Numerical simulations - supporting design of facilities and interpretations

Transcription

1 Numerical simulations - supporting design of facilities and interpretations Viggo H. Hansteen Synergies between ground and space based solar research 1st SOLARNET - 3rd EAST/ATST meeting Oslo, 5-8 August 2013

2 Magnetoconvective Energy in the Photosphere Granular scale Hinode/SOT movies courtesy Alan Title Supergranular scale Magnetic Flux everywhere Continual Emergence, Field Recycled rapidly Mixed Polarity in QS Unipolarity in Plage regions

3 Groundwork done early, with competing theory of acoustic heating coming at about the same time...

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5 ...and lead to provocative questions: what is...and Simulations acoustic waves the nature drive certainly of the synthetic play energy observables a role in the budget? that can chromosphere... be directly compared with observations

6 ...and lead to provocative questions: what is Simulations the nature drive of the synthetic energy observables budget? that can be directly compared with observations

7 ...and lead to provocative questions: what is the nature of the energy budget?

8 SOHO/SUMER show acoustic waves in upper chromosphere, but something important is missing from the calculations Carlsson, Judge & Wilhelm 1997, ApJ 486 L63

9 SOHO/SUMER show acoustic waves in upper chromosphere, but something important is missing from the calculations There is a chromospheric heating problem! Carlsson, Judge & Wilhelm 1997, ApJ 486 L63

10 ...and indeed observations show that... the 5-10 mhz oscillations can be followed up into the (upper) transition region the oscillations are best seen in the line shift, but are also present as variations in the line intensity Wikstøl et al, 2000 (ApJ Volume 531, Issue 2, pp )

11 Transition region (C IV nm) lines...have many characteristics that are not straight forward to explain. Peter 1999 (ApJ 516, 490)

12 The MHD equations ρ (ρu ) t + = 0 e t + (eu) + p u = F r + F c + ηj 2 + Q visc B t = (u B) + η 2 B ρu t + (ρuu + τ) = p + j B gρ with some equation of state... T g,p g = EOS(e, )

13 The MHD equations ρ t + (ρu ) = 0 B t = (u B) + η 2 B Realistic models e t + (eu) + p u = F r + F c + ηj 2 + Q visc ρu t + (ρuu + τ) = p + j B gρ with some equation of state... T g,p g = EOS(e, )

14 Results from all three codes considered here have already passed various reality checks by comparison with observational data (e.g., Danilovic et al. 2008; Pereira et al. 2009a,b; Wedemeyer-Böhm & Rouppe van der Voort 2009; Hirzberger 2010). Although the three numerical solar models considered here (CO 5 BOLD, MURaM, and Stagger) result from codes with different numerical methods and from simulation boxes of different size and spatial grid resolution, their overall agreement is very good and encouraging. Beeck et al. 2012, A&A 539, 121

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16 In Norse mythology, Bifröst or Bilröst is a burning rainbow bridge between Midgard, the world, and Asgard, the realm of the gods. The bridge is made from fire, water and air, the traditional hydrodynamic variables.... The bridge's destruction at Ragnarök by the forces of Muspell is foretold.... A significant investment in code development and analysis of which physics Scholars have proposed that the bridge may have originally represented the Milky Way and have noted parallels between the bridge and another bridge in Norse mythology, Gjallarbrú. need to be included - of order 10 years... from Wikipedia

17 BIFROST Hansteen 2004, Hansteen, Carlsson, Gudiksen 2007, Sykora, Hansteen, Carlsson 2008, Gudiksen et al th order scheme, with artificial viscosity/diffusion Open vertical boundaries, horizontally periodic Possible to introduce field through bottom boundary Realistic EOS Detailed radiative transfer along 48 rays Multi group opacities (4 bins) with scattering NLTE losses in the chromosphere, optically thin in corona Conduction along field lines Operator split and solved by using multi grid method Time dependent Hydrogen ionization Generalized Ohm s Law

