Magnetic braking, ambipolar diffusion, and the formation of cloud cores and protostars. I. Axisymmetric solutions

Research output: Contribution to journalArticle

Abstract

We formulate and solve the problem of ambipolar-diffusion and/or magnetic-braking initiated formation and contraction of protostellar cores in self-gravitating, magnetically supported, rotating, isothermal model molecular clouds. If it were not for ambipolar diffusion and magnetic braking, the model clouds, which are oblate, aligned rotators (J ∥ B) initially in exact equilibrium states (with gravitational and external-pressure forces balanced by magnetic, thermal-pressure, and centrifugal forces), would undergo no evolution at all. We follow the evolution up to six orders of magnitude enhancement of the central density (e.g., from 3 × 103 to 3 × 109 cm-3). A thermally and magnetically supercritical core forms because of ambipolar diffusion. It is characterized by a compact, uniform-density central region, shrinking both in size and mass, surrounded by a "tail" of matter left behind, in which a near power-law density profile is established, as found earlier by Mouschovias et al. in the absence of magnetic braking. The envelope remains well supported by magnetic forces. Magnetic braking leads to a very rapid decrease of the specific angular momentum everywhere in a model cloud, so that centrifugal forces play a negligible role in the formation and evolution of protostellar cores, at least up to central densities of ∼3 × 109 cm-3. Typically, the evolution of the angular velocity Ωc of the compact, uniform-density central part of the core exhibits three distinct phases: (1) an exponential decrease of Ωc(t) due to effective magnetic braking, before ambipolar diffusion induces any significant redistribution of mass in the central flux tubes; (2) a constant-Ωc phase, which lasts until a magnetically supercritical core forms in the subcritical cloud; and (3) a constant angular momentum (J) phase, coinciding with the rapid contraction phase of the supercritical core. We predict the typical structure, mass, size, magnetic field strength, angular momentum, etc., of protostellar cores; for example, by the end of a typical run, a core's specific angular momentum (J/M) is reduced by two orders of magnitude, to a value comparable to that of wide binary systems. Moreover we find that, even in the absence of magnetic braking, the gravitational field of the nonhomologously contracting, oblate central region increases just as rapidly as the centrifugal acceleration (∝r-3), so that centrifugal forces do not become important during these stages of evolution.

Original languageEnglish (US)
Pages (from-to)720-741
Number of pages22
JournalAstrophysical Journal
Volume432
Issue number2
StatePublished - Sep 10 1994

Fingerprint

ambipolar diffusion
braking
protostars
angular momentum
centrifugal force
contraction
power law
magnetic field
angular velocity
molecular clouds
gravitational fields
field strength
envelopes
tubes
augmentation
profiles

Keywords

  • Diffusion
  • ISM: magnetic fields
  • MHD
  • Stars: formation
  • Stars: pre-main-sequence
  • Stars: rotation

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Magnetic braking, ambipolar diffusion, and the formation of cloud cores and protostars. I. Axisymmetric solutions. / Basu, Shantanu; Mouschovias, Telemachos Ch.

In: Astrophysical Journal, Vol. 432, No. 2, 10.09.1994, p. 720-741.

Research output: Contribution to journalArticle

@article{671fefb845324b619daa2a025f8cbb67,
title = "Magnetic braking, ambipolar diffusion, and the formation of cloud cores and protostars. I. Axisymmetric solutions",
abstract = "We formulate and solve the problem of ambipolar-diffusion and/or magnetic-braking initiated formation and contraction of protostellar cores in self-gravitating, magnetically supported, rotating, isothermal model molecular clouds. If it were not for ambipolar diffusion and magnetic braking, the model clouds, which are oblate, aligned rotators (J ∥ B) initially in exact equilibrium states (with gravitational and external-pressure forces balanced by magnetic, thermal-pressure, and centrifugal forces), would undergo no evolution at all. We follow the evolution up to six orders of magnitude enhancement of the central density (e.g., from 3 × 103 to 3 × 109 cm-3). A thermally and magnetically supercritical core forms because of ambipolar diffusion. It is characterized by a compact, uniform-density central region, shrinking both in size and mass, surrounded by a {"}tail{"} of matter left behind, in which a near power-law density profile is established, as found earlier by Mouschovias et al. in the absence of magnetic braking. The envelope remains well supported by magnetic forces. Magnetic braking leads to a very rapid decrease of the specific angular momentum everywhere in a model cloud, so that centrifugal forces play a negligible role in the formation and evolution of protostellar cores, at least up to central densities of ∼3 × 109 cm-3. Typically, the evolution of the angular velocity Ωc of the compact, uniform-density central part of the core exhibits three distinct phases: (1) an exponential decrease of Ωc(t) due to effective magnetic braking, before ambipolar diffusion induces any significant redistribution of mass in the central flux tubes; (2) a constant-Ωc phase, which lasts until a magnetically supercritical core forms in the subcritical cloud; and (3) a constant angular momentum (J) phase, coinciding with the rapid contraction phase of the supercritical core. We predict the typical structure, mass, size, magnetic field strength, angular momentum, etc., of protostellar cores; for example, by the end of a typical run, a core's specific angular momentum (J/M) is reduced by two orders of magnitude, to a value comparable to that of wide binary systems. Moreover we find that, even in the absence of magnetic braking, the gravitational field of the nonhomologously contracting, oblate central region increases just as rapidly as the centrifugal acceleration (∝r-3), so that centrifugal forces do not become important during these stages of evolution.",
keywords = "Diffusion, ISM: magnetic fields, MHD, Stars: formation, Stars: pre-main-sequence, Stars: rotation",
author = "Shantanu Basu and Mouschovias, {Telemachos Ch}",
year = "1994",
month = "9",
day = "10",
language = "English (US)",
volume = "432",
pages = "720--741",
journal = "Astrophysical Journal",
issn = "0004-637X",
publisher = "IOP Publishing Ltd.",
number = "2",

