Fast methods to track grain coagulation and ionization. I. Analytic derivation. (arXiv:2103.00002v1 [astro-ph.GA])
<a href="http://arxiv.org/find/astro-ph/1/au:+Marchand_P/0/1/0/all/0/1">Pierre Marchand</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Guillet_V/0/1/0/all/0/1">Vincent Guillet</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lebreuilly_U/0/1/0/all/0/1">Ugo Lebreuilly</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Low_M/0/1/0/all/0/1">Mordecai-Mark Mac Low</a>
Dust grains play a major role in many astrophysical contexts. They influence
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 implement numerically by
itself, it is difficult to couple it with multi-dimensional hydrodynamics
numerical simulations because of its high computational cost. We propose here a
simple method to track 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 other processes than coagulation, it is
mathematically exact, fast, inexpensive, and can be used to evaluate the impact
of grain coagulation in most astrophysical contexts. Although other processes
modifying the size-distribution, as fragmentation cannot be coupled to this
method, it is applicable to all coagulation kernels in which local physical
conditions and grain properties can be separated. We also describe another
method to calculate the average electric charge of grains and the density of
ions and electrons in environments 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 needed to
model non-ideal magnetohydrodynamics.
Dust grains play a major role in many astrophysical contexts. They influence
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 implement numerically by
itself, it is difficult to couple it with multi-dimensional hydrodynamics
numerical simulations because of its high computational cost. We propose here a
simple method to track 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 other processes than coagulation, it is
mathematically exact, fast, inexpensive, and can be used to evaluate the impact
of grain coagulation in most astrophysical contexts. Although other processes
modifying the size-distribution, as fragmentation cannot be coupled to this
method, it is applicable to all coagulation kernels in which local physical
conditions and grain properties can be separated. We also describe another
method to calculate the average electric charge of grains and the density of
ions and electrons in environments 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 needed to
model non-ideal magnetohydrodynamics.
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