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Novae and Mixing
John ZuHone
ASCI/Alliances Center for
Thermonuclear Flashes
University of Chicago
Overview
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Purpose
What is FLASH?
Mixing in Novae
Setting Up the Problem
Doing the Problem
Conclusions
Purpose
• To develop a numerical simulation using the
FLASH code to simulate mixing of flulds at
the surface of a white dwarf star
• Understanding this mixing will contribute to
our understanding of novae explosions in
binary systems containing a white dwarf
star
What is FLASH?
• FLASH is a three dimensional
hydrodynamics code that solves the Euler
equations of hydrodynamics
• FLASH uses an adaptive mesh of points
that can adjust to areas of the grid that need
more refinement for increased accuracy
• FLASH also can account for other physics,
such as nuclear reactions and gravity
What is FLASH?
• Euler equations of hydrodynamics
rt + • rv = 0
rvt + • rvv + P = rg
rEt + • (rE + P) v = rv • g
where
E = e + ½v2
What is FLASH?
• Pressure obtained using equation of state
– ideal gas
P = (g - 1)re
– other equations of state (i.e. for degenerate
Fermi gases, radiation, etc.)
• For reactive flows track each species
rXlt + • rXlv = 0
Mixing in Novae
• What is a nova?
– novae occur in binary star systems consisting of
a white dwarf star and a companion star
– the white dwarf accretes material into an
accretion disk around it from the companion
– some of this material ends up in a H-He
envelope on the surface of the white dwarf
Mixing in Novae
– this material gets heated and compressed by the
action of gravity
– at the base of this layer, turbulent mixing mixes
the stellar composition with the white dwarf
composition (C, N, O, etc.)
– temperatures and pressures are driven high
enough for thermonuclear runaway to occur
(via the CNO cycle) and the radiation causes
the brightness increase and blows the layer off
Setting Up the Problem
• Initial Conditions
– what we want is a stable model of a white
dwarf star and an accretion envelope in
hydrostatic equilibrium
– we get close enough to the surface where
Cartesian coordinates (x, y, z) and a constant
gravitational field are valid approximations
Setting Up the Problem
• Hydrostatic Equilibrium
– to ensure a stable solution we must set up the
initial model to be in hydrostatic equilibrium,
meaning v = 0 everywhere
– momentum equation reduces to
P = rg
– set this up using finite difference method,
taking an average of densities
Setting Up the Problem
• Procedure for initial model
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set a density at the interface
set temperature, elemental abundances
call equation of state to get pressure
iterate hydrostatic equilibrium condition and
equation of state to get pressure, density, etc. in
rest of domain
Setting Up the Problem
• Region I: 50% C,
50% O, T1 = 107 K
• Region II: 75% H,
25% He, T2 = 108 K
• Density at interface:
ro = 3.4 × 103 g cm-3
Doing the Problem
• Loading the model into FLASH
– load the model in and see if the simulation is in
hydrostatic equilibrium
– it ISN’T!
– high velocities at interface and boundary
– begin to examine the model for possible flaws
Doing the Problem
• Question: Is the model itself really in
hydrostatic equilibrium?
– test the condition, discover that the model is in
hydrostatic equilibrium to about one part in
1012
• Question: Is the resolution high enough?
– try increasing number of points read in,
increase refinement, still no change
Doing the Problem
• Question: Is the density jump across the
interface hurting accuracy?
– smooth out density jump by linearly changing
temperature and abundances
– velocities slightly lower, but still present
– try this for a number of different sizes of
smoothing regions, still no change
Doing the Problem
• Check the equation of state
– the Helmholtz equation of state we were using
was complex
– accounts for gas, degenerate electrons, and
radiation
– switch to gamma equation of state to see if
anything improves
– NO IMPROVEMENT!
Movie Time!
(maybe)
Doing the Problem
• Two important resolutions
– there was an error in temperature calculation
which was caused by a mismatch in precision
of numerical constants
– we found that if we used the same number of
points in FLASH as we did the initial model
some of the inconsistency was resolved
Doing the Problem
• Which brings us to where we currently
are…
– we believe that by our linear interpolation for
the density is too imprecise
– we are currently implementing a quadratic
interpolation for the density
Conclusions
• What have we learned?
– stability is important
– the need for there to be a check within FLASH
itself for hydrostatic equilibrium
– the need to carefully examine all parts of a code
to look for possible mistakes
– consistency!
Conclusions
• Thanks to:
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Mike Zingale and Jonathan Dursi
Prof. Don Lamb
the ASCI FLASH Center
the University of Chicago