}

TY - JOUR

T1 - Magnetic braking, ambipolar diffusion, and the formation of cloud cores and protostars. I. Axisymmetric solutions

AU - Basu, Shantanu

AU - Mouschovias, Telemachos Ch

PY - 1994/9/10

Y1 - 1994/9/10

N2 - We formulate and solve the problem of ambipolar-diffusion and/or magnetic-braking initiated formation and contraction of protostellar cores in self-gravitating, magnetically supported, rotating, isothermal model molecular clouds. If it were not for ambipolar diffusion and magnetic braking, the model clouds, which are oblate, aligned rotators (J ∥ B) initially in exact equilibrium states (with gravitational and external-pressure forces balanced by magnetic, thermal-pressure, and centrifugal forces), would undergo no evolution at all. We follow the evolution up to six orders of magnitude enhancement of the central density (e.g., from 3 × 103 to 3 × 109 cm-3). A thermally and magnetically supercritical core forms because of ambipolar diffusion. It is characterized by a compact, uniform-density central region, shrinking both in size and mass, surrounded by a "tail" of matter left behind, in which a near power-law density profile is established, as found earlier by Mouschovias et al. in the absence of magnetic braking. The envelope remains well supported by magnetic forces. Magnetic braking leads to a very rapid decrease of the specific angular momentum everywhere in a model cloud, so that centrifugal forces play a negligible role in the formation and evolution of protostellar cores, at least up to central densities of ∼3 × 109 cm-3. Typically, the evolution of the angular velocity Ωc of the compact, uniform-density central part of the core exhibits three distinct phases: (1) an exponential decrease of Ωc(t) due to effective magnetic braking, before ambipolar diffusion induces any significant redistribution of mass in the central flux tubes; (2) a constant-Ωc phase, which lasts until a magnetically supercritical core forms in the subcritical cloud; and (3) a constant angular momentum (J) phase, coinciding with the rapid contraction phase of the supercritical core. We predict the typical structure, mass, size, magnetic field strength, angular momentum, etc., of protostellar cores; for example, by the end of a typical run, a core's specific angular momentum (J/M) is reduced by two orders of magnitude, to a value comparable to that of wide binary systems. Moreover we find that, even in the absence of magnetic braking, the gravitational field of the nonhomologously contracting, oblate central region increases just as rapidly as the centrifugal acceleration (∝r-3), so that centrifugal forces do not become important during these stages of evolution.

AB - We formulate and solve the problem of ambipolar-diffusion and/or magnetic-braking initiated formation and contraction of protostellar cores in self-gravitating, magnetically supported, rotating, isothermal model molecular clouds. If it were not for ambipolar diffusion and magnetic braking, the model clouds, which are oblate, aligned rotators (J ∥ B) initially in exact equilibrium states (with gravitational and external-pressure forces balanced by magnetic, thermal-pressure, and centrifugal forces), would undergo no evolution at all. We follow the evolution up to six orders of magnitude enhancement of the central density (e.g., from 3 × 103 to 3 × 109 cm-3). A thermally and magnetically supercritical core forms because of ambipolar diffusion. It is characterized by a compact, uniform-density central region, shrinking both in size and mass, surrounded by a "tail" of matter left behind, in which a near power-law density profile is established, as found earlier by Mouschovias et al. in the absence of magnetic braking. The envelope remains well supported by magnetic forces. Magnetic braking leads to a very rapid decrease of the specific angular momentum everywhere in a model cloud, so that centrifugal forces play a negligible role in the formation and evolution of protostellar cores, at least up to central densities of ∼3 × 109 cm-3. Typically, the evolution of the angular velocity Ωc of the compact, uniform-density central part of the core exhibits three distinct phases: (1) an exponential decrease of Ωc(t) due to effective magnetic braking, before ambipolar diffusion induces any significant redistribution of mass in the central flux tubes; (2) a constant-Ωc phase, which lasts until a magnetically supercritical core forms in the subcritical cloud; and (3) a constant angular momentum (J) phase, coinciding with the rapid contraction phase of the supercritical core. We predict the typical structure, mass, size, magnetic field strength, angular momentum, etc., of protostellar cores; for example, by the end of a typical run, a core's specific angular momentum (J/M) is reduced by two orders of magnitude, to a value comparable to that of wide binary systems. Moreover we find that, even in the absence of magnetic braking, the gravitational field of the nonhomologously contracting, oblate central region increases just as rapidly as the centrifugal acceleration (∝r-3), so that centrifugal forces do not become important during these stages of evolution.

KW - Diffusion

KW - ISM: magnetic fields

KW - MHD

KW - Stars: formation

KW - Stars: pre-main-sequence

KW - Stars: rotation

UR - http://www.scopus.com/inward/record.url?scp=12044251203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12044251203&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:12044251203

VL - 432

SP - 720

EP - 741

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

ER -