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Investigation of Mass Flows in the Transition Region and Corona in a Three-Dimensional Numerical Model Approach

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Investigation of Mass Flows in the Transition Region and Corona in a Three-Dimensional Numerical Model Approach A&A 531, A97 (2011) Astronomy DOI: 10.1051/0004-6361/201016047 & c ESO 2011 Astrophysics Investigation of mass flows in the transition region and corona in a three-dimensional numerical model approach P. Zacharias1, H. Peter2, and S. Bingert2 1 Kiepenheuer-Institut für Sonnenphysik, Schöneckstrasse 6, 79104 Freiburg, Germany e-mail: [email protected] 2 Max Planck Institute for Solar System Research, Max-Planck Strasse 2, 37191 Katlenburg-Lindau, Germany Received 2 November 2010 / Accepted 4 April 2011 ABSTRACT Context. The origin of solar transition region redshifts is not completely understood. Current research is addressing this issue by investigating three-dimensional magneto-hydrodynamic models that extend from the photosphere to the corona. Aims. By studying the average properties of emission line profiles synthesized from the simulation runs and comparing them to observations with present-day instrumentation, we investigate the origin of mass flows in the solar transition region and corona. Methods. Doppler shifts were determined from the emission line profiles of various extreme-ultraviolet emission lines formed in the range of T = 104−106 K. Plasma velocities and mass flows were investigated for their contribution to the observed Doppler shifts in the model. In particular, the temporal evolution of plasma flows along the magnetic field lines was analyzed. Results. Comparing observed vs. modeled Doppler shifts shows a good correlation in the temperature range log(T/[K]) = 4.5−5.7, which is the basis of our search for the origin of the line shifts. The vertical velocity obtained when weighting the velocity by the density squared is shown to be almost identical to the corresponding Doppler shift. Therefore, a direct comparison between Doppler shifts and the model parameters is allowed. A simple interpretation of Doppler shifts in terms of mass flux leads to overestimating the mass flux. Upflows in the model appear in the form of cool pockets of gas that heat up slowly as they rise. Their low temperature means that these pockets are not observed as blueshifts in the transition region and coronal lines. For a set of magnetic field lines, two different flow phases could be identified. The coronal part of the field line is intermittently connected to subjacent layers of either strong or weak heating, leading either to mass flows into the loop (observed as a blueshift) or to the draining of the loop (observed as a redshift). Key words. stars: coronae – Sun: corona – Sun: transition region – Sun: UV radiation – techniques: spectroscopic 1. Introduction Spadaro et al. (2006) used one-dimensional coronal loop models to show that the redshifts can be the result of transient heating Persistent average redshifts of emission lines from the solar tran- near the loop footpoints. Recently, Hansteen et al. (2010)have sition region were observed by Doschek et al. (1976)forthe shown that transition region redshifts are naturally produced in first time. Early observations from rockets (e.g., Hassler et al. episodically heated models where the average volumetric heat- 1991) had limited potential and did not provide a conclusive pic- ing scale height lies between 50 and 200 km. The authors suggest ture of the nature of these redshifts. The evaluation of SUMER that chromospheric material is heated in place to coronal tem- (Solar Ultraviolet Measurements of Emitted Radiation, Wilhelm peratures or that rapidly heated coronal material leads to a con- et al. 1995) observations onboard SOHO led to the conclusion duction front heating the chromospheric material below. Both that redshifts in the transition region predominately present ver- options lead to a high-pressure plug of material at upper tran- tical motions that turn into blueshifts at higher temperatures sition region temperatures that relaxes towards equilibrium by (Peter 1999; Peter & Judge 1999). These redshifts have been ex- expelling material. plained by a variety of models including the return of previously In this paper, we describe the investigation of a small ac- heated spicular material (Athay & Holzer 1982; Athay 1984) tive region by means of a three-dimensional (3D) magneto- or nanoflare-induced waves generated in the corona that would hydrodynamic (MHD) model. We synthesize transition region produce a net redshift in transition region lines (Hansteen 1993). lines that have been typically observed by SUMER. The synthe- For a more comprehensive discussion of coronal loops in rela- sized emission may be compared directly to observations. The tion to the Doppler shift observations see Peter & Judge (1999). mass balance in the model simulation is investigated as is the re- Peter et al. (2004, 2006) found that three-dimensional numerical lation of the Doppler shifts to the magnetic