AR Magne)c Energy What do we know? What can we learn? Dana Longcope Montana State University

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1 AR Magne)c Energy What do we know? What can we learn? Dana Longcope Montana State University

2 What we know: Magne)c energy is stored slowly in AR field. Sudden release* of a frac)on of stored energy produces flares & CMEs. What this knowledge can do for us: Quan)ta)ve measurements are crucial for basic studies of flares & CMEs. Key to flare/cme science Help forecast occurrence/severity of flares, CMEs & space weather. Key to flare/cme forecas3ng How well do we know what we know? 1. How well can we measure the magne)c energy stored in an AR at any )me? 2. How well can we measure the frac)on available for release? 3. How well can we measure the energy actually released in a par)cular flare? 4. How well can we measure energy flux during storage? * Release = conversion to other forms: kine)c, radia)on, thermal, NT par)cles

3 1. Measuring magne)c energy the state of the art: NLFFF* Measure B(x,y,z 0 ) over some horizontal surface z=z 0 Assume ( B) B = 0 for all z > z 0 (β=0 i.e. Force- Free Field ) Use favorite algorithm to extrapolate from measurement to B(x,y,z) over volume V within z > z 0 Sun et al Integrate over volume W ff,v = 1 8π V 2 B(x, y,z) dxdydz *NLFFF = non- linear force- free field

4 Issues with the state of the art Measured B(x,y,z 0 ) must be adjusted to conform w/ FFF assump)on Different algorithms for extrapola)on and/or FFF adjustment yield different solu)ons different energies (Schrijver et al. 2008, Metcalf et al. 2008, DeRosa et al. 2009, 2015) β > 0 produces error in energy rel. error ~ 1.5 β (Peter et al. 2015) Energy affected by choice of V especially loca)on of z 0 since energy is concentrated low Thin current layers common/important in models & simula)ons (CSs, QSLs) rare in data & extrapola)ons (cf Metcalf et al. 2008) No quan)ta)ve use of coronal data (cf Malanushenko et al. 2011, 2012, 2014 Aschwanden 2013) Schrijver et al DeRosa et al Thalmann & Wiegelmann. 2008

5 2. Available energy the state of the art: Free Energy ΔW Assume B z (x,y,z 0 ) unchanged during flare/cme Field with minimum energy: poten)al B 0 = 0 Subtract this energy to obtain Free Energy ( ) ΔW = W ff W 0 = 1 8π B 2 2 B 0 Issues with the state of the art V dxdydz Observed: surface field does change (Wang et al. 2002, Sudol & Harvey 2005) ΔW ~ 5% - 20% of W ff comparable to accuracy of NLFFF Can we even accurately (repeatably) measure W 0? Other conserved quan))es (i.e. helicity) prevents the field from achieving its minimum much of ΔW not truly available Is energy in lowest layer (i.e. most of it) reduced over en)re AR in a flare? flare kernels (chr- spheric response) occupy small frac)on of AR large- scale organiza)on (e.g. ribbons) suggests release in high corona can this effec)vely tap energy stored low down?

6 3. Measuring the energy drop state of the art Sun et al differen)al use of NLFFF less affected by systema)c errors some measurements of drops 55% ΔW: Schrijver et al % ΔW: Sun et al % ΔW: Feng et al Measuring the energy release where we stand (Emslie et al. 2004, 2005, 2012) Radia)ve losses over all λ only losses from flare (esp. UV & vis.) Kine)c energy of ejected material omit work done by solar wind(?) MHD waves leaving AR (25% - 60% of release Longcope & Tarr 2012) NT par)cles accounted for in later radia)ve losses? Thermal conduc)on radiated from TR and chr- sphere Thermal energy of flare plasma eventually lost through above channels double coun)ng?

7 4. Energy flux the state of the art: Poyn)ng flux Measure p- spheric velocity field v(x,y,z 0 ) horizontal & ver)cal. Use B(x,y,z 0,t) in feature- tracking methods like LCT, DAVE or MEF (Fisher & Welsch 2008, Schuck 2006, 2008, Longcope 2004) Compute Poyn)ng flux upward through z=z 0 S z (x, y,z 0 ) = 1 4π B ( v B) z ˆ Time integrate over build- up Issues with the state of the art Technical challenges w/ velocity measurements (see Welsch et al. 2007) Build- up is very slow (1 5 days) makes data- driven modeling very challenging requires mul)- day, round- the- clock observa)on of B(x,y,z 0,t) Steady losses may off- set some accumula)on: e.g. coronal hea)ng in AR requires P ~ erg/day (@ 10 7 erg/cm 2 /s) (stored energy comes from rather thin margin!?)

8 Making progress Measure B(x,y,z 0 ) at z 0 where FFF is beser approx n: chr- spheric VMGs May help extrapola)on algorithms at least reduce discrepancies (but precision is different from accuracy!) S)ll have errors ~ 1.5 β from seung β=0 (Peter et al. 2015) Omits region with significant free energy (chr- sphere) where field changes much more during flare source of flare energy? Make use of coronal data in extrapola)on How can coronal B observa)ons be incorporated? Coronal images provide informa)on use it (sensi)ve to J layers?) Efforts s)ll preliminary development needed Less energy in corona BUT perhaps most important for flaring Next gen. coronal models beyond the NLFFF Dynamics (aka simula)ons) )me- scale & length- scale challenges Include β 0?? Permit thin layers Measuring energy release flare modeling to produce energy inventory