Gravo-Turbulence

The goal is to study how different initial conditions lead to a state of gravitational collapse and characterize the turbulence and to either back-out how viable formation mechanisms for MC's or determine that IC's are not important to MC evolution.

Possible different IC's to use:

• Pure density perturbations (with either an Isothermal eq of state - or IICooling to trigger thermal instabilities)
• Initial solenoidal velocity fields (virial equilibrium)
• Compressive flows (2 finite streams)?
• Magnetically critical clouds

Density Perturbations

Goal is to put a cloud with random perturbations following a given power spectra P_\xi(k)=Ak^\beta for k_{\min} <= k <= k_{\max} where \xi=\log(\rho). The perturbations will be windowed on a region with a finite radius embedded in a much lower density region. Since \int{P_\xi(k)dk} = \int{\hat{\xi}(k)k^2dk} we must have \hat{\xi}(k) \propto k^\alpha where \alpha = \beta-2

Initially I tried a somewhat flat spectra \alpha=0 in 2D from k_min=4 to kmax=48 or from 6 pc to .5 pc. This actually corresponds to a \beta=1 and led to higher power at shorter wavelengths. As a result, the local density enhancements had typical size scales of .5 pc (8 cells) corresponding to k=k_{\max} .

The clump density was 400 and the temperature was 10K giving an overall Jeans length of 1.1 pc and free fall time of 1.7 Myr.

Most of these had densities of at least 800 (twice the mean) with several having densities of 1600 and a few with densities of 3200. The ones with a density of 800 would be stable to collapse and those with a density of 1600 have Jeans lengths of .26 pc and could potentially collapse - although the timescales would be similar to the timescales for the global collapse. This is in fact what we see… Two particles form before the entire thing collapses and then forms a binary system with periodic ejections of material. Not sure if this is a protection issue, or material being slingshotted from the secondary. Eventually the particles become unbound and begin to seemingly accelerate upwards. This may be related to the way periodic BC's handle self gravity (which won't be a problem in 3D), or may be related to the particle kick #157.

Below is the initial density perturbation and here is the movie​

So i modified the mean density to be 10, set \alpha=-2 so \beta-1 and strengthened the perturbation. Below is the initial density perturbation and here is the movie​

In all of these, there was initial pressure equilibrium (so different temperatues), although I was using a gamma=1.001 which assumes an isothermal gas. Consider what happens when a gas at a density of 1 and a temperature of 100 K mixes with a gas at a density of 100 and a temperature of 1 K.

The new density is \rho=100+1=101

The new energy is E=10^5+10^5=2\times 10^5

The new pressure is P=2\times 10^2

And the new temperature is T=200/101 \approx 2

So the dense gas at 100 K is instantly heated to 2 K and the equation of state is violated

If instead the gas is at the same temperature everywhere, then initial differences in density will cause expansion

movie​

An alternative is to use the IICooling and to start with a much larger domain at a lower density with a small perturbation that will cause it to self-consistently develop large density perturbations.

Fixed Parameters
rho	10 particles/cc
T	160 K
cs	1.02 km/s
tff	11.2 Myr
LJ	30 pc

movie​

Here is another movie of density that zooms in as the cloud collapses. A few bugs were fixed and phi-gradient refinement was used and there is no longer an explosion…

movie​

Velocity Perturbations

Virial equilibrium requires 2T=V where V=\frac{3GM^2}{5R}

Or in the case of 2D V=\frac{GM}{2}(\log(R)-\frac{1}{4})

If the kinetic energy is put into solenoidal motions with a spectral index \alpha = -1 so that \hat{v}(k)\propto k^{\alpha}, then energy dissipates fairly quickly and the whole thing collapses

movie​

And here is another movie with phi-gradient refinement and with a steeper initial velocity profile \hat{v}(k)\propto k^{-3/2} so that E_{1D}(k) \propto k^{-2}

movie​

And here is a movie showing cloud temperature early on. You can see the dense filaments cool to 10K.

