Numerical Simulations of Supergranulation and

Solar Oscillations

Åke Nordlund

Niels Bohr Institute, Univ. of Copenhagen

with

Bob Stein (MSU)

David Benson, Dali Georgobiani

Sasha Kosovichev, Junwei Zhao (Stanford)

Experiment settings: Code

Staggered mesh code conservative, with radiative transfer

fast – about 5 CPU-microseconds / mesh-update includes 4-bin radiative transfer

massively parallel OpenMP up to about 250 CPUs MPI up to thousands of CPUs (just developed) Hybrid MPI/OMP for clusters with shared mem. nodes

e.g. DCSC/KU: 118 nodes x dual-CPUs x dual core AMD = 472 cores (corresponds to ~90 million zone-updates / sec)

Stagger Code:Scaling on Columbia (Altix)

With OpenMP

With MPI

Size     N-cpu µsec/pnt

125x500x125 1 5.9

250x500x250 64 8.6

500x500x500 64 7.8

500x500x500 125 9.3

500x500x500 250 11.9

Size     N-cpu µsec/pnt

250x500x250 1 4.3

250x500x250 50 4.7

500x500x500 50 5.3

500x500x500 100 6.1

500x500x500 250 6.7

Supergranulation Simulation48 Mm wide x 20 Mm deep

63 hours (1.3 turnover time) f-plane rotation (surface shear layer) No magnetic field (yet) Low resolution:

• 100 km horizontal, • 12-70 km vertical

Mean Atmosphere: Ionization of Hydrogen and Helium

What can we learn?

Use the model and data as a test bed SOHO/MDI synthetic data

what does SOHO/MDI actually measure, and how well? Local helioseismology

what do the various methods measure, and how well?

Nature of the flow field What is ‘supergranulation’? How does it fit in with larger & smaller scales?

Data sets available onStanford Helioseismology Archive

Upflows at surface come from small area at bottom (left)Downflows at surface converge to supergranule boundaries (right)

Animation

Time evolution at various depths

Velocity at the same depths

The solar velocity spectrum

Power spectra are often plotted log-log, which means the power per unit x-axis is really k P(k), rather than just P(k)!

Solar velocity spectrum

MDI doppler (Hathaway) TRACE

correlation tracking (Shine)

MDI correlation tracking (Shine)

3-D simulations (Stein & Nordlund)

V ~ k

V~k-1/3

constantV

Velocity spectrum:

v(k) = (k P(k))1/2

Rotation subtracted solar Doppler image

Ni 6768 response function

simulation MDI

k- Diagram

Sub-sonic filtering

~ 7 km/s~ 7 km/s

P-mode power (red), convective power (black) – time average (blue)

Hi-res MDI

Note that it matters very much how one

computes power spectra

Velocity spectrumonly distinct scale is granulation

Vhoriz (sim)

Vz(sim)

V MDI

- - - - convection

…. oscillations

A continuous solar velocity spectrum!

Supergranulation may stand out a little

But the flow is nearly scale-invariant amplitudes scale inversely with size lifetimes scale with the square of the size

A Nearly Scale Free Spectrum!Doppler Image of the Sun (SOHO/MDI)

Solar horizontal velocity (observed)Scales differ by factor 2 – which is which?

400 Mm

200 Mm

100 Mm

50 Mm

Solar horizontal velocity (model)Scales differ by factor 2 – which is which?

24 Mm12 Mm

6 Mm3 Mm

Solar velocity spectrum

Time-Distance Diagram

f-mode Travel Times vs Simulated Flow Fields (divergence)

Right side image shows the f-mode outgoing and ingoing travel time differences, and the left side image shows the divergence computed from simulation. (From Junwei Zhao)

f-mode Travel Times vs Simulated Flow Fields (Horizontal)

Right side image shows the f-mode north-going and south-going travel time differences, and the left side image shows the Vn-s

averaged from simulation. (From Junwei Zhao & Aaron Birch)

Local Correlation Tracking

Sunspots

Sunspot, initial time evolution

Sunspot, time evolution (rep.)

Temperature, hor. & vert. magn. field,hor. & vert. velocity, surface intensity

Velocity, as seen by VAPOR(top perspective)

Sunspot,log magnetic pressure

Sunspot, field lines with density iso-surface (~solar surface)

Field line detail

Key result: A continuous solar velocity spectrum

Supergranulation may stand out a little

But the flow is nearly scale-invariant amplitudes scale inversely with size lifetimes scale with the square of the size

Data sets available onStanford Helioseismology Archive

Experiments:Forthcoming

AR magnetic fields add B from MDI magnetogram (as in Gudiksen &

Nordlund)

Quiet Sun magnetic fields advect initially horizontal field from the bottom b.c.

Rise of magnetic flux tube Insert flux tube near bottom, study emergence through

surface

Coronal & chromospheric heating similar to Gudiksen & Nordlund, but “real driving”

The End The End