Photon Scattering in 3D Radiative MHD

Simulations

Wolfgang HayekMPA/RSAA/UIO

Collaborators

Radiative Transfer and Stellar Atmospheres:Martin Asplund, Regner Trampedach, Remo Collet

Developers of the Bifrost Code:Boris Gudiksen, Mats Carlsson, Viggo Hansteen, Jorrit Leenaarts, Juan Martinez Sykora

Overview

1. 3D Model Atmospheres

2. The 3D Radiative Transfer Solver

3. Effects in the Sun

4. Metal-poor stars

Image: SOHO (ESA/NASA)

Cool stellar atmospheres

‣ Energy transport mainly through radiation and convection

‣ Rapid transition of optical depth at the surface

‣ Requires models that include hydrodynamics and radiative transfer

Model Requirements

‣ Plane parallel model⇒ Box-in-a-star

‣ Large-Eddy simulation

‣ Assumption of ergodicity

‣ Large enough to cover granule dynamics

‣ Deep enough to cover several pressure scale heights

Governing equations!"

!t+!·"u = 0Mass conservation

!"u!t

+! ["(u" u)] +!#visc +!p = #"gMomentum

!e

!t+! (eu) + p!u = Qrad + QviscEnergy conservation

p = p(!, e)EOS andRadiative Transfer

n ·!I = "!I + !S

Temperature Slice

Radiative Transfer

‣ Radiative cooling drives convection

‣ Includes scattering and absorption processes

‣ Scattering previously treated as absorption

‣ Skartlien (2000): Scattering in 3D time-dependent MHD simulations

Scattering Processes

‣ Continuum:Electron scatteringRayleigh scattering

‣ Lines:van Regemorter approximation for scattering probabilities

‣ Approximation: coherent scattering

H I

Radiative Transfer

‣ Time-independent, assume static medium

‣ Look up precomputed quantities (LTE)

‣ Use multi-group opacities

‣ Include coherent scattering term in S

‣ J-S splitting yields heating/cooling rates

S = (1! !)J + !B

n ·!I = "!I + !S

!F = "!J + !S

The Gauss-Seidel Scheme

‣ Trujillo Bueno & Fabiani Bendicho (1995)

‣ Uses Short Characteristics

‣ Start with first-guess source function (previous time step)

‣ Compute corrections during the sweep

Parallelization

‣ MPI parallelism for high resolution or refined opacity treatment

‣ Subdomain decompo-sition best for MHD

‣ Ray decomposition best for radiation, but...• Load balancing issues• Large comm. load• Limited node memory

Parallelization

‣ Use serial solver on MHD subdomains

‣ Flexible for massively parallel applications

‣ SCs have small stencil

‣ Needs iterative solution (but scattering needs iterations anyway)

‣ Store incoming intensities in ghost zones

SC vs LC Feautrier‣ Gauss-Seidel yields fast convergence, but

formal solution may be slower

‣ Reaches similar computation speeds as Skartlien’s LC-Feautrier method

‣ Feautrier method: no full subdomain decomposition yet (no vertical divisions)

‣ RT compute speeds: ~seconds per timestep, Wolfgang’s programming speed: ~months

Test simulation:Solar photosphere

‣ Three cases:LTEContinuum scatteringCont. + line scattering

‣ Check impact on the temperature structure

‣ Implications for line formation

Importance of Scattering

‣ Line and continuum scattering (opacity group means)

Solar photosphere

‣ Red: scattering as absorption, Blue: true scattering

Solar photosphere

‣ Scattering reduces re-heating of the upper photosphere

Solar photosphere

‣ Green: line scattering as absorption, other colors as before

A very metal-poor Sun

‣ Hypothetical star (?)

‣ Solar Teff and logg

‣ MARCS opacities, Mihalas-Hummer-Däppen EOS

‣ Opacity binning

[Fe/H]=-3.0

Electron Densities

‣ Metals are important electron donors

Rosseland Opacities

‣ Metal-poor Sun lacks line opacities

Sun vs. metal-poor Sun

‣ Expansion cooling vs. radiative heating in upper photosphere

LTE vs. Cont. Scattering

‣ Mean structure and RMS deviation, Teff=5910 K

What about giants?

‣ Rayleigh scattering is an important opacity source!

What about giants?

‣ After ~7 hours of simulation time, VERY preliminary

Summary

1. Fully parallel code for scattering radiative transfer in 3D (M)HD simulations

2. Continuum scattering is not important in solar-type stars, independent of metallicity

3. More important in giant stars, to be done very soon...

Thanks for listening...

