Local shear instabilities in weakly ionized, weakly magnetized disks

Chondrule Formation and Protoplanetary Disk Heating by Current Sheets in Nonideal Magnetohydrodynamic Turbulence

“…Ionization fraction is a key parameter in determining whether a disk will be turbulent or not, since the MRI is confined to regions where the ionization fraction is high enough to ensure good coupling between ions and neutrals. This occurs when the neutral-ion collision rate ( ni ) is significantly greater (by 3-100 at least) than the rotation rate (Blaes & Balbus 1994;Mac Low et al 1995;Hawley & Stone 1998). The critical ionization fraction is calculated to be…”

“…Here, c is the speed of light, e ¼ n e =n n is the electron fraction, and T g is the ambient gas temperature. For the last equality in equation (2), we adopt the value of the electrical conductivity e from Draine, Roberge, & Dalgarno (1983) and Blaes & Balbus (1994). Subscripts e, i, and n denote quantities pertaining to electron, ion, and neutral components, respectively.…”

“…In this case, Ohmic dissipation acts to stabilize wavelengths shorter than the resistive diffusion scale k 2 =v A , where v A ¼ B=(4 n ) 1=2 is the Alfvén speed. In other words, the critical wavelength at which MRI sets in is given by k crit ¼ max (k BH ; k ) (Blaes & Balbus 1994;Sano et al 2000). When k > k BH , the perturbation growth becomes much slower.…”

“…On the theoretical side, magnetorotational instability (MRI) provided a solution to the long-standing problem of identifying the cause of anomalous viscosity, which allows mass accretion of the disk , collectively referred to as BH91 hereafter). When applied to partially ionized disks, it remains an efficient mechanism for generating turbulence as long as ions are sufficiently well coupled to neutrals, i.e., if the neutral-ion collision rate far exceeds the orbital rotation rate: ni 3 (Blaes & Balbus 1994;Mac Low et al 1995;Hawley & Stone 1998). However, large regions in protoplanetary disks, especially near the disk midplane, have a relatively low ionization fraction ($10 À12 ), and hence are thought to be magnetically dead (Gammie 1996;Glassgold, Najita, & Igea 1997).…”

X-ray ionization of protostellar disks

“…For this instability to be effective, the electron fraction in the disk has to be larger than some critical value, x C r « 10~1 4 -10~1 3 (Blaes & Balbus 1994, Gammie 1996. Thus, when we speak of large and small ionization fractions, it is with respect to this very small value of x cr .…”