Magnetic field lines in 3D MHD models of the solar corona
Jörn Warnecke Max-Planck-Institut für
Sonnensystemforschung
Göttingen
synthetic corona from 3D MHD model
Lab experiment of a coronal loop
Oz, Myers, Yamada, Ji, Kulsrud, Xie (2011) Phys. Plas. 8, 102107
► MRX
There is a constant (in space and time) current through the structure that heats up the plasma
What does it need to model these structures? The point is to get the emission right…
3D MHD model accounting for the magnetic and the thermal structure of the atmosphere including the synthesis of the coronal emission ► conservation of mass ► conservation of momentum: gravity, Lorentz force ► energy equation: – optically thin radiative losses – heat conduction || B (Spitzer: ~T5/2 ∇||T ) – heat input – here: Ohmic heating: ~η j 2
► induction equation ► boundary conditions → provided / driven by observations to get a “realistic” model corona ► synthesize observable emission line profiles from corona
essential to get coronal pressure right !
problem: heat conduction
sets the time step → δ t ~1 ms …
Magnetohydrodynamics (MHD)
but… the devil is in the detail…
3D MHD box model of the corona
The Pencil Code Brandenburg & Dobler (2002) Comp Phys Comm 147, 471 https://code.google.com/p/pencil-code/
► high-order finite-difference modular code for compressible 3D MHD ► horizontal motions in photosphere as driver → “modified” field line braiding (Parker 1972)
► start with observed photospheric magnetogram
► energy dissipation through Ohmic-type heating ~ η j2
► concept similar to Gudiksen & Nodlund (2002, 2005a,b) ► full energy equation (heat conduction, rad. losses) → important for coronal pressure (spectral diagnostics)
photospheric magnetic field
formation height of 105 K emission
density cut
Bin
gert
& P
eter
(201
1) A
&A
530,
A11
2
3D MHD coronal model including spectral synthesis
photospheric magnetic field
105 K isosurface
density cut
→ full energy equation (heat conduction, radiative losses)
► up to 1024 x 1024 x 512 grid ► horizontally periodic, open top ► non-uniform mesh
Pencil Code Brandenburg & Dobler (2002) Comp Phys Comm 147, 471
► efficient parallelization (MPI)
3D MHD model: T, ρ, v, B
comparison
real observations Hinode / EIS Fe XV 284 Å
160”x125”
synthesized coronal emission Mg X 625 Å
intensity map (inv.) Doppler map
compare
spectral synthesis
Bingert & Peter (2011) A&A 530, A112 Peter (2010) A&A 521, A51
An evolved active region → stable loops
Temporal evolution of loops – 3D model
magnetic field at lower boundary driven by horizontal motions Bingert & Peter (2011) A&A 530, A112
► coronal box model above an active region ► field line braiding → currents → dissipation ► heating η j2 variable in time and space → produces discrete loop structures → these evolve in time
Peter & Bingert (2012) A&A 548, A1
Ohmic-type heating η j2 provides proper distribution of heating rate in space and time to produce observable structures !
Line of sight effects: “rotation” of snapshot
Peter & Bingert (2012) A&A 548, A1
Thermal structure of field lines in the loop
Magnetic field
j || B
Ohmic heating per Particle
Hohm/N ~ exp (-z/H)
Current along the the loop
j along loop negative in coronal region
I = j||.A = j.B/|B| . A A=|B0|/|B| . π(0.5 Mm)^2
J!
Model of an emerging
active region
Coronal model driven by emerging flux simulation
Che
n, B
inge
rt, P
eter
, Che
ung
(201
3)
27.2 hr 25.2 hr 23.0 hr
+3000!
B z [
G]!
–3000!
0!
flux-emergence simulation from / similar to Cheung et al (2010) ApJ 720, 233
– flux rope rises from bottom and breaks through surface → pair of sunspots
coronal simulation
– use photospheric layer (T, ρ, v, B) as time-dependent lower boundary
→ magnetic field expands → coronal loops form
146 x 73 Mm2
Coronal model driven by emerging flux simulation synthesized coronal emission (1.5 106 K )
Chen, Bingert, Peter, Cheung (2013) 1!
100!
1000!
10!
+3000!
–3000!
0!
► loops form at different places at different times
► loop footpoints are in sunspot periphery (penumbra)
34 min out of 10 hrs
view from top: Bvert @ bottom + AIA 193 Å!
view from side: AIA 193 Å!
DN
/ pi
x / s!
B z [
G]!
146 x 73 Mm2
Comparison of observations and model
→ these 3D models give a realistic description of coronal structures in active regions.
Magnetic field and current structure
90°
Ohmic heating per Particle
Current along the loop
current along loop: different sign in two legs → downward directed in both legs
J!J!
Conclusions
Conclusions
► 3D MHD models of model solar corona with spectral synthesis – driven by photospheric motions: fieldline braiding – emerging active region – good match to many observable solar features: → in statistical sense / average properties → and for 1:1 comparison of solar structures
Currents in two experiments Equilibrium AR loops → show properties as expected → current roughly constant along the magnetic tube hosting the coronal loop → similar to lab experiment
Emerging AR loops: → interaction with overlying field → downward directed currents in both legs of the loop ! → maybe similar to flares
current along the loop: same sign and value → constant current through loops
current along loop:���different sign in two legs → downward directed in both legs
J!J! J!is this quite different behavior
of the currents also found in laboratory experiments?