Numerical Simulation of a Solar Active Region I

Authors: Alain Vincent Paul Charbonneau Caroline Dubé

Publish Date: 2012/03/16

Volume: 278, Issue: 2, Pages: 367-391

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Abstract

We present threedimensional unsteady modeling and numerical simulations of a coronal active region carried out within the compressible singlefluid MHD approximation We focus on AR 9077 on 14 July 2000 and the triggering of the X57 GOES Xray class “Bastille Day” flare We simulate only the lower corona although we include a virtual photosphere and chromosphere below The boundary conditions at the base of this layer are set using temperature maps from line intensities and lineofsight magnetograms SOHO/MDI From the latter we generate vector magnetograms using the forcefree approximation these vector magnetograms are then used to produce the boundary condition on the velocity field using a minimum energy principle Longcope Astrophys J 612 1181 2004 The reconnection process is modeled through a dynamical hyperresistivity which is activated when the current exceeds a critical value Klimas et al J Geophys Res 109 2218 2004 Comparing the time series of Xray fluxes recorded by GOES with modeled time series of various mean physical variables such as current density Poynting energy flux or radiative loss inside the active region we can demonstrate that the model properly captures the evolution of an active region over a day and in particular is able to explain the initiation of the flare at the observed timeThe computations were done at the Réseau Québécois de Calcul de Haute Performance RQCHP Montréal Québec Alain Vincent and Paul Charbonneau are supported through NSERC Individual Research Grants We thank Jacques Richer from RQCHP for his help with OpenMP as well as Benoît Rolland Benoît Tremblay Léonie Petitclerc Frédérique Baron Ali Benslimane and Michel JeanPhilippe Côté for their contributions to data preprocessing Finally we thank the anonymous reviewer and the editor for their constructive remarksThe mean current density 〈J〉z A m−2 decreases from 10−3 A m−2 at the transition layer to 10−6 A m−2 at 100 000 km The strongest gradients of B are located at the transition layer consistent with the flare being localized just above the transition layer A sudden burst of J occurs above the transition layer likely due to the occurrence of strong shear gradients immediately below We do not simulate what happens inside the chromosphere and below but the origin of the flare is likely to be found there The reconnection at the top of the slinky arcade system could result from this burst of J near the transition layer Due to our reconnection model the Joule heating takes place at the same location where J exceeds J c There are also magnetic loops there Figure 5 In our simple MHD model and our low numerical resolution there is only a slight avalanche oriented eastwest and best seen on an animated movie of electric hyperresistivity ηxy Figure 8 but this is located around 8000 – 12 000 km above the transition zone and not at the top of the arcade system Although plasma and radiative effects are neglected in our model our results are consistent at least qualitatively with observations eg Liu and Zhang 2001The magnetic hyperresistivity 〈η〉z Ω m first increases slightly to reach a maximum around 10 000 km and then decays from about 10−4 Ω m to 10−5 Ω m at 40 000 km and above Note that we would have to take higher values of η max Equation 10 to reach 40 MK during reconnection as observed Aschwanden and Alexander 2001Joule heating seen in γ−1〈ηJ 2〉z W m−3 starting from 10−12 W m−3 at the transition layer to 10−18 W m−3 around 20 000 km of altitude The peak occurs 10 000 km above the transition layer where the maximal value reaches ≈ 10−7 W m−3 at the flare center This is consistent with reconnection taking place mostly within the first 100 000 km above the transition layerRadiative cooling gamma1 E mathrmrz = gamma1langle n mathrme2 LT rangle z~mboxWm3 is also maximal near 10 000 km and does not vary much up to 40 000 km where it starts to decay in a manner similar to Sz

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