HMI

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HMI Photospheric Flows

1. Review of methods to determine surface plasma
   flow
2. Comparisons between methods
3. Data requirements
4. Necessary computational resources
5. Possible improvements to methods.

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General Approach

• From 2D data arrays, f1(x1,x2) f2(x1,x2), find
  vector flow v(x1,x2) consistent with
• Observed evolution, ?f(x1,x2) f2(x1,x2)
  f1(x1,x2)
• Other possible assumptions
• Magnetic induction eqn., ?Bn/?t ?t?(vnBt-vtBn)
• Continuity equation, ?f/?t ?t?(vtf) 0
• Doppler velocities more later
• v(x1,x2) might have 2 or 3 components

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General Approach, contd

• Ideally, with finite difference equations,
  cadence should beat Courant cadence ? ?tC
  ?x/vmax
• analog of numerical Courant condition
• time step limited by propagation speed of
  information
• ?x ? pixel size vmax ? expected max. flow speed
• low cadence is ?t gt ?tC
• ?t ? ?tC very rare in solar physics!
• (usually, ?t gtgt ?tC)

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HMI Capabilities

• Pixels .5 363 km, resolution 1.5 1100
  km
• Photospheric csound ? (?kT/m)1/2 ? 9 km/s
• Courant Cadence
• ?tHMI ? (363 km)/(9 km/s) ? 40 sec.
• LOS Mag. Field Cadence, ?tLOS 60 sec.
• Vector Mag. Field ?tVEC 600 sec.
• Typical v 2 km/s, and resolution 1100 km, so
  ?tPRACTICAL 550 sec.

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Current Methods

• Local Correlation Tracking (LCT)
• Inductive Methods (ILCT, MEF, )
• Feature Tracking (FT)

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1. Local Correlation Tracking (LCT)

• Take subregions, ? pixels wide, of f1 f2, find,
  e.g.,
• shift ?x that minimizes difference ?f or
• shift ?x of peak in (Fourier) correlation funcn
• Sub-pixel shifts found by interpolation SLOW!
• Most algorithms solve advection equation,
• ?f/?t (vt??t) f 0
• Can be used on intensity images, LOS, vector
  magnetograms from HMI.
• Cadence must be slow enough that ?fnoise lt
  ?fadvection
• Workable with very low cadence data ?t ? 100?tC

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LCT applied to magnetograms Démoulin Bergers
(2003) analysis of photospheric flux transport

• Motion of flux across photosphere, uf, is a
  combination of horizontal vertical flows acting
  on non-vertical fields.

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LCT, contd

• Hence, flows uLCT from LCT on magnetograms
• are not generally identical to plasma velocity v
• solve advection equation, not continuity equation
• Given vector B, can assume uf uLCT, and thereby
  find v from uLCT.
• Q How good does LCT do? A Pretty good!

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A Comparable Data SetFlare Genesis Experiment

• Balloon-borne (Antarctic) observations of NOAA
  8844, 25 Jan 2000
• 54 vector magnetograms, 2.3/5.3 min. per
• hi-res .18 pixels (130.5 km), 520 x 520 pix
• LCT differenced over ti /-10, for Dt 85 min.
• Doppler maps, too! (No info. on method.)
• Tracking of white light images underway

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FGE Movie
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FGE White Light vs. Mag
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FGE Larger ?
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Modifications to LCT

• Near future Improvement in sub-pixel
  interpolation added speed.
• Future Convert to FORTRAN parallelize.
• Compute on tiles, not on each pixel.

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2. Inductive Methods

• Use finite diff. approx. to magnetic induction
  equations normal comp. as addl constraint.
• Purely inductive methods need ?t ? ?tC
• Methods currently available ILCT, MEF, Kusano et
  al. (2002), MSR (Georgoulis et al., 2005, in
  prep.)
• All methods return (vx, vy, vz) at photosphere,
  where (v?B) 0 parallel flow unconstrained by
  indn eqn.
• Post-processing with Doppler data can give v B
• NB NOT Doppler from Stokes I (Chae et al., 2004)

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Inductively Derived Flows are Consistent with
Induction Eqns Normal Component!
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What about other components?
Directly measured
Derived by new method?
Derived Inductively
From NLFFF Extrapolation?
at photosphere, z 0
above photosphere, z gt 0
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A) ILCT Modify LCT solution to match induction
equation
Let

• Solve for ?,? with 2D divergence and 2D curl
  (n-comp), and the approximation that ufuLCT

NB if only BLOS is known, we can still solve for
?,? !
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B) Minimum Energy Fit (MEF)

• Also uses induction equations normal component
  to derive flow, with additional assumption that
  integral of squared velocity is minimized.
• Applicable to vector magnetograms.
• More from D. Longcope, shortly!

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Other Inductive Methods

• Kusano et al. (2002) get v from LCT flow, derive
  additional flow for consistency with induction
  equation.
• Georgoulis (2005, in prep) Use (i) minium
  structure (ii) coplanarity assumptions, with
  (iii) induction equation to derive (iv) velocity
  perpendicular to magnetic field. (System
  overconstrained.)

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Prelim. Comparison of Inductive Methods

• Used MHD simulations of Magara (2001)
• Given B(x,y,z0,t), practioners computed
  v(x,y,z0,t), and were then told actual v.

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Some Prelim Comparisons
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Some Prelim Comparisons
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Some Prelim Comparisons
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Some Prelim Comparisons
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3. Feature Tracking

• Useful with WL images magnetograms.
• Algorithms
• White Light L. Strous
• Active region fields B. Welsch, G. Barnes
• Quiet Sun fields C. DeForest, M. Hagenaar, C.
  Parnell, B. Welsch
• Does not return v(x,y) rather, gives velocity of
  patches of photosphere.
• Easily incorporated in pipeline.

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Feature Tracking in AR 8038
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Conclusions

• Planned data cadences are compatible with
  existing velocity inversion algorithms.
• LCT can be used to derive flows in HMIs
  intensity, LOS, and vector field maps.
• ILCT, MEF suitable for determining
  three-component photospheric magnetic flows.
• Doppler data from Stokes profiles (zero crossing
  of V, or central minima of Q,U) desirable.
• Significant improvement in computational
  performance of LCT algorithms is needed for
  real-time analysis.