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?