18 BIFROST Hansteen 2004, Hansteen, Carlsson, Gudiksen 2007, Sykora, Hansteen, Carlsson 2008, Gudiksen et al th order scheme, with artificial viscosity/diffusion Open vertical boundaries, horizontally periodic Possible to introduce field through bottom boundary Realistic EOS Detailed radiative transfer along 48 rays Multi group opacities (4 bins) with scattering NLTE losses in the chromosphere, optically thin in corona Conduction along field lines Operator split and solved by using multi grid method Time dependent Hydrogen ionization Generalized Ohm s Law

19 BIFROST Hansteen 2004, Hansteen, Carlsson, Gudiksen 2007, Sykora, Hansteen, Carlsson 2008, Gudiksen et al th order scheme, with artificial viscosity/diffusion Open vertical boundaries, horizontally periodic Possible to introduce field through bottom boundary Realistic EOS Detailed radiative transfer along 48 rays Multi group opacities (4 bins) with scattering NLTE losses in the chromosphere, optically thin in corona Conduction along field lines Operator split and solved by using multi grid method Time dependent Hydrogen ionization Generalized Ohm s Law

20 BIFROST Hansteen 2004, Hansteen, Carlsson, Gudiksen 2007, Sykora, Hansteen, Carlsson 2008, Gudiksen et al th order scheme, with artificial viscosity/diffusion Open vertical boundaries, horizontally periodic Possible to introduce field through bottom boundary Realistic EOS Detailed radiative transfer along 48 rays Multi group opacities (4 bins) with scattering NLTE losses in the chromosphere, optically thin in corona Conduction along field lines Operator split and solved by using multi grid method Time dependent Hydrogen ionization Generalized Ohm s Law

21 Equation of State The basic assumption is that the plasma is in LTE so that all needed quantities can be looked up as functions of density and internal energy. P g (,e), T g (,e), R(,e) For radiation with scattering we also need B bin (,e), bin (,e), bin(,e)

22 Equation of State The basic assumption is that the plasma is in LTE so that all needed quantities can be looked up as functions of density and internal energy. P g (,e), T g (,e), R(,e) For radiation with scattering we also need B bin (,e), bin (,e), bin(,e) Can remove Hydrogen from tables if running explicit time dependent ionization of Hydrogen

23 Optically thick radiation Z r F r =4 (B J ) d Assume opacities in LTE and coherent scattering Calculate group mean opacities and group mean source functions The resulting non-lte 3D scattering problem is solved by iteration Scattering crucial for proper description of upper photosphere/lower chromosphere Nordlund 1982 A&A 107, 1; Skartlien 2000 ApJ 536, 465

24 non-lte radiative losses in Mg II, Ca II, H Q X = L Xm (T )E Xm ( ) N X m N X (T )A X N H n e the optically thin radiative loss function the probability that this energy escapes from the atmosphere the fraction of atoms in the given ionization stage Carlsson & Leenaarts 2012, A&A 539, 39 =

25 non-lte radiative losses in Mg II, Ca II, H Q X = L Xm (T )E Xm ( ) N X m N X (T )A X N H n e the optically thin radiative loss function Incoming radiation field from corona also the probability that this energy escapes from the included for upper chromosphere atmosphere the fraction of atoms in the given ionization stage Carlsson & Leenaarts 2012, A&A 539, 39 =

26 Thermal Conduction Numerical analysis severely strained by Courant condition - which with conduction scales as the grid size squared (Δs 2 ). An implicit operator to solve diffusive part of operator Proceed by operator splitting High order explicit method with Hyman time-stepping is used to solve MHD Multigrid method is used to solve diffusive operator

27 What does it all cost? (Bifrost) Cray XT4 Intel (SGI ICE) Radiation + Conduction + MHD Conduction + MHD MHD Note that for coronal runs, with short Δt, radiation need only be run every 30 timesteps or so...

