Density, Velocity, and Magnetic Field Structure in Turbulent Molecular Cloud Models

We use three-dimensional (3D) numerical magnetohydrodynamic simulations to follow the evolution of cold, turbulent, gaseous systems with parameters chosen to represent conditions in giant molecular clouds (GMCs). We present results of three model cloud simulations in which the mean magnetic field strength is varied (B0 = 1.4-14 ?G for GMC parameters), but an identical initial turbulent velocity field is introduced. We describe the energy evolution, showing that (1) turbulence decays rapidly, with the turbulent energy reduced by a factor 2 after 0.4-0.8 flow crossing times (~2-4 Myr for GMC parameters), and (2) the magnetically supercritical cloud models gravitationally collapse after time ?6 Myr, while the magnetically subcritical cloud does not collapse. We compare density, velocity, and magnetic field structure in three sets of model snapshots with matched values of the Mach number ? 9,7,5. We show that the distributions of volume density and column density are both approximately log-normal, with mean mass-weighted volume density a factor 3-6 times the unperturbed value, but mean mass-weighted column density only a factor 1.1-1.4 times the unperturbed value. We introduce a spatial binning algorithm to investigate the dependence of kinetic quantities on spatial scale for regions of column density contrast (ROCs) on the plane of the sky. We show that the average velocity dispersion for the distribution of ROCs is only weakly correlated with scale, similar to mean size-line width distributions for clumps within GMCs. We find that ROCs are often superpositions of spatially unconnected regions that cannot easily be separated using velocity information; we argue that the same difficulty may affect observed GMC clumps. We suggest that it may be possible to deduce the mean 3D size-line width relation using the lower envelope of the 2D size-line width distribution. We analyze magnetic field structure and show that in the high-density regime n 103 cm-3, total magnetic field strengths increase with density with logarithmic slope ~1/3-2/3. We find that mean line-of-sight magnetic field strengths may vary widely across a projected cloud and are not positively correlated with column density. We compute simulated interstellar polarization maps at varying observer orientations and determine that the Chandrasekhar-Fermi formula multiplied by a factor ~0.5 yields a good estimate of the plane-of sky magnetic field strength, provided the dispersion in polarization angles is 25?.

[1]  A Search for Larson-type Relations in Numerical Simulations of the ISM: Evidence for Nonconstant Column Densities , 1996, astro-ph/9607175.

[2]  R. Wilson,et al.  Filamentary structure in the Orion molecular cloud , 1986 .

[3]  B. Elmegreen Cloud/Intercloud Structure from Nonlinear Magnetic Waves , 1997 .

[4]  J. Alves,et al.  Dust Extinction and Molecular Cloud Structure: L977 , 1998, astro-ph/9805141.

[5]  R. Larson Turbulence and star formation in molecular clouds , 1980 .

[6]  A. Wolfendale,et al.  The size-line width relation and the mass of molecular hydrogen , 1990 .

[7]  M. Heyer,et al.  Application of Principal Component Analysis to Large-Scale Spectral Line Imaging Studies of the Interstellar Medium , 1997 .

[8]  F. Adams,et al.  Star Formation in Molecular Clouds: Observation and Theory , 1987 .

[9]  C. Lada,et al.  Book-Review - the Physics of Star Formation and Early Stellar Evolution , 1991 .

[10]  E. Zweibel,et al.  On the virial theorem for turbulent molecular clouds , 1992 .

[11]  A. Goodman,et al.  On the dispersion in direction of interstellar polarization , 1991 .

[12]  A. R. Rivolo,et al.  Mass, luminosity, and line width relations of Galactic molecular clouds , 1987 .

[13]  B. Elmegreen Star Formation in a Crossing Time , 1999, astro-ph/9911172.

[14]  James M. Stone,et al.  MOCCT: A numerical technique for astrophysical MHD , 1995 .

[15]  M. Norman,et al.  ZEUS-2D : a radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. II : The magnetohydrodynamic algorithms and tests , 1992 .

[16]  J. Alves,et al.  Infrared Extinction and the Structure of the IC 5146 Dark Cloud , 1999 .

[17]  A. Boss,et al.  Protostars and Planets VI , 2000 .

[18]  Andreas Burkert,et al.  Kinetic Energy Decay Rates of Supersonic and Super-Alfvénic Turbulence in Star-Forming Clouds , 1998 .

[19]  M. Norman,et al.  ZEUS-2D: A radiation magnetohydrodynamics code for astrophysical flows in two space dimensions. I - The hydrodynamic algorithms and tests. II - The magnetohydrodynamic algorithms and tests , 1992 .

