Modelling stellar atmospheres with full Zeeman treatment

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1 1 / 16 Modelling stellar atmospheres with full Zeeman treatment Katharina M. Bischof, Martin J. Stift M. J. Stift s Supercomputing Group FWF project P16003 Institute f. Astronomy Vienna, Austria CP#AP workshop 12 th of September 2007

2 2 / 16 Contents 1 2 3

3 2 / 16 Contents 1 2 3

4 2 / 16 Contents 1 2 3

5 3 / 16 Outline of the problem Outline of the problem Bagnulo et al., 2001, A&A 369, 889 Properties of magnetic CP stars: upper main sequence stars T eff ranging from to K spectrum and photometric variability peculiar and stratified abundances magnetic fields, B ranging from 100 G to 35 kg, up to 100 kg at magnetic poles

6 3 / 16 Outline of the problem Outline of the problem Bagnulo et al., 2001, A&A 369, 889 Properties of magnetic CP stars: upper main sequence stars T eff ranging from to K spectrum and photometric variability peculiar and stratified abundances magnetic fields, B ranging from 100 G to 35 kg, up to 100 kg at magnetic poles

7 3 / 16 Outline of the problem Outline of the problem Bagnulo et al., 2001, A&A 369, 889 Properties of magnetic CP stars: upper main sequence stars T eff ranging from to K spectrum and photometric variability peculiar and stratified abundances magnetic fields, B ranging from 100 G to 35 kg, up to 100 kg at magnetic poles

8 3 / 16 Outline of the problem Outline of the problem Bagnulo et al., 2001, A&A 369, 889 Properties of magnetic CP stars: upper main sequence stars T eff ranging from to K spectrum and photometric variability peculiar and stratified abundances magnetic fields, B ranging from 100 G to 35 kg, up to 100 kg at magnetic poles

9 4 / 16 Outline of the problem Outline of the problem requirements specification for the atmospheric model code temperature range (of interest): to K peculiar and stratified abundances arbitrary inclination of the field in plane parallel models full Zeeman treatment, polarised Feautrier solver hydrostatic equilibrium with magnetic pressure VALD line data, CoCoS simplifications: plane parallel, Kurucz continuum routines, no dynamic phenomena considered, no microturbulence.

10 5 / 16 Software engineering Polarised radiation transfer Temperature correction Program features: ATLAS12 continua for comparability with standard models consistent with spectral synthesis (COSSAM) and radiative diffusion (CARAT) code written in Ada95 thread parallel modularised, object oriented

11 5 / 16 Software engineering Polarised radiation transfer Temperature correction Program features: ATLAS12 continua for comparability with standard models consistent with spectral synthesis (COSSAM) and radiative diffusion (CARAT) code written in Ada95 thread parallel modularised, object oriented

12 5 / 16 Software engineering Polarised radiation transfer Temperature correction Program features: ATLAS12 continua for comparability with standard models consistent with spectral synthesis (COSSAM) and radiative diffusion (CARAT) code written in Ada95 thread parallel modularised, object oriented

13 5 / 16 Software engineering Polarised radiation transfer Temperature correction Program features: ATLAS12 continua for comparability with standard models consistent with spectral synthesis (COSSAM) and radiative diffusion (CARAT) code written in Ada95 thread parallel modularised, object oriented

14 6 / 16 Software engineering Polarised radiation transfer Temperature correction Polarised radiation transfer equation d dz I = K I + K (S, 0, 0, 0) Stokes vector I = (I, Q, U, V ) absorption matrix K = κ c 1 + κ o Φ line absorption matrix Φ = Show details φ I φ Q φ U φ V φ Q φ I φ V φ U φ U φ V φ I φ Q φ V φ U φ Q φ I z, I B γ χ x y

15 7 / 16 Zeeman Feautrier solver Software engineering Polarised radiation transfer Temperature correction Feautrier equation can be generalised to the magnetic case in the presence of blends (see Alecian and Stift, 2004, A&A 416, 703) d J dτ 5000 = XH dh and dτ 5000 = X( J S) with X := K κ 5000 µ d dτ 5000 (X 1 d J dτ 5000 ) = X( J S) (inner points) dx 1 dτ 5000 d J dτ X 1 d 2 J dτ = X( J S) (boundary condition) N equations, N unknowns B 1 J1 C 1 J2 = L 1 A n Jn 1 + B n Jn C n Jn+1 = L n A N JN 1 + B N JN = L N

16 Temperature correction Software engineering Polarised radiation transfer Temperature correction Dreizler s Lucy Unsöld scheme adapted for polarised radiation transport equations: (see Dreizler, 2003, ASPC 288, 69) momenta of the polarised radiation transport equation differences ( X = X Equilibrium X Model ) of flux, intensity and radiation pressure two flux criteria local balance of emitted versus absorbed energy d(h I ) z dτ 5000 = 0 (constant flux) cannot be used in deep layers where the atmosphere becomes diffusive and S J local Planck function. nonlocal condition of constant flux: 0 Show momenta HI dωdν σ 4π T 4 eff = 0 (desired value of the flux) inefficient in regions with small opacities 8 / 16

