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Inductive Flow Estimation for HMI

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 )

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Inductive Flow Estimation for HMI

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

  2. 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 AP) • E can be used to drive time dependent simulations of coronal magnetic evolution… • Abbett et al. (in progress)

  3. 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.)

  4. Magnetic evolution can be used to estimate E or v. • Faraday’s Law relates evolution of B to E: • The vertical component constrains Eh, or its associated flow field, • Here, we’ve used the “flux transport velocity” Demoulin & Berger (2003) (flow v|| along B is unconstrained)

  5. 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 “electrostatic potential” “inductive potential” Welsch et al. 2004, Longcope 2004

  6. In tests with MHD data, we found this purely inductive electric field estimate to be pretty good*. *cf., other flow estimates by MEF, ILCT, LCT, DAVE (Welsch & Fisher 2008)

  7. (DBr/Dt) 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. 2004 used this “hybrid” solution. DAVE or other tracking data could be used here.

  8. vLOS v vLOS vLOS Aside: Doppler shifts do not constrain E. v v 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 Bn changes sign (Chae et al. 2004, Lites 2005).

  9. A variety of estimates of E or v can be made, depending upon available magnetic information. • Knowledge of only BLOSand (DBLOS/Dt) is enough to directly (and crudely) estimate Eh. • If vector B and (DBR/Dt) are known, then a purely inductive estimate of v or E can be made. • 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.

  10. 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:0905.0529!

  11. Fin

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