Explosions and Shock Waves

1
Explosions and Shock Waves

• 10 February 2003
• Astronomy G9001 - Spring 2003
• Prof. Mordecai-Mark Mac Low

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Shock Waves in the ISM

• supernova remnants
• stellar wind bubbles
• H II regions
• stellar jets
• spiral arms
• accretion flows
• thermal instability

point blast waves
3
Point Explosions

• Sedovs dimensional analysis
• relevant physical variables are E, ?0, R, t
• combine to find a dimensionless constant

4
Blast Wave Equation of Motion
Cioffi, McKee, and Bertschinger (1988)
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Similarity Solutions
Ryu Vishniac 1987

• The interior structure of an adiabatic blast wave
  from a point explosion has no intrinsic scale.
• Specification of the time or radius determines
  the rest of the structure.
• Non-dimensionalization of equations of gas flow
  allows derivation.

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Dynamical Overstability
ram
thermal
Vishniac (1983)
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Development and Saturation

• Vishniac overstability occurs (Ryu Vishniac
  1987, 1988)
• for ? lt 1.2 in blast waves
• for ? lt 1.1 in shells
• Growth rate of t1/2
• Saturates when flows in shell become supersonic
  (ML Norman 1992)
• Transonic turbulence in shell

8
Experimental Verification

• Laser vaporization of foam target
• Nitrogen has ?1.4 (adiabatic diatomic gas)
• Xenon has many lines, so can radiatively cool
  with effective ?1.05

N2
Xe
Grun et al. 1991 (PRL)
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Nonlinear Thin Shell Instability
ram
ram
Vishniac (1994)

• Nonlinear instability
• Displacements must be as large as layer thickness
• Occurs in shock-bounded layer if thin

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Nonlinear Development

• Leads to steadily thickening turbulent layer
  (Blondin Marks 1996)

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Explosions in a Stratified Medium

• Explosions in exponentially stratified medium
  formally reach infinite velocity in finite time
  (Kompaneets 1959)
• Explosions in medium with ?1/r2 expand at
  constant rate. In steeper power laws they
  accelerate, in shallower they decelerate (see
  Ostriker McKee 1988, Koo McKee 1990)

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Rayleigh-Taylor instabilities in shells
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Supernova Remnants
free expansion R ? t
Sedov Solution (adiabatic) R ? t2/5
pressure-driven snowplow (cooled shell) R ? (t - t0)3/10 not R ? t2/7
mntm-driven snowplow (cooled interior) R ? t1/4

• developmental stages
• numerical solution (Cioffi, McKee Bertschinger
  1988)

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Stellar Wind Bubbles

• Double shock structure, separated by a contact
  discontinuity
• Outer shell quickly
  cools, interior only
  cools if very dense
• Hot interior pressure
  driven (Rt3/5)
• Cold interior mntm
  driven (Rt1/2)

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Stellar Wind Bubbles

• Similarity solution for shell structure (Castor,
  McCray Weaver 1976, Weaver et al. 1977)
• Interior dominated by conductive evaporation

?
T
shell
center
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Hot ISM

• To explain observed hot medium, consider filling
  factor of supernova remnants
• Cox Smith (1975), McKee Ostriker (1977)
• How to compute expansion of SNRs in clumpy,
  inhomogeneous medium?
• MO77 assumed dense, round clouds embedded in
  low-density intercloud gas
• SNRs expand quickly through low-density gas, so
  they found very high filling factors.

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Multiple Supernovae Superbubbles

• Most Type II SNe from massive stars occur in OB
  associations
• Later SNe occur within earlier SNRs
• Later blast waves quickly decelerate to sound
  speed of hot interior, maintaining pressure (ML
  McCray 1988)
• Multiple SNR expands like wind-driven bubble with
  LmechNSNESN/?tSN

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Multiple Supernovae Turbulence
ML, Avillez, Balsara, Kim 2001, astro-ph

• Computational model of disk
• 1 x 1 x 20 kpc2
• SN driving
• vertical strat.
• 1.25 pc res
• radiative cooling

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Galactic Fountain

• Hot gas in plane must rise
• Shapiro Field (1976) computed consequences
• Gas at 106 K allowed to radiatively cool
• Incorporating self-photoionization gives good
  match to column densities of C IV, N V, and O VI
  (Shapiro Benjamin 1991)
• Result of cooling shown numerically to be
  falling, dense clouds (Avillez 2000)

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Starburst winds

• With sufficiently high star formation (and SN)
  rate, hot gas entirely escapes potential
• X-ray and Ha emission observed many kpc away from
  starburst galaxies
• Winds may energize, pollute nearby IGM, but cant
  sweep away rest of ISM (ML Ferrara 1999, Fujita
  et al. in prep)
• winds accelerate down steepest density gradients
• far more energy required to sweep ISM than just
  the gravitational binding energy suggested by
  Dekel Silk (1986)

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Where to go next?

