Radiative Transfer with Sphray(Smoothed Particle

Hydrodynamics Ray Tracer)

Gabriel Altay

Advisor: Rupert Croft

Partner in Crime: Inti Pelupessy

Carnegie Mellon University

ComponentNumerical

MethodsRelevant

ForcesRelevant Velocity

Dark EnergyCo-moving Coordinates

? ?

Dark MatterN-Body

(Particle Mesh, BH Tree …)

GravityParticle Velocity

10’s - 100’s of km/s

Baryonic Matter

Smoothed Particle Hydrodynamics (SPH) / Adaptive Mesh Refinement

(AMR)

Gravity +(Magneto)

Hydrodynamics

Sound Speed10’s - 100’s of km/s

RadiationRay Tracing /

Moment Methods / Monte Carlo

ElectromagnetismLight Speed300,000 km/s

Cosmological Simulations Detailed Physics vs. Run Time

• N-body• Hydrodynamics• Feedback• Radiative Transfer

• Dark Matter + • Adiabatic Ideal Gas +• SF, Cooling, SN, BH …• Ionization State

(The SPH in Sphray)

RT Comparison Project I

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 Testastro-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)

Code Verification: Temperature (astro-ph/0603199)

A More Challenging Testastro-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. 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!