The Formation of High Mass Stars

1
The Formation of High Mass Stars
Zurich September 17, 2007 Next Generation of
Computational Models

• Richard I. Klein
• UC Berkeley, Department of Astronomy
• and
• Lawrence Livermore National Laboratory
• Collaborators
• Mark Krumholz (Princeton University) and Chris
  McKee (UC Berkeley)

This work was performed under the auspices of the
U.S. Department of Energy by the University of
California Lawrence Livermore National Laboratory
under contract No. W-7405-Eng-48.
UCRL-PRES-229278
2
Outstanding Challenges of Massive Star Formation

• What is the formation Mechanism Gravitational
  collapse of an unstable turbulent cloud
  Competitive Bondi-Hoyle accretion Collisional
  Coalescence?
• How can gravitationally collapsing clouds
  overcome the Eddington limit due to radiation
  pressure?
• What determines the upper limit for High Mass
  Stars? (120Msun ? 150Msun)
• How do feedback mechanisms such as protostellar
  outflows and radiation affect protostellar
  evolution? These mechanisms can also have a
  dramatic effect on cluster formation
• How do the systems in which massive stars are
  present form?

3
Theoretical Challenges of High Mass Star Formation

• Effects of Strong Radiation Pressure
• Massive stars M ? 20 M? have tK lt tform (Shu et
  al. 1987) and begin nuclear burning during
  accretion phase
• Radiates enormous energy
• For M ? 100 M?
• however ?dust gtgt ?T
• But, observations show M 100 M? (Massey 1998,
  2003)
• Fundamental Problem How is it possible to
  sustain a sufficiently high-mass accretion rate
  onto protostellar core despite Eddington
  barrier?
• Does radiation pressure provide a natural limit
  to the formation of high mass stars?

4
Theoretical Challenges of High Mass Star
Formation (cont.)

• Effects of Protostellar outflows
• Massive stars produce strong radiation driven
  stellar winds with momentum fluxes
• Massive YSO have observed (CO) protostellar
  outflows where
  (Richer et al. 2000 Cesaroni 2004)
• If outflows where spherically symmetric this
  would create a greater obstacle to massive star
  formation than radiation pressure
• but, flows are found to be collimated with
  collimation factors 2-10 (Beuther 2002, 2003,
  2004)
• Fundamental Problem How do outflows effect the
  formation of Massive stars? Do outflows limit
  the mass of a star?

5
Physical Effects in High-Mass Star Formation

• Photoionization
• Effects quenched for moderate accretion rates
  10-4 M? /yr
• for spherically
  symmetric infall
• In disk accretion, material above and below disk
  confine ionized region close to stellar surface
• Outflows are sufficient to quench ionization
  (Tan and McKee 2003)
• Omit Photoionization as a first approximation
• Magnetic fields
• Gravity dominates magnetic fields when M gt MB ?
  B3/n2 so magnetic fields are dynamically
  unimportant for high mass cores (Shu et al. 1987)
• At high densities B ? n1/2 so MB ? n-1/2 and
  since n ? 106 in massive star forming regions, MB
  is substantially reduced
• Observations of magnetic fields in high mass
  cores inconlcusive
• Neglect of magnetic fields is a reasonable first
  approximation

6
Physical Effects in High-Mass Star Formation
(cont.)

• Dust
• Critical role in massive star formation ? couples
  gas to radiation flux from central star
• ? need radiation transport and multi-species
  models with good microphysics
• Photostellar outflows
• Molecular outflows in neighborhood of massive
  stars 10-4 - 10-2 M? /yr. Force required to
  drive such outflows Fco gt 10 100 LBOL/c
• Outflows may be important to protostellar
  evolution
• Three-Dimensional Effects
• Interaction of radiation with infalling envelope
  subject to radiation driven instabilities
• Interaction of protostellar outflow with
  infalling envelope possibly unstable
• Accretion disks develop non-axisymmetric
  structures in turbulent flows
• Three dimensional simulations are crucial

7
Equations of Gravito-Radiation Hydrodynamics to
order v/c (Krumholz, Klein McKee 2007a)
(Continuity)
(Gas momentum)
(Gas energy)
(Poisson)
(Radiation energy)
(Flux-limited diffusion approximation)
Equations exact to (v/c) in static diffusion
regime.
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High Mass Star Formation Simulation Physics

