# Novae and Mixing - PowerPoint PPT Presentation

1 / 23

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

## Related searches for Novae and Mixing

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Novae and Mixing

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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

¶r/¶t + Ñ • rv = 0

¶rv/¶t + Ñ • rvv + ÑP = rg

¶rE/¶t + Ñ • (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 + Ñ • 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

ÑP = rg

• 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:

ro = 3.4 × 103 g cm-3

### Doing the Problem

• 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!

## MovieTime!

(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