References

Collapse

• ​Hunter 1962 The Instability of the Collapse of a Self-Gravitating Gas Cloud.
• ​Lin et al 1965 The Gravitational Collapse of a Uniform Spheroid.
• ​Larson 1969 Numerical calculations of the dynamics of collapsing proto-star
• ​Penston 1969 Dynamics of self-gravitating gaseous spheres-II. Collapses of gas spheres with cooling and the behaviour of polytropic gas spheres
• ​Penston 1969 Dynamics of self-gravitating gaseous spheres-III. Analytical results in the free-fall of isothermal cases
• ​Shu 1977 Self-similar collapse of isothermal spheres and star formation
• ​Hunter 1977 The collapse of unstable isothermal spheres
• ​Tereby, Shu, & Cassen 1984 The collapse of the cores of slowly rotating isothermal clouds
• ​Foster & Chevalier 1993 Gravitational Collapse of an Isothermal Sphere
• ​Hartmann et al 1994 Protostellar collapse in a self-gravitating sheet

Chronologically

• ​Hunter 1962 The Instability of the Collapse of a Self-Gravitating Gas Cloud.
• ​Lin et al 1965 The Gravitational Collapse of a Uniform Spheroid.
• ​Strittmatter 1966 Gravitational collapse in the presence of a magnetic field
• ​Larson 1969 Numerical calculations of the dynamics of collapsing proto-star
• ​Penston 1969 Dynamics of self-gravitating gaseous spheres-II. Collapses of gas spheres with cooling and the behaviour of polytropic gas spheres
• ​Penston 1969 Dynamics of self-gravitating gaseous spheres-III. Analytical results in the free-fall of isothermal cases
• ​Low & Lyndin-Bell The minimum Jeans mass or when fragmentation must stop
• ​Mouschovias 1976 Nonhomologous contraction and equilibria of self-gravitating, magnetic interstellar clouds embedded in an intercloud medium: Star formation. I Formulation of the problem and method of solution
• ​Mouschovias 1976 Nonhomologous contraction and equilibria of self-gravitating, magnetic interstellar clouds embedded in an intercloud medium: Star formation. II - Results
• ​Mouschovias & Spitzer 1976 Note on the collapse of magnetic interstellar clouds
• ​Woodward 1976 Shock-driven implosion of interstellar gas clouds and star formation
• ​Hunter 1977 The collapse of unstable isothermal spheres
• ​Rees & Ostriker 1977 Cooling, dynamics and fragmentation of massive gas clouds - Clues to the masses and radii of galaxies and clusters
• ​Shu 1977 Self-similar collapse of isothermal spheres and star formation
• ​Silk 1977 On the fragmentation of cosmic gas clouds. II - Opacity-limited star formation
• ​Boss 1980 Protostellar formation in rotating interstellar clouds. I - Numerical methods and tests
• ​Boss 1980 Protostellar formation in rotating interstellar clouds. II - Axially symmetric collapse
• ​Boss 1980 Protostellar formation in rotating interstellar clouds. III - Nonaxisymmetric collapse
• ​Cohn 1980 Late core collapse in star clusters and the gravothermal instability
• ​Goldreich & Weber 1980 Homologously collapsing stellar cores
• ​Larson 1981 Turbulence and star formation in molecular clouds
• ​Boss 1984 Protostellar formation in rotating interstellar clouds. IV Nonisothermal collapse
• ​Fillmore & Goldreich 1984 Self-similar gravitational collapse in an expanding universe
• ​Miyama et al 1984 Criteria for collapse and fragmentation of rotating, isothermal clouds
• ​Tereby, Shu, & Cassen 1984 The collapse of the cores of slowly rotating isothermal clouds
• ​Larson 1985 Cloud fragmentation and stellar masses
• ​Boss 1986 Protostellar formation in rotating interstellar clouds. V - Nonisothermal collapse and fragmentation
• ​Hunter et al 1986 Star formation in colliding gas flows
• ​Bonazzola et al, 1987 Jeans collapse in a turbulent medium
• ​Boss 1987 Protostellar formation in rotating interstellar clouds. VI - Nonuniform initial conditions
• ​Shu, Adams, & Lizano 1987 Star formation in molecular clouds - Observation and theory
• ​Boss 1988 Protostellar formation in rotating interstellar clouds. VII - Opacity and fragmentation
• ​Boss 1989 Protostellar formation in rotating interstellar clouds. VIII - Inner core formation
• ​Shu & Lizano 1989 Molecular cloud cores and bimodal star formation
