\mathrm{acc.}$, the time at which the accretion rate onto the star drops below $10^{-11}\,M_\odot/\mathrm{yr}$. Fourth column: $t_\mathrm{IR.ex}$, the time when the disc would be undetectable due to lack of IR excess; we estimate this as the time when the surface density of small dust at $r=1\,\mathrm{AU}$ drops below $1/\kappa_0$, with a reference opacity of small dust grains $\kappa_0 = 1000\,\mathrm{cm}^2/\mathrm{g}$. Last column: fraction of dust mass lost to wind (note the somewhat inconsistent vertical axis range due to values spanning different orders of magnitude across the different setups; see also Fig. \ref{['fig:f_wind.w.r.t.Rc']}). As shown in the legend in the first and fourth columns (which relate to dust timescales), the upward triangles indicate runs where the dust disc radii initially expand due to significant diffusion, while circles indicate those setups which do not (cfr. top row of Fig. \ref{['fig:Evo__FUV=1000_ALPHA=1e-03_lam=3']}).