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As we are heading towards the next solar cycle, presumably with a relatively small amplitude, it is of significant interest to reconstruct and describe the past grand minima on the basis of actual observations of the time. The Dalton Minimum is often considered one of the grand minima captured in the coverage of telescopic observations. Nevertheless, the reconstructions of the sunspot group number vary significantly, and the existing butterfly diagrams have a large data gap during the period. This is partially because most long-term observations have remained unexplored in historical archives. Therefore, to improve our understanding on the Dalton Minimum, we have located two series of Thadd\"aus Derfflinger's observational records (a summary manuscript and logbooks) as well as his Brander's 5.5-feet azimuthal-quadrant preserved in the Kremsm\"unster Observatory. We have revised the existing Derfflinger's sunspot group number with Waldmeier classification and eliminated all the existing 'spotless days' to remove contaminations from solar meridian observations. We have reconstructed the butterfly diagram on the basis of his observations and illustrated sunspot distributions in both solar hemispheres. Our article aims to revise the trend of Derfflinger's sunspot group number and to bridge a data gap of the existing butterfly diagrams around the Dalton Minimum. Our results confirm that the Dalton Minimum is significantly different from the Maunder Minimum, both in terms of cycle amplitudes and sunspot distributions. Therefore, the Dalton Minimum is more likely a secular minimum in the long-term solar activity, while further investigations for the observations at that time are required., Comment: main text 17 pages, references 7 pages, and 8 figures; accepted for publication in the ApJ

The quality of today's research is often tightly limited to the available computing power and scalability of codes to many processors. For example, tackling the problem of heating the solar corona requires a most realistic description of the plasma dynamics and the magnetic field. Numerically solving such a magneto-hydrodynamical (MHD) description of a small active region (AR) on the Sun requires millions of computation hours on current high-performance computing (HPC) hardware. The aim of this work is to describe methods for an efficient parallelization of boundary conditions and data input/output (IO) strategies that allow for a better scaling towards thousands of processors (CPUs). The Pencil Code is tested before and after optimization to compare the performance and scalability of a coronal MHD model above an AR. We present a novel boundary condition for non-vertical magnetic fields in the photosphere, where we approach the realistic pressure increase below the photosphere. With that, magnetic flux bundles become narrower with depth and the flux density increases accordingly. The scalability is improved by more than one order of magnitude through the HPC-friendly boundary conditions and IO strategies. This work describes also the necessary nudging methods to drive the MHD model with observed magnetic fields from the Sun's photosphere. In addition, we present the upper and lower atmospheric boundary conditions (photospheric and towards the outer corona), including swamp layers to diminish perturbations before they reach the boundaries. Altogether, these methods enable more realistic 3D MHD simulations than previous models regarding the coronal heating problem above an AR -- simply because of the ability to use a large amount of CPUs efficiently in parallel., Comment: 26 pages, 12 figures, 1 table, accepted at GAFD

We investigate the collective behaviour of particle orbits in the vicinity of magnetic reconnection in Earth's magneto-tail. Various regions of different kinds of orbital stability of particle motions are found. We locate regimes of temporary capture of particle orbits in configuration space as well as locations, where strong particle accelerations take place. With this study we are able to provide a detailed map, i.e. the topology, of high and low acceleration centers close to the reconnection site. Quasi-regular and chaotic kinds of motions of elementary particles can be determined as well. The orbital stability of particle orbits is obtained by a statistical analysis of the outcome of the system of variational equations of particle orbits within the framework of particle-in-cell simulations. Using the concept of Lyapunov Characteristic Numbers to ensembles of particle orbits we introduce Lyapunov Ensemble Averages to describe the response of particle orbits to local perturbations induced by the electro-magnetic field., Comment: 21 pages, 10 figures, https://aip.scitation.org/doi/10.1063/1.5093392

The electromotive force (EMF) describes how the evolution and generation of a large-scale magnetic field is influenced by small-scale turbulence. Recent studies of in-situ measurements have shown a significant peak in the EMF while a coronal mass ejection (CME) shock front passes by the spacecraft. The goal of this study is to use the EMF as an indicator for the arrival of CME shock fronts. With Helios spacecraft measurements we carry out a statistical study on the EMF during CMEs in the inner heliosphere. We develop an automated shock front detection algorithm using the EMF as the main detection criterion and compare the results to an existing CME database. The properties of the EMF during the recorded events are discussed as a function of the heliocentric distance. Our algorithm reproduces most of the the events from Kilpua et al. (2015) and finds many additional CME-like events which proves the EMF as a good shock front indicator. The largest peaks in the EMF are found from 0 to 50 minutes after the initial shock. We find a power law of -1.54 and -2.18 for two different formulations of the EMF with the heliocentric distance., Comment: 6 pages, 5 figures, published