• ​Mouschovias 1991 Magnetic braking, ambipolar diffusion, cloud cores, and star formation - Natural length scales and protostellar masses
• ​Falgarone 1992 The small-scale density and velocity structure of quiescent molecular clouds
• ​Fiedler & Mouschovias 1992 Ambipolar diffusion and star formation: Formation and contraction of axisymmetric cloud cores. I - Formulation of the problem and method of solution
• ​Boss 1993 Collapse and fragmentation of molecular cloud cores. I - Moderately centrally condensed cores
• ​Fiedler & Mouschovias 1993 Ambipolar Diffusion and Star Formation: Formation and Contraction of Axisymmetric Cloud Cores. II. Results
• ​Foster & Chevalier 1993 Gravitational Collapse of an Isothermal Sphere
• ​Galli & Shu 1993 Collapse of Magnetized Molecular Cloud Cores. I. Semianalytical Solution
• ​Galli & Shu 1993 Collapse of Magnetized Molecular Cloud Cores. II. Numerical Results
• ​Hartmann et al 1994 Protostellar collapse in a self-gravitating sheet
• ​Boss 1995 Collapse and fragmentation of molecular cloud cores. 2: Collapse induced by stellar shock waves
• ​Boss 1995 Collapse and Fragmentation of Molecular Cloud Cores. III. Initial Differential Rotation
• ​Boss 1996 Collapse and Fragmentation of Molecular Cloud Cores. IV. Oblate Clouds and Small Cluster Formation
• ​Gammie 1996 Linear Theory of Magnetized, Viscous, Self-gravitating Gas Disks
• ​Gammie & Ostriker 1996 Can Nonlinear Hydromagnetic Waves Support a Self-gravitating Cloud?
• ​Hartmann et al 1996 Sheet Models of Protostellar Collapse
• ​Boss 1997 Collapse and Fragmentation of Molecular Cloud Cores. V. Loss of Magnetic Field Support
• ​McLaughlin & Pudritz 1997 Gravitational Collapse and Star Formation in Logotropic and Nonisothermal Spheres
• ​Pudritz et al 1997 Collapse and Outflow: Towards an Integrated Theory of Star Formation
• ​Truelove 1997 The Jeans Condition: A New Constraint on Spatial Resolution in Simulations of Isothermal Self-gravitational Hydrodynamics
• ​Bate 1998 Collapse of a Molecular Cloud Core to Stellar Densities: The First Three-dimensional Calculations
• ​Klessen et al 1998 Fragmentation of Molecular Clouds: The Initial Phase of a Stellar Cluster
• ​Masunaga et al. 1998 A Radiation Hydrodynamic Model for Protostellar Collapse. I. The First Collapse
• ​Nakano 1998 Star Formation in Magnetic Clouds
• ​Truelove et al. 1998 Self-gravitational Hydrodynamics with Three-dimensional Adaptive Mesh Refinement: Methodology and Applications to Molecular Cloud Collapse and Fragmentation
• ​Ballesteros-Paredes 1999 Clouds as Turbulent Density Fluctuations: Implications for Pressure Confinement and Spectral Line Data Interpretation
• ​Ballesteros-Paredes 1999 Turbulent Flow-driven Molecular Cloud Formation: A Solution to the Post-T Tauri Problem?
• ​Boss 1999 Collapse and Fragmentation of Molecular Cloud Cores. VI. Slowly Rotating Magnetic Clouds
• ​Ostriker 1999 Kinetic and Structural Evolution of Self-gravitating, Magnetized Clouds: 2.5-dimensional Simulations of Decaying Turbulence
• ​Boss et al 2000 The Jeans Condition and Collapsing Molecular Cloud Cores: Filaments or Binaries?
• ​Heitsch et al 2000 Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence
• ​Hennebelle & Perault 2000 Dynamical condensation in a magnetized and thermally bistable flow. Application to interstellar cirrus
• ​Klessen et al 2000 The Formation of Stellar Clusters: Gaussian Cloud Conditions. I.x
• ​Klessen et al 2000 Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence
• ​Klessen et al 2000 One-Point Probability Distribution Functions of Supersonic Turbulent Flows in Self-gravitating Media
• ​Li et al 2000 Simulations of Star Formation out of a Turbulence Molecular Cloud
• ​Masunaga & Inutsuka 2000 A Radiation Hydrodynamic Model for Protostellar Collapse. II. The Second Collapse and the Birth of a Protostar
• ​Aikawa et al 2001 Molecular Evolution in Collapsing Prestellar Cores
• ​Boss & Hartmann 2001 Protostellar Collapse in a Rotating, Self-gravitating Sheet
• ​Hartmann et al. 2001 Rapid Formation of Molecular Clouds and Stars in the Solar Neighborhood
• ​Heitsch et al 2001 Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbulence
