Excitation of Oscillations in the Sun and Stars Bob Stein - MSU Dali Georgobiani - MSU Regner Trampedach - MSU Martin Asplund - ANU Hans-Gunther Ludwig - Lund Aake Nordlund - Copenhagen

P-Mode Excitation P-modes are excited by PdV work of turbulent and non-adiabatic gas pressure fluctuations, = Reynolds stresses and entropy fluctuations P-modes are excited by PdV work of turbulent and non-adiabatic gas Pressure fluctuations, = Reynolds stresses and Entropy fluctuations

P-Mode Excitation Pressure fluctuationMode compression Mode energy Eigenfunction

P-Mode Excitation Alternatives Goldreich, Murray & Kumar, 1994 Samadi & Goupil, 2001

Use Convection Simulation to Evaluate Excitation

Computation 3D, Compressible EOS includes ionization Solve –Conservation equations mass, momentum & internal energy –Induction equation –Radiative transfer equation Open boundaries –Fix entropy of inflowing plasma at bottom

Method Spatial derivatives - Finite difference –6 th order compact or 3 rd order spline Time advance - Explicit –3 rd order predictor-corrector Diffusion

Radiation Transfer LTE Non-gray - multi-group Formal Solution Calculate J - B by integrating Feautrier equations along one vertical and 4 slanted rays through each grid point on the surface.

5 Rays Through Each Surface Grid Point Interpolate source function to rays at each height

Opacity is binned, according to its magnitude, into 4 bins.

Advantage Wavelengths with same  (z) are grouped together, so integral over  and sum over commute

Solar Convection

Energy Fluxes

Mean Atmosphere

Entropy Profile

Dynamic Effects Non-linear effects –The mean of a dynamic atmosphere is not equal to a static atmosphere –e.g. Planck function is a non-linear function of temperature, except in the infrared T rad > T gas Slow rates –Not enough time to reach equilibrium –e.g. Ionization and recombination slow compared to dynamic times in chromosphere electron density > than LTE

A Granule is a fountain velocity arrows, temperature color

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

Stein & Nordlund, ApJL 1989

Upflows diverge. Fluid reaching surface comes from small area below the surface

Upflows are slow and have nearly the same velocity.

Downflows converge. Fluid from surface is compressed to small area below surface

Downflows are fast. In 9 min some fluid reaches the bottom.

Vertical Velocity red, yellow down & blue, green up surface 8 Mm below Size of horizontal cells increases with depth.

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

Vorticity Downflows are turbulent, upflows are more laminar.

Vorticity surface and depth.

Vorticity Distribution Down Up

Fluid Parcels reaching the surface Radiate away their Energy and Entropy Z S E  Q 

Entropy Green & blue are low entropy downflows, red is high entropy upflows

Entropy Distribution

P-Mode Oscillations: Stochastic Excitation Nordlund & Stein, ApJ, 546, 576, 2001 Stein & Nordlund, ApJ, 546, 585, 2001

Simulation Radial Modes

P-Modes = resonant oscillations Cavity: surface small H , depth large T, C s

P-Mode Spectrum

Oscillation Spectrum, l =740

P-Mode Intensity - Velocity Phase

p-mode frequencies 1D Standard model 3D Convection model

Never See Hot Gas

3D Effects Inhomogeneous T (see only cool gas), P turb Raises atmosphere 1 scale height

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

P-Mode Excitation Mode energy

Mode Mass Mode mass increases toward low frequencies, because low frequency modes penetrate deeper

P-Mode Excitation Mode compression Eigenfunction

Mode Compression Mode compression decreases toward low frequencies, reduces low frequency excitation.

P-Mode Excitation Pressure fluctuation

Pressure Fluctuations Pressure fluctuations decrease toward high frequency, Reduces high frequency excitation.

P-Mode excitation Decreases at low frequencies because of mode properties: –mode mass increases toward low frequencies –mode compression decreases toward low frequencies Decreases at high frequencies because of convection properties: –Turbulent and non-adiabatic gas pressure fluctuations produced by convection and convective motions are low frequency.

Turbulent & Gas Pressure P turb & non-adiabatic P gas work comparable near surface, P turb work dominates below surface

Turbulent and Gas Pressure Most p-mode driving is by turbulent pressure.

P-Mode Excitation

Excitation primarily by downflows down & up flows interfere destructively

P-Mode Oscillations: Impulsive Excitation Skartlien, Stein & Nordlund, ApJ, 541, 468, 2000

Wave Generation Granule disappears Intensity darkens Velocity Pulse: up/down Energy Flux: up/down

Vertical Divergence -> Horizontal Convergence Diverging Vertical Flow Converging Horizontal Flow

Rarefaction -> Compression RarefactionCompression

Other Stars

Excitation Spectra Decreasing g Increaseing T eff

Reynolds Stress vs. Entropy Fluctuations Star A Sun Eta Boo

Excitation P turbulent P non-ad gas

Excitation (log g, T eff )

P-Mode Excitation Excitation increases with decreasing gravity Excitation increases with increasing effective temperature Excitation by turbulent pressure is comparable to excitation by non-adiabatic gas pressure (entropy) fluctuations MLT

The End