[Paper Review] On the Ionisation Fraction in Protoplanetary Disks I: Comparing Different Reaction Networks

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

Astrophysics and Star Formation Studies17 references102 citations

TL;DR

This paper compares gas-phase and gas-grain chemical reaction networks to model ionisation fractions in protoplanetary disks under X-ray irradiation. It finds that complex networks predict significantly larger magnetically inactive (dead) zones than simple models, especially when heavy metals are present, and that grain growth and settling are essential for disks to become magnetically active and turbulent.

ABSTRACT

We calculate the ionisation fraction in protostellar disk models using a number of different chemical reaction networks, including gas-phase and gas-grain reaction schemes. The disk models we consider are conventional alpha-disks, which include viscous heating and radiative cooling. The primary source of ionisation is assumed to be X-ray irradiation from the central star. We consider a number of gas-phase chemical networks. In general we find that the simple models predict higher fractional ionisation levels and more extensive active zones than the more complex models. When heavy metal atoms are included the simple models predict that the disk is magnetically active throughout. The complex models predict that extensive regions of the disk remain magnetically uncoupled even with a fractional abundance of magnesium of 10(-8). The addition of submicron sized grains with a concentration of 10(-12) causes the size of the dead zone to increase dramatically for all kinetic models considered. We find that the simple and complex gas-grain reaction schemes agree on the size and structure of the resulting dead zone. We examine the effects of depleting the concentration of small grains as a crude means of modeling the growth of grains during planet formation. We find that a depletion factor of 10(-4) causes the gas-grain chemistry to converge to the gas-phase chemistry when heavy metals are absent. 10(-8) is required when magnesium is included. This suggests that efficient grain growth and settling will be required in protoplanetary disks, before a substantial fraction of the disk mass in the planet forming zone between 1 - 10 AU becomes magnetically active and turbulent.

Motivation & Objective

• To assess how different chemical reaction networks affect predictions of ionisation fraction and magnetic activity in protoplanetary disks.
• To investigate the role of heavy metals (e.g., magnesium) and submicron grains in determining the extent of magnetically active versus dead zones.
• To evaluate the validity of simplified chemical models (e.g., Oppenheimer & Dalgarno 1974) in representing complex gas-phase and gas-grain chemistry.
• To determine the grain depletion factors required for gas-grain chemistry to converge with gas-phase chemistry in the presence and absence of metals.
• To examine the implications of these findings for the onset of MHD turbulence and planet formation in disks.

Proposed method

• Uses a standard α-disk model with viscous heating and radiative cooling, assuming X-ray ionisation as the primary ionisation source.
• Applies multiple chemical reaction networks: a simple five-species model (Oppenheimer & Dalgarno 1974) and more complex networks derived from the UMIST database.
• Incorporates gas-grain interactions by including submicron-sized grains with a fixed concentration ($x_{\text{gr}} = 10^{-12}$) to model electron scavenging.
• Varies elemental abundances (e.g., $x_{\text{Mg}} = 10^{-8}$ to $10^{-12}$) and grain depletion factors ($10^{-4}$ to $10^{-8}$) to test convergence between models.
• Calculates ionisation fraction, magnetic Reynolds number, and spatial extent of magnetically active regions using steady-state chemical equilibrium solutions.
• Compares results across models to assess consistency and identify conditions under which simplified models break down.

Experimental results

Research questions

• RQ1 How do different chemical reaction networks (simple vs. complex) affect predictions of ionisation fraction and magnetic activity in protoplanetary disks?
• RQ2 What is the impact of including heavy metals (e.g., magnesium) on the size and structure of magnetically inactive (dead) zones?
• RQ3 How do submicron-sized grains influence the ionisation fraction and the extent of dead zones across different chemical models?
• RQ4 What grain depletion factor is required for gas-grain chemistry to reproduce the ionisation fraction predicted by gas-phase chemistry?
• RQ5 Under what conditions can simplified gas-phase chemical models reliably predict the ionisation structure of protoplanetary disks?

Key findings

• The simple Oppenheimer & Dalgarno (1974) model predicts globally magnetically active disks when $x_{\text{Mg}} \geq 10^{-11}$, while complex gas-phase networks predict extensive dead zones even at $x_{\text{Mg}} = 10^{-8}$.
• Complex gas-phase networks predict larger dead zones than simple models due to the dominance of molecular ions in electron recombination, even at moderate metal abundances.
• The addition of submicron grains with $x_{\text{gr}} = 10^{-12}$ dramatically increases the size of the dead zone in all models, due to efficient electron scavenging.
• Gas-grain chemical networks show excellent agreement in predicting the size and structure of the active zone, as grains dominate the ionisation fraction regardless of the underlying reaction network.
• A grain depletion factor of $\sim 10^{-4}$ is required to reproduce gas-phase chemistry without metals, while $\sim 10^{-8}$ is needed when metals are included.
• The results imply that efficient grain growth and settling are essential before gas-phase models can reliably predict ionisation fractions and magnetic activity in disks.