Flows and the Photospheric Magnetic Field Dynamics at Interior – Corona Interface Brian Welsch, George Fisher, Yan Li, & the UCB/SSL MURI & CISM Teams HMI Team Mtg., 2006M1-H2: Mag. Activity

14 Feb 2006HMI+AIA, M1-H2: Mag. Activity2 The ‘Store and Release Paradigm’ (cf., earthquakes) motivates studying photospheric flows. 1. Slow photospheric motions (v ~ 1 km/s) add magnetic energy to the coronal field, as Poynting flux. -- E x B  -(v x B) x B 2.The “frozen-in flux” condition prevents relaxation B  B (P), so free energy is stored in the corona – “latency.” 3.With enough free energy, the corona reaches an unstable configuration (??) and “spontaneously” relaxes toward B (P). Most CME models – flux cancellation, breakout, tether cutting, kink instability – accord with this picture. (But even Chen’s [1996] “energy injection” paradigm also invokes photospheric flows!)

Velocity inversions generate a 2D map v(x 1,x 2 ) from some 2D image, f 1 (x 1,x 2 ), to another, f 2 (x 1,x 2 ). The map depends upon: 1.the difference  f(x 1,x 2 ) = f 2 (x 1,x 2 ) – f 1 (x 1,x 2 ) 2.assumption(s) relating v(x 1,x 2 ) to  f/  t, e.g.: –continuity equation,  f/  t +  t  (v t f) = 0, or –advection equation,  f/  t + (v t   t )f = 0, etc. We apply Fourier Local Correlation Tracking (FLCT, Welsch et al. 2004), which assumes advection, to magnetograms. (More on FLCT in M3: Mag. Data Products, Thurs.)

Demoulin & Berger (2003) argued that LCT applied to magnetograms does not necessarily give plasma velocities. u f  v n B h -v h B n is the flux transport velocity u f is the apparent velocity (2 components) v is the actual plasma velocity (3 comps) Motion of flux across photosphere, u f, can be a combination of horizontal & vertical flows acting on non- vertical fields.

14 Feb 2006HMI+AIA, M1-H2: Mag. Activity5 Ishii et al. (1998) explained complicated photospheric evolution in AR 5395 in terms of a complex, 3D flux system. (a) schematic magnetogram; (b) sketch of 3D structure

Demoulin & Berger (2003) also argued that the flux transport velocity, with vector magnetograms, determines the fluxes of magnetic energy & helicity into the corona.  E/  t = -  dS(B h  u f ) B n dS and  H/  t  -  dS(A h  u f ) B n dS, where B n = (  h x A h )  n

14 Feb 2006HMI+AIA, M1-H2: Mag. Activity7 We have implemented a preliminary, automated “Magnetic Evolution Pipeline” (MEP). cron checks for new magnetograms with wget New MDI magnetograms are downloaded, deprojected, and tracked using FLCT. The output stream includes deprojected m-grams, FLCT flows (.png graphics files & ASCII data files), and tracking parameters. Full documentation & all codes (and bugs!) are on line.

14 Feb 2006HMI+AIA, M1-H2: Mag. Activity8 Electric fields derived from pipelined velocities will be used as inputs for MHD models of the solar corona. HMIs vector magnetogram coverage will improve accuracy of MHD boundary condition. Hoped-for near term (1-2 years) improvements: 1.Extension of disk-side pipeline to global pipeline, via estimation of far-side magnetic evolution. 2.Feature tracking, for estimation of flux cancellation rates. 3.Coronal models, e.g., magnetic charge topology (MCT).

14 Feb 2006HMI+AIA, M1-H2: Mag. Activity9 References Démoulin & Berger, 2003: Magnetic Energy and Helicity Fluxes at the Photospheric Level, Démoulin, P., and Berger, M. A. Sol. Phys., v. 215, # 2, p Ishii et al, 1998: Emergence of a Twisted Magnetic Flux Bundle as a Source of Strong Flare Activity, Ishii, T.T., Kurokawa, H., & Takeuchi, T.T., ApJ, v. 499, 898. Schuck, 2005: Local Correlation Tracking and the Magnetic Induction Equation, Schuck, P., ApJ, v. 632, L53. Welsch et al., 2004: ILCT: Recovering Photospheric Velocities from Magnetograms by Combining the Induction Equation with Local Correlation Tracking, Welsch, B. T., Fisher, G. H., Abbett, W.P., and Regnier, S., ApJ, v. 610, #2, p