Extra Material

1. H- bf, H- ff

2. H bf, H ff

3. H2- ff, H+H, H2, H2+

4. He-, He, He+

5. Various metals (CNO, Ne, Na, Mg, ...)

6. OH, CH, H20, CO, H+He, H2+H, H2+He, H2+H2

Opacity Sources

Flux Divergence

‣ Flux divergence yields heating/cooling rates

‣ ∇F round-off problematic in the optically thin

‣ J-S round-off problematic in the optically thick

‣ No energy transfer through scattering!

!F = "!J + !S

F = n!

I !n,n!" d!!

3D vs. 1D

‣ No dynamical cooling in 1D (Image: Asplund et al., 2001)

10 Jun 2005 22:18 AR AR251-AA43-12.tex XMLPublishSM(2004/02/24) P1: KUVAR REVIEWS IN ADVANCE10.1146/annurev.astro.42.053102.134001

12.10 ASPLUND

Figure 2 Same as Figure 1 but for [Fe/H] = !3.0 (Asplund & Garcıa Pcrez 2001). Notethat the 3D model has temperatures much below the radiative equilibrium expectations inthe optically thin layers due to the dominance of expansion cooling in upflows over radiativeheating owing to spectral lines. The large difference in temperature with the 1D model canhave a profound impact on lines sensitive to those atmospheric layers.

quantitative manner (e.g., Atroshchenko & Gadun 1994; Kiselman & Nordlund1995; Gadun & Pavlenko 1997; Kiselman 1997; Uitenbroek 1998; Asplund et al.1999, 2000a,b,c, 2004, 2005; Asplund 2000, 2004a,b; Allende Prieto, Lambert &Asplund 2001, 2002; Asplund & Garcıa Perez 2001; Shchukina & Trujillo Bueno2001; Allende Prieto et al. 2002; Nissen et al. 2002; Steffen & Holweger 2002;Shchukina, Trujillo Bueno & Asplund 2005). The current state-of-the-art in 3Dhydrodynamical modeling of stellar atmospheres (e.g., Stein & Nordlund 1998;Freytag, Steffen & Dorch 2002; Carlsson et al. 2004; Vogler 2004) solves the stan-dard equations for conservation of mass, momentum, and energy in connection withthe 3D radiative transfer equation for a representative volume of the stellar surfacecovering typically >10 granules at any one time. The vertical extent is normally"10 pressure scale-heights, which in the Sun corresponds to approximately 3 Mm(3 # 106 m) below the surface to at least up to the temperature minimum around0.5 Mm above. The numerical resolution is typically "1003 gridpoints, which ap-pears to be sufficient for line-formation purposes (Asplund et al. 2000a). Realisticequation-of-state and opacities with line-blanketing accounted for through opacitybinning (Nordlund 1982) are used; tests show that the predicted radiative heatingagrees to typically approximately 1% with detailed opacity sampling calculations

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Interpolation

‣ Need second-order formal solution

‣ Need second-order interpolation (χ, S, I)

‣ Reduced SC diffusion!

χ, S, I

?

3D Radiative Transfer

10000

8000

6000

Tem

pera

ture

in K

‣ Temperature contrast at depth z=145 km (Sun)

3D Radiative Transfer

‣ (Rosseland) Opacity contrast at depth z=145 km

‣ Flux divergence is sensitive to the numerical method

10-5

10lo

g(κ R

oss)

in c

m-1

10-6

10-7

‣Does not depend on a specific transition (e.g. quantum mechanical coupling of angular momenta)‣Electrons dominate collisional de-excitation

!! =1

(Aij/Cij) + 1

Cij

Aij= 20.6!3neT

!1/2PN,I

!!E

kt

"

T^-1/2 is wrong!!!T^-3/2!!!!

! = " + # ! = "/#

The (M)HD Solver

‣ Finite Difference method on a staggered mesh

‣ Explicit time stepping (3rd order Runge-Kutta)

‣ Quenched hyperviscosity stabilization

‣ Massively MPI parallel (subdomain decomposition)

• • • • •• • • • •• • • • •• • • • •• • • • •

• • • •• • • •• • • •• • • •• • • •

• • • • •• • • • •• • • • •• • • • •

• scalars • vectors

∆x

3D Spectral Line Formation

‣ Line shifts, broadening, intensity contrast

‣ Finite resolution, unresolved stellar disk: overlay of spectra

‣ Line asymmetry traces velocity field above the optical surface

3D Spectral Line Formation

Observational Test

‣ Model bisectors vs. observations (Asplund et al., 2000)

1DFe I 6804.2Fe I 6271.2Fe I 6240.6