Clusters of small eruptive flares produced by magnetic reconnection in the sun

We report on the formation of small solar flares produced by patchy magnetic reconnection between interacting magnetic loops. A three-dimensional (3D) magnetohydrodynamic (MHD) numerical experiment was performed, where a uniform magnetic flux sheet was injected into a fully developed convective layer. The gradual emergence of the field into the solar atmosphere results in a network of magnetic loops, which interact dynamically forming current layers at their interfaces. The formation and ejection of plasmoids out of the current layers leads to patchy reconnection and the spontaneous formation of several small (size ? 1-2Mm) flares. We find that these flares are short-lived (30 s - 3 min) bursts of energy in the range O(10^25 - 10^27) ergs, which is basically the nanoflare-microflare range. Their persistent formation and co-operative action and evolution leads to recurrent emission of fast EUV/X-ray jets and considerable plasma heating in the active corona.Comment: 5 pages, 5 figure

Eruption of magnetic flux ropes during flux emergence

Aims: We investigate the formation of flux ropes in a flux emergence region and their rise into the outer atmosphere of the Sun. Methods: We perform 3D numerical experiments solving the time-dependent and resistive MHD equations. Results: A sub-photospheric twisted flux tube rises from the solar interior and expands into the corona. A flux rope is formed within the expanding field, due to shearing and reconnection of field lines at low atmospheric heights. If the tube emerges into a non-magnetized atmosphere, the flux rope rises, but remains confined inside the expanding magnetized volume. On the contrary, if the expanding tube is allowed to reconnect with a preexisting coronal field, the flux rope experiences a full eruption with a rise profile which is in qualitative agreement with erupting filaments and Coronal Mass Ejections

Flux emergence and coronal eruption

Our aim is to study the photospheric flux distribution of a twisted flux tube that emerges from the solar interior. We also report on the eruption of a new flux rope when the emerging tube rises into a pre-existing magnetic field in the corona. To study the evolution, we use 3D numerical simulations by solving the time-dependent and resistive MHD equations. We qualitatively compare our numerical results with MDI magnetograms of emerging flux at the solar surface. We find that the photospheric magnetic flux distribution consists of two regions of opposite polarities and elongated magnetic tails on the two sides of the polarity inversion line (PIL), depending on the azimuthal nature of the emerging field lines and the initial field strength of the rising tube. Their shape is progressively deformed due to plasma motions towards the PIL. Our results are in qualitative agreement with observational studies of magnetic flux emergence in active regions (ARs). Moreover, if the initial twist of the emerging tube is small, the photospheric magnetic field develops an undulating shape and does not possess tails. In all cases, we find that a new flux rope is formed above the original axis of the emerging tube that may erupt into the corona, depending on the strength of the ambient field.Comment: 5 pages, 3 figures, accepted for publication in A&

Modelling magnetic flux emergence in the solar convection zone

[Abridged] Bipolar magnetic regions are formed when loops of magnetic flux emerge at the solar photosphere. Our aim is to investigate the flux emergence process in a simulation of granular convection. In particular we aim to determine the circumstances under which magnetic buoyancy enhances the flux emergence rate (which is otherwise driven solely by the convective upflows). We use three-dimensional numerical simulations, solving the equations of compressible magnetohydrodynamics in a horizontally-periodic Cartesian domain. A horizontal magnetic flux tube is inserted into fully developed hydrodynamic convection. We systematically vary the initial field strength, the tube thickness, the initial entropy distribution along the tube axis and the magnetic Reynolds number. Focusing upon the low magnetic Prandtl number regime (Pm<1) at moderate magnetic Reynolds number, we find that the flux tube is always susceptible to convective disruption to some extent. However, stronger flux tubes tend to maintain their structure more effectively than weaker ones. Magnetic buoyancy does enhance the flux emergence rates in the strongest initial field cases, and this enhancement becomes more pronounced when we increase the width of the flux tube. This is also the case at higher magnetic Reynolds numbers, although the flux emergence rates are generally lower in these less dissipative simulations because the convective disruption of the flux tube is much more effective in these cases. These simulations seem to be relatively insensitive to the precise choice of initial conditions: for a given flow, the evolution of the flux tube is determined primarily by the initial magnetic field distribution and the magnetic Reynolds number.Comment: 12 pages, 15 figures, 2 tables. Accepted for publication in Astronomy and Astrophysic

Validation and Benchmarking of a Practical Free Magnetic Energy and Relative Magnetic Helicity Budget Calculation in Solar Magnetic Structures

