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

BALLTRACKING

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

Established Tracking Methods

• Standard LCT (Simon 1988). – Excellent results but slow (approx 4 days for 8hrs MDI

High Resolution data)

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• 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 MDIMichaelson Doppler

Interferometer

BFIBroadband 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

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

Balltracking 1: Filtering and derotation

Filtered image

Inverse transform

Phase adjust

Mask2D Fourier Transform

Raw Image

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):

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V(xi,yi,t) : smoothed velocity

: spatial smoothing radius

t : 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

t, r : Sampling intervals

v, u, : 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

: 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

• Very efficient and robust tracking method• Accuracy close to the maximum possible• Useful for tracking any flow with features at a

characteristic spatial scale

BALLTRACKING

• Fast enough for automated, real time analysis of large data sets

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