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Novae and Mixing John ZuHone ASCI/Alliances Center for Thermonuclear Flashes University of Chicago Overview Purpose What is FLASH? Mixing in Novae Setting Up the Problem Doing the Problem Conclusions Purpose

Novae and Mixing

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Novae and Mixing

John ZuHone

ASCI/Alliances Center for Thermonuclear Flashes

University of Chicago

- Purpose
- What is FLASH?
- Mixing in Novae
- Setting Up the Problem
- Doing the Problem
- Conclusions

- 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

- 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

- Euler equations of hydrodynamics
¶r/¶t + Ñ • rv = 0

¶rv/¶t + Ñ • rvv + ÑP = rg

¶rE/¶t + Ñ • (rE + P) v = rv • g

where

E = e + ½v2

- Pressure obtained using equation of state
- ideal gas
P = (g- 1)re

- other equations of state (i.e. for degenerate Fermi gases, radiation, etc.)

- ideal gas
- For reactive flows track each species
¶rXl/¶t + Ñ • rXlv = 0

- 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

- 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

- 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

- 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
ÑP = rg

- set this up using finite difference method, taking an average of densities

- Procedure for initial model
- 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

- 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

- 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

- 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

- 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

- 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!

MovieTime!

(maybe)

- 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

- 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

- 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!

- Thanks to:
- Mike Zingale and Jonathan Dursi
- Prof. Don Lamb
- the ASCI FLASH Center
- the University of Chicago