Solar Convection: What it is & How to Calculate it. Bob Stein.

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Presentation transcript:

Solar Convection: What it is & How to Calculate it. Bob Stein

The Sun is Dynamic, Convection is the Driver  Transports Energy  Transports Angular Momentum  Generates Magnetic Fields by Dynamo  Excites Acoustic and Magnetic Waves

The Solar Surface Hot gas rises (floats up) -> Brighter Cool gas sinks (pulled down by gravity) -> Darker ~ 1000 km Convection (boiling water)

The Solar Surface

The Solar Surface Convection Sunspots: Magnetic fields, Cooler -> Darker

Observed as Doppler Shift at the solar surface

Magnetic Field

The Sun in X-Rays

The Solar Wind

Models & Observations SIMULATION Calculate Observables OBSERVATIONS Disagree improve physics Agree investigate causes

Comparison Simulations vs. Observations Images Intensity distribution Spectrum Line profiles Magnetic Field distribution Resonant Oscillations

Emergent Intensity

Intensity Histogram

Line Profiles Average Profile Iron: Majority species Equilibrium populations Heavy-> small Doppler width Weak lines

Field Distribution simulationobserved Both simulated and observed distributions are stretched exponentials.

P-Mode Excitation Triangles = simulation, Squares = observations (l=0-3) Excitation decreases both at low and high frequencies

Causes: convection

Convection is Driven by Radiative Cooling at Surface: Fluid Radiates away its Energy & Entropy -> Denser -> pulled down by Gravity Z S E  Q 

Stratified convective flow: diverging upflows, turbulent downflows Velocity arrows, temperature fluctuation image (red hot, blue cool)

Stein & Nordlund, ApJL 1989

Downflows: cell size increases with depth

Vorticity: Downdrafts are Turbulent

Turbulent downdraft

Never See Hot Gas

Causes: Oscillations

Simulation Modes

Oscillations Excited by Turbulent Pressure & Entropy Fluctuations Entropy Fluctuations

Peak Excitation ~ 5 minutes

Turbulent Pressure > Entropy Fluctuations

Oscillations Excited close to Surface

Causes: Magnetic Field

Magnetic Field Reorganization

Exponential Distribution

Magnetic Field Lines

Methodology

Equations: Conservation of Mass Conservation of Momentum Conservation of Energy Induction

 E P p y, V y, B y P z, V z, B z ExEx EyEy EzEz Variables Staggered in Space Center: i,j,k Faces: i-1/2,j-1/2,k-1/2

Spatial Derivatives: 6 th order Finite Difference

Time Advance: 3 rd order Runge-Kutta n=1-3

Characteristic Boundary Conditions Unique Conservative Equations Non-unique Wave-like Equations

Characteristic Equations

Characteristic Boundary Conditions Boundary Conditions on OUTGOING characteristics is the Characteristic Equations evaluated using one-sided derivatives For INCOMING characteristics the normal derivatives in the characteristic directions must be evaluated using the physics boundary conditions.

For (non-magnetic) Gas

The End