Download Modeling Time Dependent Winds - Center for Computational Sciences

Modeling Time Dependent
Astrophysical Winds
Peter Vitello
Lawrence Livermore National Laboratory
Livermore, CA 94550-9234
University of Kentucky
01/31/07
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.
Winds are extremely common
astrophysical phenomena
• Gas pressure driven:
– Solar wind (~10-14 Mo/yr - source of interplanetary plasma)
– X-ray heated stellar winds in X-ray binaries
– X-ray heated stellar and AGN accretion disks (~10-2 Mo/yr)
• Radiation pressure driven:
– Stellar wind in hot OB stars (10-6 – 10-5 Mo/yr)
– Cataclysmic Variable Stellar accretion disks (~10-8 Mo/yr)
– Active Galactic Nuclei accretion disks (~1 Mo/yr)
• Magnetic pressure driven:
– Centrifugally driven outflows in dense molecular clouds
collapsing into proto-stellar accretion disks (~10-4 Mo/yr)
– X-wind from magnetized proto-star and accretion disk (~10-7
Mo/yr)
– Magnetized active Galactic Nuclei accretion disks
(~1 Mo/yr)
Astrophysical winds are
non-spherical
• Solar wind originates in open magnetic field lies
in coronal holes
• Stellar winds from stars rotating near break-up
are denser and cooler in the equatorial plane
• Winds from accretion disks vary strongly with
distance in the disk from the central object
• Stellar winds in X-ray binary systems differ on
the direction towards and away from the X-ray
companion
• Non-radial stellar pulsations generate nonuniform photosphere conditions for stellar
winds
Astrophysical winds are
non-steady
• Accretion disk winds show stable and unstable regions
(turbulent outflow and/or fountain effect)
• Line radiation winds inherently unstable at short
wavelengths
• Wind accretion in binaries to form an accretion disk is
turbulent
• Velocity shears from non-spherical flows should drive
turbulence
• Until recently our computational ability to simulate nonspherical, time dependent winds has been extremely
limited
In a X-ray binary source the X-ray emission is
powered by wind accretion and the wind is
modified by the X-rays
Preliminary 2-D FLASH simulation of Vela
X-1
OB star
4.4
10.8
log T (K)
8.3
log n (cm-3)
radiatively driven wind
7.3
7.4
log x
X-ray source
(compact
star)
v (km s-1)
3500
-1.1
10
Asymmetries affect the predicted X-ray spectrum in
ways that cannot be captured by simple models.
Mauche LLNL 2006
Disk wind fountain and
spiral stellar wind
Accretion disk wind fountain
Proga & Kallman 2004
Rotating stellar winds from localized
emission sites Dessart 2004
Physics involved in modeling
astrophysical winds
•
•
•
•
•
•
•
•
Hydrodynamics
Gravity
Rotation
Radiation pressure
Heating / Cooling
Ionization
Radiation transfer
Magnetic field
• Too much physics is needed to start
from scratch and continuously build
new computational simulation models
Re-use of hydrodynamic codes
• Hydrodynamics is one aspect of wind modeling
that is shared by many other disciplines
• Adopting existing hydrodynamic simulation
codes is the basis of wind modeling advances
• Early wind modeling used ODE solvers for
steady state 1D modeling
• Recent modeling has used ZEUS and FLASH
which are 2D/3D hydrodynamic codes which
were designed to be adaptable to different types
of astrophysics problems
Evolution of numerical
astrophysical modeling
• Numerical astrophysical modeling has evolved
enormously in the last 30 years
– 1D (70’s) -> 2D (80’s) -> 3D (90’s)
– Steady state modeling -> time dependent
– Low resolution (~100 zones) -> high resolution
( > 108 zones)
• 1 mainframe -> massively parallel (>10,000 cpu’s)
• A few hours -> millions of cpu hours
• Simple mesh -> locally refined mesh (AMR)
Computation speed has gone up and
cost has gone down
• Supercomputers
– Cray-1
• LANL in 1976
• 160 MFlop / 8 MB main memory
– Blue Gene/L
•
•
•
•
LLNL in 2005
280 TFlop / 32 TB memory
216 cpu’s (64k)
800 TB storage
• Cost per GFlop
– 1976 ($55,000,000)
• Cray-1
– 1997 ($30,000)
• 16 Pentium Pro processor Beowulf cluster
– 2006 ($1)
• ATI PC add-in graphic card (X1900)
Supernova modeling has DOE backing
for massive simulations
• Univ. of Chicago used 2.7 million hours of
supercomputing time to simulation of a
supernova from a whole star simulation of a
white dwarf with their FLASH code.
