Ambipolar diffusion, cloud cores, and star formation: Two-dimensional, cylindrically symmetric contraction. I. The issues, formulation of the problem, and method of solution

Telemachos Ch Mouschovias, Scott A. Morton

Research output: Contribution to journalArticle

Abstract

The role of ambipolar diffusion in the formation of molecular cloud cores and protostars is examined critically. The origin and physical meaning of a criterion for quasistatic or dynamic core contraction in otherwise magnetically supported clouds is explained briefly on the basis of analytical considerations. The relative magnitude of three natural length scales, which are unavoidably present in (realistic, three-dimensional) molecular clouds, determines the typical mass that can go into a protostar (∼ 1 M). We formulate the problem of the self-initiated contraction (due to ambipolar diffusion) of cylindrically symmetric, self-gravitating, isothermal, magnetic clouds embedded in a medium of constant thermal and magnetic pressures. If it were not for ambipolar diffusion, these model clouds would exist in exact equilibrium states indefinitely. The equations themselves contain three dimensionless free parameters: the ratio αc of magnetic and thermal pressures in the core of the initial equilibrium state; the ratio vff of the initial free-fall and neutral-ion collision times (divided by π1/2) in the core; and the exponent k in the parametrization ni ∝ nnk of the ion density in terms of the neutral density. The boundary conditions introduce, in general, two additional free parameters, namely, the ratio of the initial surface and central neutral densities, and the ratio of the initial surface and central magnetic field strengths. The initial conditions introduce no new free parameters in the problem. In fact, they remove one free parameter if α is taken to be constant in the initial equilibrium state. The numerical method developed to follow the evolution of these model clouds, which involves an adaptive grid, is characterized by a fractional error ≃10-5 in the approximation of the forces everywhere in a model cloud except at the surface, where the error increases to ≃10-2 without degrading the accuracy anywhere else in the interior; a maximum relative error of the implicit time-integrator one to two orders of magnitude smaller than that introduced by spatial discretization; and a numerical diffusion of magnetic flux, introduced by the advection scheme, typically a few ×10-5. The results, including an extensive parameter study, as they relate to the formation of cores and protostars are described in a following paper.

Original languageEnglish (US)
Pages (from-to)296-316
Number of pages21
JournalAstrophysical Journal
Volume371
Issue number1
DOIs
StatePublished - Apr 10 1991

Fingerprint

ambipolar diffusion
contraction
star formation
protostars
formulations
molecular clouds
magnetic clouds
free fall
ion
integrators
advection
numerical method
magnetic flux
field strength
boundary condition
collision
grids
parameter
method
exponents

Keywords

  • Diffusion
  • Hydrodynamics
  • Interstellar: magnetic fields
  • Plasmas
  • Stars: formation
  • Stars: pre-main-sequence

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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title = "Ambipolar diffusion, cloud cores, and star formation: Two-dimensional, cylindrically symmetric contraction. I. The issues, formulation of the problem, and method of solution",
abstract = "The role of ambipolar diffusion in the formation of molecular cloud cores and protostars is examined critically. The origin and physical meaning of a criterion for quasistatic or dynamic core contraction in otherwise magnetically supported clouds is explained briefly on the basis of analytical considerations. The relative magnitude of three natural length scales, which are unavoidably present in (realistic, three-dimensional) molecular clouds, determines the typical mass that can go into a protostar (∼ 1 M⊙). We formulate the problem of the self-initiated contraction (due to ambipolar diffusion) of cylindrically symmetric, self-gravitating, isothermal, magnetic clouds embedded in a medium of constant thermal and magnetic pressures. If it were not for ambipolar diffusion, these model clouds would exist in exact equilibrium states indefinitely. The equations themselves contain three dimensionless free parameters: the ratio αc of magnetic and thermal pressures in the core of the initial equilibrium state; the ratio vff of the initial free-fall and neutral-ion collision times (divided by π1/2) in the core; and the exponent k in the parametrization ni ∝ nnk of the ion density in terms of the neutral density. The boundary conditions introduce, in general, two additional free parameters, namely, the ratio of the initial surface and central neutral densities, and the ratio of the initial surface and central magnetic field strengths. The initial conditions introduce no new free parameters in the problem. In fact, they remove one free parameter if α is taken to be constant in the initial equilibrium state. The numerical method developed to follow the evolution of these model clouds, which involves an adaptive grid, is characterized by a fractional error ≃10-5 in the approximation of the forces everywhere in a model cloud except at the surface, where the error increases to ≃10-2 without degrading the accuracy anywhere else in the interior; a maximum relative error of the implicit time-integrator one to two orders of magnitude smaller than that introduced by spatial discretization; and a numerical diffusion of magnetic flux, introduced by the advection scheme, typically a few ×10-5. The results, including an extensive parameter study, as they relate to the formation of cores and protostars are described in a following paper.",
keywords = "Diffusion, Hydrodynamics, Interstellar: magnetic fields, Plasmas, Stars: formation, Stars: pre-main-sequence",
author = "Mouschovias, {Telemachos Ch} and Morton, {Scott A.}",
year = "1991",
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T1 - Ambipolar diffusion, cloud cores, and star formation

T2 - Two-dimensional, cylindrically symmetric contraction. I. The issues, formulation of the problem, and method of solution

AU - Mouschovias, Telemachos Ch

AU - Morton, Scott A.

PY - 1991/4/10

Y1 - 1991/4/10

N2 - The role of ambipolar diffusion in the formation of molecular cloud cores and protostars is examined critically. The origin and physical meaning of a criterion for quasistatic or dynamic core contraction in otherwise magnetically supported clouds is explained briefly on the basis of analytical considerations. The relative magnitude of three natural length scales, which are unavoidably present in (realistic, three-dimensional) molecular clouds, determines the typical mass that can go into a protostar (∼ 1 M⊙). We formulate the problem of the self-initiated contraction (due to ambipolar diffusion) of cylindrically symmetric, self-gravitating, isothermal, magnetic clouds embedded in a medium of constant thermal and magnetic pressures. If it were not for ambipolar diffusion, these model clouds would exist in exact equilibrium states indefinitely. The equations themselves contain three dimensionless free parameters: the ratio αc of magnetic and thermal pressures in the core of the initial equilibrium state; the ratio vff of the initial free-fall and neutral-ion collision times (divided by π1/2) in the core; and the exponent k in the parametrization ni ∝ nnk of the ion density in terms of the neutral density. The boundary conditions introduce, in general, two additional free parameters, namely, the ratio of the initial surface and central neutral densities, and the ratio of the initial surface and central magnetic field strengths. The initial conditions introduce no new free parameters in the problem. In fact, they remove one free parameter if α is taken to be constant in the initial equilibrium state. The numerical method developed to follow the evolution of these model clouds, which involves an adaptive grid, is characterized by a fractional error ≃10-5 in the approximation of the forces everywhere in a model cloud except at the surface, where the error increases to ≃10-2 without degrading the accuracy anywhere else in the interior; a maximum relative error of the implicit time-integrator one to two orders of magnitude smaller than that introduced by spatial discretization; and a numerical diffusion of magnetic flux, introduced by the advection scheme, typically a few ×10-5. The results, including an extensive parameter study, as they relate to the formation of cores and protostars are described in a following paper.

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