Fast methods for tracking grain coagulation and ionization

Abstract

Dust grains play a major role in many astrophysical contexts. They affect the chemical, magnetic, dynamical, and optical properties of their environment, from galaxies down to the interstellar medium, star-forming regions, and protoplanetary disks. Their coagulation leads to shifts in their size distribution and ultimately to the formation of planets. However, although the coagulation process is reasonably uncomplicated to numerically implement by itself, it is difficult to couple it with multidimensional hydrodynamics numerical simulations because of its high computational cost. We propose here a simple method for tracking the coagulation of grains at far lower cost. Given an initial grain size distribution, the state of the distribution at time t is solely determined by the value of a single variable integrated along the trajectory, independently of the specific path taken by the grains. Although this method cannot account for processes other than coagulation, it is mathematically exact, fast, inexpensive, and can be used to evaluate the effect of grain coagulation in most astrophysical contexts. It is applicable to all coagulation kernels in which local physical conditions and grain properties can be separated. We also describe another method for calculating the average electric charge of grains and the density of ions and electrons in environments that are shielded from radiation fields, given the density and temperature of the gas, the cosmic-ray ionization rate, and the average mass of the ions. The equations we provide are fast to integrate numerically and can be used in multidimensional numerical simulations to self-consistently calculate on the fly the local resistivities that are required to model nonideal magnetohydrodynamics.

Impact of Dust Size Distribution Including Large Dust Grains on Magnetic Resistivity: An Analytical Approach

“…Recently, Marchand et al (2021) proposed a similar method that also can be used to calculate magnetic resistivity analytically. Our numerical tests showed that our method seems to be more robust and applicable over a wide parameter range (e.g., when the dust grains are highly depleted).…”

“…When we implemented and tested their algorithm, we found that it did not converge in the limit where the total dust charge goes to zero. This is because their method uses ψ as the basic variable and use equations (A.3) and (A.4) of Marchand et al (2021) to determine ò and n i . However, their equation (A.4) becomes singular when ò = 1 and á ñ = Z 0 ¯, i.e., gas-phase recombination determines the ionization state.…”

Universal protoplanetary disk size under complete non-ideal magnetohydrodynamics: The interplay between ion-neutral friction, Hall effect, and the Ohmic dissipation

“…Applying n M /n e ≈ 107 (Marchand et al 2021) and σ coll w M ≈ 2.4 × 10 −9 (cm 3 s −1 )C s (km s −1 ) 0.6 ≈ 9.1 10 −10 (Pinto & Galli 2008), we obtain k ≈ 5.2 × 10 13 cm −3 G −1 , which is not far from the value measured directly from simulations.…”

“…where number density ratio between ions and electrons n M /n e ≈ 107 is applied (Marchand et al 2021). Since the Hall effect drifts the magnetic field outward, the equilibrium radius shrinks as the local value of B z decreases.…”

Fast methods for tracking grain coagulation and ionization

“…We detail an extension of the ionization model of Marchand et al (2021) to include the thermal ionization of one gas species. It is possible to increase the number of ionized species by adding their contribution in the same manner, at the price of a higher numerical cost.…”