Magnetic Helicity and Solar Eruptions Alexander Nindos Section of Astrogeophysics Physics Department University of Ioannina Ioannina GR Greece

Outline Objective Data base The concept of magnetic helicity Computations of the AR’s coronal helicity Helicity content of ARs and photospheric complexity The role of the overlying field Conclusions

Objective Whether the amount of magnetic helicity stored into the corona is a necessary condition for CME initiation. Helicity content of ARs versus the complexity of their photospheric magnetic fields. What is the role of the overlying field.

How to do it? Study A.Rs that emerge on the visible side of the solar disk, at least 150” away from filaments. EFRs sometimes are associated with eruptions of nearby filaments (Bruzek 1952; Feynman & Martin 1995; Wang & Sheeley 1999) Here we investigate whether the AR itself that forms after the bipole emergence erupts or not. At the beginning of emergence most A.Rs’s twist is not necessarily zero (e.g. Leka et al. 1996) but usually small (Pevtsov et al. 2003). Consequently, monitoring the helicity evolution of such A.Rs becomes less ambiguous.

Database Find A.Rs emerging within longitudes E45 and E00. Get rid of those that emerge with significant twist. Compute the coronal H at the beginning of flux emergence. Follow the A.R and compute its coronal H just before its first CME or when it reaches W45 (whichever happens first). 18 A.Rs give CME before crossing W45 and 25 do not.

A Typical Example

H quantifies how much a set of flux tubes are sheared and/or wounded around each other, w/ each flux tube contributing proportionally to the square of its magnetic flux H=2  1  2 Magnetic Helicity H is meaningful only when B is fully contained inside V (at any point of the surface S surrounding V, B n =0). This is because A is defined through a gauge transformation A’=A + div Φ → H is gauge-invariant only when B n =0. In ideal MHD, H is a conserved quantity. H can be regarded as an almost conserved quantity even in resistive MHD (H’s dissipation rate negligible in all non-ideal processes, including reconnection.

Coronal Helicity: the LFFF approximation Coronal field under the linear force-free field assumption (Alissandrakis 1981) Compute coronal helicity H c as a function of the derived alpha Follow Berger (1985) and Demoulin et al. (2002) and get

The alpha best Method For each AR use MDI magnetograms and compute alpha: (1) at the beginning of flux emergence and (2) just before its first CME or when it reaches W45 (whichever happens first). Determine alpha iteratively and as objectively as possible: 1. Compute the coronal field assuming a given alpha. 2. Compute the mean distance d mean btw the coronal loops and the closest computed lines. 3. Through successive steps, select the alpha that gives the best global fit, ie, lowest d mean The derived alpha  satisfactory if ≈ 2-4 Mm (close to pixel size of coronal images)

Two Typical Examples One hour before CME At W45 No CME

ARs for which alpha best method works

Coronal Helicity: a second approach Compute H c at the time of the first CME or when the AR reaches W45 using: H c : the coronal helicity we need to compute H c,emerg : the helicity already stored in the corona at the beginning of flux emergence (use alpha best method: it should be almost potential). ΔH inj : the total accumulated helicity injected into the corona from the time flux emergence begins until the time we are interested in.

Compute helicity injected into the corona Use MDI LOS images Remove differential rotation Compute horizontal velocities using LCT method LCT does NOT detect v t but (Demoulin & Berger 2003) Then either combine it with dH/dt| n and dH/dt| t and get the whole helicity flux density G A = -2(A p v LCT ) B n Or even better get LCT results and use as helicity flux density (Pariat et al. 2005)

Helicity flux densities

A Typical Example Magnetic flux Helicity injection rate ΔH inj : Accumulated change of helicity

All A.Rs together Crosses: A.Rs for which alpha best method did not work satisfactorily

Helicities from alpha best methodHelicities using ΔH inj Right panel shows smaller helicities; reflects intrinsic difficulties of lfff and alpha best method. However, the conclusion from both sets is the same: the null hypothesis (ie there is no association btw the CME initiation and whether the AR’s H is bigger or smaller than the median value of the sample’s H) is rejected at the >99% confidence level.

Photospheric configuration and eruptions R: total unsigned flux within 15 Mm of the PIL (Schrijver 2007) The null hypothesis (ie there is no association btw the CME initiation and whether the AR’s R is bigger or smaller than the median value of the sample’s R) is rejected at the >99% confidence level

Helicity and photospheric configuration

Helicity and overlying field n = -(r/B pot ) (dln B pot )/dr  n quantifies how rapidly the nearly potential field decreases with height

Conclusions This work provides direct observational support for the paradigm that the helicity accumulation is a necessary condition for CME initiation. Complex photospheric configurations contain more helicity and are more likely to erupt. The fast decrease of the overlying field facilitates the eruption