1. A Semi-Analytic Model of Type Ia Supernova Turbulent Deflagration
Kevin Jumper
Advised by Dr. Robert Fisher
April 22, 2011

2. 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 Web.

3. 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
A Visualization of a Type Ia Supernova
Credit: Dr. Robert Fisher, University of Massachusetts Dartmouth

4. 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

5. The Semi-Analytic Model
One dimensional – a single flame bubble expands and vertically rises through the star
The Morison equation governs bubble motion
t = time
R = bubble radius
ρ1 = bubble (ash) density
ρ2 = background star (fuel) density
V = bubble volume
g = gravitational acceleration
CD = coefficient of drag
Proceeds until breakout

6. The Semi-Analytic Model (Continued)
The coefficient of drag depends on the Reynolds Numbers (Re).
Coefficient of Drag vs. Reynolds Number
3.0
2.5
2.0
Coefficient of Drag
1.5
Δx is grid resolution
Higher Reynolds numbers indicate greater fluid turbulence.
1.0
0.5
0.0 20 40 60 80
100
120
140
Reynolds Number

7. 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

8. 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.

9. 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 3 2
Log [Speed (km/s)] 1
400
800
1200
1600
Position (km)

10. Comparison with 3-D Simulations
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 8 7 6
Log [Area (km^2)] 5 4 3
400
800
1200
1600
Position (km)

11. 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 12 11 10 9 8
Log [Volume (km^3)] 7 6 5 4
400
800
1200
1600
Position (km)

12. 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
0.040
0.035
0.030
0.025
Fractional Burnt Mass
0.020
0.015
0.010
0.005
0.000
400
800
1200
1600
Position (km)

13. 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

14. A Semi-Analytic Model of Type Ia Supernovae
Questions?