Physical modeling of coronal magnetic fields and currents Participants: E. Elkina,, B. Nikutowski,, A. Otto, J. Santos (Moscow,Lindau,, Fairbanks, São José dos Campos) Goal: Forward modeling to understand the magnetic coupling that controls the solar atmosphere from (below) the photosphere
Direct chromospheric / coronal B-field and j observations are rare, e.g. From a chromospheric observation the magnetic field and perpendicular current density (Jperp) was derived [Solanki et al., Lagg et al., 2003] -> -> Hence, modeling approaches have to be developed using with the observed dynamically evolving photospheric B-fields
Our approach an outline Extrapolation vs. modeling of coronal magnetic fields Current free extrapolation (J =0) Force free extrapolation (only Jperp = 0) Physical modeling: all kinds of currents allowed What causes currents? (The question of energy input) -> Photospheric motion and how to diagnoze it In the horizontal direction Flux emergence -> MHD models Consequences of currents, e.g., Direct dissipation: At what rate? Reconnection: Where, when and how? -> Kinetic models
Photospheric magnetic carpet The the lineof-sight component (Bz) of the photospheric magnetic field can be used to extrapolate current-free (potential) B- fields >the lowest energy state [Title & Schrijver, 98] -> How can we add coronal physics to this approach?
Energy source for the corona: Plasma convection below the photosphere (to the right: helioseismology of AR10488, 30.10.03, lower panel: 16 Mm deep) [Gizon, Kosovichev et al., 05] -> Dynamo -> B fields -> upward Poynting flux estimated, e.g., as compare to necessary fluxes: Quiet regions 300 W m -2 Active regions (0.5-1) 10 4 W m -2 Coronal holes 800 W m -2
Energy transport to the corona: 1. Wave picture (not considered here) e.g. microflares at the footpoint of coronal fields (funnels) [Axford and McKenzie 1993] -> generation of Alfven waves -> Open question: Dissipation of these waves in the corona, see, e.g., [Marsch & Tu] over the years...
Problem of coronal dissipation Criterion for dissipation: Magnetic Reynolds number -> of the order of unity For Spitzer (Coulomb-collision based) resistivity + typical coronal plasma velocities and sizes (10 Mm) -> R m ~ 10 10! And: for Spitzer resistivity and typical plasma velocities R m becomes ~ 1 only in current sheets as thin as 1 cm! while the (Coulomb-) collisional mean free path is l mfp = 1 n kt 2 e 2 10 -> Dissipation beyond Coulomb-collisions is needed! 8 T cm 6 10 K 2 10 9 n cm 3 1
Energy transport to the corona: 2. Currents and their dissipation Example: A solar wind acceleration model [Fisk et al., 99] A: Newly emerging flux rises -> B: Currents are formed between antiparallel B field components ( current sheets ) -> Open questions: locations of currents current dissipation
Photospheric Bz-field dynamics Starting point: photospheric B field dynamics (cf. animation of the photospheric line-of sight field to the left for 15:23 on October 17th till 07:00 UT on October 18th) Goal: Prediction of the location of coronal current concentrations (SOHO/MDI 17.-18.10.1996; area 40 x 40 ~ 23 Mm x 23 Mm)
Derivation of the horizontal velocity by local correlation tracking Vector magnetogram of AR8210 on May 1st 1998, 17:13 UT Variation of the Bz component between 17:13UT and 21:29 UT [from Santos et al., 2005]
ILCT = LCT + induction equation for Bn and Bt to obtain Vn and Vt: Velocities obtained by ILCT Bz variation, consistent with Bt & V [Welsh et al., 2004] [from Santos et al., 2005]
Next step: Plasma simulation, here coupling to the neutral gas [Büchner et al., 2005; Otto et al., 2006]
Initial & boundary conditions Initial condition: Force free B-field & plasma equilibrium Boundary condition deduced from the photospheric plasma motion: 400 300 Y 200 100 0 0 100 200 300 400 X In the chromosphere neutral gas and plasma motion are strongly coupled Temperature stratification at t=0 [Büchner et al. 2005, Otto et al., 2006]
Result: Jperp near a magnetic null
Or: Jpar for torsional motion (case without magnetic null)
Location of Jpar without null Quasi-separatrix layers (QSL) form if the magnetic connectivity in the complex coronal B-field changes consierably -> Measure: Q where a,b,c,d are the elements of the Jacobian: [Titov et al. 2003] (Q = aspect ratio of the ellipse conjugate to initially circular flux tubes)
Dissipation by wave-particle interaction The ensemble averaging of the Vlasov equation for with reveals Theoretical (quasilinear) estimates of the anomalous (effective) collision frequency : and for the collision frequency : But what is the wave energy at sun? Invisible! > kinetic simulations are needed! In a simulation one then can directly determine the effective collision frequency
