Intermittent heating in the solar corona employing a 3D MHD model

We investigate the spatial and temporal evolution of the heating of the corona of a cool star such as our Sun in a three-dimensional magneto-hydrodynamic (3D MHD) model. We solve the 3D MHD problem numerically in a box representing part of the (solar) corona. The energy balance includes Spitzer heat conduction along the magnetic field and optically thin radiative losses. The self-consistent heating mechanism is based on the braiding of magnetic field lines rooted in the convective photosphere. Magnetic stress induced by photospheric motions leads to currents in the atmosphere which heat the corona through Ohmic dissipation. While the horizontally averaged quantities, such as heating rate, temperature or density, are relatively constant in time, the simulated corona is highly variable and dynamic, on average reaching temperatures and densities as found in observations. The strongest heating per particle is found in the transition region from the chromosphere to the corona. The heating is concentrated in current sheets roughly aligned with the magnetic field and is transient in time and space. This supports the idea that numerous small heating events heat the corona, often referred to a nanoflares

Parametrization of coronal heating: spatial distribution and observable consequences

We investigate the difference in the spatial distribution of the energy input for parametrizations of different mechanisms to heat the corona of the Sun and possible impacts on the coronal emission. We use a 3D MHD model of a solar active region as a reference and compare the Ohmic-type heating in this model to parametrizations for alternating current (AC) and direct current (DC) heating models, in particular, we use Alfven wave and MHD turbulence heating. We extract the quantities needed for these two parametrizations from the reference model and investigate the spatial distribution of the heat input in all three cases, globally and along individual field lines. To study differences in the resulting coronal emission we employ 1D loop models with a prescribed heat input based on the heating rate we extracted along a bundle of field lines. On average, all heating implementations show a roughly drop of the heating rate with height. This also holds for individual field lines. While all mechanism show a concentration of the energy input towards the low parts of the atmosphere, for individual field lines the concentration towards the footpoints is much stronger for the DC mechanisms than for the Alfven wave AC case. In contrast, the AC model gives a stronger concentration of the emission towards the footpoints. This is because the more homogeneous distribution of the energy input leads to higher coronal temperatures and a more extended transition region. The significant difference in the concentration of the heat input towards the foot points for the AC and DC mechanisms, and the pointed difference in the spatial distribution of the coronal emission for these cases shows that the two mechanisms should be discriminable by observations. Before drawing final conclusions, these parametrizations should be implemented in new 3D models in a more self-consistent way.Comment: accepted for publication in A&A, 10 pages, 9 figure

Coronal loops above an Active Region - observation versus model

We conducted a high-resolution numerical simulation of the solar corona above a stable active region. The aim is to test the field-line braiding mechanism for a sufficient coronal energy input. We also check the applicability of scaling laws for coronal loop properties like the temperature and density. Our 3D-MHD model is driven from below by Hinode observations of the photosphere, in particular a high-cadence time series of line-of-sight magnetograms and horizontal velocities derived from the magnetograms. This driving applies stress to the magnetic field and thereby delivers magnetic energy into the corona, where currents are induced that heat the coronal plasma by Ohmic dissipation. We compute synthetic coronal emission that we directly compare to coronal observations of the same active region taken by Hinode. In the model, coronal loops form at the same places as they are found in coronal observations. Even the shapes of the synthetic loops in 3D space match those found from a stereoscopic reconstruction based on STEREO spacecraft data. Some loops turn out to be slightly over-dense in the model, as expected from observations. This shows that the spatial and temporal distribution of the Ohmic heating produces the structure and dynamics of a coronal loops system close to what is found in observations.Comment: 7 pages, 7 figures, special issu

