[Paper Review] On the Ionisation Fraction in Protoplanetary Disks II: The Effect of Turbulent Mixing on Gas--phase Chemistry

M. Ilgner, Richard P. Nelson|ArXiv.org|Sep 19, 2005

Astrophysics and Star Formation Studies27 references40 citations

TL;DR

This paper investigates how turbulent mixing affects ionisation fractions in protoplanetary disks, using gas-phase chemical networks to model vertical diffusion of species. It finds that when magnesium abundances exceed a threshold ($x_{\rm Mg} \sim 10^{-10}$–$10^{-8}$), turbulent diffusion can suppress recombination by metal ions, eliminating magnetically decoupled 'dead zones' and enabling self-sustaining MHD turbulence.

ABSTRACT

We calculate the ionisation fraction in protostellar disk models using two different gas-phase chemical networks, and examine the effect of turbulent mixing by modelling the diffusion of chemical species vertically through the disk. The aim is to determine in which regions of the disk gas can couple to a magnetic field and sustain MHD turbulence. We find that the effect of diffusion depends crucially on the elemental abundance of heavy metals (magnesium) included in the chemical model. In the absence of heavy metals, diffusion has essentially no effect on the ionisation structure of the disks, as the recombination time scale is much shorter than the turbulent diffusion time scale. When metals are included with an elemental abundance above a threshold value, the diffusion can dramatically reduce the size of the magnetically decoupled region, or even remove it altogther. For a complex chemistry the elemental abundance of magnesium required to remove the dead zone is 10(-10) - 10(-8). We also find that diffusion can modify the reaction pathways, giving rise to dominant species when diffusion is switched on that are minor species when diffusion is absent. This suggests that there may be chemical signatures of diffusive mixing that could be used to indirectly detect turbulent activity in protoplanetary disks. We find examples of models in which the dead zone in the outer disk region is rendered deeper when diffusion is switched on. Overall these results suggest that global MHD turbulence in protoplanetary disks may be self-sustaining under favourable circumstances, as turbulent mixing can help maintain the ionisation fraction above that necessary to ensure good coupling between the gas and magnetic field.

Motivation & Objective

• To determine how turbulent mixing influences the ionisation structure in protoplanetary disks, particularly in relation to magnetic field coupling.
• To assess whether turbulent diffusion can reduce or eliminate magnetically decoupled regions ('dead zones') in disks with low ionisation.
• To investigate the role of heavy metals, especially magnesium, in modifying recombination pathways and ionisation fractions under diffusive conditions.
• To explore whether chemical signatures of turbulent mixing could serve as indirect observational diagnostics for disk turbulence.
• To evaluate the conditions under which global MHD turbulence might become self-sustaining through feedback between diffusion and ionisation chemistry.

Proposed method

• Modeling protoplanetary disks as standard $\alpha$-disks with X-ray ionisation as the primary ionisation source.
• Using two gas-phase chemical networks: the simplified Oppenheimer & Dalgarno (1974) network and a complex network based on the UMIST database.
• Implementing vertical turbulent diffusion by equating the diffusion coefficient $\mathcal{D}$ to the kinematic viscosity $\nu$.
• Solving the time-dependent diffusion-reaction equations for all chemical species, including electrons and key ions.
• Comparing ionisation fractions and dead zone structure with and without diffusion, for varying magnesium abundances.
• Analyzing changes in dominant ion species and recombination pathways due to mixing effects.

Experimental results

Research questions

• RQ1 Can turbulent mixing reduce or eliminate the magnetically decoupled 'dead zone' in protoplanetary disks?
• RQ2 How does the inclusion of heavy metals like magnesium alter the effectiveness of turbulent diffusion in maintaining ionisation?
• RQ3 What threshold abundance of magnesium is required for diffusion to significantly suppress recombination and sustain magnetic coupling?
• RQ4 Do changes in dominant ion species under diffusion indicate detectable chemical signatures of turbulence?
• RQ5 Under what conditions can turbulent mixing lead to self-sustaining MHD turbulence in disks?

Key findings

• When magnesium abundance exceeds $x_{\rm Mg} = 10^{-10}$, turbulent diffusion can eliminate the dead zone beyond $R \geq 2$ AU in the UMIST-based model.
• For the Oppenheimer & Dalgarno network, a magnesium abundance of $x_{\rm Mg} = 10^{-12}$ is sufficient to remove the dead zone beyond $R \geq 2$ AU when diffusion is active.
• Diffusion has minimal effect on dead zones in models without heavy metals, due to rapid recombination of molecular ions with electrons.
• The recombination time for metal ions (e.g., Mg+) is orders of magnitude longer than for molecular ions, enabling diffusion to outpace electron loss when metals are present.
• Turbulent mixing alters chemical pathways, causing a shift in dominant ions near the dead zone boundary, suggesting potential chemical tracers of turbulence.
• In some cases, diffusion can deepen the dead zone in outer disk regions by diluting electron fractions below the critical threshold for magnetic coupling.