The emergence of dipolar magnetic features on the solar surface is an idealization. Most of the magnetic flux emergence occurs in complex multipolar regions. Here, we show that the surface pattern of magnetic structures alone can reveal the sign of the underlying magnetic helicity in the nearly force-free coronal regions above. The sign of the magnetic helicity can be predicted to good accuracy by considering the three-dimensional position vectors of three spots on the sphere ordered by their relative strengths at the surface and compute from them the skew product. This product, which is a pseudoscalar, is shown to be a good proxy for the sign of the coronal magnetic helicity., Comment: 7 pages, 3 figures, 2 tables, published

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., Comment: 9 pages, 8 figures, published

Electromotive force is an essential quantity in dynamo theory. During a coronal mass ejection (CME), magnetic helicity gets decoupled from the Sun and advected into the heliosphere with the solar wind. Eventually, a heliospheric magnetic transient event might pass by a spacecraft, such as the Helios space observatories. Our aim is to investigate the electromotive force, the kinetic helicity effect ($\alpha$ term), the turbulent diffusion ($\beta$ term) and the cross-helicity effect ($\gamma$ term) in the inner heliosphere below 1 au. We set up a one-dimensional model of the solar wind velocity and magnetic field for a hypothetic interplanetary CME. Because turbulent structures within the solar wind evolve much slower than this structure needs to pass by the spacecraft, we use a reduced curl operator to compute the current density and vorticity. We test our CME shock-front model against an observed magnetic transient that passes by the Helios-2 spacecraft. At the peak of the fluctuations in this event we find strongly enhanced $\alpha$, $\beta$ and $\gamma$ terms, as well as a strong peak in the total electromotive force. Our method allows us to automatically identify magnetic transient events from any in-situ spacecraft observations that contain magnetic field and plasma velocity data of the solar wind., Comment: 10 pages, 14 figures, published

Plasma beta is an important and fundamental physical quantity in order to understand plasma dynamics, particularly in the context of magnetically active stars, because it tells about the domination of magnetic versus thermodynamic processes on the plasma motion. We estimate the value ranges of plasma beta in different regions within the solar atmosphere and we describe a possible mechanism that helps forming a penumbra. For that we evaluate data from a 3D magnetohydrodynamic model of the solar corona above a magnetically active region. We compare our results with previously established data that is based on magnetic field extrapolations and that was matched for some observations. Our model data suggest that plasma beta in the photosphere should be considered to be larger than unity outside of sunspots. However, in the corona we also find that the beta value range reaches lower than previously thought, which coincides with a recent observation. We present an idea based on a gravity-driven process in a high-beta regime that might be responsible for the formation of the penumbra around sunspot umbra, where the vertical field strength reaches a given threshold. This process would also explain counter-Evershed flows. Regarding the thermal and magnetic pressure within the mixed-polarity solar atmosphere, including non-vertical magnetic field and quiet regions, plasma beta may reach unity at practically any height from the photosphere to the outer corona., Comment: 5 pages, 2 figures, published

To understand the essential physics needed to reproduce magnetic reconnection events in 2.5-D particle-in-cell (PIC) simulations, we revisit the Geospace Environmental Modeling (GEM) setup. We set up a 2-D Harris current sheet (that also specifies the initial conditions) to evolve the reconnection of antiparallel magnetic fields. In contrast to the GEM setup, we use a much smaller initial perturbation to trigger the reconnection and evolve it more self-consistently. From PIC simulation data with high-quality particle statistics we study a symmetric reconnection site, including separatrix layers, as well as the inflow and the outflow regions. The velocity distribution functions (VDFs) of electrons have a fine structure and vary strongly depending on their location within the reconnection setup. The goal is to start cataloging multidimensional fine-structured electron velocity distributions showing different reconnection processes in the Earth's magnetotail under various conditions. This will enable a direct comparison with observations from, e.g., the NASA Magnetospheric MultiScale (MMS) mission, to identify reconnection-related events. We find regions with strong non-gyrotropy also near the separatrix layer and provide a refined criterion to identify an electron diffusion region in the magnetotail. The good statistical significance of this work for relatively small analysis areas reveals the gradual changes within the fine structure of electron VDFs depending on their sampling site., Comment: 17 pages, 11 figures, published

