MHD simulations of Coronal Mass Ejections in the global corona P. Pagano 1 D.H. Mackay 1 , A. Yeates 2 1 University of St Andrews, 2 Durham University − − − − − − − − − − −− 2nd SolarNet Meeting, Palermo February 2nd 2015
Coronal Mass Ejection Coronal plasma and magnetic field Speed: ∼ 450 km / s Speed range: 100 to 3000 km / s Space Weather impact Three components structure
Ejection of Flux Rope The ejection of a flux rope is believed to be the progenitor of CMEs. It is also a component of the flare standard model. Cheng et al., 2011
Boundary conditions of Space Weather At ∼ 4 R ⊙ CME are blown in the solar wind Magnetized plasmoid the Solar Wind can deflect the ICME The CME plasmoid can rotate The ”Bz” component of the magnetic field (perpendicular to ecliptic) is crucial for the impact of the ICME on the Earth-magneosphere
Boundary conditions of Space Weather Space Weather forecast: arrival time and properties of CMEs For Space Weather forecast, we need: efficiency on computation accuracy on the injection of the CME in the solar wind
Life of flux Rope: formation Patsourakos et al., 2013 Formation of flux rope: accumulation of free magnetic energy Flux rope formation Slow formation: days or weeks Quasi-static evolution. ( t >> τ Alf ) Magnetic evolution: β << 1 everywhere
Life of flux Rope: ejection Flux rope ejection: release of energy Flux rope ejection Fast ejection: flux rope travels out of the corona in ∼ 2 hours Highly dynamic evolution. ( t ∼ τ Alf ) Full MHD: plasma is locally compressed. ( β ≥ 1)
Strategy: Pagano et al.,2013. We couple two models. Model the life span of Flux Rope Global Non-Linear Force Free Field (GNLFFF) evolution model Flux rope formation Decribes a magnetically dominated evolution Models the evolution of corona for weeks Computationally efficient: magnetofrictional technique MHD Simulation with the MPI-AMRVAC code Flux rope ejection Accounts for plasma and magnetic field Models multi- β domain
Ejection of the flux rope: 3D MHD Simulation MPI-AMRVAC: KU Leuven MHD ∂ρ ∂ t + � ∇ · ( ρ� v ) = 0 , (1) ∇ × � B ) × � v ) + ∇ p − ( � ∂ρ� v B ) + � ∇ · ( ρ� v � = + ρ� g , (2) ∂ t 4 π ∂� B v × � ∂ t − � ∇ × ( � B ) = 0 , (3) ∂ e ∂ t + � v − n 2 χ ( T ) − ∇ · � ∇ · [( e + p ) � v ] = ρ� g · � F c , (4) ∇ · � B = 0 (5) � B 2 γ − 1 = e − 1 p v 2 − 2 ρ� 8 π , (6) g = − GM ⊙ � ˆ r , (7) r 2
What we achieved so far... Pagano et al.,2013, A&A, 554, A77 it is possible to couple the GNLFFF model with the MHD AMRVAC code we follow the life span of a flux rope from formation to ejection the stress accumulated during the formation justifies a flux rope ejection
What we achieved so far... Pagano et al.,2013, A&A, 560, A38 we study the role of the gravitational stratification on the early progation of a CME we identify the parameter space where ejections are more likely
What we achieved so far... Pagano et al.,2014, A&A, 568, A120 Non ideal MHD simulation of flux rope ejection Study of the role of thermal conduction and radiative cooling Synthesis of SDO/AIA observations
CME MHD simulation of the global corona Coupling MHD simulation with Global code The Global code uses a series of Magnetograms as boundary conditions Accounts for flux emergence and flux cancellation at the solar surface Predicts the formation of most flux ropes
A vec implementation MHD ( � A ) ∂ρ ∂ t + � ∇ · ( ρ� v ) = 0 , (8) v ) + ∇ p − ( � ∇ × � ∇ × � A ) × ( ∇ × � ∂ρ� v A ) + � ∇ · ( ρ� v � = + ρ� g , (9) ∂ t 4 π ∂� A v × ( � ∇ × � ∂ t = � A ) , (10) ∂ e ∂ t + � v − n 2 χ ( T ) − ∇ · � v ] = ρ� ∇ · [( e + p ) � g · � F c , (11) v 2 − ( � ∇ × � A ) 2 γ − 1 = e − 1 p 2 ρ� , (12) 8 π g = − GM ⊙ � ˆ r , (13) r 2
Advantages of the � A formulation ∇ · � B = 0 Direct coupling with GNLFFF and back Mind that: Stencil of the numerical model Boundary conditions in terms of � A
⊲ ⊲⊲ ⊲⊲ Computational efficiency of the GNLFFF model Accuracy and generality of MPI-AMRVAC MHD simulations
t t CPU ∼ 0 . 0005 t t CPU ∼ 15 —- From magnetograms to GNLFFF From GNLFFF to MHD Feasible approach for Space Weather Forecast. GNLFFF ∼ 30 K more efficient than MHD
PRELIMINARY SIMULATION Magnetic configuration from the evolution of actual magnetograms We can study the reaction of the global magnetic field to the ejection The post ejection magnetic field can become initial conditions for the GNLFFF model
� A -MHD 2D Test � � A MHD B MHD
� A -MHD 3D Spherical Test Initial Condition
� A -MHD 3D Spherical Test Final evolution
� A -MHD 3D Spherical Test Difference � A -MHD/MHD
Conclusions MHD simulation of flux rope ejections The coupling of GNLFFF and MPI-AMRVAC is a reliable technique to model the life span of a flux rope This model is able to reproduce the main features of a flux rope ejection (time scale, shape) We idenfied a parameter space where the ejections are favoured Using also Non-Ideal term in the MHD simulation we can reproduce AIA/SDO observations of flux rope ejections MHD simulation of flux rope ejection in the global corona We developed a new numerical model to solve MHD equations in terms of the potential vector A We run MHD simulations of the global corona during flux rope ejections The mutual coupling of GNLFFF and MPI-AMRVAC will lead to a feasible way to provide Space Weather models with accurate and realistic boundary conditions opening the way to a new generation of Space Weather forecasting tools.
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