### Abstract

The problem of the formation and contraction of fragments (or cores) in magnetically supported parent molecular clouds was formulated in a previous paper. Three dimensionless free parameters appear in the evolution equations: the initial ratio of the free-fall and neutral-ion collision times (in the uniform reference state), v_{ff.0}, the exponent k in the relation between the ion and neutral densities n_{i} ∝ n^{k}_{n}, and the initial ratio of the magnetic and thermal pressures, α_{0}. The initial central mass-to-flux ratio in units of the critical value for gravitational collapse, μ_{0}, enters through the initial conditions. We follow both the quasistatic and dynamic phases of contraction and demonstrate that ambipolar diffusion leads to self-initiated protostar formation ("quasistatic" meaning motion with negligible acceleration). A typical cloud core forms and contracts quasistatically on the flux-loss time scale until the central mass-to-flux ratio (dM/dΦ_{B})_{c} exceeds the critical value. During quasistatic contraction, the magnetic field lines are essentially "held in place" as the neutrals contract through them, and the field strength increases by less than a factor of 2. Despite subsequent dynamic contraction perpendicular to magnetic field lines, thermal pressure continues to balance gravity along field lines, hereby enforcing quasistatic contraction in this direction. We follow the contraction until the central density n_{c} increases by a factor of 10^{6} (typically from 3 × 10^{2} to 3 × 10^{8} cm^{-3}). The envelope remains magnetically supported. The results from our parameter study show that decreasing v_{ff.0} speeds up ambipolar diffusion shortens the quasistatic phase of contraction, and causes (dM/dΦ_{B})_{c} to increase by a greater amount above the critical value. The enhancement of the central magnetic field B_{c}, however, is not sensitive to the value of v_{ff.0}. A smaller k leads to progressively more rapid ambipolar diffusion as n_{c} increases. Reducing μ_{0} lengthens the duration of the quasistatic phase and results in a larger reduction of a core's magnetic flux, but the dynamic phase of contraction is independent of μ_{0}. The value of (dM/dΦ_{B})_{c} in our models is initially 1.9-16.3 times smaller than the critical value, but increases (because of ambipolar diffusion) by a factor of 10-50 by the time n_{c} has increased by a factor ≈10^{6}. The value of α_{0} mainly affects the relaxation of clouds from their initial states into the corresponding equilibrium states under flux-freezing, in which α is related to μ_{0} by α_{c},_{eq}μ^{2}_{0} ≈ constant.

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

Pages (from-to) | 680-700 |

Number of pages | 21 |

Journal | Astrophysical Journal |

Volume | 415 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 1993 |

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### Keywords

- Diffusion
- Hydromagnetics
- ISM: clouds
- ISM: magnetic fields
- Plasmas
- Stars: formation

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

**Ambipolar diffusion and star formation : Formation and contraction of axisymmetric cloud cores. II. Results.** / Fiedler, Robert A.; Mouschovias, Telemachos Ch.

Research output: Contribution to journal › Article

*Astrophysical Journal*, vol. 415, no. 2, pp. 680-700. https://doi.org/10.1086/173193

}

TY - JOUR

T1 - Ambipolar diffusion and star formation

T2 - Formation and contraction of axisymmetric cloud cores. II. Results

AU - Fiedler, Robert A.

