TOWARDS A REALISTIC, DATA-DRIVEN THERMODYNAMIC MHD MODEL OF THE GLOBAL SOLAR CORONA Cooper Downs, Ilia I. Roussev, Bart van der Holst, Noe Lugaz, Igor V. Sokolov, and Tamas I. Gombosi arXiv: submitted 12/08/2009 to ApJ

Abstract They implemented a thermodynamic energy equation into the global corona model. They compared the model results to full sun EUV and soft X-Ray observations. They found that a relative simple empirical heating model is adequate in reproducing structures observed in the low corona. They showed that the interplay between coronal heating and electron heat conduction provides significant feedback onto the 3D magnetic topology in the low corona.

Coronal Heating Problem How the solar corona can be heated to 1MK? Wave or nanoflare? Hinode – Temperature structure in coronal loop (Tripathi et al. 2009, Kano et al. 2008) – Heating at footpoint of AR loop (Hara et al. 2008) – Timescale of nanoflare (Terzo) – Upflow in plage (Imada et al. 2007) – High temperature plasma (Reale et al. 2009, Ishibashi et al.) Many simulations – Antolin, P. PhD Thesis – Matsumoto, T. PhD Thesis

Parameterized heating It is difficult to include the small-scale micro physics of plasma responsible for coronal heating in 3D models. As a result, heating models are often parameterized as a heating term that depends on various local magnetic and thermodynamic properties that is included in the energy equation. There are the large number of ad-hoc heating models (e.g. Aschwanden & Schrijver (2002); Schrijver et al. (2004); Abbett (2007); Mok et al. (2008)).

Data driven approach Constraining physical theories and scenarios through as many observable manifestations available is important. They modify the global corona model of the Space Weather Modeling Framework (Toth et al. 2005) to include the transition region between the chromosphere and the corona. The now relevant non-MHD terms (radiation, heat conduction, and coronal heating) are added to the MHD energy equation.

2. The simulation Tool They use Space Weather Modeling Framework (SWMF) Solar Corona model (Cohen et al. 2007) and Wang-Sheeley-Arge (WSA) model (Arge et al. 2004). The advantage of this tool is its ability to simulate the complete 3D environment of any event and Carrington Rotation. The initial magnetic configuration is extrapolated using the Potential Field Source Surface Method (Altschuler et al. 1977).

2.2. Including Additional Thermodynamic Terms Heat conduction Radiative Loses Heating Model 1 Heating Model 2 Total unsigned magnetic flux at the solar surface Constant Local heating weighting function

2.2. Including Additional Thermodynamic Terms Coronal hole heating Open field cutoff – Open field (coronal hole) => only “coronal hole heating” is applied – Closed field => both are applied

2.3. Boundary Conditions Chromospheric boundary – Chromospheric values are set to be – Broadening method in transition region Radiative Energy Balance (REB) Model – In high transition region,

2.4. Geometric Considerations Sun-centered 48x48x48R sun cube. Average cell size is smallest at the surface (~7000km). The block-adaptive mesh and adaptive mesh refinement capability.

3. Model Runs MDI magnetogram, CR 1913, centered on Aug 27, Solar minimum. Compared with SOHO EIT(171, 195, and 284A), and Yohkoh SXT observation.

Run A Run B Run C Run D Observation

Run C and D Run C (Uniform Heating)Run D (Exponential + AR Heating) This result suggests a complex relationship both between the thermodynamics of the low corona and the global structure of the solar wind.

4. Detailed analysis (Run D) Run D (Exponential Heating + AR heating)Yohkoh SXT AlMg response

PFSSM (Altschuler et al. 1977) Standard SC model (Cohen et al. 2007) Run D

Obs. Standard SC model (Cohen et al. 2007)

Standard SC model (Cohen et al. 2007) Run D Temperature Distribution R=1.01 R=1.03 R=1.10

Standard SC model (Cohen et al. 2007) Run D Electron Density Distribution R=1.01 R=1.03 R=1.10