Efficient tracking of photospheric flows

1. BALLTRACKING Efficient tracking of photospheric flows H.E.Potts, D.A.Diver, R.K.Barrett University of Glasgow, UK Funded by PPARC Rolling Grant PPA/G/0/2001/00472

2. The Why and The How Why? • Investigate small scale interactions between magnetic elements and photosphere • Contribution to magnetic energy budget How? • Quite hard: • Typical diameter ~1 Mm • Granules only live for 5–15 mins • Typical supergranular velocity 500ms-1 , but much faster ‘random walk’ • Only advected ~0.5 Mm by supergranular flow in lifetime • Need lots of data! MDI continuum data

3. Established Tracking Methods • Standard LCT (Simon 1988). • Excellent results but slow (approx 4 days for 8hrs MDI High Resolution data) • CST (Strous 1995) • Complex, and limited to high resolution images. Need to be careful about selection effects • Simulated data needed

4. What will Solar-B give us? 10 – 20 times more data to process!

5. Balltracking 1: Filtering and derotation Filtering: • Continuum data is dominated by p-mode oscillations • 2D Fourier filter applied to remove all but granulation information. No time filtering used Derotation • Minimal remapping – just rigid derotation. Any more sophisticated scaling done on processed data set • Much smaller dataset (eg. 6GB raw vs. 10MB processed) • Reduces interpolation errors • Done in Fourier space Both done in a single operation for speed

6. Balltracking 1: Filtering and derotation Raw Image Filtered image 2D Fourier Transform Mask Phase adjust Inverse transform FILTER DEROTATE

7. Balltracking 2 : Tracking • Surface made from smoothed granulation data • Massy ‘balls’ dropped onto the surface. • Balls ‘float’ on surface and settle to local minima • Balls are then pushed around by travelling granulation patterns • Balls removed if too close to each other • Damping force for stability

8. Balltracking 3: Smoothing • Set of irregularly spaced ball trajectories • Smooth in space and time to get underlying velocity V(i,j): V(xi,yi,t): smoothed velocity s : spatial smoothing radius Dt : time smoothing interval rn,t : distance from (xi,yi) to ball

9. How accurate is possible? • Random Velocity > Directed velocity • Estimate error in smoothed velocity: • But adjacent measurements are not independent: • Best possible, regardless of sampling frequency: RS ,TS: Smoothing lengths Dt, Dr : Sampling intervals sv, su, : STD of smoothed and random velocity

10. How smooth is smooth enough

11. Making Test data • Make uniform density array of randomly positioned cells • Assign a size and lifetime to each cell. • Specify velocity field v • Cell is advected by underlying velocity field, and repelled by surrounding cells • As a cells dies replace, with spatial frequency S : S : local cell replacement rate v : specified velocity field t : mean cell lifetime n0 : mean cell density

12. Results from simulated granulation

13. Real results - Supergranule evolution 4 hour average 2.5 × 2.5 arcmin Passive flow tracers

14. Supergranular lanes • 36h Quiet sun • Granulation pattern found from velocity field using a lane finding algorithm • Note differential rotation

15. Conclusions BALLTRACKING • Very efficient and robust tracking method • Accuracy close to the maximum possible • Useful for tracking any flow with features at a characteristic spatial scale • Fast enough for automated, real time analysis of large data sets

16. Publications Balltracking method: • Potts HE, Barrett RK, Diver, DA Balltracking: An ultra efficient method for tracking photosperic flows. Submitted to A&A, November 2003 Interpolation errors in LCT: • Potts HE, Barrett R, Diver, DA Reduction of interpolation errors when using LCT for motion detection. Submitted to Solar Physics, June 2003