Holography Applied to Artificial Data A. Birch D. Braun NWRA, CoRA Division S. Hanasoge (Stanford)

Outline Simulated Data Holography Results Background models Power spectra Holography Results Frequency dependence Positive travel-time shifts

Numerical Simulations Code by Shravan Hanasoge (Hanasoge et al. 2007) Propagate linear waves through arbitrary backgrounds (restrictions: must be convectively stable) 256x256x300 grid (200 Mm^2 x 36 Mm)

Background Models Sound Speed (cm/s) Stabalized S Polytrope + iso Density (cgs) Acoustic Cutoff (mHz)

Power Spectra: Stabilized Model S

Power Spectra Model MDI

Sound-Speed Perturbations Fan, Braun, & Chou (1995) for the sound-speed perturbation Use epsilon=0.1. For the “shallow” case: D=1 Mm For the “deep” case: D=10 Mm In both cases: R=20 Mm Note that epsilon=1, D=1 was a good match to Hankel analysis phase shifts

Travel-Time Shifts Shallow Deep

Frequency Dependence Shallow, D=1 Mm Deep, D=10 Mm 3 mHz 4 mHz 5 mHz

Polytrope with isothermal atmo. Shallow, D=1 Mm Deep, D=10 Mm 3 mHz 4 mHz 5 mHz

Positive Travel-Time Shifts (?) (Braun & Birch 2007, Sol Phys. submitted)

Compare D=1 with MDI observations 3 mHz 4 mHz 5 mHz

Conclusions support NASA (NNG07EI5IC) NASA/Stanford/HMI project Frequency dependence is a useful constraint on models In simple models, a shallow sound-speed perturbation produces something like the observed frequency dependence Increase in sound-speed can lead to increased travel times ! Lots of work to do: modeling & theory support NASA (NNG07EI5IC) NASA/Stanford/HMI project

Power Spectra Simulation (Polytrope) Sun (MDI Full Disk)

Positive Travel-Time Shifts Ridge-Like Filter Phase-Speed Filter