Transcript The Formation of High Mass Stars

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
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?
UCRL-PRES-229278- 2
Theoretical Challenges of High Mass Star Formation
1.
Effects of Strong Radiation Pressure
— Massive stars M  20 M have tK < tform (Shu et al. 1987) and begin
nuclear burning during accretion phase
 Radiates enormous energy
 For M  100 M
4Gmp cM
L* ~ Ledd 
~ 3 106 LΟ
T
however dust >> T
 f rad  f grav for M  10 M Ο
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?
UCRL-PRES-229278- 3
Theoretical Challenges of High Mass Star
Formation (cont.)
2.
Effects of Protostellar outflows
— Massive stars produce strong radiation driven stellar winds with
momentum fluxes
Ýv  L /c
M
— Massive YSO have observed (CO) protostellar outflows where
Ýv ~ 100 L /c (Richer et al. 2000; Cesaroni 2004)
M

 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?
UCRL-PRES-229278- 4
Physical Effects in High-Mass Star Formation
•
Photoionization:
— Effects quenched for moderate accretion rates ~10-4 M /yr
4GM*Sm H
MÝcrit 
 (2)
2
1/ 2


 S 1/ 2
M*
5
1
 2 10 
  49 1  M sun yr
10Msun  10 s 
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 > 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
UCRL-PRES-229278- 5
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 > 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
UCRL-PRES-229278- 6
Equations of Gravito-Radiation Hydrodynamics
to order v/c (Krumholz, Klein & McKee 2007a)

      0
t
(Continuity)

        P     R F (Gas momentum)
t
c
(Gas energy)
 P
 R

e    e        4  c   2  1   F
t
 R
 c


2  4G    M i x  xi  (Poisson)
i


(Radiation energy)
  c

 

E
 3  R2

   
E    Li x  xi    4  cE    2 P  1  E    
E 
t
 2

 R
 i
 R

F
 cE 
E
R
(Flux-limited diffusion approximation)
Equations exact to (v/c) in static diffusion regime.
UCRL-PRES-229278- 7
High Mass Star Formation Simulation Physics
•
•
Euler equations of compressible gas dynamics with gravity
•
•
Model of dust opacity based on Pollack et al. (1994) (6 species)
Radiative transfer and radiation pressure in the gray, flux-limited
diffusion approximation  radiative feedback
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
UCRL-PRES-229278- 8
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
I.
Hydrodynamics: is solved with conservative, high order, time explicit
Godunov scheme with Approximate Riemann Solver
 Multi-fluid Hydrodynamics
II.
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
UCRL-PRES-229278- 9
Physics Implementation (cont.)

III.

IV.
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)
UCRL-PRES-229278- 10
HMSF Initial Conditions: Non-Turbulent
r –3/2 density profile, r = 0.1–0.2 pc, M = 100–200 Msun,
slow solid-body rotation:  = 0.02, dynamic range = 8192UCRL-PRES-229278- 11
Non-Turbulent IC: Early Evolution
At early stages the star accretes steadily and a Keplerian
disk forms. Cylindrical symmetry is maintained.
UCRL-PRES-229278- 12
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.
UCRL-PRES-229278- 13
Continued Expansion of Radiation Bubble
UCRL-PRES-229278- 14
High Mass Disk and Formation of Expanding
Radiation Driven Bubble
UCRL-PRES-229278- 15
Rayleigh-Taylor Instability in Radiation Driven
Bubble
UCRL-PRES-229278- 16
Collapse of radiation driven bubble
UCRL-PRES-229278- 17
HMSF: Turbulent Initial Conditions
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
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
UCRL-PRES-229278- 18
HMSF Protostellar Evolution
Turbulent ICs
Non Turbulent ICs
UCRL-PRES-229278- 19
Radius, Accretion Rate and Luminosity of
Primary Star
start of
Deuterium
burning
accretion
luminosity
Principal source of
raising temperature in
the core is accretion
luminosity which is the
dominant source of
energy prior to nuclear
burning
UCRL-PRES-229278- 20
Temperature Distribution in 100 Solar Mass Core
ALL
T>50 K, RT
T>50 K, BAR
T>100 K, RT
T>300 K, RT
T>100 K, BAR
T>300 K, BAR
Accretion luminosity transported by radiation heats a radius of 1000 AU of
the core to > 50K and substantial parts of the core to > 100K
UCRL-PRES-229278- 21
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
UCRL-PRES-229278- 22
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
UCRL-PRES-229278- 23
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,)
UCRL-PRES-229278- 24
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 star’s dust destruction radius
•
•
Because grains are small, outflow cavities are optically thin.
•
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)
Due to high outflow velocities, there is no time for dust grains to
regrow inside outflow cavities. Grains reach only ~10–3m by the time
they escape the core.
Thin cavities can be very effective at collimating protostellar radiation,
reducing the radiation pressure force in the equatorial plane
UCRL-PRES-229278- 25
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 Z=ab; M=50M ZAMS; 50M envelope
• With no wind cavity; frad > fgrav everywhere except inside the accretion disk accretion halted
• With wind cavity, frad < fgrav outside disk radius  accretion can continue
UCRL-PRES-229278- 26
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
UCRL-PRES-229278- 27
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 > 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 > 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 > 106 - 107
•
For galaxy simulations to incorporate star formation
Galaxy  GMCs  Clumps  Cores  Stars
Dynamic Range > 3x108 - 3x1010
UCRL-PRES-229278- 28
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.
UCRL-PRES-229278- 29
Back up Slides
UCRL-PRES-229278- 30
Radiation Transport Results in Suppression of
Large Scale Fragmentation in Massive Star
Formation
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
0.26 pc
6700 AU
Most of the available mass in turbulent cloud goes into one massive star.
UCRL-PRES-229278- 31
High Mass Disk at 27,000 yr. (Krumholz, Klein & McKee 2007b)
0.6 pc radius
Disk radius 3000 AU
UCRL-PRES-229278- 32
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)
UCRL-PRES-229278- 33
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
UCRL-PRES-229278- 34