Efficient tracking of photospheric flows 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 Efficient tracking method Picture shows an overview of the method

The Why and The How Why? How? 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 Sub pixel movements

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

What will Solar-B give us? SOHO Solar-B Instrument MDI Michaelson Doppler Interferometer BFI Broadband Filter Imager Max Resolution 0.6 arcsec 0.08 arcsec CCD size 1024 x 1024 2048 x 2048/4096 Max image rate 60s 10s 10 – 20 times more data to process!

Balltracking 1: Filtering and derotation 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

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

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

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

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

How smooth is smooth enough

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

Results from simulated granulation

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

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

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

Publications Balltracking method: Interpolation errors in LCT: 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