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

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

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

(The SPH in Sphray)

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

Nice Things About Sphray

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).

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/0508416)

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

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/0307117)

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 Output @ t = 10 Myr, 100Myr, 500Myr years ~ 4 trec

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

Ionization structure another view

Code Verification: Temperature (astro-ph/0603199)

Temperature profile

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 Output @ t = 600,000 years ~ 5 trec

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

Temperature

Hydrogen I

Hydrogen II

Helium I

Helium II

Helium III

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

Thanks!