• Euler equations of compressible gas dynamics with
  gravity
• Radiative transfer and radiation pressure in the
  gray, flux-limited diffusion approximation ?
  radiative feedback
• Model of dust opacity based on Pollack et al.
  (1994) (6 species)
• Outflows hydromagnetic outflow models
• Dynamical Feedback
• Eulerian sink particles
• Created when the density in a cell exceeds the
  local Jeans density (Krumholz, McKee, Klein
  2004)
• Free to move through the grid and continue to
  accrete gas
• Sink particles feed radiation and (for some runs)
  winds back into the grid based on a protostellar
  model
• Model includes accretion, KH contraction,
  deuterium and hydrogen burning (McKee Tan
  2003), x-winds
• Capability to handle the enormous range of scales
  involved ? AMR

9
Physics Implementation

• Our AMR code is a combination of C and FORTRAN
  90 ? Uses parallel MPI-based Box Lib Library
• ORION is our magneto-radiation-hydrodynamics AMR
  code
• We Solve Parallel, 3-D coupled
  self-gravitating-Radiation-Hydrodynamics on
  Adaptive Meshes ? Multi-Scale Physics
• Hydrodynamics is solved with conservative, high
  order, time explicit Godunov scheme with
  Approximate Riemann Solver
• ? Multi-fluid Hydrodynamics
• Self-Gravity We employ parallel, scalable,
  multi-grid solution algorithms
• ? We use implicit multi-grid iteration to first
  solve Poisson Equation on a single level

10
Physics Implementation (cont.)

• Level solutions are then coupled and iterated to
  convergence to obtain solution for gravitational
  potential on all levels
• Radiation Transfer Non-Equilibrium
  Flux-Limited diffusion including important O(v/c)
  terms - Radiation solved implicity with parallel
  multi-grid, iteration scheme taking into account
  multi-level solves
• ? Solutions must be obtained which couple all
  grids at a single refinement level, or even
  across multiple level
• Ideal MHD fully 2nd order unsplit Godunov MHD
• We are now implementing this in our AMR
  self-gravity rad-hydro code
• Much better dissipation properties than split
  staggered mesh schemes (Crockett, Collella,
  Fisher, Klein McKee JCP 2004)

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HMSF Initial Conditions Non-Turbulent
r 3/2 density profile, r 0.10.2 pc, M
100200 Msun, slow solid-body rotation ? 0.02,
dynamic range 8192
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Non-Turbulent IC Early Evolution
At early stages the star accretes steadily and a
Keplerian disk forms. Cylindrical symmetry is
maintained.
13
Non-Turbulent IC Radiation Bubble Formation
At higher luminosities, radiation pressure forms
bubbles above and below the accretion disk.
Bubble growth is up-down and cylindrically
asymmetric.
14
Continued Expansion of Radiation Bubble
15
High Mass Disk and Formation of Expanding
Radiation Driven Bubble
16
Rayleigh-Taylor Instability in Radiation Driven
Bubble
17
Collapse of radiation driven bubble
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HMSF Turbulent Initial Conditions
r 3/2 density profile, Gaussian random velocity
field with power on large scales, kinetic energy
potential energy ? Mach number 8.5, dynamic
range 16,348
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HMSF Protostellar Evolution
Turbulent ICs
Non Turbulent ICs
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Radius, Accretion Rate and Luminosity of Primary
Star
start of Deuterium burning
Principal source of raising temperature in the
core is accretion luminosity which is the
dominant source of energy prior to nuclear burning
accretion luminosity
21
Temperature Distribution in 100 Solar Mass Core
Tgt100 K, RT
Tgt50 K, RT
ALL
Tgt300 K, RT
Tgt100 K, BAR
Tgt300 K, BAR
Tgt50 K, BAR
Accretion luminosity transported by radiation
heats a radius of 1000 AU of the core to gt 50K
and substantial parts of the core to gt 100K
22
Evolution of 100 Solar Mass Turbulent
Protostellar Core
Radiative heating results in the formation of a
primary high mass star and 2 low mass stars in
the disk
23
Evolution of 100 Solar Mass Turbulent Isothermal
Protostellar Core
Isothermal or barotropic models result in the
formation of a multitude of low mass stars only ?
erroneous fragmentation
24
Observing Massive Disks with ALMA
Integrated TB in simulated 1000 s / pointing ALMA
observation of disk at 0.5 kpc in CH3CN 220.7472
GHz (KKM 2007c, ApJ,)
25
Effects of Protostellar Outflows

• High mass protostars have outflows that look like
  larger versions of low mass protostellar outflows
  (Beuther et al. 2004)
• Outflows are launched inside stars dust
  destruction radius
• Due to high outflow velocities, there is no time
  for dust grains to regrow inside outflow
  cavities. Grains reach only 103?m by the time
  they escape the core.
• Because grains are small, outflow cavities are
  optically thin.
• Thin cavities can be very effective at
  collimating protostellar radiation, reducing the
  radiation pressure force in the equatorial plane
• Krumholz, McKee Klein, (2005) using toy
  Monte-Carlo radiative transfer calculations find
  outflows cause a factor of 5 10 radiation
  pressure force reduction
• Outflows may be responsible for driving
  turbulence in clumps (Li Nakamura 2006)
• ?

