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Magnetic Helicity Reversal in the Corona at Small Plasma Beta

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Magnetic Helicity Reversal in the Corona at Small Plasma Beta The Astrophysical Journal, 869:2 (9pp), 2018 December 10 https://doi.org/10.3847/1538-4357/aae97a Preprint typeset using LATEX style emulateapj pab v. 21/02/18 Magnetic Helicity Reversal in the Corona at Small Plasma Beta Philippe-A. Bourdin1, , Nishant K. Singh2;3, , Axel Brandenburg3;4;5;6, 1 Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, A-8042 Graz, Austria 2 Max-Planck-Institut f¨urSonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 G¨ottingen,Germany 3 Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden 4 JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80303, USA 5 Department of Astronomy, AlbaNova University Center, Stockholm University, SE-10691 Stockholm, Sweden and 6 Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA Received 2018 April 11; revised 2018 October 17; accepted 2018 October 17; published 2018 December 5 Abstract Solar and stellar dynamos shed small-scale and large-scale magnetic helicity of opposite signs. However, solar wind observations and simulations have shown that some distance above the dynamo both the small- scale and large-scale magnetic helicities have reversed signs. With realistic simulations of the solar corona above an active region now being available, we have access to the magnetic field and current density along coronal loops. We show that a sign reversal in the horizontal averages of the magnetic helicity occurs when the local maximum of the plasma beta drops below unity and the field becomes nearly fully force free. Hence, this reversal is expected to occur well within the solar corona and would not directly be accessible to in-situ measurements with the Parker Solar Probe or SolarOrbiter. We also show that the reversal is associated with subtle changes in the relative dominance of structures with positive and negative magnetic helicity. Keywords: Sun: corona | Sun: magnetic fields | solar wind | dynamo | magnetohydrodynamics (MHD) | methods: numerical 1. Introduction coronal exterior (Warnecke et al. 2011, 2012). This unex- Magnetic helicity is an important invariant in ideal and pected behavior is what is referred to as magnetic helicity nearly ideal magnetohydrodynamics (MHD); see Biskamp reversal. Such reversals have also been found in analytic so- (2003) and the original work of Woltjer(1958). It plays lutions of simple dynamo models with a force-free exterior a crucial role in characterizing the topological complexity (Bonanno 2016) and in mean-field models with magnetic of coronal magnetic fields (Berger & Field 1984), and it helicity fluxes included (Brandenburg et al. 2009). is also responsible for the possibility of premature quench- Numerical simulations are currently the best way of test- ing of the underlying dynamo (Gruzinov & Diamond 1994). ing and studying in detail the idea of the magnetic helicity An obvious remedy to the dynamo problem is to let excess reversal. Here, we consider the magnetic helicity that was magnetic helicity escape through the boundaries (Black- found to emerge from the MHD simulations of Bourdin, man & Field 2000; Kleeorin et al. 2000), especially through Bingert, & Peter(2013, hereafter BBP), who used a so- coronal mass ejections (Blackman & Brandenburg 2003) lar magnetogram of an active region (AR) as a boundary and the solar differential rotation, which also acts on open condition. Reconnection and the associated coronal heat- field lines rooted in magnetically quiet regions of the pho- ing were driven by random footpoint motions, as envisaged in the early work of Parker(1972). The simulations of tosphere (DeVore 2000); see Berger & Ruzmaikin(2000) 1 for estimates of the relative importance of different contri- BBP used the Pencil Code and covered a larger domain 2 3 butions to the total magnetic helicity flux. Much of the (235 × 156 Mm ) compared to earlier ones with the Stag- magnetic helicity transported by differential rotation out ger Code (Gudiksen & Nordlund 2002, 2005a,b). through the surface has entered through the equator; see The AR model of BBP is observationally driven by Brandenburg & Sandin(2004). Its contribution to the net line-of-sight magnetograms taken from Hinode/SOT-NFI magnetic helicity loss may therefore be subdominant. Nev- (Kosugi et al. 2007; Tsuneta et al. 2008). The model pro- ertheless, estimates for the Sun invariably result in a total vides a sufficient amount of energy to the corona (Bourdin arXiv:1804.04153v2 [astro-ph.SR] 8 Dec 2018 loss of ∓1046 Mx2 per 11 year cycle (Berger & Ruzmaikin et al. 2015). It also compares well with various coronal ob- 2000; DeVore 2000; Brandenburg & Sandin 2004; Branden- servations (BBP) and shows similarities to coronal scaling burg 2009) in the northern and southern