• ​Klessen et al 2000 Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbulence
• ​Klessen 2001 The Formation of Stellar Clusters: Mass Spectra from Turbulent Molecular Cloud Fragmentation
• ​Ossenkopf 2001 On the structure of self-gravitating molecular clouds
• ​Ostriker 2001 Density, Velocity, and Magnetic Field Structure in Turbulent Molecular Cloud Models
• ​Abel et al 2002 The Formation of the First Star in the Universe
• ​Boss 2002 Collapse and Fragmentation of Molecular Cloud Cores. VII. Magnetic Fields and Multiple Protostar Formation
• ​Elmegreen 2002 Star Formation from Galaxies to Globules
• ​Padoan & Nordlund 2002 The Stellar Initial Mass Function from Turbulent Fragmentation
• ​de Vega & Sanchez 2002 Statistical mechanics of the self-gravitating gas: I. Thermodynamic limit and phase diagrams
• ​Aikawa et al 2003 Molecular Evolution in Collapsing Prestellar Cores. II. The Effect of Grain-Surface Reactions
• ​Ballesteros-Paredes 2003 Dynamic cores in hydrostatic disguise
  • SPH Turbulent driving of various sorts with self-gravity turned on. (Periodic BC) 205,379 particles
• ​Hennebelle et al. 2003 Protostellar collapse induced by compression
• ​Larson 2003 The physics of star formation
• ​Li et al 2003 The Formation of Stellar Clusters in Turbulent Molecular Clouds: Effects of the Equation of State
• ​Vazques-Semadeni et al 2003 A Holistic Scenario of Turbulent Molecular Cloud Evolution and Control of the Star Formation Efficiency: First Tests
• ​Vazques-Semadeni et al. 2003 The Origin of Molecular Cloud Turbulence and its Role on Determining the Star Formation Efficiency
• ​Goodwin et al. 2004 Simulating star formation in molecular cloud cores. I. The influence of low levels of turbulence on fragmentation and multiplicity
• ​Goodwin et al. 2004 Simulating star formation in molecular cores. II. The effects of different levels of turbulence
• ​Hennebelle et al. 2004 Protostellar collapse induced by compression - II. Rotation and fragmentation
• ​Aikawa et al 2005Molecular Evolution in Collapsing Prestellar Cores. III. Contraction of a Bonnor-Ebert Sphere
• ​Boss 2005 Collapse and Fragmentation of Molecular Cloud Cores. VIII. Magnetically Supported Infinite Sheets
• ​Clark and Bonnell 2005 The onset of collapse in turbulently supported molecular clouds
• ​Heitsch et al 2005 Formation of Structure in Molecular Clouds: A Case Study
• ​Jappsen et al 2005 The stellar mass spectrum from non-isothermal gravoturbulent fragmentation
• ​Klessen et al 2005 Quiescent and Coherent Cores from Gravoturbulent Fragmentation
• ​Li et al 2004 The Lifetimes and Evolution of Molecular Cloud Cores
• ​Li et al 2005 Control of Star Formation in Galaxies by Gravitational Instability
• ​Vazquez-Semadeni 2005 The Lifetimes and Evolution of Molecular Cloud Cores
• ​Vazquez-Semadeni et al. 2005 Star Formation Efficiency in Driven, Supercritical, Turbulent Clouds
• ​Ballesteros-Paredes 2006 The Mass Spectra of Cores in Turbulent Molecular Clouds and Implications for the Initial Mass Function
• ​Ballesteros-Paredes 2006 Six myths on the virial theorem for interstellar clouds
• ​Bonnell and Bate 2006 Star formation through gravitational collapse and competitive accretion
• ​Bonnell and Bate 2006 The Jeans mass and the origin of the knee in the IMF
• ​Heitsch et al 2006 The Birth of Molecular Clouds: Formation of Atomic Precursors in Colliding Flows
• ​Vazques-Semadeni et al 2006 Molecular Cloud Evolution. I. Molecular Cloud and Thin Cold Neutral Medium Sheet Formation
• ​Ballesteros-Paredes 2007 Molecular Cloud Turbulence and Star Formation
• ​Boss 2007 Collapse and Fragmentation of Molecular Cloud Cores. IX. Magnetic Braking of Initially Filamentary Clouds
• ​Glover & Mac Low 2007 Simulating the Formation of Molecular Clouds. I. Slow Formation by Gravitational Collapse from Static Initial Conditions
• ​Glover & Mac Low 2007 Simulating the Formation of Molecular Clouds. II. Rapid Formation from Turbulent Initial Conditions
• ​Goodman et al. 2009 A role for self-gravity at multiple length scales in the process of star formation
• ​Hennebelle et al 2007 Diffuse interstellar medium and the formation of molecular clouds