• CHIMERA code (PRISM collaboration) is one of
the proposed ‘peta-applications’ for the next
generation PFlop machines.
• New 3D simulations which are resulting in many
TBytes of data is forcing the development of fast
large scale parallel file systems and parallel
graphic data visualization tools.
FLASH - An Astrophysics Community Code
Shortly: Relativistic accretion onto NS
Flame-vortex interactions
Compressed turbulence
Type Ia Supernova
The Flash
code
Gravitational collapse/Jeans instability
1. Parallel, adaptive-mesh simulation code
Wave breaking on white dwarfs
2. Can solve a broad range of (astro)physics problems
3. Portable: runs on many massively-parallel systems
4. The largest run on 64k processors
Intracluster interactions
6. Not a single code,Laser-driven
but component
based:
shock instabilities
Nova outbursts on white dwarfs
Rayleigh-Taylor instability
combine to form many different applications
Helium burning on neutron stars
Magnetic
Rayleigh-Taylor
Cellular detonation
Orzag/Tang MHD
vortex
Lynn Reid
ASC Center for Astrophysical Thermonuclear Flashes
(University of Chicago)
Richtmyer-Meshkov instability
FLASH is a Community Code
Breakdown of Responses
Haven't used yet,
plan to in future
8%
Not using
17%
Primary
research
tool
41%
Sample code/
concept testing/
educational
25%
V&V
9%
Breakdown of
FLASH code
research areas for
primary research
tool users
Variety of User Expertise
• Complete
beginners
- execute only
•
More advance
- Generate new problems, analyze
- Change parameters in text files
- Generate new simulations with initial conditions, parameters
- Write alternate API routines for specialized output
•
Expert
- New research
- Can override any aspect of the code
- Can install completely new algorithms or meshes
- Can contribute to core functionality
- Still benefits from framework and infrastructure,
verification
What happens in wind modeling when the
spatial resolution increases?
• A consequence of high resolution time
dependent 2D/3D modeling is the appearance
of fine scale hydrodynamic instabilities
• Nature loves chaos and finds ways to mix gradients in
flows whenever it can.
• Several of the classic flow instabilities (Kelvin-Helmholtz,
Rayleigh-Taylor, and Richtmyer-Meshkov) are clearly
evident in numerical models of astrophysical winds.
• Other flow instabilities can come from magnetic stress
and radiation pressure.
• These instabilities lead to turbulent flow which can
strongly modify density, velocity and temperature
structures in winds.
Kelvin-Helmholtz velocity shear instability
• Kelvin-Helmholtz instability occurs when
two fluids of different density flow past
each other at different speeds.
A KHI on Saturn caused by the interaction
between two bands of the planet's atmosphere.
Wave clouds forming over
Mount Duval.
Rayleigh-Taylor gravity accelerated
density shear instability
• The Rayleigh-Taylor instability occurs any time a
dense, heavy fluid is being accelerated by light fluid.
Hydrodynamics simulation of the RTI
RTI fingers evident in the Crab Nebula
in which hot gas from the explosion is
ramming into the surrounding
Interstellar medium.
Richtmyer-Meshkov accelerated density
shear instability
• The Richtmyer-Meshkov instability occurs when
an interface between fluids of differing density is
impulsively accelerated, e.g. by the passage of a
shock wave.
