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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: Small introduction to the physics of radiative transfer

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slide1

Unstructured grids for Astrophysics

Gas dynamics and

radiative transfer

C.P. Dullemond

Max Planck Institute for Astronomy

Heidelberg, Germany

overview
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
radiative transfer
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:

difficulty of dust 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.
  • 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.
slide6

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

Planetary birth site in the Orion Nebula

Hubble

Space

Telescope

Image

disk structure

z

R

Hydrostatic equilibrium:

Disk structure

1 AU

10 AU

100 AU

Need temperature!

disk structure1

z

R

Moving radiation through matter:

Interaction radiation - matter:

Disk structure

1 AU

Radiative transfer

10 AU

100 AU

example infrared spectra of disks
Example: Infrared spectra of disks

Dust continuum

spectra of a

number of

protoplanetary

disks

Furlan et al. 2006

example infrared spectra of disks1
Example: Infrared spectra of disks

Gas (CO) emission lines

from a protoplanetary

disk

Goto, Dullemond et al. 2008

radiative transfer2
Radiative transfer

Emission/absorption lines:

Hot surface layer

Cool surface layer

Flux

Flux

slide17

But Nature is not smooth

or axisymmetric...

disks are clumpy spiraly asymmetric
Disks are clumpy / spiraly / asymmetric

AB Aurigae:

a proto-

planetary

disk

Fukagawa et al. 2004

complex geometries huge size ranges
Complex geometries, huge size ranges

Eagle Nebula

(M16)

Picture credit: T.A. Rector & B.A. Wolpa

complex geometries huge size ranges1
Complex geometries, huge size ranges

Eagle Nebula

(M16)

Picture Credit: J. Hester & P. Scowen

complex geometries huge size ranges2
Complex geometries, huge size ranges

Eagle Nebula

(M16)

Picture Credit: J. Hester & P. Scowen

complex geometries huge size ranges3

size of our solar system

Complex geometries, huge size ranges

Eagle Nebula

(M16)

Picture Credit: J. Hester & P. Scowen

formation of stars
Formation of stars

By Matthew Bate

Uni Exeter, UK

formation of planets clumps waves
Formation of planets: clumps, waves

Rice, Lodato et al. 2004

bottom lines
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.
slide26

Current methods:

Adaptive Mesh Refinement

(AMR)

current methods amr
Current methods: AMR

Paramesh library

can zoom in arbitrarily much
Can zoom in arbitrarily much...

Abel, Bryan and Norman 1999

problems
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
slide30

Unstructured grids are now

slowly being recognized in

the astrophysical community

a new hydro scheme by volker springel
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 springel1
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
Delaunay grids for radiative transfer

Model of a protoplanetary disk

by Christian Brinch (Leiden University, the Netherlands)

slide34

RADMC-3D

A new 3-D versatile radiative

transfer package for astrophysics

(in progress)

based on 2-D code RADMC

radmc 3d features
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
example
Example

Simple model

of star formation

example1
Example

Simple model

of star formation

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