• ​Krumholz et al 2007 Radiation-Hydrodynamic Simulations of Collapse and Fragmentation in Massive Protostellar Cores
• ​McKee Ostriker 2007 Theory of Star Formation
• ​Price & Bate 2007 The impact of magnetic fields on single and binary star formation
• ​Vazques-Semadeni et al 2007 Molecular Cloud Evolution. II. From Cloud Formation to the Early Stages of Star Formation in Decaying Conditions
• ​Furesz et al. 2008 Kinematic Structure of the Orion Nebula Cluster and its Surroundings
• ​Heitsch et al 2008 Cooling, Gravity, and Geometry: Flow-driven Massive Core Formation
• ​Heitsch & Hartmann 2008 Rapid Molecular Cloud and Star Formation: Mechanisms and Movies
• ​Hennebelle et al. 2008 From the warm magnetized atomic medium to molecular clouds
• ​Hennebelle & Chabrier 2008 Analytical Theory for the Initial Mass Function: CO Clumps and Prestellar Cores
• ​Nakamura & Li 2008 Magnetically Regulated Star Formation in Three Dimensions: The Case of the Taurus Molecular Cloud Complex
  • 128³ isothermal MHD with AD and feedback 2.4 pc → .02 pc
  • B=15 microG (beta=1/24) subcritical
• ​Offner et al 2008 Driven and Decaying Turbulence Simulations of Low-Mass Star Formation: From Clumps to Cores to Protostars
  • 1100/cc 10K
• ​Offner et al. 2008 The Kinematics of Molecular Cloud Cores in the Presence of Driven and Decaying Turbulence: Comparisons with Observations
• ​Price & Bate 2008 The effect of magnetic fields on star cluster formation
• ​Banerjee et al 2009 Clump morphology and evolution in MHD simulations of molecular cloud formation
• ​Hennebelle & Chabrier 2009 Analytical Theory for the Initial Mass Function. II. Properties of the Flow
• ​Heyer et al. 2009 Re-Examining Larson's Scaling Relationships in Galactic Molecular Clouds
• ​Offner et al 2009 The Shapes of Molecular Cloud Cores in Simulations and Observations
• ​Price & Bate 2009 Inefficient star formation: the combined effects of magnetic fields and radiative feedback
• ​Ciardi & Hennebelle 2010 Outflows and mass accretion in collapsing dense cores with misaligned rotation axis and magnetic field
• ​Federrath et al 2010 Modeling Collapse and Accretion in Turbulent Gas Clouds: Implementation and Comparison of Sink Particles in AMR and SPH
• ​Federrath et al 2010 Comparing the statistics of interstellar turbulence in simulations and observations. Solenoidal versus compressive turbulence forcing
• ​Tomida 2010 Radiation Magnetohydrodynamics Simulation of Proto-stellar Collapse: Two-component Molecular Outflow
• ​Wang et al 2010 Outflow Feedback Regulated Massive Star Formation in Parsec-Scale Cluster-Forming Clumps
• ​Ballesteros-Paredes 2011 Gravity or turbulence? Velocity dispersion-size relation
• ​Ballesteros-Paredes 2011 Gravity or turbulence? II. Evolving column density PDFs in molecular clouds
• ​Cho & Kim 2011 Enhanced core formation rate in a turbulent cloud by self-gravity
  • 512³ Isothermal MHD fixed grid
  • beta=.1
  • J=4 (l_box/l_jeans)
  • M=10
  • Power law tail
  • Line-width size relation
• ​Clark et al 2011 Gravitational Fragmentation in Turbulent Primordial Gas and the Initial Mass Function of Population III Stars
• ​Collins et al 2011 Mass and Magnetic Distributions in Self-gravitating Super-Alfvénic Turbulence with Adaptive Mesh Refinement
  • ENZO 128³+4 = 2048³; 10pc → 1000 AU; MHD Isothermal 10K; n=300/cc; B=.6+-2.7 microG (no AD) (supercritical)
  • power law tail for density (1.64) and B (2.74)
  • B = rho^.48
  • sigma = rho^.25 for cores
  • CMF = 2.1+-.6
• ​Hopkins et al 2011 Self-Regulated Star Formation in Galaxies via Momentum Input from Massive Stars
• ​Kritsuk et al 2011 On the Density Distribution in Star-forming Interstellar Clouds
  • ENZO 512³+5x2=524,288³; 5pc → 2 AU; Isothermal 10K; n=500/cc
  • Power law tail to density pdf
• ​Krumholz et al 2011 Which Phase of the Interstellar Medium Correlates with the Star Formation Rate?
• ​Padoan & Nordlund 2011 The Star Formation Rate of Supersonic Magnetohydrodynamic Turbulence
• ​Peters et al 2011 The Interplay of Magnetic Fields, Fragmentation, and Ionization Feedback in High-mass Star Formation

