Finding Photospheric Flows with I+LCT 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

Outline Context: Why do we care? Background: What has been done before? I+LCT: What’s this new approach? Results: How well does it work? Punchline: What have we learned?

Context: Why study photospheric velocities? Coronal magnetic field flares and/or erupts. –Can affect Earth: satellites, power grids, etc. We don’t know how flares/eruptions work! –But we’d like to know! –Clearly magnetically driven… Evolution of the coronal magnetic field is driven (primarily?) by evolution of the field at the photosphere.

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!) Q: How do photospheric flows affect corona?

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.

Previous methods, cont’d: 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 prob’ly better!) Shifts are features’ apparent transverse velocities,, not ‘real’ flow v  …

Demoulin & Berger (Sol. Phys. 2003) showed isn’t necessarily just horizontal motion: Apparent horizontal motion can be true horizontal motion, or vertical motion of a tilted flux tube.

What are the implications of the D&B conjecture for determining v z, v  ? One additional equation can close system! Since velocities along B can’t change B z, we assume (According to D&B, assuming v  = implies v z = 0.)

Then algebra yields all components of v! B is averaged from times {t i, t i+1 }, so u LCT and v  are flows at t i+1/2 Need vector B! Derived flows should be consistent with

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).

LCT movie to follow. Details: G. Fisher’s 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.

Now use LCT w/D&B 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

Vectors are v  (km/s), contours are v z (red receding, blue approaching).

The D&B conjecture also greatly simplifies the z-component of the ideal induction equation: (Only z-component is completely determined by photospheric vector magnetograms.) Since and B z are known, we can compute expected from, and compare it with the observed.

To get flow consistent w/LCT & ind’n eqn: Express u as Div. gives Poisson’s equation for  : Approximate u I+LCT by u LCT and take curl to get Poisson’s equation for  :

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 you’re at it. Can test both LCT and algebraic method!

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! –code’s B  can diverge from observed B  MHD codes require specification of data in guard/ghost cells below z = 0! Metcalf’s Na D line method can be used to measure, so other comps of ind. eqn. can be used to derive velocities.

Sources of Error: Inaccuracy in D&B approximation. –Diffusion ignored! –Evolution of emerging field ignored over  t. Errors in mag’gram data, esp. LCT’s intrinsic errors: –Aliasing –Many flows possible w/, so LCT fails Comparisons with MHD simulations are apples to oranges? ???

Tests of I+LCT 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 v z ? Compare LCT on magnetograms with LCT on other features (e.g., white light).