• Current plan is to devote one more week to
  ZEUS-3D, examining MHD problems
• Then spend similar amounts of time on
• Flashcode (AMR, Riemann solver, MPI)
• GADGET (SPH, self-gravity methods, MPI)
• Cloudy (photoionization computations)
• Alternatives
• spend more time on ZEUS-3D
• study ZEUS-MP as an example of an MPI code
  instead of one of the other codes (based on
  ZEUS-3D so some things familiar)

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Multidimensional Computations

• Directional splitting
• XYZ XZY YZX...
• Centering
• velocities are face centered, not edge centered

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Different coordinate systems

• Non-cartesian rectilinear coordinate systems in
  ZEUS all difference equations in covariant form.

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Ratioed grids

• ZEUS includes ratioed grids (see sample prob).
• add multiple ggen namelists
• set lgrid.f. until last one, then .t.
• x1rat1.03 is a typical value
• To compute grid sizes
• Best not to exceed 101 zone aspect ratioes.
• dxmax(dxmin)n

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Parallelization

• Additional issues
• How to coordinate multiple processors
• How to minimize communications
• Common types of parallel machines
• shared memory, single program
• eg SGI Origin 2000, dual or quad proc PCs
• multiple memory, multiple program
• eg Beowulf Linux clusters, Cray T3E, ASCI systems

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Shared Memory

• Multiple processors share same memory
• Only one processor can access memory location at
  a time
• Synchronization by controlling who reads, writes
  shared memory

U of Minn Supercomputing Inst.
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Shared Memory

• Advantages
• Easy for user
• Speed of memory access
• Disadvantages
• Memory bandwidth limited.
• Increase of processors without increase of
  bandwidth will cause severe bottlenecks

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Distributed Memory

• Multiple processors with private memory
• Data shared across network
• User responsible for synchronization

U of Minn Supercomputing Inst.
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Distributed Memory

• Advantages
• Memory scalable with number of processors. More
  processors, more memory.
• Each processor can read its own memory quickly
• Disadvantages
• Difficult to map data structure to memory
  organization
• User responsible for sending and receiving data
  among processors
• To minimize overhead, data should be transferred
  early and in large chunks.

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Methods

• Shared memory
• data parallel
• loop level parallelization
• Implementation
• OpenMP
• Fortran90
• High Performance Fortran (HPF)
• Examples
• ZEUS-3D

• Distributed memory
• block parallel
• tiled grids
• Implementation
• Message Passing Interface (MPI)
• Parallel Virtual Machine (PVM)
• Examples
• ZEUS-MP
• Flashcode
• GADGET

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OpenMP

• Designate inner loops that can be distributed
  across processors with DOACROSS command.
• Dependencies between loop instances prevent
  parallelization
• Execution of each loop usually depends on values
  from neighboring parts of grid.
• ZEUS-3D only parallelizes out to 8-10 processors
  with OpenMP

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Cache Optimization

• Modern processors retrieve 64 bytes or more at a
  time from main memory
• However it takes hundreds of cycles
• Cache is small amount of very fast memory on
  microprocessor chip
• Retrievals from cache take only a few cycles.
• If successive operations can work on cached data,
  speed much higher
• Fastest changing array index should be inner
  loop, even if code rearrangement required

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Parallel ZEUS-3D

• To run ZEUS-3D in parallel, set the variable
  iutask 1 in setup block, recompile.
• inserts DOACROSS directives
• compiles with parallel flags turned on if OS
  supports them.
• Set the number of processors for the job (usually
  with an environment variable)
• Run is otherwise similar to serial.

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Use of IDL
pause

• Quick and dirty movies
• for i1,30 do begin
• asin(findgen(10000.))
• hdfrd,fzhd_string(i,form(i3.3))aa,dd,
  xx
• plot,x,d4.dat end
• Scaling, autoscaling, logscaling 2D arrays
• tvscl,alog(d)
• tv,bytscl(d,maxdmax,mindmin)
• Array manipulation, resizing
• tvscl,rebin(d,nx,ny,/s) nx, ny multiple
• tvscl,rebin(reform(dj,,),nx,ny,/s)

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More IDL

• plots, contours
• plot,x,di,,k,xtitleTitle,psym-3
• oplot,x,di10,,k
• contour,reform(di,,),nlev10
• slicer3D
• dp ptr_new(alog10(d))
• slicer3D,dp
• Subroutines, functions