Alphabetically

• ​Abel et al 2002 The Formation of the First Star in the Universe
• ​Aikawa et al 2001 Molecular Evolution in Collapsing Prestellar Cores
• ​Aikawa et al 2003 Molecular Evolution in Collapsing Prestellar Cores. II. The Effect of Grain-Surface Reactions
• ​Aikawa et al 2005Molecular Evolution in Collapsing Prestellar Cores. III. Contraction of a Bonnor-Ebert Sphere
• ​Ballesteros-Paredes 1999 Clouds as Turbulent Density Fluctuations: Implications for Pressure Confinement and Spectral Line Data Interpretation
• ​Ballesteros-Paredes 1999 Turbulent Flow-driven Molecular Cloud Formation: A Solution to the Post-T Tauri Problem
• ​Ballesteros-Paredes 2003 Dynamic cores in hydrostatic disguise
  • SPH Turbulent driving of various sorts with self-gavity turned on. (Periodic BC) 205379 particles
• ​Ballesteros-Paredes 2006 The Mass Spectra of Cores in Turbulent Molecular Clouds and Implications for the Initial Mass Function
• ​Ballesteros-Paredes 2006 Six myths on the virial theorem for interstellar clouds
• ​Ballesteros-Paredes 2007 Molecular Cloud Turbulence and Star Formation
• ​Ballesteros-Paredes 2011 Gravity or turbulence? Velocity dispersion-size relation
• ​Ballesteros-Paredes 2011 Gravity or turbulence? II. Evolving column density PDFs in molecular clouds
• ​Banerjee et al 2009 Clump morphology and evolution in MHD simulations of molecular cloud formation
• ​Bate 1998 Collapse of a Molecular Cloud Core to Stellar Densities: The First Three-dimensional Calculations
• ​Bonazzola et al, 1987 Jeans collapse in a turbulent medium
• ​Bonnell and Bate 2006 Star formation through gravitational collapse and competitive accretion
• ​Bonnell and Bate 2006 The Jeans mass and the origin of the knee in the IMF
• ​Boss 1980 Protostellar formation in rotating interstellar clouds. I -0 Numerical methods and tests
• ​Boss 1980 Protostellar formation in rotating interstellar clouds. II -0 Axially symmetric collapse
• ​Boss 1980 Protostellar formation in rotating interstellar clouds. III -0 Nonaxisymmetric collapse
• ​Boss 1984 Protostellar formation in rotating interstellar clouds. IV Nonisothermal collapse
• ​Boss 1986 Protostellar formation in rotating interstellar clouds. V -0 Nonisothermal collapse and fragmentation
• ​Boss 1987 Protostellar formation in rotating interstellar clouds. VI -0 Nonuniform initial conditions
• ​Boss 1988 Protostellar formation in rotating interstellar clouds. VII -0 Opacity and fragmentation
• ​Boss 1989 Protostellar formation in rotating interstellar clouds. VIII -0 Inner core formation
• ​Boss 1993 Collapse and fragmentation of molecular cloud cores. I -0 Moderately centrally condensed cores
• ​Boss 1995 Collapse and fragmentation of molecular cloud cores. 2: Collapse induced by stellar shock waves
• ​Boss 1995 Collapse and Fragmentation of Molecular Cloud Cores. III. Initial Differential Rotation
• ​Boss 1996 Collapse and Fragmentation of Molecular Cloud Cores. IV. Oblate Clouds and Small Cluster Formation
• ​Boss 1997 Collapse and Fragmentation of Molecular Cloud Cores. V. Loss of Magnetic Field Support
• ​Boss 1999 Collapse and Fragmentation of Molecular Cloud Cores. VI. Slowly Rotating Magnetic Clouds
• ​Boss et al 2000 The Jeans Condition and Collapsing Molecular Cloud Cores: Filaments or Binaries
• ​Boss & Hartmann 2001 Protostellar Collapse in a Rotating, Self-gravitating Sheet