26
Protostellar Outflows in High-Mass Star Formation
Temperature Distribution
Radiation and Gravitational Forces

• Temperature distribution from Monte Carlo
  diffusion (Whitney, et. al. 2003) Radiation
  transfer with ray solution to get radiative
  forces
• Envelope rotationally flattened density dist.
  cavity shape Za?b M50M? ZAMS 50M? envelope
• With no wind cavity frad gt fgrav everywhere
  except inside the accretion disk? accretion
  halted
• With wind cavity, frad lt fgrav outside disk
  radius ? accretion can continue

27
HMSF with Outflows Very Early 3-D Evolution
Early results show that radiation is collimated
effectively by outflow cavities radiation energy
density is factor of 5 higher inside cavity
28
Advances Necessary in Algorithmic Performance and
Scalability for High Mass Star Formation

• State-of-the-art simulations follow collapse from
  the scale of turbulent cores to stars (KKM 2007)
• Dynamic range gt
  104
• Simulations will require more realistic initial
  conditions in core derived from the outer scale
  imposed by turbulent clumps (M several X 103
  M? )
• Simulations are just beginning to follow
  collapse
• from turbulent Clumps ?Cores ? Stars with
  radiative feedback and AMR
• Dynamic Range gt 105
• Current state-of-the-art (Krumholz, Klein McKee
  2006, 07) require months to evolve high mass
  stars on parallel machines ( 256 processors)
  with Grey Radiation Transfer ? multi-frequency
  will be several times more expensive
• Future simulations will evolve GMCs ? Clumps ?
  Cores ? Stars
• Dynamic Range gt 106 - 107
• For galaxy simulations to incorporate star
  formation
• Galaxy ? GMCs ? Clumps ? Cores ?
  Stars
• Dynamic Range gt 3x108 - 3x1010

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Summary and Future Directions

• 3-D high resolution AMR simulations with ORION
  achieves protostellar masses considerably above
  previous 2-D axisymmetric gray simulations
• Two new mechanisms have been shown to overcome
  radiation pressure barrier to achieve high mass
  star formation
• 3-D Rayleigh-Taylor instabilities in radiation
  driven bubbles appear to be important in allowing
  accretion onto protostellar core
• Protostellar outflows resulting in optically thin
  cavities promote focusing of radiation and
  reduction of radiation pressure ? enhances
  accretion
• Radiation feedback from accreting protostars
  inhibits fragmentation
• ALMA observations will help distinguish between
  competing models of high mass star formation ?
  gravitational core collapse predicts large scale
  disks
• Future Directions
• Multi-frequency radiation-hydrodynamics and
  inclusion of ionization
• Improvement in flux limited diffusion
  (Monte-Carlo Sn transport Variable Edd Tensor)
• Improvement in dust physics (e.g. shattering
  coagulation multi-species)
• Evolution of wind outflow models and interaction
  with infalling envelope
• Self consistent evolution of high mass turbulent
  cores from large scale turbulent clump
• Inclusion of MHD ? can launch hydromagnetic wind
  possible photon bubble instab. ?

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Back up Slides
31
Radiation Transport Results in Suppression of
Large Scale Fragmentation in Massive Star
Formation
0.26 pc
6700 AU
Most of the available mass in turbulent cloud
goes into one massive star.
32
High Mass Disk at 27,000 yr. (Krumholz, Klein
McKee 2007b)
0.6 pc radius
Disk radius 3000 AU
33
Observing Massive Disks
Integrated TB in simulated 1000 s / pointing ALMA
observation of disk at 0.5 kpc in CH3CN 220.7472
GHz (KKM 2007c, ApJ, in press)
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Adaptive Mesh Overview

• A block-structured refinement strategy combines
  the advantages of adaptive mesh refinement with
  the efficiencies provided by uniform grids
• For hyperbolic systems, such as the advection
  component of fluid dynamics, explicit difference
  schemes can be used which minimize communication
• A serial algorithm can proceed one grid at a time
• A parallel algorithm can process many grids at
  once. Library support for this approach is
  provided by CCSE at LBL.
• For parabolic and elliptic systems, such as those
  associated with radiation diffusion, implicit
  difference schemes must be used. Solutions must
  be obtained which couple all grids at a single
  refinement level, or even across multiple levels.
• Interactive solvers based on multigrid provide
  efficient solutions.
• We use the hypre parallel multigrid library
  developed in CASC for this part of the algorithm