A Semi-Analytic Model of Type Ia Supernova Turbulent Deflagration

Kevin JumperAdvised by Dr. Robert Fisher

April 22, 2011

Introduction: Overview of a Type Ia Supernova

• Progenitor – the white dwarf, composed of carbon and oxygen, in which little burning occurs

• Progenitor accretes mass from a companion until it nears a limiting mass

• Progenitor temperature increases

• Carbon ignites in the progenitor, creating a “flame bubble”

• Detonation occurs shortly thereafter Credit: NASA, ESA, and A. Field (STScI), from Briget Falck. “Type Ia

Supernova Cosmology with ADEPT.“ John Hopkins University. 2007. Web.

Introduction: Deflagration (Burning Phase)

• Flame bubble (orange) rises through star (green) until it breaches the stellar surface (breakout)

• Deflagration phase determines spectral properties

• Fractional burnt mass is important for describing deflagration

Credit: Dr. Robert Fisher, University of Massachusetts Dartmouth

A Visualization of a Type Ia Supernova

Introduction:Why Do we Care?

• Nearly uniform luminosity – “standard candles”

• Allows accurate measurement of distances in space

• We want to understand the mechanics of supernovae before using them as such

The Semi-Analytic Model• One dimensional – a single flame bubble

expands and vertically rises through the star• The Morison equation governs bubble motion

t = timeR = bubble radiusρ1 = bubble (ash) densityρ2 = background star (fuel) density

• Proceeds until breakout

V = bubble volumeg = gravitational accelerationCD = coefficient of drag

The Semi-Analytic Model (Continued)

• The coefficient of drag depends on the Reynolds Numbers (Re).

Coefficient of Drag vs. Reynolds Number

• Δx is grid resolution

•Higher Reynolds numbers indicate greater fluid turbulence. Reynolds Number

Coeffi

cien

t of D

rag

0 40 12080 100 1406020

0.0

0.5

1.0

1.5

2.0

2.5

3.0

The Three-Dimensional Simulation

• Used by a graduate student in my research group

• Considers the entire star

• Proceeds past breakout

• Grid resolution is limited to 8 kilometers

• Longer execution time than semi-analytic model

Project Objectives

• Analyze the evolution of the flame bubble.

• Determine the fractional mass of the progenitor burned during deflagration.

• Compare the semi-analytic model results against the 3-D simulation.

Comparison with 3-D Simulations

• There is good agreement initially between the model (blue) and the simulation (black).

•The model predicts that the bubble’s speed is eventually described by a power law.

Log Speed vs. Position

Position (km)

Log

[Spe

ed (k

m/s

)]

0 400 800 1200 1600

0

1

2

3

•There is good agreement initially.

•The model and simulation diverge beyond the flame-polishing scale.

•The bubble becomes turbulent, increasing its surface area and making it less regular.

•The model’s area eventually obeys a power law.

Log Area vs. Position

Position (km)

Log

[Are

a (k

m^2

)]

0 400 800 1200 1600

3

4

5

6

7

8

Comparison with 3-D Simulations

•The model has greater volume until an offset of about 600 km.

•Note that the star is denser at lower positions.

•Volume also obeyed a power law.

Log Volume vs. Position

Position (km)

0 400 800 1200 1600

4

5

6

7

8

9

10

11

12

Log

[Vol

ume

(km

^3)]

Comparison with 3-D Simulations

•As predicted, the model’s fractional burnt mass is higher (about 3%).

•The simulation predicts about 1% at breakout.

•The assumptions of the model need to be re-examined.

Fractional Burnt Mass vs. Position

Position (km)

0 400 800 1200 1600

Frac

tiona

l Bur

nt M

ass

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

Comparison with 3-D Simulations

Future Work

• Try to narrow the discrepancy so that the model and simulation agree within a factor of two

• Consider the effects of the progenitor’s rotation on deflagration

Questions?

A Semi-Analytic Model of Type Ia Supernovae