Magnetic Jam in the Corona of the Sun

The outer solar atmosphere, the corona, contains plasma at temperatures of more than a million K, more than 100 times hotter that solar surface. How this gas is heated is a fundamental question tightly interwoven with the structure of the magnetic field in the upper atmosphere. Conducting numerical experiments based on magnetohydrodynamics we account for both the evolving three-dimensional structure of the atmosphere and the complex interaction of magnetic field and plasma. Together this defines the formation and evolution of coronal loops, the basic building block prominently seen in X-rays and extreme ultraviolet (EUV) images. The structures seen as coronal loops in the EUV can evolve quite differently from the magnetic field. While the magnetic field continuously expands as new magnetic flux emerges through the solar surface, the plasma gets heated on successively emerging fieldlines creating an EUV loop that remains roughly at the same place. For each snapshot the EUV images outline the magnetic field, but in contrast to the traditional view, the temporal evolution of the magnetic field and the EUV loops can be different. Through this we show that the thermal and the magnetic evolution in the outer atmosphere of a cool star has to be treated together, and cannot be simply separated as done mostly so far.Comment: Final version published online on 27 April 2015, Nature Physics 12 pages and 8 figure

A model for the formation of the active region corona driven by magnetic flux emergence

We present the first model that couples the formation of the corona of a solar active region to a model of the emergence of a sunspot pair. This allows us to study when, where, and why active region loops form, and how they evolve. We use a 3D radiation MHD simulation of the emergence of an active region through the upper convection zone and the photosphere as a lower boundary for a 3D MHD coronal model. The latter accounts for the braiding of the magnetic fieldlines, which induces currents in the corona heating up the plasma. We synthesize the coronal emission for a direct comparison to observations. Starting with a basically field-free atmosphere we follow the filling of the corona with magnetic field and plasma. Numerous individually identifiable hot coronal loops form, and reach temperatures well above 1 MK with densities comparable to observations. The footpoints of these loops are found where small patches of magnetic flux concentrations move into the sunspots. The loop formation is triggered by an increase of upwards-directed Poynting flux at their footpoints in the photosphere. In the synthesized EUV emission these loops develop within a few minutes. The first EUV loop appears as a thin tube, then rises and expands significantly in the horizontal direction. Later, the spatially inhomogeneous heat input leads to a fragmented system of multiple loops or strands in a growing envelope.Comment: 13 pages, 10 figures, accepted to publication in A&

Current systems of coronal loops in 3D MHD simulations

We study the magnetic field and current structure associated with a coronal loop. Through this we investigate to what extent the assumptions of a force-free magnetic field break down and where they might be justified. We analyse a 3D MHD model of the solar corona in an emerging active region with the focus on the structure of the forming coronal loops. The lower boundary of this simulation is taken from a model of an emerging active region. As a consequence of the emerging magnetic flux and the horizontal motions at the surface a coronal loop forms self-consistently. We investigate the current density along magnetic field inside (and outside) this loop and study the magnetic and plasma properties in and around it. We find that the total current along the loop changes its sign from being antiparallel to parallel to the magnetic field. This is caused by the inclination of the loop together with the footpoint motion. Around the loop the currents form a complex non-force-free helical structure. This is directly related to a bipolar current structure at the loop footpoints at the base of the corona and a local reduction of the background magnetic field (i.e. outside the loop) caused by the plasma flow into and along the loop. The locally reduced magnetic pressure in the loop allows the loop to sustain a higher density, which is crucial for the emission in extreme UV. The acting of the flow on the magnetic field hosting the loop turns out to be also responsible for the observed squashing of the loop. The complex magnetic field and current system surrounding it can be modeled only in 3D MHD models where the magnetic field has to balance the plasma pressure. A 1D coronal loop model or a force-free extrapolation can not capture the current system and the complex interaction of the plasma and the magnetic field in the coronal loop, despite the fact that the loop is under low-$\beta$ conditions.Comment: 10 pages, 11 figures, published in A&

Investigation of mass flows in the transition region and corona in a three-dimensional numerical model approach

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. 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. Doppler shifts were determined from the emission line profiles of various extreme-ultraviolet emission lines formed in the range of $T=10^4-10^6$ 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. 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 or to the draining of the loop.Comment: 7 pages, 7 figure