28 What does it all cost? (Bifrost) Cray XT4 Intel (SGI ICE) Radiation + Conduction + MHD Typical time steps are of order a few x 10-3 s Conduction + MHD so a 1 hour run takes of order 70 days to complete for 64 3 grid points per core MHD Note that for coronal runs, with short Δt, radiation need only be run every 30 timesteps or so...

29 Initial condition - how to set B? Corona Transition region Chromosphere Photosphere

30 Initial condition - how to set B? Corona Transition region Chromosphere Photosphere

31 abs(b) at y=12 Mm

32 Ortiz et al in prep; de la Cruz et al in prep Observations Need to compare apples with apples Simulations T,ρ,B,u... => IQUV Spectral and Stokes Synthesis IQUV => T,ρ,B,u... Inversions Or combinations of the two

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35 Coronal Heating from field line braiding - nano flares dense, non-lte tenous, optically thin B 2 /2μ0 ηj 2

36 Coronal Heating from field line braiding - nano flares Magnetic heating dominates dense, non-lte tenous, optically thin B 2 /2μ0 ηj 2

37 Resulting temperature structure see also Hansteen et al. 2010, ApJ 718.

38 p (B2 ) <Q J / > AC 500 km 1000 km 3000 km 9200 km

39 ηj 2 highly variable in space and time

40 200 km 3 regions

41 Important part of IRIS project is to model the lines observed, in particular those from the upper chromosphere, TR and corona

42 Three papers on Mg II h/k line formation: Leenarts et al. 2013a,b and Pereira et al (in prep) Pereira et al. (in preparation, 2013) Simulated Mg II k images with IRIS spectral resolution Simulated Mg II k spectra along slit

43 Three papers on Mg II h/k line formation: Leenarts et al. 2013a,b and Pereira et al (in prep) Pereira et al. (in preparation, 2013) Simulated Mg II k images with IRIS spectral resolution Simulated Mg II k spectra along slit

44 C II nm p (Itot ) Rathore et al. 2013

45 C II nm p (Itot ) Rathore et al. 2013

46 The formation of the OI Å and CI Å lines in solar atmosphere Hsiao-Hsuan Lin,Jorrit Leenaart, Mats Carlsson Institute of Theoretical Astrophysics, The intersystem line from neutral oxygen at nm and the allowed line from neutral carbon at nm are both within the FUV range of the NASA/SMEX mission Interface Region Imaging Spectrograph (IRIS). The ratio between OI nm and CI nm has been reported showing drastic changes during solar flares (Skylab observations and others). The ratio has also been reported to be dependent on the electron density and could possibly provide a density diagnostic in the solar chromosphere. In this work we try to understand the formation properties of O I and C I to enable full radiative transfer calculations with the RH code even in big 3D model atmospheres. We find that the oxygen ionization degree is strongly coupled to the ionization degree of hydrogen. The intensity of the CI line is sensitive to the line profile of Lyman-alpha. For this reason, hydrogen has The ratio between O I Å intersystem line (2s 2 2p 4 3 P2-2s 2 2p 3 3s 5 S2) and C I Å permitted line (2s 2 2p 2 1 D2-2s 2 2p 4d 1 F3) has been reported strong enhancement during the solar flare([1],[2]). It is postulated that the huge enhancement of the C I line indicates the flaring region where these lines originated should have high electron densities. This phenomenon requires more detailed study as the range of these two lines will also been covered by NASA/SMEX mission Interface Region Imaging Spectrograph(IRIS). In this Method We employed the radiative transfer code RH([3]) to run the full calculation on O I and C I formation. We need to run with hydrogen first, and took the solution as the feed of the run of O I C I combined afterwards. The results presented here is based on the simplified O I atomic model([4]) and the full C I model from Diper. The calculations are based on the plane-parallel atmosphere model FAL-C([5]). References [1] Cheng, C. C., Feldman, U., & Doschek, F. A Astron. Astrophys. 86, 377 [2] Cheng, C. C Solar. Phys. 56, 205 [3] Uitenbroek, H ApJ. 557, 389 [4] Carlsson, M. & Judge, P.G ApJ, 402, 344 [5] Fontenla,J.M.,Avrett, E. H., & Loeser, R. 1990, ApJ, 355, 700 Lin et al. 2013