hemispheres, re- laws, e.g., for the temperature along loops that were de- spectively. One would therefore expect to see that the mag- rived from earlier observational and theoretical works (cf. netic helicity shed at the solar surface agrees with what is Bourdin et al. 2016). passing through the solar wind at larger distances. How- The coronal EUV emission is synthesized from the MHD ever, this does not seem to be the case because in the so- model using the Chianti atomic database (Dere et al. lar wind, the magnetic helicity was found to have mostly 1997; Young et al. 2003) using the method of Peter et al. a positive sign in the northern heliosphere (Brandenburg (2004, 2006). The 3D structure of the AR loop sys- et al. 2011), whereas at the solar surface it is mostly neg- tem matches the reconstruction from Stereo observations. ative in the north (Seehafer 1990). A similar result was Also, the plasma flow dynamics along those loops matches also obtained in numerical simulations of dynamos with a the Doppler shift pattern observed by Hinode/EIS (Cul- hane et al. 2007) in the coronal Fe XII emission line. [email protected] 1 https://github.com/pencil-code 2 Bourdin, Singh, & Brandenburg The magnetograms for driving these simulations from the s = cV ln P − cP ln ρ + s0 is the specific entropy, s0 is a con- bottom boundary give just the line-of-sight magnetic field, stant, cP and cV are the specific heats at constant pressure or Bz near disk center. During the first hour of solar time, and constant volume, respectively, χij = χ0δij +χSpitzB^iB^j we do not yet apply any large-scale driving motions de- is the thermal diffusivity, B^ is the unit vector of the mag- rived from the observed movements of magnetic patches in netic field, ν is the kinematic viscosity, η is the magnetic the photosphere. We only apply the horizontal small-scale diffusivity, χ is the Spitzer field-aligned heat conduc- velocities that mimic granulation. Therefore, these photo- Spitz tivity, χ0 is an isotropic contribution, g is the gravitational spheric horizontal motions are purely stochastic and sta- acceleration, and S is the traceless rate-of-strain tensor with tistically mirrorsymmetric, and there is no obvious mecha- 1 1 the components Sij = 2 (ui;j + uj;i) − 3 δijuk;k. Here, we nism to break the statistical mirrorsymmetry of the model. solve for A because then B is automatically divergence free. In particular, there is no Coriolis force or differential rota- Instead of solving for s, we use the logarithmic temperature tion. Nonetheless, it turns out that helicity emerges readily ln T , which is directly related to s and ln ρ. Using the log- within the initial phase of our model. arithmic density ln ρ, we are able to capture many orders Although there is no direct injection of helicity, the model of magnitude in the density stratification that our model can still produce magnetic helicity through a complex ar- atmosphere covers. rangement of multipolar spots (Bourdin & Brandenburg 2018). We use a magnetogram of a small and stable AR 2.2. Physical details about the simulations observed during 2007 November 14 in the southern hemi- For the radiative cooling function ρΛ(T ), we use a real- sphere. Indeed, we find helicity, as is readily demonstrated istic tabulation of Λ provided by Cook et al.(1989). In by looking at the vertical profile of the mean current helic- that work, the important emission peak from highly ion- ity density, hJ · Bi , where J = r × B/µ is the current xy 0 ized iron lines is included, which efficiently cools the model density, B is the magnetic field, µ is the vacuum perme- 0 corona. The characteristic half-time of this cooling is below ability, and h:::i denotes horizontal averages. We find xy 30 minutes. that the profiles generally show a sign reversal within the During the first 35 minutes of physical time, however, first 5{15 Mm above the surface. This is equally remarkable this loss term is turned off together with the heat conduc- because the upper regions are topologically connected with tion along the field. This is to prevent excessive cooling the lower ones through the same large-scale structures. Any of the corona during the initial phase in which the gran- small-scale magnetic fields seem to be interspersed within ular motions cause magnetic disturbances that still need other structures and are still associated with the large-scale to propagate from the photosphere into the corona. The magnetic loops extending from one footpoint to the other. simulation is then continued for another about 35 minutes The purpose of this work is to quantify the magnetic after all physical terms in the equations are turned on. Fur- helicity reversal in detail and to associate it with coronal ther details about the switching on can be found in Bourdin heating along EUV-emissive loops. We further characterize et al.(2014) and Bourdin(2014).
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