AU - Mouschovias, Telemachos Ch

PY - 1993/10/1

Y1 - 1993/10/1

N2 - The problem of the formation and contraction of fragments (or cores) in magnetically supported parent molecular clouds was formulated in a previous paper. Three dimensionless free parameters appear in the evolution equations: the initial ratio of the free-fall and neutral-ion collision times (in the uniform reference state), vff.0, the exponent k in the relation between the ion and neutral densities ni ∝ nkn, and the initial ratio of the magnetic and thermal pressures, α0. The initial central mass-to-flux ratio in units of the critical value for gravitational collapse, μ0, enters through the initial conditions. We follow both the quasistatic and dynamic phases of contraction and demonstrate that ambipolar diffusion leads to self-initiated protostar formation ("quasistatic" meaning motion with negligible acceleration). A typical cloud core forms and contracts quasistatically on the flux-loss time scale until the central mass-to-flux ratio (dM/dΦB)c exceeds the critical value. During quasistatic contraction, the magnetic field lines are essentially "held in place" as the neutrals contract through them, and the field strength increases by less than a factor of 2. Despite subsequent dynamic contraction perpendicular to magnetic field lines, thermal pressure continues to balance gravity along field lines, hereby enforcing quasistatic contraction in this direction. We follow the contraction until the central density nc increases by a factor of 106 (typically from 3 × 102 to 3 × 108 cm-3). The envelope remains magnetically supported. The results from our parameter study show that decreasing vff.0 speeds up ambipolar diffusion shortens the quasistatic phase of contraction, and causes (dM/dΦB)c to increase by a greater amount above the critical value. The enhancement of the central magnetic field Bc, however, is not sensitive to the value of vff.0. A smaller k leads to progressively more rapid ambipolar diffusion as nc increases. Reducing μ0 lengthens the duration of the quasistatic phase and results in a larger reduction of a core's magnetic flux, but the dynamic phase of contraction is independent of μ0. The value of (dM/dΦB)c in our models is initially 1.9-16.3 times smaller than the critical value, but increases (because of ambipolar diffusion) by a factor of 10-50 by the time nc has increased by a factor ≈106. The value of α0 mainly affects the relaxation of clouds from their initial states into the corresponding equilibrium states under flux-freezing, in which α is related to μ0 by αc,eqμ20 ≈ constant.

AB - The problem of the formation and contraction of fragments (or cores) in magnetically supported parent molecular clouds was formulated in a previous paper. Three dimensionless free parameters appear in the evolution equations: the initial ratio of the free-fall and neutral-ion collision times (in the uniform reference state), vff.0, the exponent k in the relation between the ion and neutral densities ni ∝ nkn, and the initial ratio of the magnetic and thermal pressures, α0. The initial central mass-to-flux ratio in units of the critical value for gravitational collapse, μ0, enters through the initial conditions. We follow both the quasistatic and dynamic phases of contraction and demonstrate that ambipolar diffusion leads to self-initiated protostar formation ("quasistatic" meaning motion with negligible acceleration). A typical cloud core forms and contracts quasistatically on the flux-loss time scale until the central mass-to-flux ratio (dM/dΦB)c exceeds the critical value. During quasistatic contraction, the magnetic field lines are essentially "held in place" as the neutrals contract through them, and the field strength increases by less than a factor of 2. Despite subsequent dynamic contraction perpendicular to magnetic field lines, thermal pressure continues to balance gravity along field lines, hereby enforcing quasistatic contraction in this direction. We follow the contraction until the central density nc increases by a factor of 106 (typically from 3 × 102 to 3 × 108 cm-3). The envelope remains magnetically supported. The results from our parameter study show that decreasing vff.0 speeds up ambipolar diffusion shortens the quasistatic phase of contraction, and causes (dM/dΦB)c to increase by a greater amount above the critical value. The enhancement of the central magnetic field Bc, however, is not sensitive to the value of vff.0. A smaller k leads to progressively more rapid ambipolar diffusion as nc increases. Reducing μ0 lengthens the duration of the quasistatic phase and results in a larger reduction of a core's magnetic flux, but the dynamic phase of contraction is independent of μ0. The value of (dM/dΦB)c in our models is initially 1.9-16.3 times smaller than the critical value, but increases (because of ambipolar diffusion) by a factor of 10-50 by the time nc has increased by a factor ≈106. The value of α0 mainly affects the relaxation of clouds from their initial states into the corresponding equilibrium states under flux-freezing, in which α is related to μ0 by αc,eqμ20 ≈ constant.

KW - Diffusion

KW - Hydromagnetics

KW - ISM: clouds

KW - ISM: magnetic fields

KW - Plasmas

KW - Stars: formation

UR - http://www.scopus.com/inward/record.url?scp=12044257461&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12044257461&partnerID=8YFLogxK

U2 - 10.1086/173193

DO - 10.1086/173193

M3 - Article

AN - SCOPUS:12044257461

VL - 415

SP - 680

EP - 700

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

ER -