We investigate the combined effect of solar wind, Poynting-Robertson drag, and the frozen-in interplanetary magnetic field on the motion of charged dust grains in our solar system. For this reason we derive a secular theory of motion by the means of averaging method and validate it with numerical simulations of the un-averaged equations of motions. The theory predicts that the secular motion of charged particles is mainly affected by the z-component of the solar magnetic axis, or the normal component of the interplanetary magnetic field. The normal component of the interplanetary magnetic field leads to an increase or decrease of semi-major axis depending on its functional form and sign of charge of the dust grain. It is generally accepted that the combined effects of solar wind and photon absorption and re-emmision (Poynting-Robertson drag) lead to a decrease in semi-major axis on secular time scales. On the contrary, we demonstrate that the interplanetary magnetic field may counteract these drag forces under certain circumstances. We derive a simple relation between the parameters of the magnetic field, the physical properties of the dust grain as well as the shape and orientation of the orbital ellipse of the particle, which is a necessary conditions for the stabilization in semi-major axis., Comment: 32 pages, 5 figures, 2 tables

Context. The structure and heating of coronal loops are investigated since decades. Established scaling laws relate fundamental quantities like the loop apex temperature, pressure, length, and the coronal heating. Aims. We test such scaling laws against a large-scale 3D MHD model of the Solar corona, which became feasible with nowadays high-performance computing. Methods. We drive an active region simulation a with photospheric observations and found strong similarities to the observed coronal loops in X-rays and EUV wavelength. A 3D reconstruction of stereoscopic observations showed that our model loops have a realistic spatial structure. We compare scaling laws to our model data extracted along an ensemble of field lines. Finally, we fit a new scaling law that represents well hot loops and also cooler structures, which was not possible before only based on observations. Results. Our model data gives some support for scaling laws that were established for hot and EUV-emissive coronal loops. For the RTV scaling law we find an offset to our model data, which can be explained by 1D considerations of a static loop with a constant heat input and conduction. With a fit to our model data we set up a new scaling law for the coronal heat input along magnetic field lines. Conclusions. RTV-like scaling laws were fitted to hot loops and therefore do not predict well the coronal heat input for cooler structures that are hardly observable. The basic differences between 1D and self-consistent 3D modeling account for deviations between our and earlier scaling laws. We also conclude that a heating mechanism by MHD-turbulent dissipation within a braided flux tube would heat the corona stronger than consistent with our model corona., Comment: 8 pages, 9 figures, published

Context. We have conducted a 3D MHD simulation of the solar corona above an active region (AR) in full scale and high resolution, which shows coronal loops, and plasma flows within them, similar to observations. Aims. We want to find the connection between the photospheric energy input by field-line braiding with the coronal energy conversion by Ohmic dissipation of induced currents. Methods. To this end we compare the coronal energy input and dissipation within our simulation domain above different fields of view, e.g. for a small loops system in the AR core. We also choose an ensemble of field lines to compare, e.g., the magnetic energy input to the heating per particle along these field lines. Results. We find an enhanced Ohmic dissipation of currents in the corona above areas that also have enhanced upwards-directed Poynting flux. These regions coincide with the regions where hot coronal loops within the AR core are observed. The coronal density plays a role in estimating the coronal temperature due to the generated heat input. A minimum flux density of about 200 Gauss is needed in the photosphere to heat a field line to coronal temperatures of about 1 MK. Conclusions. This suggests that the field-line braiding mechanism provides the coronal energy input and that the Ohmic dissipation of induced currents dominates the coronal heating mechanism., Comment: 8 pages, 8 figures, published

Many applications in Solar physics need a 1D atmospheric model as initial condition or as reference for inversions of observational data. The VAL atmospheric models are based on observations and are widely used since decades. Complementary to that, the FAL models implement radiative hydrodynamics and showed the shortcomings of the VAL models since almost equally long time. In this work, we present a new 1D layered atmosphere that spans not only from the photosphere to the transition region, but from the solar interior up to far in the corona. We also discuss typical mistakes that are done when switching on simulations based on such an initial condition and show how the initial condition can be equilibrated so that a simulation can start smoothly. The 1D atmosphere we present here served well as initial condition for HD and MHD simulations and should also be considered as reference data for solving inverse problems., Comment: 10 pages, 3 figures, published version

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 issue