A Semi-Analytic Model of Type Ia Supernova Turbulent Deflagration

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 BrigetFalck. “Type Ia Supernova Cosmology with ADEPT.“ John Hopkins University. 2007. 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 importantfor 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 0 20 40 60 100 120 140 80 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 0 800 1200 1600 0 400 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 0 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 0 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 0 400 800 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. Questions? A Semi-Analytic Model of Type Ia Supernovae