Finding Photospheric Flows with I LCT

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Finding Photospheric Flows with ILCT

• or,Everything you always wanted to know about
  velocity at the photosphere,
• but were afraid to ask.

B. T. Welsch, G. H. Fisher, and W.P. Abbett
Space Sciences Lab, University of California
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Outline

• Context Why do we care?
• Background What has been done before?
• ILCT Whats this new approach?
• Results How well does it work?
• Punchline What have we learned?

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Context Why study photospheric velocities?

• Coronal magnetic field flares and/or erupts.
• Can affect Earth satellites, power grids, etc.
• We dont know how flares/eruptions work!
• But wed like to know!
• Clearly magnetically driven
• Evolution of the coronal magnetic field is driven
  (primarily?) by evolution of the field at the
  photosphere.

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Q How do photospheric flows affect corona?

• Coronal field is line-tied to photospheric
  field drive coronal MHD code with observed
  photospheric B(x,y,t) and v(x,y,t) MURI goal
• Flux of energy into corona (Poynting)
• Flux of helicity into corona
• ( is inward normal to corona, ? is perp to
  not B!)

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Background How have flows in magnetic
photosphere been measured?

• Doppler can give line-of-sight velocity.
• Magnetogram data B(x,y) alters line profile, so
  interpreting line shift in magnetogram data as
  Doppler shift is not necessarily appropriate!
  (Why? Ask Metcalf!)
• Other data sets often unavailable.

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Previous methods, contd

• Local Correlation Tracking (LCT) finds shifts
  that maximize local correlation functions between
  successive images (white light, G-band, etc.)
• To drive MHD codes, correlate photospheric
  magnetograms (chromospheric probly better!)
• Shifts are features apparent transverse
  velocities, , not real flow v?

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Demoulin Berger (Sol. Phys. 2003) showed
isnt necessarily just horizontal motion

• Apparent horizontal motion can be true horizontal
  motion, or vertical motion of a tilted flux tube.

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What are the implications of the DB conjecture
for determining vz, v? ?

• One additional equation can close system!
• Since velocities along B cant change Bz , we
  assume
• (According to DB, assuming v?
  implies vz 0.)

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Then algebra yields all components of v!

• B is averaged from times ti, ti1, so
• uLCT and v? are flows at ti1/2
• Need vector B!
• Derived flows should be consistent with
  

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Apply to solar data!

• NOAA A.R. 8210, 1 May 1998
• Halo CME on this day MURI/SHINE event
• IVM data 15 magnetograms, 18 min. cad.
• CME shortly after IVM sequence.
• Reduced by Stephane Regnier at M.S.U.
• One of two data sets with vector magnetogram
  coverage around time of halo CME, with good
  interplanetary coverage (Canfield Li).

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LCT movie to follow. Details

• G. Fishers LCT code --- standard FFT correlation
  function
• Sub-region of MDI full-disk magnetogram
• 24 hours, 15 min. cadence, 5 min. avg.d
• 100 G threshold normal field strength
• Ran separately on (/-) masks, then combined ---
  significant difference near PIL.

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Now use LCT w/DB to find v

• Used first and last images in IVM sequence
• higher cadence led to spurious shifts
• 4 hours elapsed time
• LCT with 50 G threshold, (/-) masks

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Vectors are v?(km/s), contours are vz (red
receding, blue approaching).
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The DB conjecture also greatly simplifies the
z-component of the ideal induction equation

• (Only z-component is completely determined by
  photospheric vector magnetograms.)
• Since and Bz are known, we can compute
  expected from , and
  compare it with the observed .

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To get flow consistent w/LCT indn eqn

• Express u as
• Div. gives Poissons equation for f
• Approximate uILCT by uLCT and take curl to get
  Poissons equation for y

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Q How to check accuracy of methods?

• Compare with ANMHD simulations!
• Generate false magnetograms with this anelastic
  MHD code --- velocities known!
• Want , so simulate flux emergence.
• Simulate convection, too, while youre at it.
• Can test both LCT and algebraic method!

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Still working on this! Current issues

• z component of induction equation does not
  adequately constrain v !
• Both LCT z-comp. of ind. eqn. ignore evolution
  of B? --- bad for simulations!
• codes B? can diverge from observed B?
• MHD codes require specification of data in
  guard/ghost cells below z 0!
• Metcalfs Na D line method can be used to measure
  , so other comps of ind. eqn. can
  be used to derive velocities.

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Sources of Error

• Inaccuracy in DB approximation.
• Diffusion ignored!
• Evolution of emerging field ignored over Dt.
• Errors in maggram data, esp.
• LCTs intrinsic errors
• Aliasing
• Many flows possible w/ , so
  LCT fails
• Comparisons with MHD simulations are apples to
  oranges?
• ???

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Tests of ILCT with other data?

• Use shift of line center from magnetogram
  inversion to find Doppler shift. (Messy work ---
  ask Metcalf!)
• Use SOI/MDI data (w/five-minute oscillations
  removed) to determine vz?
• Compare LCT on magnetograms with LCT on other
  features (e.g., white light).