47 Effect on density sensitive line ratio Statistical equilibrium ne non-equilibrium ne Olluri et al. 2013, Apj 767, 43

48 Synthetic IRIS spectral data Pereira, Carlsson, Lin, Rathore, Leenaarts, Wiesmann, Hansteen, 2013 FUV 2 NUV

49 Synthetic IRIS Slit Jaws C II Mg II core Si IV Mg II cont

50 IRIS simulator - use of simulations to plan observations

51 Release of numerical simulation as as part of IRIS data product FITS files cell centered, index and z-axis starting in convection zone and increasing upwards

52 Bifrost coordinate system Variables on staggered grid Internal units (Mm, hs, 10-7 g cm -3, Mm/hs etc) * Uz, Bz X Y * Ux, Bx * * Uy, By e, ρ, Tg, Z

53 FITS files Z Variables all cell centered SI units (Mm, s, kg m -3, m/s, etc) Y * e, ρ, Tg, Ux, Uy, Uz, Bx, By, Bz,... X

54 File Format Level 2: D(x,y,z) one file per variable per timestep (481 MB) Level 3: D(x,y,z,t) one file per variable (240/76 GB) Level 2 Level 3 with provided SW Level 3 transpose (D(z,t,x,y)) with provided SW it=385+indgen(160) br_make_fits_level3, en024048,it, tg, /log,/byte br_transpose_fits_level3, BIFROST_en024048_tg_im.fits

55 Variables e, Ux, Uy, Uz, ρ, Bx, By, Bz Tg, Pg, Ne, Q en024048: 2.5 TB

56 Synthetic observations Need to define FITS keywords What lines/resolutions/approximations?

57 Documents Paper describing simulation characteristics Papers describing formation of Mg lines, C II, C I & O I, non-equilibrium ionization,... ITN giving technical details format, keywords, auxiliary software Bifrost document describing how to create FITS files from Bifrost files, relation between Bifrost conventions and FITS files conventions

58 Enhanced network 24x24x17 Mm (2.5 Mm below, 14.5 Mm above z=0) 504x504x496 grid 48 km horizontal, km vertical polarities separated by 8 Mm < B >=30-50 G en024048_hion (1600s)

59 Winebarger et al. 2013, ApJ 771, 21

60 IRIS lines: absolute I in upper chromosphere/lower TR HRTS QS atlas (stray light continuum ) Bifrost (synthetic spectra) SUMER QS & CH atlas (continuum level)

61 IRIS lines: absolute I in upper chromosphere/lower TR HRTS QS atlas (stray light continuum ) Bifrost (synthetic spectra) For your amusement: in order to achieve a good fit between the synthetic absolute intensities and observed atlas intensities Si abundance was set to 8.1 i.e. coronal O was set to 8.69 i.e. Asplund abundance SUMER QS & CH atlas (continuum level)

62 Conclusions Realistic models a very important tool used in all phases of, e.g., the IRIS project writing of proposal planning of instrument design construction of data pipeline: from observation to QL software (with exception of telemetry reformatting) debugging of same software planning of observation programs analysis of data and isolation of specific physical effects occurring in solar atmosphere

63 Diffusion coefficients and the hyperdiffusive operator ν x = v 1 xc f + v 2 x u x + v 3 x u ( B 2 ) 1/2 + γp with c f = ρ appears in equations with terms such as (ρu x ) t =... x ( ρν x u x x ) +... etc... where the first derivative is replaced by d +,x(f) = max x±1 3 f max x±1 f +,x(f)

64 Heating via magnetic dissipation Q Joule = E J J = B where the resistive part of the electric field is E η x = { 1 2 (η(1) y + η z (1) ) + 1 } 2 (η(2) y + η z (2) ) where the resistivities are given by η (1) j = x j Pr M (v 1 c f + v 2 u j ) η (2) j = x2 j Pr M v 3 u J x