1. The Importance of Curvature and Density Gradients for Nucleosynthesis by Detonations in Type Ia Supernovae
Broxton Miles + Dean Townsley
Fifty One Ergs 2017, Corvallis, Oregon
June 8, 2017

2. Requirements of Our Models
The observable features of Type Ias are primarily determined by two things
Light curves powered by Ni56 abundance
Spectral features determined by abundances of IMEs
This means that our simulations/calculations/models need to accurately predict these abundances.
Why should you believe our or anyone’s calculations?
The burning structures are never fully resolved
We resort to sub-grid models and post-processing.
Models can be tuned look like Type Ias, but are these physical?
Are our simulations accurately capturing the physical processes involved in these explosions?

3. A Verification Study
The original purpose of this work was to create a set of benchmark yields with which we could make comparisons
Fully resolved (not really, more like resolved as possible)
Large nuclear reaction networks
Species
Take a sub-Chandrasekhar mass white dwarf and send a detonation through it.
FLASH Hydrodynamics code for the explosion simulation
Integrated the nuclear reaction network from the Modules for Experiments in Stellar Astrophysics (MESA)

4. Explosion Simulation
We take a 0.8 solar mass, 50/50 carbon oxygen white dwarf, and send a detonation through it.
Detonation initiated by a ~100 km temperature gradient in the center with a peak temperature of 1.98e9 K 1D
205 isotope network
Lagrangian tracer particles recorded density-temperature histories for post- processing
MESA also used for post-processing.

5. First Results
Here we look at the abundance profiles in mass from the hydro and the mesa post-processing
One would hope they would be the same
They are clearly not
Ni56 Yields
Hydro: .11 Msolar
Post-Processing: .056 Msolar
Which is “correct”?

6. Detonations
If we’re not resolving the detonation in hydro, we shouldn’t trust the abundances that come out of it.
However, directly post-processing the particles probably isn’t a great idea either
The unresolved structure is imprinted in the temperature-density histories.
We need some method to reconstruct the unresolved portion of the detonation, that takes into account all of the important pieces of detonation physics.

7. Detonations – The Zel’dovich-von Neumann-DÖring (ZND) detonation model
Independently developed by three different scientists in the 1940s…
One dimensional model of detonations
Unreacted material is met by a shock which brings the material to peak pressure.
Chemical reactions occur in an exothermic reaction zone behind the shock
The reaction zone terminates at the sonic point, where the flow is then causally disconnected from the detonation.
All energy from the reaction zone is available to power the shock
IOP

8. Curved Detonations The ideal detonation is planar.
Detonations in type Ias have only positive curvature
This causes the flow to be divergent
Energy is lost to radial flow ( the x-direction in this picture)
The sonic point moves to the point where the energy loss to radial motion is equal the energy produced from the reaction zones
Moves inward  less energy available to power the detonation
Aslim 1996

9. Curvature in Type Ias
In 1D, the curvature of the detonation in the white dwarf is determined by its radial position in the star
That is kappa = 1/radius of curvature = 1/radius
For low densities and sufficient curvatures, the detonation is no longer able to propagate and burning ceases.
Black lines from Dunkley et al 2013

10. Post-Processing and Curvature
Thanks to Kevin Moore, we now have a tool that allows us to do ZND calculations with curvature
EZND
Uses the MESA reaction network
Takes density, temperature, radius of curvature, and detonation velocity and does a ZND integration
The density, temperature, and radius of curvature are all taken from the progenitor environment.
What do we use for the detonation velocity?

11. Shock/Detonation Speed
Here is the calculated speed compared to the eigenvalue speeds, the lowest speed sufficient for a steady state detonation, in these conditions
Why does the eigenvalue line just stop?
There is no eigenvalue detonation possible at that point.
Why are the measured speeds so much higher at lower densities?

12. Shock/Detonation Speed
At this point in the star, the shock is traveling down a density gradient.
The shock strengthening from this seems to be able to overcome the effects of curvature
This effect has been studied in detail within the context of shock breakout and shockwaves in a terrestrial context

13. Reconstructed Post-Processing
With this tool, we can now attempt to reconstruct the unresolved portion of the detonation in our post-processing.
When we reach a density with a detonation structure we can resolve, the hydro, bare post- processing, and reconstructed post-processing should match.

14. Full star reconstruction
The reconstruction tends to lie between the two.
The bare post-processing is actually not too bad when compared to the reconstruction.
In the regions where the detonation structure can be resolved all three match

15. Reconstructed Track

16. Summary
Due to the unresolved nature of the detonation in the hydro simulation, any abundances produced from the hydro are suspect.
The strength of the detonation is determined by the competing weakening affect of curvature and a strengthening affect from traveling down the density gradient of the progenitor.
Nucleosynthesis can occur where it would otherwise be unexpected
This will be much more complicated in multi-d since detonations will travel in different directions with respect to the gradient
By reconstructing the unresolved structure of the detonation, we can now have greater confidence in the nucleosynthetic results of our post-processing calculations.

17. Extra Slides

19. Yields Table Hydro Bare Post-Processing Reconstructed Ni56 0.119 0.057
0.059
Si28
0.247
0.307
0.300
S32
0.158
0.171
Ca40
0.04
0.031
0.033