17 9 / 16 Combining the flux criteria Software engineering Polarised radiation transfer Temperature correction T = π 4σT 3 R S d [Kν «J 0 ν] I dν 1 R [Kν] 0 I,IS S νdν {z } local energy conservation S R + d [Kν J 0 ν] I dν 2 R J I [Kν] 0 I,IS νdν f 0 H I (0) fg {z } surface flux S R + d [Kν J 0 ν] I dν 3 R J I [Kν] 0 I,IS νdν Z τ 0 1 f R 0 [Kν H ν] I dν H I κ 5000 H I dτ 5000 {z } global energy conservation «

18 10 / 16 Results and comparisons Comparison with Carpenter s results Comparisons with LLMODELS Summary Two effects enhanced line blanketing magnetic pressure Comparison with the results of Carpenter (enhanced line blanketing and magnetic pressure see Carpenter, 1985, ApJ 289, 660, Carpenter, 1983, PhD Thesis ) LLMODELS (enhanced line blanketing, see Kochukhov et al., 2005, A&A 433, 671, Khan and Shulyak, 2006a, A&A 448, 1153, Khan and Shulyak, 2006b, A&A 454, 933)

19 11 / 16 Comparison with Carpenter s results Comparisons with LLMODELS Summary Comparison with Carpenter s results CAMAS results Carpenter, 1985, ApJ 289, 660

20 12 / 16 Comparisons with LLMODELS Comparison with Carpenter s results Comparisons with LLMODELS Summary differences between the field less and the isotropic model CAMAS results Kochukhov et al., 2005, A&A 433, 671

21 12 / 16 Comparisons with LLMODELS Comparison with Carpenter s results Comparisons with LLMODELS Summary differences between the field less and the isotropic model CAMAS results Kochukhov et al., 2005, A&A 433, 671

22 13 / 16 Depth scales Comparison with Carpenter s results Comparisons with LLMODELS Summary τ ross is affected by (magnetic) line blanketing, τ 5000 is not directly affected

23 14 / 16 Depth scales Comparison with Carpenter s results Comparisons with LLMODELS Summary τ ross is affected by (magnetic) line blanketing, τ 5000 is not directly affected

24 15 / 16 Comparison with LLMODELS Comparison with Carpenter s results Comparisons with LLMODELS Summary differences between the anisotropic and the isotropic model CAMAS results

25 15 / 16 Comparison with LLMODELS Comparison with Carpenter s results Comparisons with LLMODELS Summary differences between the anisotropic and the isotropic model Khan and Shulyak, 2006b, A&A 454, 933

26 Comparison with LLMODELS Comparison with Carpenter s results Comparisons with LLMODELS Summary differences between the anisotropic and the isotropic model CAMAS results Khan and Shulyak, 2006b, A&A 454, 933 Zoom 15 / 16

27 16 / 16 Summary Comparison with Carpenter s results Comparisons with LLMODELS Summary The Zeeman effect enhances the opacity. This affects the optical depth and the temperature structure. CAMAS essentially confirms the results of LLMODELS. The isotropic models are largely identical, however the anisotropic models with strong magnetic fields exhibit notable differences that need to be clarified. The atmospheres computed with CAMAS will be used (among others) for the modelling of diffusion processes. Acknowledgements: this work was supported by the Austrian Science Funds (FWF project P16003 of M.J.Stift). KMB wants to thank Bob Kurucz for the useful discussions on the ATLAS code, Christian Stütz and the VALD team for the line data and Holger Pikall for tree weeks of CPU-time.

28 17 / 16 Bibliography I Appendix References Alecian, G. and Stift, M. J.: 2004, A&A 416, 703 Bagnulo, S., Wade, G. A., Donati, J.-F., Landstreet, J. D., Leone, F., Monin, D. N., and Stift, M. J.: 2001, A&A 369, 889 Carpenter, K. G.: 1983, Ph.D. thesis, AA(Ohio State Univ., Columbus.) Carpenter, K. G.: 1985, ApJ 289, 660 Dreizler, S.: 2003, in I. Hubeny, D. Mihalas, and K. Werner (eds.), ASP Conf. Ser. 288: Stellar Atmosphere Modeling, Vol. 288 of ASP Conference Series, p. 69, Review of temperature correction schemes, Damping Khan, S. A. and Shulyak, D. V.: 2006a, A&A 448, 1153 Khan, S. A. and Shulyak, D. V.: 2006b, A&A 454, 933 Kochukhov, O., Khan, S., and Shulyak, D.: 2005, A&A 433, 671

29 Appendix References Comparison with LLMODELS differences between the anisotropic and the isotropic model CAMAS results Khan and Shulyak, 2006b, A&A 454, 933 Return 18 / 16