structure in order to models spanning the region from the photosphere to the corona elucidate the nature of the transition region redshifts. are producing redshifts in transition region lines. The 3D MHD model is introduced in Sect. 2. Section 3 fo- In these models, coronal heating comes from the Joule dis- cuses on the spectral line synthesis from the simulation results sipation of currents produced by the braiding of the magnetic and on the comparison with observations. The origin and nature field through photospheric plasma motions; however, details of the modeled Doppler shifts is investigated in Sect. 4,before on the origin of the redshifts have not been identified so far. results are discussed in Sect. 5. Article published by EDP Sciences A97, page 1 of 7 A&A 531, A97 (2011) 2. The coronal 3D MHD model 6.0 We are applying a 3D MHD model of the solar atmosphere above a small active region in a computational box of the size 5.5 50 × 50 × 30 Mm3. A detailed description of the model can be found in Bingert & Peter (2011). The simulations are car- 5.0 ried out using the Pencil-code (Brandenburg & Dobler 2002), a high-order finite-difference code for compressible MHD. The temperature [K] > 4.5 set of equations being solved includes the continuity equation, 10 the induction equation, the Navier-Stokes equation, and the en- 4.0 ergy equation with an anisotropic Spitzer heat conduction term < log (Spitzer 1962) and an optical thin radiative loss function (Cook et al. 1989). 0 10 20 30 For the lower boundary we constructed a map of the mag- height above photosphere [Mm] netic field based on two observed magnetograms, one from an active region, spatially scaled down by a factor of five, and an- Fig. 1. Height dependence of the average temperature in horizontal lay- other one from a quiet Sun area. Thus, the resulting magnetic ers of the simulation box (solid line). Diamonds indicate the forma- map represents the quiet Sun with some activity added by a pore tion temperature of the emission lines that are investigated in this study (compare Table 1, column labeled log Tcontrib). The dashed lines show and is supposed to be typical for the magnetic field underlying the minimum and maximum temperature in the horizontal layers. the transition region of the Sun outside active regions. The main difference between the model presented in this study and the one described by Bingert & Peter (2011)isthe The deposited energy is efficiently redistributed by heat conduc- higher grid point resolution of our simulation, allowing for a tion, the rate of which is comparable to the Ohmic heating rate, slightly lower magnetic diffusivity. The resolution of 2563 grid except for low temperatures, where radiative losses dominate. points corresponds to a grid spacing of 195 km in the horizon- The boundary conditions are chosen such that the simula- tal direction and 75−285 km in the vertical direction, where a tion box is periodic in (x,y) and closed for mass flux on both nonequidistant grid is applied. This corresponds to a maximum the top and bottom. At the bottom boundary, the temperatures resolvable vertical temperature gradient of about 2 K/m, when and densities are set to the average photospheric temperature and 6 assuming a temperature difference of 10 K across five grid density values at τ = 1. The magnetic field at the lower bound- points. This number is confirmed by the 3D model discussed ary is driven by horizontal motions mimicking the photospheric by Peter et al. (2006), see their Fig. 5. In a static 1D empirical horizontal granular motions. This leads to the braiding of the model based on an emission measure inversion, Mariska (1992) magnetic field lines and the induction of currents, which are sub- found a maximum temperature gradient of the order of 10 K/m sequently dissipated by Ohmic heating. As a result, the plasma (his Table 6.1). Flows present in our 3D model are assumed to is heated and driven, leading to a dynamic corona. The simu- smooth out steep temperature gradients, resulting in temperature lation was run – for some 30 min – to a state where the be- changes that are less substantial than expected for the case of the havior is independent of the initial condition. This point of time static 1D empirical models (see Fig. 5 of Peter et al. 2006). Thus, is defined as t = 0 min in our study. The simulation produces it can be assumed that temperature gradients in the 3D model a dynamic transition region and corona with flows up to and are being properly resolved. However, to synthesize transition above the sound speed and with the horizontally averaged quan- region emission lines, the temperatures and densities as com- tities, such as the average temperature (see Fig. 1) and density puted in the 3D MHD model have to be interpolated (Sect. 3.1; as a function of height, showing only a little variation over time. for details see Peter et al. 2006). Below about 4 Mm, the computational domain contains material The viscosity and heat conduction terms as published by at and below chromospheric temperatures.
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