Unstructured grids for AstrophysicsUnstructured grids for Astrophysics

Gas dynamics andGas dynamics andradiative transferradiative transfer

C.P. DullemondC.P. DullemondMax Planck Institute for AstronomyMax Planck Institute for Astronomy

Heidelberg, GermanyHeidelberg, Germany

OverviewOverview• Radiative transfer (RT) in astrophysics:Radiative transfer (RT) in astrophysics:

– Small introduction to the physics of radiative transferSmall introduction to the physics of radiative transfer– Example of protoplanetary disks: how to link theory to Example of protoplanetary disks: how to link theory to

observations.observations.

• Future of RT in astrophysics:complex geometriesFuture of RT in astrophysics:complex geometries– ExamplesExamples

• Current techniques: Adaptive Mesh RefinementCurrent techniques: Adaptive Mesh Refinement

• Future techniques: Unstructured gridsFuture techniques: Unstructured grids– ExamplesExamples

• My new all-round astro RT package: RADMC-3DMy new all-round astro RT package: RADMC-3D– Need CG library for unstructured grids Need CG library for unstructured grids

Radiative transferRadiative transfer

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dIνds= ρ κ ν (Sν − Iν )

Radiative transfer equation:Radiative transfer equation:

Over length scales larger than 1/Over length scales larger than 1/ intensity I tends to intensity I tends to

approach source function S. approach source function S.

Photon mean free path:Photon mean free path:

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lfree,ν =1

ρ κ ν

Optical depth of a Optical depth of a cloud of size L:cloud of size L:

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τ =L

lfree,ν= Lρκ ν

In case of local thermodynamic In case of local thermodynamic equilibrium: S is Planck function:equilibrium: S is Planck function:

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Sν = Bν (T)

Radiative transferRadiative transfer

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Iνobs = Iν

0e−τν + (1− e−τν ) Bν (T)

Difficulty of dust radiative Difficulty of dust radiative transfertransfer

• If temperature of dust is given (ignoring scattering for the If temperature of dust is given (ignoring scattering for the moment), then radiative transfer is a mere integral along a moment), then radiative transfer is a mere integral along a ray: i.e. easy.ray: i.e. easy.

• Problem:Problem: dust temperature is affected by radiation, even the dust temperature is affected by radiation, even the radiation it emits itself.radiation it emits itself.

• Therefore:Therefore: must solve radiative transfer and thermal must solve radiative transfer and thermal balance simultaneously. balance simultaneously.

• Difficulty:Difficulty: each point in cloud can heat (and receive heat each point in cloud can heat (and receive heat from) each other point.from) each other point.

Example:Example:

Studying Planetary BirthplacesStudying Planetary Birthplaces

the so called the so called ““Protoplanetary Disks”Protoplanetary Disks”

Planetary birth site in the Planetary birth site in the Orion NebulaOrion Nebula

Here is the star hiddenHere is the star hidden

= 500x Distance Earth-Sun= 500x Distance Earth-Sun= 16x Distance Neptune-Sonne= 16x Distance Neptune-Sonne

HubbleHubbleSpaceSpaceTelescopeTelescopeImageImage

Disk structureDisk structure

1 AU10 AU

100 AU

z

R

Hydrostatic equilibrium:Hydrostatic equilibrium:

Need temperature!Need temperature!

Disk structureDisk structure

1 AU10 AU

100 AU

z

R

Moving radiation through matter:Moving radiation through matter:

Interaction radiation - matter:Interaction radiation - matter:

Radiative transferRadiative transfer

““Virtual Telescope”Virtual Telescope”

HD163296

Model:Model: Observations:Observations:

Example: Infrared spectra Example: Infrared spectra of disksof disks

Furlan et al. 2006Furlan et al. 2006

Dust continuumDust continuumspectra of aspectra of anumber of number of protoplanetaryprotoplanetarydisksdisks

Example: Infrared spectra Example: Infrared spectra of disksof disks

Goto, Dullemond et al. 2008Goto, Dullemond et al. 2008

Gas (CO) emission linesGas (CO) emission linesfrom a protoplanetaryfrom a protoplanetarydiskdisk

Radiative transferRadiative transferEmission/absorption lines:Emission/absorption lines:

Hot surface layerHot surface layer

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τ ≤1

€

τ >>1

FluxFlux

Cool surface layerCool surface layer

FluxFlux

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Iνobs = Iν

0e−τν + (1− e−τν ) Bν (T)

Disk has hot translucent Disk has hot translucent surface layersurface layer

Viewing a protoplanetary Viewing a protoplanetary diskdisk

Viewing a protoplanetary Viewing a protoplanetary diskdisk

But But NatureNature is not smooth is not smoothor axisymmetric...or axisymmetric...

