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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

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Novae and Mixing

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Novae and Mixing

John ZuHone

ASCI/Alliances Center for Thermonuclear Flashes

University of Chicago

Overview l.jpg


  • Purpose

  • What is FLASH?

  • Mixing in Novae

  • Setting Up the Problem

  • Doing the Problem

  • Conclusions

Purpose l.jpg


  • 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

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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

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What is FLASH?

  • Euler equations of hydrodynamics

    ¶r/¶t + Ñ • rv = 0

    ¶rv/¶t + Ñ • rvv + ÑP = rg

    ¶rE/¶t + Ñ • (rE + P) v = rv • g


    E = e + ½v2

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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 + Ñ • rXlv = 0

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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

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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

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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

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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

      ÑP = rg

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

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Setting Up the Problem

  • 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

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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

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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

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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

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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

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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


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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

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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

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  • 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!

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  • Thanks to:

    • Mike Zingale and Jonathan Dursi

    • Prof. Don Lamb

    • the ASCI FLASH Center

    • the University of Chicago

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