Unstructured grids for Astrophysics Gas dynamics and radiative transfer

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

2. Overview • 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 • Examples • Current techniques: Adaptive Mesh Refinement • Future techniques: Unstructured grids • Examples • My new all-round astro RT package: RADMC-3D • Need CG library for unstructured grids

3. 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:

4. Radiative transfer

5. 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. • Problem: dust temperature is affected by radiation, even the radiation it emits itself. • Therefore: must solve radiative transfer and thermal balance simultaneously. • Difficulty: each point in cloud can heat (and receive heat from) each other point.

6. Example: Studying Planetary Birthplaces the so called “Protoplanetary Disks”

7. Here is the star hidden = 500x Distance Earth-Sun = 16x Distance Neptune-Sonne Planetary birth site in the Orion Nebula Hubble Space Telescope Image

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

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

10. HD163296 “Virtual Telescope” Model: Observations:

11. Example: Infrared spectra of disks Dust continuum spectra of a number of protoplanetary disks Furlan et al. 2006

12. Example: Infrared spectra of disks Gas (CO) emission lines from a protoplanetary disk Goto, Dullemond et al. 2008

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

14. Disk has hot translucent surface layer

15. Viewing a protoplanetary disk

16. Viewing a protoplanetary disk

17. But Nature is not smooth or axisymmetric...

18. Disks are clumpy / spiraly / asymmetric AB Aurigae: a proto- planetary disk Fukagawa et al. 2004

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

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

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

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

23. Formation of stars By Matthew Bate Uni Exeter, UK

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

25. Bottom lines... • Modern astrophysical simulations are evolving more and more to full 3-D • Such models often cover huge ranges of scales: • Star formation: from parsec to solar radius = 108 • Planet formation: from 10 AU to Earth radius = 105 • Galaxy formation: from kilopc to central BH = 1012 • etc. • Grid refinement essential. Currently usually AMR type. • Unstructured grids may (will) revolutionize this field.

26. Current methods: Adaptive Mesh Refinement (AMR)

27. Current methods: AMR Paramesh library

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

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

30. Unstructured grids are now slowly being recognized in the astrophysical community

31. 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.

32. 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.

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

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

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

36. Example Simple model of star formation

37. Example Simple model of star formation

38. Synthetic observations λ=1000 μm

39. Synthetic observations λ=100 μm

40. Synthetic observations λ=50 μm

41. Synthetic observations λ=40 μm

42. Synthetic observations λ=30 μm

43. Synthetic observations λ=20 μm

44. Synthetic observations λ=10 μm

45. Conclusions • 3-D complex models are more and more common in astrophysics. • 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. • Unstructured grids now slowly start being used in mainstream RT software (though still very much in its infancy)

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