• ​Boss 2002 Collapse and Fragmentation of Molecular Cloud Cores. VII. Magnetic Fields and Multiple Protostar Formation
• ​Boss 2005 Collapse and Fragmentation of Molecular Cloud Cores. VIII. Magnetically Supported Infinite Sheets
• ​Boss 2007 Collapse and Fragmentation of Molecular Cloud Cores. IX. Magnetic Braking of Initially Filamentary Clouds
• ​Cho & Kim 2011 Enhanced core formation rate in a turbulent cloud by self-gravity
  • 512³ Isothermal MHD fixed grid
  • beta=.1
  • J=4 (l_box/l_jeans)
  • M=10
  • Power law tail
  • Line-width size relation
• ​Ciardi & Hennebelle 2010 Outflows and mass accretion in collapsing dense cores with misaligned rotation axis and magnetic field
• ​Clark and Bonnell 2005 The onset of collapse in turbulently supported molecular clouds
• ​Clark et al 2011 Gravitational Fragmentation in Turbulent Primordial Gas and the Initial Mass Function of Population III Stars
• ​Cohn 1980 Late core collapse in star clusters and the gravothermal instability
• ​Collins et al 2011 Mass and Magnetic Distributions in Self-gravitating Super-Alfvénic Turbulence with Adaptive Mesh Refinement
  • ENZO 128³+4 = 2048³; 10pc → 1000 AU; MHD Isothermal 10K; n=300/cc; B=.6+-2.7 microG (no AD) (supercritical)
  • power law tail for density (1.64) and B (2.74)
  • B = rho^.48
  • sigma = rho^.25 for cores
  • CMF = 2.1+-.6
• ​de Vega & Sanchez 2002 Statistical mechanics of the self-gravitating gas: I. Thermodynamic limit and phase diagrams
• ​Elmegreen 2002 Star Formation from Galaxies to Globules
• ​Falgarone 1992 The small-scale density and velocity structure of quiescent molecular clouds
• ​Federrath et al 2010 Modeling Collapse and Accretion in Turbulent Gas Clouds: Implementation and Comparison of Sink Particles in AMR and SPH
• ​Federrath et al 2010 Comparing the statistics of interstellar turbulence in simulations and observations. Solenoidal versus compressive turbulence forcing
• ​Fiedler & Mouschovias 1992 Ambipolar diffusion and star formation: Formation and contraction of axisymmetric cloud cores. I -0 Formulation of the problem and method of solution
• ​Fiedler & Mouschovias 1993 Ambipolar Diffusion and Star Formation: Formation and Contraction of Axisymmetric Cloud Cores. II. Results
• ​Fillmore & Goldreich 1984 Self-similar gravitational collapse in an expanding universe
• ​Foster & Chevalier 1993 Gravitational Collapse of an Isothermal Sphere
• ​Furesz et al. 2008 Kinematic Structure of the Orion Nebula Cluster and its Surroundings
• ​Galli & Shu 1993 Collapse of Magnetized Molecular Cloud Cores. I. Semianalytical Solution
• ​Galli & Shu 1993 Collapse of Magnetized Molecular Cloud Cores. II. Numerical Results
• ​Gammie 1996 Linear Theory of Magnetized, Viscous, Self-gravitating Gas Disks
• ​Gammie & Ostriker 1996 Can Nonlinear Hydromagnetic Waves Support a Self-gravitating Cloud
• ​Glover & Mac Low 2007 Simulating the Formation of Molecular Clouds. I. Slow Formation by Gravitational Collapse from Static Initial Conditions
• ​Glover & Mac Low 2007 Simulating the Formation of Molecular Clouds. II. Rapid Formation from Turbulent Initial Conditions
• ​Goodman et al. 2009 A role for self-gravity at multiple length scales in the process of star formation
• ​Goldreich & Weber 1980 Homologously collapsing stellar cores
• ​Goodwin et al. 2004 Simulating star formation in molecular cloud cores. I. The influence of low levels of turbulence on fragmentation and multiplicity