Time
Experiment observing the shock-acceleration of a thin,
perturbed layer of heavy gas embedded in a lowerdensity gas show new combinations of the three
primary flow topologies discovered recently.
1996 APS-DFD Gallery of Fluid Motion by Paul Rightley,
Robert Benjamin and Peter Vorobieff.
The wind tunnel problem shows the complexity
of flows with even simple internal structures
• The problem uses a twodimensional rectangular
domain with an internal
step.
• On the left-hand side we
use a supersonic inflow.
• This problem was run
using FLASH with 5
levels of adaptive mesh
refinement (AMR).
Detail of the KHI at the slip line behind the Mach
stem for 2, 3, 4, and 5 levels of refinement
2-D Rayleigh-Taylor /
Kelvin-Helmholtz Instability
• 2 and 3-D RTI calculations were carried out as
part of the validation program for the FLASH
code (Kevin Olson)
• The images show a narrow spike of dense fluid
falling under the influence of gravity, and
bubbles of light fluid rising up on the sides.
• The small features are the result of a KelvinHelmholtz instability at the interface of the fluids.
• With 10 levels of refinement, the effective
uniform grid resolution of this calculation is
16,384 x 4,096.
Density field of the 2-D Rayleigh-Taylor
simulation at a late stage in the calculation
Resolution study of the accretion flow in the vicinity
of the neutron star. (from ~7x109 to 3x107 cm)
Earlier simulation
log density
r/R
log density (g/cm3)
8
OB star
10
r/R
Blondin et al.
(1990–1995)
14
5x1012 cm
1x1011 cm
Recent simulation
Mauche LLNL 2006
15
Resolution study of the accretion flow in the vicinity
of the neutron star. (from ~7x109 to 3x107 cm)
Applying FLASH to “simple”
thermally driven stellar winds
• The simplist form of astrophysical wind is
the thermally (gas pressure) driven wind
• For steady state, spherical initial
conditions analytic solutions exist
• Looking at high resolution at winds with
even simple, smoothly varying conditions
at the base of the wind can lead to
turbulent flow
2D simulation of a thermally driven wind
from a star with a perturbed photosphere
• Boundary conditions
– Stellar mass: 2 Mo
– Stellar radius: 0.1 Ro
– Photosphere temperature:
• Cosine variation: 2x107- 4 x107 K ( T = To + T1cos(6pq) )
– Radiation pressure:
• Cosine variation: G = 0.45 – 0.55 (G = Go + G1cos(6pq) )
• AMR mesh
– 8 levels of refinement
– 1.4x106 mesh zones
– Maximum resolution
• 3.3x104 radial zones x 512 angular zones
• 1.7x107 zones if uniform mesh used
Wind flow is stable if temperature and
radiation pressure reinforce each other
Vr
Boundary conditions
T = 2x107 - 2x106 cos(6pq)
G = 0.5 - 0.05 cos(6pq)
log10(den)
Temperature
Wind stability mode is dependent
upon initial conditions
Vr
Boundary conditions
T = 2x107 - 2x106 cos(6pq)
G = 0.5 + 0.05 cos(6pq)
log10(den)
Temperature
Radial velocity evolution
Larger temperature perturbation leads to
a more chaotic flow
Initial temperature profile
Boundary conditions
T = 3x107 - 1x107 cos(6pq)
G = 0.5 + 0.05 cos(6pq)
Final temperature profile
Density profile evolution
Initial
log10(den)
profile
Boundary conditions
T = 3x107 - 1x107 cos(6pq)
G = 0.5 - 0.05 cos(6pq)
Final
log10(den)
profile
Velocity profile evolution
Initial vr
Final vr
Final vq
Conclusion
• Simulations of astrophysical winds today can be
done with spatial resolution that was impossible
even a few years ago
• This increased resolution unfortunately leads to
a lot of computational effort being used to deal
with hydrodynamic instabilities
• What is needed to be done next is to be able to
advance the level of physics in the models