Novae and Mixing

1
Novae and Mixing

• John ZuHone
• ASCI/Alliances Center for Thermonuclear Flashes
• University of Chicago

2
Overview

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

3
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

4
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

5
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
• where
• E e ½v2

6
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

7
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

8
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

9
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

10
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

11
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

12
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

13
(No Transcript)
14
(No Transcript)
15
Doing the Problem

• Loading the model into FLASH
• load the model in and see if the simulation is in
  hydrostatic equilibrium
• it ISNT!
• high velocities at interface and boundary
• begin to examine the model for possible flaws

16
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

17
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

18
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!

19
Movie Time!

• (maybe)

20
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

21
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

22
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!

23
Conclusions

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