### Abstract

The problem of the self-initiated (due to ambipolar diffusion) formation and contraction of protostellar fragments in model molecular clouds was formulated in a previous paper in axisymmetric geometry, taking advantage of a recent result by Fiedler and Mouschovias; namely, that balance of forces along magnetic field lines is rapidly established and maintained even during dynamic contraction (i.e., collapse) perpendicular to the field lines, at least up to central densities ≃3 × 10^{9} cm^{-3}. We describe a method for solving the reduced, multifluid, nonlinear, magnetohydrodynamic equations that govern the time evolution of such model clouds; algebraic equations for the equilibrium abundances of charged species are solved at each time step. The method consists of an implicit time integrator; an advective difference scheme that possesses the transportive property; a second-order difference approximation of forces inside a cell; an integral approximation of the gravitational and magnetic fields; and an adaptive mesh capable of reliably following the formation and evolution of cloud cores and of resolving length scales smaller than ≃10 AU at densities ≃10^{9} cm^{-3} with only about 100 points to cover the radial extent (typically ≃4.3 pc) of the entire cloud. The accuracy of the method is discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 561-569 |

Number of pages | 9 |

Journal | Astrophysical Journal |

Volume | 421 |

Issue number | 2 |

State | Published - Feb 1 1994 |

### Fingerprint

### Keywords

- Diffusion
- ISM: magnetic fields
- MHD
- Methods: numerical
- Plasmas
- Stars: formation

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*421*(2), 561-569.

**Ambipolar diffusion, interstellar dust, and the formation of cloud cores and protostars. II. Numerical method of solution.** / Morton, Scott A.; Mouschovias, Telemachos Ch; Ciolek, Glenn E.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 421, no. 2, pp. 561-569.

}

TY - JOUR

T1 - Ambipolar diffusion, interstellar dust, and the formation of cloud cores and protostars. II. Numerical method of solution

AU - Morton, Scott A.

AU - Mouschovias, Telemachos Ch

AU - Ciolek, Glenn E.

PY - 1994/2/1

Y1 - 1994/2/1

N2 - The problem of the self-initiated (due to ambipolar diffusion) formation and contraction of protostellar fragments in model molecular clouds was formulated in a previous paper in axisymmetric geometry, taking advantage of a recent result by Fiedler and Mouschovias; namely, that balance of forces along magnetic field lines is rapidly established and maintained even during dynamic contraction (i.e., collapse) perpendicular to the field lines, at least up to central densities ≃3 × 109 cm-3. We describe a method for solving the reduced, multifluid, nonlinear, magnetohydrodynamic equations that govern the time evolution of such model clouds; algebraic equations for the equilibrium abundances of charged species are solved at each time step. The method consists of an implicit time integrator; an advective difference scheme that possesses the transportive property; a second-order difference approximation of forces inside a cell; an integral approximation of the gravitational and magnetic fields; and an adaptive mesh capable of reliably following the formation and evolution of cloud cores and of resolving length scales smaller than ≃10 AU at densities ≃109 cm-3 with only about 100 points to cover the radial extent (typically ≃4.3 pc) of the entire cloud. The accuracy of the method is discussed.

AB - The problem of the self-initiated (due to ambipolar diffusion) formation and contraction of protostellar fragments in model molecular clouds was formulated in a previous paper in axisymmetric geometry, taking advantage of a recent result by Fiedler and Mouschovias; namely, that balance of forces along magnetic field lines is rapidly established and maintained even during dynamic contraction (i.e., collapse) perpendicular to the field lines, at least up to central densities ≃3 × 109 cm-3. We describe a method for solving the reduced, multifluid, nonlinear, magnetohydrodynamic equations that govern the time evolution of such model clouds; algebraic equations for the equilibrium abundances of charged species are solved at each time step. The method consists of an implicit time integrator; an advective difference scheme that possesses the transportive property; a second-order difference approximation of forces inside a cell; an integral approximation of the gravitational and magnetic fields; and an adaptive mesh capable of reliably following the formation and evolution of cloud cores and of resolving length scales smaller than ≃10 AU at densities ≃109 cm-3 with only about 100 points to cover the radial extent (typically ≃4.3 pc) of the entire cloud. The accuracy of the method is discussed.

KW - Diffusion

KW - ISM: magnetic fields

KW - MHD

KW - Methods: numerical

KW - Plasmas

KW - Stars: formation

UR - http://www.scopus.com/inward/record.url?scp=12044250469&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12044250469&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:12044250469

VL - 421

SP - 561

EP - 569

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

ER -