Data for Helioseismology Testing: Large-Scale Stein-Nordlund Simulations Dali Georgobiani Michigan State University Presenting the results of Bob Stein (MSU) & Åke Nordlund (Denmark) with David Benson (MSU) Stanford, August 6, 2007

Stein–Nordlund RHD Simulations Conservative compressible 3D (M)HD equations LTR non-gray radiation transfer Realistic EOS and opacities  No free parameters (except for diffusion model).  Wave excitation and damping occur naturally.  There is an excellent correspondence between the code results and observations. 48 Mm 20 Mm

Simulations Supergranulation scale: 48 Mm x 48 Mm x 20 Mm Resolution: 100 km horizontal, 12–75 km vertical Numerical method: staggered variables Spatial differencing: 6 th order centered finite difference Time advancement: 3 rd order Runge-Kutta

Boundary Conditions Density: logarithmic extrapolation on top and bottom Velocity at the top is taken to be constant at its value at the last physical point Energy (per unit mass): top – slowly evolving average, bottom – fixed energy in inflows Initialization Start from existing 12x12x9 Mm simulation Extend adiabatically to 20 Mm and relax for a solar day to develop structures Double horizontally + small fraction of stretched fluctuations to remove symmetry Relax to develop large-scale structures

Radiation Treatment LTR Non-grey, 4 bin multigroup Equation of State Tabular EOS Includes ionization, excitation H, He, H 2, other abundant elements

Vertical velocity

Horizontal velocity divergence

Vertical velocity, horizontal slices at various heights

Vertical velocity, vertical slice

Image of the vertical momentum showing a granule 30 Mm across. This is a snapshot at a depth of 16.8 Mm.

96 Mm by 96 Mm wide simulations

Vertical Velocity at 2.5 & 8 Mm depth Boxes show domain of earlier simulations at 6, 12, 24 & 48 Mm widths.

Available Datasets Website (some info) Contact Bob Stein (more 2 datasets: 8.5 hr (511 min) solar time, no rotation 58.5 hr, with rotation Simulated data are being ingested into the new SDO JSOC database Thanks to Rick Bogart for his extensive help with archiving!

Archived Data Description Data are in FITS format Temporal cadence is 1 minute 3D spatial grid is 500x500x500 A snapshot of a variable occupies approximately 500 MB of disk space First and third directions are horizontal Second direction is vertical Vertical grid is provided separately

Data Set 1 Duration: 511 minutes, or hours No rotation 5 variables: horizontal velocities V x, V z, vertical velocity V y, temperature, density. Each variable is stored in a different directory, each snapshot in a separate file. Every 20 minutes of data are in one sub- directory.

Data Set 2 Duration: 58 hours 29 minutes Uniform background rotation 9 variables: horizontal velocities V x, V z, vertical velocity V y, temperature, density, pressure, internal energy, electron density and   Each snapshot of a variable is stored in a separate file; 9 variables at each time step are combined to be retrieved together (The data will be available for retrieval soon – maybe, in September)

Units of Variables Length is in 10 8 cm = 1 Mm Time is in 10 2 s Velocities V x, V z, and V y are in 10 km/s Temperature is in K Density is in g/cm 3 Pressure is in 10 5 dynes/cm 2 Internal energy is in 10 5 dynes/cm 2 Electron density is log cm -3

These simulations provide an excellent opportunity to validate various techniques, widely used in solar physics and helio- seismology for directly obtaining otherwise inaccessible properties (subsurface flows, structures etc.) On the other hand, these analysis techniques also help to examine how realistic the simulations are

Data Analysis Power spectrum Tests of time-distance methods Compare the results for the simulations and the SOHO/MDI high-res observations (211.5 Mm by Mm patch, 512 min)

Power Spectra SimulationsMDI high-res data

Time-Distance Diagram

TD Diagrams at Various Depths

Exploring Simulated Surface Structures Spatial filtering Spectral analysis f-mode time-distance analysis Local correlation tracking

Large Structures

Time-Distance Analysis

Local Correlation Tracking Correlation coefficient Is 0.99 But velocity amplitudes are under- estimated (~1.8 times lower than in simulations)

These and other results of the simulated data analysis were published in Georgobiani, D.; Zhao, J.; Kosovichev, A.; Benson, D.; Stein, R.; Nordlund, A. "Local Helioseismology and Correlation Tracking Analysis of Surface Structures in Realistic Simulations of Solar Convection" Astrophysical Journal 2007, Vol. 657, p.1157 Zhao, J.; Georgobiani, D.; Kosovichev, A.; Benson, D.; Stein, R.; Nordlund, A. "Validation of Time-Distance Helioseismology by Use of Realistic Simulations of Solar Convection" Astrophysical Journal 2007, Vol. 659, p.848

Summary - Advantages  More Time – Distance calculations?  Acoustic holography?  MHD: sunspot simulations (Nordlund)  Spectra? Mode asymmetries? Future Plans  Large domain – supergranulation scale  Deep - includes lower turning points  Fast code (parallelizes well)

Mean Atmosphere Temperature, Density and Pressure