• ​Goodwin et al. 2004 Simulating star formation in molecular cores. II. The effects of different levels of turbulence
• ​Hartmann et al 1994 Protostellar collapse in a self-gravitating sheet
• ​Hartmann et al 1996 Sheet Models of Protostellar Collapse
• ​Hartmann et al. 2001 Rapid Formation of Molecular Clouds and Stars in the Solar Neighborhood
• ​Heitsch et al 2000 Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence
• ​Heitsch et al 2001 Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbulence
• ​Heitsch et al 2005 Formation of Structure in Molecular Clouds: A Case Study
• ​Heitsch et al 2006 The Birth of Molecular Clouds: Formation of Atomic Precursors in Colliding Flows
• ​Heitsch et al 2008 Cooling, Gravity, and Geometry: Flow-driven Massive Core Formation
• ​Heitsch & Hartmann 2008 Rapid Molecular Cloud and Star Formation: Mechanisms and Movies
• ​Hennebelle & Perault 2000 Dynamical condensation in a magnetized and thermally bistable flow. Application to interstellar cirrus
• ​Hennebelle et al. 2003 Protostellar collapse induced by compression
• ​Hennebelle et al. 2004 Protostellar collapse induced by compression -0 II. Rotation and fragmentation
• ​Hennebelle et al 2007 Diffuse interstellar medium and the formation of molecular clouds
• ​Hennebelle et al. 2008 From the warm magnetized atomic medium to molecular clouds
• ​Hennebelle & Chabrier 2008 Analytical Theory for the Initial Mass Function: CO Clumps and Prestellar Cores
• ​Hennebelle & Chabrier 2009 Analytical Theory for the Initial Mass Function. II. Properties of the Flow
• ​Heyer et al. 2009 Re-Examining Larson's Scaling Relationships in Galactic Molecular Clouds
• ​Hopkins et al 2011 Self-Regulated Star Formation in Galaxies via Momentum Input from Massive Stars
• ​Hunter 1962 The Instability of the Collapse of a Self-Gravitating Gas Cloud
• ​Hunter 1977 The collapse of unstable isothermal spheres
• ​Hunter et al 1986 Star formation in colliding gas flows
• ​Jappsen et al 2005 The stellar mass spectrum from non-isothermal gravoturbulent fragmentation
• ​Klessen et al 1998 Fragmentation of Molecular Clouds: The Initial Phase of a Stellar Cluster
• ​Klessen et al 2000 The Formation of Stellar Clusters: Gaussian Cloud Conditions. I.x
• ​Klessen et al 2000 Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence
• ​Klessen et al 2000 One-Point Probability Distribution Functions of Supersonic Turbulent Flows in Self-gravitating Media
• ​Klessen et al 2000 Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbulence
• ​Klessen 2001 The Formation of Stellar Clusters: Mass Spectra from Turbulent Molecular Cloud Fragmentation
• ​Klessen et al 2005 Quiescent and Coherent Cores from Gravoturbulent Fragmentation
• ​Kritsuk et al 2011 On the Density Distribution in Star-forming Interstellar Clouds
  • ENZO 512³+5x2=524,288³; 5pc → 2 AU; Isothermal 10K; n=500/cc
  • Power law tail to density pdf
• ​Krumholz et al 2007 Radiation-Hydrodynamic Simulations of Collapse and Fragmentation in Massive Protostellar Cores
• ​Krumholz et al 2011 Which Phase of the Interstellar Medium Correlates with the Star Formation Rate
• ​Larson 1969 Numerical calculations of the dynamics of collapsing proto-star
• ​Larson 1981 Turbulence and star formation in molecular clouds
• ​Larson 1985 Cloud fragmentation and stellar masses
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