[20]  E. Vázquez-Semadeni Hierarchical Structure in Nearly Pressureless Flows as a Consequence of Self-similar Statistics , 1994 .

[21]  James M. Stone,et al.  Kinetic and Structural Evolution of Self-gravitating, Magnetized Clouds: 2.5-Dimensional Simulations of Decaying Turbulence , 1998, astro-ph/9810321.

[22]  Leo Blitz,et al.  DETERMINING STRUCTURE IN MOLECULAR CLOUDS , 1994 .

[23]  Neal J. Evans Physical conditions in regions of star formation , 1999 .

[24]  L. Hartmann,et al.  Turbulent Flow-driven Molecular Cloud Formation: A Solution to the Post-T Tauri Problem? , 1999, astro-ph/9907053.

[25]  The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds , 1998, astro-ph/9809177.

[26]  Elizabeth A. Lada,et al.  Dust Extinction and Molecular Gas in the Dark Cloud IC 5146 , 1994 .

[27]  J. Scalo,et al.  Clouds as Turbulent Density Fluctuations: Implications for Pressure Confinement and Spectral Line Data Interpretation , 1998, astro-ph/9806059.

[28]  E. Ostriker,et al.  Can Nonlinear Hydromagnetic Waves Support a Self-gravitating Cloud? , 1996, astro-ph/9601095.

[29]  J. Stutzki,et al.  High spatial resolution isotopic CO and CS observations of M17 SW - The clumpy structure of the molecular cloud core , 1989 .

[30]  P. Padoan,et al.  Supersonic Turbulence in the Interstellar Medium: Stellar Extinction Determinations as Probes of the Structure and Dynamics of Dark Clouds , 1996, astro-ph/9603061.

[31]  Richard M. Crutcher,et al.  Magnetic Fields in Molecular Clouds: Observations Confront Theory , 1998 .

[32]  A. Pouquet,et al.  A Turbulent Model for the Interstellar Medium. II. Magnetic Fields and Rotation , 1994 .

[33]  R. Klessen,et al.  Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence , 1999, astro-ph/9911068.

[34]  B. Zuckerman,et al.  Radio radiation from interstellar molecules , 1974 .

[35]  T. Passot,et al.  Density probability distribution in one-dimensional polytropic gas dynamics , 1998, physics/9802019.

[36]  P. Padoan,et al.  Interstellar Turbulence: The Density PDFs of Supersonic Random Flows , 1999 .

[37]  P. Padoan,et al.  A Super-Alfvénic Model of Dark Clouds , 1999, astro-ph/9901288.

[38]  W. Roberts,et al.  Ambiguities in the Identification of Giant Molecular Cloud Complexes from Longitude-Velocity Diagrams , 1992 .

[39]  Jonathan P. Williams,et al.  Molecular Clouds Are Not Fractal: A Characteristic Size Scale in Taurus , 1997 .

[40]  E. Ostriker,et al.  Dissipation in Compressible Magnetohydrodynamic Turbulence , 1998, astro-ph/9809357.

[41]  L. Spitzer,et al.  Star formation in magnetic dust clouds , 1956 .

[42]  Enrico Fermi,et al.  Magnetic fields in spiral arms , 1953 .

[43]  Alyssa A. Goodman,et al.  The Spectral Correlation Function: A New Tool for Analyzing Spectral Line Maps , 1999, astro-ph/9903454.

[44]  Jonathan P. Williams,et al.  The Density Structure in the Rosette Molecular Cloud: Signposts of Evolution , 1995 .

[45]  F. Bertoldi,et al.  Pressure-confined clumps in magnetized molecular clouds , 1992 .

[46]  E. Zweibel,et al.  Magnetic field-line tangling and polarization measurements in clumpy molecular gas , 1990 .

[47]  J. Scalo,et al.  On the Probability Density Function of Galactic Gas. I. Numerical Simulations and the Significance of the Polytropic Index , 1997, astro-ph/9710075.

[48]  A. Goodman,et al.  THE MAGNETIC FIELD IN THE OPHIUCHUS DARK CLOUD COMPLEX , 1994 .

[49]  B. Elmegreen Formation and Loss of Hierarchical Structure in Two-dimensional Magnetohydrodynamic Simulations of Wave-driven Turbulence in Interstellar Clouds , 1999, astro-ph/9911156.

[50]  A. Goodman,et al.  Magnetic molecular clouds: indirect evidence for magnetic support and ambipolar diffusion , 1988 .

[51]  J. Hawley,et al.  Simulation of magnetohydrodynamic flows: A Constrained transport method , 1988 .