On the ionisation fraction in protoplanetary disks. I. Comparing different reaction networks
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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 α -disks, which include viscous heating and radiative cooling. The primary source of ionisation is assumed to be X-ray irradiation from the central star. For most calculations we adopt a specific disk model (with accretion rate ${\dot M}=10^{-7}$ $M_{\odot}$ yr -1 and $\alpha=10_{}^{-2}$), and examine the predictions made by the chemical networks concerning the ionisation fraction, magnetic Reynolds number, and spatial extent of magnetically active regions. This is to aid comparison between the different chemical models. We consider a number of gas-phase chemical networks. The simplest is the five species model proposed by Oppenheimer & Dalgarno (1974). We construct more complex models by extracting species and reactions from the UMIST data base. 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 (“dead”) even when the fractional abundance of magnesium $x_{\rm Mg}=10^{-8}$. This is because of the large number of molecular ions that are formed, which continue to dominate the recombination with free electrons in the presence of magnesium. The addition of submicron sized grains with a concentration of $x_{\rm gr}=10^{-12}$ causes the size of the “dead zone” to increase dramatically for all kinetic models considered, as the grains are highly efficient at sweeping up the free electrons. We find that the simple and complex gas-grain reaction schemes agree on the size and structure of the resulting “dead zone”, as the grains play a dominant role in determining the ionisation fraction. 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. When magnesium is included a depletion factor of 10 -8 is required to reproduce the gas-phase ionisation fraction. 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. Only after this has occurred can gas-phase chemical models be used to predict reliably the ionisation degree in protoplanetary disks.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Spectroscopy
View Paper: https://www.semanticscholar.org/paper/8566f3becf83c0971d99da97d0bcaa86aa2774d2
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Citations in the corpus
- Dead Zone Accretion Flows in Protostellar Disks (2008, methodology): “The recombination is treated using the reduced reaction network with grains described by Ilgner & Nelson (2006).”
- Global Simulations of the Inner Regions of Protoplanetary Disks with Comprehensive Disk Microphysics (2017, methodology): “The ionization of PPDs largely relies on external sources such as cosmic-rays and X-rays, leading to extremely low level of disk ionization with vertically stratified ionization structure (Sano et al. 2000; Ilgner & Nelson 2006; Bai & Goodman 2009).”
- The dynamics of Jupiter and Saturn in the gaseous protoplanetary disk (2007, background): “Thus, even if undergoing the ionizing effect of the stellar radiation, a disk might not exhibit MHD turbulence if a sufficient amount of dust is present (Ilgner and Nelson, 2006a,b).”
- ELECTRIC CHARGING OF DUST AGGREGATES AND ITS EFFECT ON DUST COAGULATION IN PROTOPLANETARY DISKS (2009, background): “As pointed out by Ilgner & Nelson (2006c), the flaring could quantitatively change the ionization state of the disk.”
- Turbulent Mixing and the Dead Zone in Protostellar Disks (2006, methodology): “…surface density, the abundance of the dust that hastens recombination (Wardle & Ng 1999; Sano et al. 2000), the presence of long-lived metal ions (Fromang et al. 2002), and the rate at which the turbulence mixes the charged species into the interior ( Inutsuka & Sano 2005; Ilgner & Nelson 2006b).”
- NONSTEADY ACCRETION IN PROTOSTARS (2008, background): “Both calculations assume that absorption of ions and electrons by grains is unimportant, which is only true if small dust is highly depleted in the active layer (e.g., Sano et al. 2000, also Ilgner & Nelson 2006a,b,c).”
- Planet-Disk Interaction and Orbital Evolution (2012, background): “Details of this layered structure depend on a large number of parameters including the sizes and abundances of dust grains (Sano et al., 2000; Ilgner & Nelson, 2006), and the intensity of external ionisation sources (Turner & Drake, 2009), in addition to the field strength and topology.”
- GLOBAL SIMULATIONS OF PROTOPLANETARY DISKS WITH OHMIC RESISTIVITY AND AMBIPOLAR DIFFUSION (2015, methodology): “Modifications to the disk chemistry Our chemical network is based on the one used by Ilgner & Nelson (2006), labeled model4, with grain surface reactions and a simplified gas-phase reaction set involving one representative metal and one molecular ion.”
- WIND-DRIVEN ACCRETION IN PROTOPLANETARY DISKS. I. SUPPRESSION OF THE MAGNETOROTATIONAL INSTABILITY AND LAUNCHING OF THE MAGNETOCENTRIFUGAL WIND (2013, methodology): “Finally, we find that the grain abundance, which has been found to play a crucial role in determining the extent of the active layer in the conventional layered accretion scenario (Ilgner & Nelson 2006; Bai & Goodman 2009), has almost no influence on the wind scenario.”
- Thanatology in protoplanetary discs - The combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones (2014, background): “S R ] 2 4 Fe b 20 14 2000; Fromang et al. 2002; Ilgner & Nelson 2006a,b) and threedimensional numerical simulations (Fleming et al. 2000; Fleming & Stone 2003; Turner et al. 2007; Ilgner & Nelson 2008).”
- Grain Retention and Formation of Planetesimals near the Snow Line in MRI-driven Turbulent Protoplanetary Disks (2007, methodology): “We approximate the size of the active layer from chemical equilibrium calculations to determine the linear stability to MRI turbulence (Ilgner & Nelson 2006 (model 4); Neal Turner private communication).”
- Dust settling in local simulations of turbulent protoplanetary disks (2006, background): “The extent of this dead zone is very uncertain, since it depends on the ionising source and on the chemistry (Sano et al. 2000; Fromang et al. 2002; Ilgner & Nelson 2006), but its existence is likely.”
- Dynamics of Protoplanetary Disks (2010, background): “…physical effect is also present in more refined calculations, which model reactions between large numbers of chemical species (Bai & Goodman 2009; Ilgner & Nelson 2006; Sano et al. 2000; Semenov, Wiebe & Henning 2004), though at a weaker level, because the more complex models include additional…”
- CHEMICAL PROCESSES IN PROTOPLANETARY DISKS (2010, background): “For effective accretion, the ionisation fraction is required to exceed a critical level which is dependent on the nature of the star-disk system (see e.g. Ilgner & Nelson (2006)).”