In earlier works we introduced and tested a nonlinear force-free (NLFF) method designed to self-consistently calculate the free magnetic energy and the relative magnetic helicity budgets of the corona of observed solar magnetic structures. The method requires, in principle, only a single, photospheric or low-chromospheric, vector magnetogram of a quiet-Sun patch or an active region and performs calculations in the absence of three-dimensional magnetic and velocity-field information. In this work we strictly validate this method using three-dimensional coronal magnetic fields. Benchmarking employs both synthetic, three-dimensional magnetohydrodynamic simulations and nonlinear force-free field extrapolations of the active-region solar corona. We find that our time-efficient NLFF method provides budgets that differ from those of more demanding semi-analytical methods by a factor of ~3, at most. This difference is expected from the physical concept and the construction of the method. Temporal correlations show more discrepancies that, however, are soundly improved for more complex, massive active regions, reaching correlation coefficients of the order of, or exceeding, 0.9. In conclusion, we argue that our NLFF method can be reliably used for a routine and fast calculation of free magnetic energy and relative magnetic helicity budgets in targeted parts of the solar magnetized corona. As explained here and in previous works, this is an asset that can lead to valuable insight into the physics and the triggering of solar eruptions.Comment: 32 pages, 14 figures, accepted by Solar Physic

Recurrent solar jets in active regions

We study the emergence of a toroidal flux tube into the solar atmosphere and its interaction with a pre-existing field of an active region. We investigate the emission of jets as a result of repeated reconnection events between colliding magnetic fields. We perform 3D simulations by solving the time-dependent, resistive MHD equations in a highly stratified atmosphere. A small active region field is constructed by the emergence of a toroidal magnetic flux tube. A current structure is build up and reconnection sets in when new emerging flux comes into contact with the ambient field of the active region. The topology of the magnetic field around the current structure is drastically modified during reconnection. The modification results in a formation of new magnetic systems that eventually collide and reconnect. We find that reconnection jets are taking place in successive recurrent phases in directions perpendicular to each other, while in each phase they release magnetic energy and hot plasma into the solar atmosphere. After a series of recurrent appearance of jets, the system approaches an equilibrium where the efficiency of the reconnection is substantially reduced. We deduce that the emergence of new magnetic flux introduces a perturbation to the active region field, which in turn causes reconnection between neighboring magnetic fields and the release of the trapped energy in the form of jet-like emissions. This is the first time that self-consistent recurrency of jets in active regions is shown in a three-dimensional experiment of magnetic flux emergence.Comment: 4 pages, 3 figures, accepted for publication (A&A

3D MHD Flux Emergence Experiments: Idealized models and coronal interactions

This paper reviews some of the many 3D numerical experiments of the emergence of magnetic fields from the solar interior and the subsequent interaction with the pre-existing coronal magnetic field. The models described here are idealized, in the sense that the internal energy equation only involves the adiabatic, Ohmic and viscous shock heating terms. However, provided the main aim is to investigate the dynamical evolution, this is adequate. Many interesting observational phenomena are explained by these models in a self-consistent manner.Comment: Review article, accepted for publication in Solar Physic

Validation of the magnetic energy vs. helicity scaling in solar magnetic structures

We assess the validity of the free magnetic energy - relative magnetic helicity diagram for solar magnetic structures. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volume-calculation nonlinear force-free (NLFF) method applied to finite coronal magnetic structures and a surface-calculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic active-region cases obtained by three-dimensional magneto-hydrodynamic (MHD) simulations and observed active-region cases, which include both eruptive and noneruptive magnetic structures. The derived energy--helicity diagram shows a consistent monotonic scaling between relative helicity and free energy with a scaling index 0.84$\pm$0.05 for both data sets and calculation methods. It also confirms the segregation between noneruptive and eruptive active regions and the existence of thresholds in both free energy and relative helicity for active regions to enter eruptive territory. We consider the previously reported energy-helicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism

Sunspot rotation. I. A consequence of flux emergence

Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the sub-photospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a Lagrangian-Remap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353 degrees over the course of the experiment

On the Saturation of Astrophysical Dynamos: Numerical Experiments with the No-cosines flow

In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and study the dynamo's mode of operation during both the linear and non-linear saturation regime: It turns out that in addition to a high growth rate in the linear regime, the dynamo saturates at a level significantly higher than normal turbulent dynamos, namely at exact equipartition when the magnetic Prandtl number is on the order of unity. Visualization of the magnetic and velocity fields at saturation will help us to understand some of the aspects of the non-linear dynamo problem.Comment: 8 pages, 5 figures, submitted to the proceedings of "Space Climate 1" to be peer-reviewed to Solar Physic