1. Radiative Transfer with Sphray (Smoothed Particle Hydrodynamics Ray Tracer)
Gabriel Altay
Advisor: Rupert Croft
Partner in Crime: Inti Pelupessy
Carnegie Mellon University
Short and sweet
Numerical Tool

2. Co-moving Coordinates ?
Component
Numerical
Methods
Relevant
Forces
Velocity
Dark Energy
Co-moving Coordinates ?
Dark Matter
N-Body
(Particle Mesh,
BH Tree …)
Gravity
Particle Velocity
10’s - 100’s of km/s
Baryonic Matter
Smoothed Particle Hydrodynamics (SPH) / Adaptive Mesh Refinement (AMR)
Gravity +
(Magneto) Hydrodynamics
Sound Speed
Radiation
Ray Tracing / Moment Methods / Monte Carlo
Electromagnetism
Light Speed
300,000 km/s
Cosmological components
Methods aggreed upon in gravity and gas dynamics
Subgrid models are not
Radiative transfer is in development

3. Cosmological Simulations Detailed Physics vs. Run Time
N-body
Hydrodynamics
Feedback
Radiative Transfer
Dark Matter +
Adiabatic Ideal Gas +
SF, Cooling, SN, BH …
Ionization State
Momentum transfer from dust

4. (The SPH in Sphray)

5. RT Comparison Project I
Variety of RT codes and methods
OTVET: moment method - diffusion
CRASH: monte carlo
IFT: sharp ionization front approx

6. Nice Things About Sphray

7. Speed Ray-cer
SPH particles are stored in an Oct-Tree structure (the number of particles in each leaf is user defined)
For each ray, Sphray uses the Plücker method to perform an Axis Aligned Bounding Box (AABB) Test to determine the particle intersections (Mahovsky and Wyvill, The Journal of Graphics Tools, 2004).

8. Time Steps
The speed which with ionization fronts travel through gas normally imposes severe time step restraints.
Use of time averaged optical depths and photo ionization rates + iterative solution of ionization fractions allows for much longer time steps.
Method introduced in the code C2-Ray (astro-ph/ )

9. SPH all the way through
No artifacts from interpolating SPH particles onto a grid.
Democratic handling of gravity, hydrodynamics and radiative transfer.

10. Monte Carlo Sampling
For each ray traced, Sphray samples a spectrum and an emission profile.
Very easy to incorporate sources with arbitrary spectra and arbitrary emission profiles + include background and diffuse ionizing radiation.
Method introduced in the code CRASH (astro-ph/ )

11. Benchmark Test astro-ph/0603199
100,000 K Blackbody Spectrum
L = 5.0*1048 ergs/s
n=.001 cm-3
100% Hydrogen (by number)
0% Helium (by number)
Initial Temperature = 100 K
Gas Initially Fully Neutral
t = 10 Myr, 100Myr, 500Myr years ~ 4 trec

12. Code Verification: Ionization Fronts (astro-ph/0603199)
Low neutral fraction near the center, ionization profile

13. Ionization structure another view

14. Code Verification: Temperature (astro-ph/0603199)

15. Temperature profile

16. A More Challenging Test astro-ph/0307117 (CRASH)
60,000 K Blackbody Spectrum
L = 1.0*1038 ergs/s
n=1.0cm-3
90% Hydrogen (by number)
10% Helium (by number)
Initial Temperature = 100 K
Gas Initially Fully Neutral
t = 600,000 years ~ 5 trec

17. The following plots are very rough comparisons
The following plots are very rough comparisons. They are two plots superimposed, one from the CRASH paper and one from Sphray results. The bottom right corners are aligned. CRASH - Red, Sphray - Green, Cloudy94 - Line

18. Temperature

19. Hydrogen I

20. Hydrogen II

21. Helium I

22. Helium II

23. Helium III

24. Possible Applications
Calculation of ionization bubbles for reionization / 21 cm maps.
Escape fraction of galactic photons
High resolution feed back models

25. Thanks!