Inductive Flow Estimation for HMI Brian Welsch, Dave Bercik, and George Fisher, SSL UC-Berkeley

Estimates of the photospheric electric field E should be useful for understanding flares and CMEs. Poynting flux of magnetic energy goes as (E x B) Flux of magnetic helicity goes as (E x A P ) E can be used to drive time dependent simulations of coronal magnetic evolution… – Abbett et al. (in progress)

Photospheric evolution typically appears ideal. Consequently, E = -(v x B)/c is usually assumed. (Cross product between v and B implies that flows v || along B are unrelated to E.)

Magnetic evolution can be used to estimate E or v.

Tracking flows aren’t exactly consistent with the induction equation’s vertical component. But an E or v consistent with the observations can be found. A Helmholtz decomposition gives: Then, and

*cf., other flow estimates by MEF, ILCT, LCT, DAVE (Welsch & Fisher 2008)

(D B r / D t) does not constrain the electrostatic potential y, but tracking data can provide more information. Taking the curl of tracking flows yields Tracking and inductive info can be combined, The ILCT method of Welsch et al used this “hybrid” solution. DAVE or other tracking data could be used here.

Aside: Doppler shifts do not constrain E. Generally, Doppler shifts cannot distinguish flows || to B (red), perp. to B (green), or in an intermediate direction (blue). With v  estimated another way & projected onto the LOS, the Doppler shift determines v || (Georgoulis & LaBonte, 2006) Doppler shifts are only unambiguous along polarity inversion lines, where B n changes sign (Chae et al. 2004, Lites 2005). v v LOS v v

A variety of estimates of E or v can be made, depending upon available magnetic information. 1.Knowledge of only B LOS and (D B LOS / D t) is enough to directly (and crudely) estimate E h. 2.If vector B and (D B R / D t) are known, then a purely inductive estimate of v or E can be made. 3.Tracking information can be combined with the inductive potential to estimate a hybrid v / E. Software to compute the inductive components of flow / electric fields has been delivered for ingestion into JSOC.

Efforts to further develop and test flow methods, and their applications, are ongoing. We’re validating flow estimation methods with synthetic magnetograms from MHD simulations: MURaM data, courtesy Mark Cheung We’re investigating correlations between flare activity and flow properties (and other properties of magnetic evolution).  See preprint arXiv: !

Fin