Dissipation after phase space filamentation due to plasma waves <- The wave-particle interaction lead to a filamentationof the velocity space down to the finest scales, hence essentially nonlinear effects have to be considered and resolved -> Since PIC codes are too noisy (shot noise), huge particle numbers would be necessary to describe the filamentation of the distribution functions -> practical noiseless Vlasov codes have to be used to investigate the collisionless dissipation in the solar corona
Scattering for Jerp (LHD) From the effective collision rate follows the effective, (turbulent) resistivity : [animation from Silin and Büchner, 2004, 05]
Scattering for Epar = const. (IA) -> electric currents in the transition region are limited and dissipated due to wave-particle scattering in self-generated potential wells [from Elkina and Büchner, 2005]
Collision frequency for Epar Blue: momentum exchange rate (simulation result): green: the theoretical estimate, using E^2 is much smaller, also the Sagdeev-formula estimate
Sub-summary - microphysics The anomalous resistivity in the corona can be driven either by Jperp, Epar, or Jpar : 1.) Jperp -> nonlinear LHD-type-instability [PIC: Büchner&Kuska,1999; Vlasov: Silin&Büchner, 2005] 2.) Epar -> weak, quasi-linear ion-acoustic instability [Sagdeev and Galeev, 1967; PIC: Dum, 1970; Büchner 2005, Elkina & Büchner 2005] 3.) Most efficient, however, is scattering in case of Jpar: -> nonlinear ion-acoustic electron-hole instabilities [Elkina & Büchner, 2006] Parametrization for MHD, e.g. vd η 0 min 1, 1 η = via a threshold (V c or gradient vc, scale L) and Eta 0 -> 0 where V c and Eta 0 strongly depend on the configuration! vd v c v d < v c
Example: EIT (195 A) Bright Point EUV BP of 17-18.10.1996 [M. Madjarska et al., 2003)
... identified by modeling as being due to reconnection with magnetic null Enhanced Jperp: after U=J/q rho > Vc A Jperp plasma instability causes sufficient collisionless resistivity -> Continued reconnection due to the observed continued footpoint motion that drives plasma through the separatrix (animation!)
Example 2: TRACE EUV-BP EUV BP, 14.6.98, 14:00 UT No null, but rotating [Brown et al., 2000] magnetic polarity
Modeled coronal currents Solid line: Dashed line: Jpar is dissipated continuously after the instability threshold Vpar =Vcrit is reached. [Büchner & Nikutowski, 2005] Jperp is dissipated intermittendly by reconnection
Generation of Jpar->Epar Torsion plus strong magnetic connectivity create Jpar -> Epar after resistivity is switched on [Büchner et al, 2004]
Epar vs. TRACE-EUV The modeled electric field Epar is enhanced in places, where TRACE [Büchner et al., 2004] observed the EUV brightening!
Did the QSL (Q) predict Epar? Epar is maximum, where (1) Q >>1 (QSL!) if and only if in addition (2) the photospheric convection had moved plasma accross the QSL
Summary We demonstrated our appraoch to a forward modeling of the magnetic coupling betwwen photosphere and corona by currents (Jpar and Jperp) Since coronal fields are practically not observed: Photospheric fields and motion should be used as input information for modeling approaches We found enhanced J, including Jperp, in regions of peculiar B-field geometry, i/o magnetic nulls Quasi-separatrix layers (QSL) appeared to be good predictors for current concentrations i/o nulls QSL have to just be affected by perpendicular plasma motion in order to cause current concentrations We used the parameters of these current concentrations as input parameters for kinetic dissipation models We then feed the kinetic results back to the fluid model
Outlook For meso-scale coronal energization processes one can carry on with the developed forward modeling approach for observations, e.g., of Solar-B: From time dependent photospheric (vector) magnetic fields: -> 1.) one can predict current concentrations by investigations of the current free B field -> 2.) then one can estimate Vn and Vt using ILCT Next one can dynamically simulate the generation of currents out of an equilibrium field- and plasma model Then -> one has to add a microphysical dissipation model This way one obtains Ohmic heating as energy input Next one can obtain E_par and electron acceleration and directly compare with x-ray observations Desirable: Emission and radiation transfer integration along the line-of-sight to directly compare with the observed radiation