Disks are clumpy / spiraly / Disks are clumpy / spiraly / asymmetricasymmetric

Fukagawa et al. 2004Fukagawa et al. 2004

AB Aurigae:AB Aurigae:

a proto-a proto-planetary planetary diskdisk

Eagle Eagle NebulaNebula(M16)(M16)

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

Complex geometries, huge Complex geometries, huge size rangessize ranges

Picture Credit: J. Hester & P. ScowenPicture Credit: J. Hester & P. Scowen

Complex geometries, huge Complex geometries, huge size rangessize ranges

Eagle Eagle NebulaNebula(M16)(M16)

Picture Credit: J. Hester & P. ScowenPicture Credit: J. Hester & P. Scowen

Complex geometries, huge Complex geometries, huge size rangessize ranges

Eagle Eagle NebulaNebula(M16)(M16)

Picture Credit: J. Hester & P. ScowenPicture Credit: J. Hester & P. Scowen

size of our solar systemsize of our solar system

Complex geometries, huge Complex geometries, huge size rangessize ranges

Eagle Eagle NebulaNebula(M16)(M16)

Formation of starsFormation of stars

By Matthew BateBy Matthew BateUni Exeter, UKUni Exeter, UK

Formation of planets: Formation of planets: clumps, wavesclumps, waves

Rice, Lodato et al. 2004Rice, Lodato et al. 2004

Bottom lines...Bottom lines...• Modern astrophysical simulations are evolving Modern astrophysical simulations are evolving

more and more to more and more to full 3-Dfull 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 = 10Star formation: from parsec to solar radius = 1088

– Planet formation: from 10 AU to Earth radius = 10Planet formation: from 10 AU to Earth radius = 1055 – Galaxy formation: from kilopc to central BH = 10Galaxy formation: from kilopc to central BH = 101212 – etc.etc.

• Grid refinement essential. Currently usually Grid refinement essential. Currently usually AMR type.AMR type.

• Unstructured grids may (will) revolutionize this Unstructured grids may (will) revolutionize this field.field.

Current methods:Current methods:

Adaptive Mesh RefinementAdaptive Mesh Refinement(AMR)(AMR)

Current methods: AMRCurrent methods: AMR

Paramesh libraryParamesh library

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

Abel, Bryan and Norman 1999Abel, Bryan and Norman 1999

ProblemsProblems• Preferential directions, may lead to artificial Preferential directions, may lead to artificial

effectseffects

• No Galilei-invarianceNo Galilei-invariance

• Jump-like transitions at refinement boundaries Jump-like transitions at refinement boundaries may cause problemsmay cause problems

• Moving objects require continuous de-Moving objects require continuous de-refinement and refinementrefinement and refinement

• Hierarchical oct-tree structure can be Hierarchical oct-tree structure can be cumbersome to handle for the usercumbersome to handle for the user

Unstructured grids are nowUnstructured grids are nowslowly being recognized inslowly being recognized in

the astrophysical communitythe astrophysical community

A new hydro scheme (by A new hydro scheme (by Volker Springel)Volker Springel)

Code is calledCode is called““Arepo”, authorArepo”, authorV. Springel (MPAV. Springel (MPAGarching, Germany)Garching, Germany)

Paper in prep.Paper in prep.

Uses Voronoi diagramUses Voronoi diagramfor grid. Nice feature:for grid. Nice feature:Cells automaticallyCells automaticallyadapt to problem.adapt to problem.

A new hydro scheme (by A new hydro scheme (by Volker Springel)Volker Springel)

Code is calledCode is called““Arepo”, authorArepo”, authorV. Springel (MPAV. Springel (MPAGarching, Germany)Garching, Germany)

Paper in prep.Paper in prep.

Uses Voronoi diagramUses Voronoi diagramfor grid. Nice feature:for grid. Nice feature:Cells automaticallyCells automaticallyadapt to problem.adapt to problem.

Delaunay grids for Delaunay grids for radiative transferradiative transfer

Model of a protoplanetary diskModel of a protoplanetary disk

by Christian Brinch (Leiden University, the Netherlands)by Christian Brinch (Leiden University, the Netherlands)

RADMC-3DRADMC-3D

A new 3-D versatile radiativeA new 3-D versatile radiativetransfer package for astrophysicstransfer package for astrophysics

(in progress)(in progress)

based on 2-D code RADMCbased on 2-D code RADMC

RADMC-3DRADMC-3D: Features: Features• Continuum and gas line transferContinuum and gas line transfer

• 1-D, 2-D and 3-D models1-D, 2-D and 3-D models

• Cartesian or spherical coordinatesCartesian or spherical coordinates

• Various gridding possibilities:Various gridding possibilities:– RegularRegular– Regular + AMRRegular + AMR– Tetrahedral / DelaunayTetrahedral / Delaunay– Voronoi Voronoi

ExampleExampleSimple modelSimple modelof star formationof star formation

ExampleExampleSimple modelSimple modelof star formationof star formation

Synthetic observationsSynthetic observationsλ=1000 μmλ=1000 μm

Synthetic observationsSynthetic observationsλ=100 μmλ=100 μm

Synthetic observationsSynthetic observationsλ=50 μmλ=50 μm

Synthetic observationsSynthetic observationsλ=40 μmλ=40 μm

Synthetic observationsSynthetic observationsλ=30 μmλ=30 μm

Synthetic observationsSynthetic observationsλ=20 μmλ=20 μm

Synthetic observationsSynthetic observationsλ=10 μmλ=10 μm

ConclusionsConclusions• 3-D complex models are more and more 3-D complex models are more and more

common in astrophysics.common in astrophysics.

• AMR currently the standard, but has problemsAMR currently the standard, but has problems

• In spite of their seeming complexity, In spite of their seeming complexity, unstructured grids may actually be easier than unstructured grids may actually be easier than AMR-like techniques, provided a good library for AMR-like techniques, provided a good library for such gridding is used.such gridding is used.

• Unstructured grids now slowly start being used Unstructured grids now slowly start being used in mainstream RT software (though still very in mainstream RT software (though still very much in its infancy)much in its infancy)

Wish listWish list• Periodic spacesPeriodic spaces

• Incremental updates, if faster than redoingIncremental updates, if faster than redoing

• Implementation on GPUs, if this brings speedupImplementation on GPUs, if this brings speedup