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

• 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

t + • v = 0

vt + • vv + P = g

Et + • (E + P) v = v • g

where

E = + ½v2

What is FLASH?

• Pressure obtained using equation of state– ideal gas

P = ( 1)– other equations of state (i.e. for degenerate

Fermi gases, radiation, etc.)

• For reactive flows track each species

Xlt + • Xlv = 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 = g– set this up using finite difference method,

taking an average of densities

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

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:

o = 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:– Mike Zingale and Jonathan Dursi– Prof. Don Lamb– the ASCI FLASH Center– the University of Chicago