Unstructured grids for Astrophysics Gas dynamics and radiative transfer C.P. Dullemond Max Planck Institute for Astronomy Heidelberg, Germany

Overview Radiative transfer (RT) in astrophysics: Radiative transfer (RT) in astrophysics: –Small introduction to the physics of radiative transfer –Example of protoplanetary disks: how to link theory to observations. Future of RT in astrophysics:complex geometries Future of RT in astrophysics:complex geometries –Examples Current techniques: Adaptive Mesh Refinement Current techniques: Adaptive Mesh Refinement Future techniques: Unstructured grids Future techniques: Unstructured grids –Examples My new all-round astro RT package: RADMC-3D My new all-round astro RT package: RADMC-3D –Need CG library for unstructured grids

Radiative transfer Radiative transfer equation: Over length scales larger than 1/ intensity I tends to approach source function S. Photon mean free path: Optical depth of a cloud of size L: In case of local thermodynamic equilibrium: S is Planck function:

Radiative transfer

Difficulty of dust radiative transfer If temperature of dust is given (ignoring scattering for the moment), then radiative transfer is a mere integral along a ray: i.e. easy. If temperature of dust is given (ignoring scattering for the moment), then radiative transfer is a mere integral along a ray: i.e. easy. Problem: dust temperature is affected by radiation, even the radiation it emits itself. Problem: dust temperature is affected by radiation, even the radiation it emits itself. Therefore: must solve radiative transfer and thermal balance simultaneously. Therefore: must solve radiative transfer and thermal balance simultaneously. Difficulty: each point in cloud can heat (and receive heat from) each other point. Difficulty: each point in cloud can heat (and receive heat from) each other point.

Example: Studying Planetary Birthplaces the so called Protoplanetary Disks

Planetary birth site in the Orion Nebula Here is the star hidden = 500x Distance Earth-Sun = 16x Distance Neptune-Sonne HubbleSpaceTelescopeImage

Disk structure 1 AU 10 AU 100 AU z R Hydrostatic equilibrium: Need temperature!

Disk structure 1 AU 10 AU 100 AU z R Moving radiation through matter: Interaction radiation - matter: Radiative transfer

Virtual Telescope HD Model:Observations:

Example: Infrared spectra of disks Furlan et al Dust continuum spectra of a number of protoplanetarydisks

Example: Infrared spectra of disks Goto, Dullemond et al Gas (CO) emission lines from a protoplanetary disk

Radiative transfer Emission/absorption lines: Hot surface layer Flux Cool surface layer Flux

Disk has hot translucent surface layer

Viewing a protoplanetary disk

But Nature is not smooth or axisymmetric...

Disks are clumpy / spiraly / asymmetric Fukagawa et al AB Aurigae: a proto- planetarydisk

Eagle Nebula (M16) Picture credit: T.A. Rector & B.A. Wolpa Complex geometries, huge size ranges

Picture Credit: J. Hester & P. Scowen Complex geometries, huge size ranges Eagle Nebula (M16)

Picture Credit: J. Hester & P. Scowen Complex geometries, huge size ranges Eagle Nebula (M16)

Picture Credit: J. Hester & P. Scowen size of our solar system Complex geometries, huge size ranges Eagle Nebula (M16)

Formation of stars By Matthew Bate Uni Exeter, UK

Formation of planets: clumps, waves Rice, Lodato et al. 2004

Bottom lines... Modern astrophysical simulations are evolving more and more to full 3-D Modern astrophysical simulations are evolving more and more to full 3-D Such models often cover huge ranges of scales: Such models often cover huge ranges of scales: –Star formation: from parsec to solar radius = 10 8 –Planet formation: from 10 AU to Earth radius = 10 5 –Galaxy formation: from kilopc to central BH = –etc. Grid refinement essential. Currently usually AMR type. Grid refinement essential. Currently usually AMR type. Unstructured grids may (will) revolutionize this field. Unstructured grids may (will) revolutionize this field.

Current methods: Adaptive Mesh Refinement (AMR)

Current methods: AMR Paramesh library

Can zoom in arbitrarily much... Abel, Bryan and Norman 1999

Problems Preferential directions, may lead to artificial effects Preferential directions, may lead to artificial effects No Galilei-invariance No Galilei-invariance Jump-like transitions at refinement boundaries may cause problems Jump-like transitions at refinement boundaries may cause problems Moving objects require continuous de- refinement and refinement Moving objects require continuous de- refinement and refinement Hierarchical oct-tree structure can be cumbersome to handle for the user Hierarchical oct-tree structure can be cumbersome to handle for the user

Unstructured grids are now slowly being recognized in the astrophysical community

A new hydro scheme (by Volker Springel) Code is called Arepo, author V. Springel (MPA Garching, Germany) Paper in prep. Uses Voronoi diagram for grid. Nice feature: Cells automatically adapt to problem.

A new hydro scheme (by Volker Springel) Code is called Arepo, author V. Springel (MPA Garching, Germany) Paper in prep. Uses Voronoi diagram for grid. Nice feature: Cells automatically adapt to problem.

Delaunay grids for radiative transfer Model of a protoplanetary disk by Christian Brinch (Leiden University, the Netherlands)

RADMC-3D A new 3-D versatile radiative transfer package for astrophysics (in progress) based on 2-D code RADMC

RADMC-3D : Features Continuum and gas line transfer Continuum and gas line transfer 1-D, 2-D and 3-D models 1-D, 2-D and 3-D models Cartesian or spherical coordinates Cartesian or spherical coordinates Various gridding possibilities: Various gridding possibilities: –Regular –Regular + AMR –Tetrahedral / Delaunay –Voronoi

Example Simple model of star formation

Example Simple model of star formation

Synthetic observations λ=1000 μm

Synthetic observations λ=100 μm

Synthetic observations λ=50 μm

Synthetic observations λ=40 μm

Synthetic observations λ=30 μm

Synthetic observations λ=20 μm

Synthetic observations λ=10 μm

Conclusions 3-D complex models are more and more common in astrophysics. 3-D complex models are more and more common in astrophysics. AMR currently the standard, but has problems AMR currently the standard, but has problems In spite of their seeming complexity, unstructured grids may actually be easier than AMR-like techniques, provided a good library for such gridding is used. In spite of their seeming complexity, unstructured grids may actually be easier than AMR-like techniques, provided a good library for such gridding is used. Unstructured grids now slowly start being used in mainstream RT software (though still very much in its infancy) Unstructured grids now slowly start being used in mainstream RT software (though still very much in its infancy)

Wish list Periodic spaces Periodic spaces Incremental updates, if faster than redoing Incremental updates, if faster than redoing Implementation on GPUs, if this brings speedup Implementation on GPUs, if this brings speedup