30 19 / 16 first depth point Appendix References d J dτ = X 1 ( J 1 (1 e τ 1X 1 ) S 1 ) J1 = d J 2 τ J (2,1) dτ 1 ( τ (2,1)) 2 d 2 J 2 dτ ( forward Taylor series) A 1 = 0 B 1 = 1 + τ (2,1) X 1 ( τ (2,1)) 2 dx 1 X 1 1 X 1 + ( τ (2,1)) 2 X dτ C 1 = 1 L1 = ( τ (2,1) ( τ (2,1)) 2 dx 1 X 1 1 )X 1 (1 e τ 1X 1 ) S 1 + ( τ (2,1)) 2 X 2 1S 1 2 dτ

31 20 / 16 inner depth points Appendix References d d J dτ X 1 = dτ n X 1 Jn+1 J n n+ 1 τ X 1 Jn J n 1 (n+1,n) n 1 τ (n,n 1) 2 2 τ (n+1,n) + τ (n,n 1) 2 A n = B n = C n = (X n 1 + X n ) 1 τ (n,n 1) τ (n+1,n 1) (X n 1 X n ) 1 (X 1 n X n) 1 + X n τ (n,n 1) τ (n+1,n 1) τ (n+1,n) τ (n+1,n 1) (X n+1 + X n ) 1 τ (n+1,n) τ (n+1,n 1) Ln = X n Sn

32 Flowchart of CAMAS Appendix References read input, initialise enter radiative equilibrium loop check convection recompute equidistant τ 5000 and interpolate model data EXIT if convergence criteria are met pretabulate continua if necessary reselect lines if necessary enter integration loop (> 90% of computation time) independent tasks use a magnetic Feautrier solver for all wavelength points and add the results calculate temperature corrections calculate and apply pressure corrections search for noise in the flux distribution and check convergence apply temperature corrections if not converged yet apply Ng acceleration (optional) 21 / 16

33 22 / 16 Feautrier solver Appendix References solve radiation transport equation as boundary value problem di ± dτ 5000 = I ± S define flux like and intensity like quantities combine equations for outward and inward rays discretize and add boundary conditions

34 22 / 16 Feautrier solver Appendix References solve radiation transport equation as boundary value problem define flux like and intensity like quantities H n = I+ n I n 2, J n = I+ n + I n 2 combine equations for outward and inward rays discretize and add boundary conditions

35 22 / 16 Feautrier solver Appendix References solve radiation transport equation as boundary value problem di ± dτ 5000 = I ± S define flux like and intensity like quantities combine equations for outward and inward rays dj dh = H, = J S dτ 5000 dτ }{{ 5000 } d 2 J dτ = J S discretize and add boundary conditions

36 22 / 16 Feautrier solver Appendix References solve radiation transport equation as boundary value problem define flux like and intensity like quantities combine equations for outward and inward rays discretize and add boundary conditions I (τ = 0) = 0, no incident radiation on the surface dj dτ 5000 τ=0 = J(τ = 0) H N = I + N J N, diffusive at innermost depth-point dj N = I + N dτ J N with I + N = S N + ds N 5000 dτ 5000

37 Appendix References Angle dependent opacity line absorption terms φ I = φ Q = φ U = φ V = φ p, b, r Faraday terms φ Q = φ U = φ V = φ p, b, r Return 1 4 (2 φ p sin 2 γ + (φ r + φ b )(1 + cos 2 γ)) 1 4 (2 φ p (φ r + φ b )) sin 2 γ cos 2χ 1 4 (2 φ p (φ r + φ b )) sin 2 γ sin 2χ 1 2 (φ r φ b ) cos γ... line absorption profiles 1 4 (2 φ p (φ r + φ b )) sin2 γ cos 2χ 1 4 (2 φ p (φ r + φ b )) sin2 γ sin 2χ 1 2 (φ r φ b ) cos γ... anomalous dispersion profiles z B I β θ x ψ y z, I B γ x χ y 23 / 16

38 24 / 16 Appendix References Combining the flux criteria Return 0th moment: d H I 4σT 3 π dh eq dτ R 5000 [K 0 νxν,eq] I dν X eq S T = 4σT 3 π R 0 R 0 dτ 5000 = [Kν J ν] I dν κ 5000 = 0, 0th moment for dhmod dτ R 5000 [K 0 νxν,mod] I dν X model T = S [Kν J ν] I dν R 0 [Kν] I,IS S + S νdν R d K I 0 dτ 5000 = [Kν H ν] I dν κ 5000 integration variable Eddington factors f τ = Kτ 1st moment: f J I }{{} K I = f0 g H I (0) + τ 0 R 0 R 0 R 0 [Kν] I,IS νdν [Kν] I,I S νdν κ 5000 R 0 J τ and g = H 0 [Kν H ν] I dν κ 5000 dτ 5000 [Kν J ν] I dν J I J I J 0

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