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James E. Leake

Publications and source records attributed to James E. Leake.

At least 19 recordsLinked to original sources

Simulating the photospheric to coronal plasma using magnetohydrodynamic characteristics III: validation including gravity, flux emergence, and an eruption

Solar eruptions arise from instabilities or loss of equilibria in the solar atmosphere, but routinely inferring the precise magnetic and plasma properties that lead to eruptions is not currently practical using synoptic solar observations. Data driven simulations offer an appealing alternative. We test our boundary data-driven magnetohydrodynamic (MHD) approach, based on the method of characteristics, on a simulation that includes full MHD, a stratified atmosphere, and the emergence of a model solar magnetic active region, from the photosphere upwards. The driven simulation is tested against a larger, ab initio ``Ground Truth'' simulation that extends downward into the convection zone. Our driven simulation accurately reproduces the dynamic emergence of the active region above the photosphere, the formation of key topological features throughout the corona, and the subsequent eruption of mass and magnetic field. The total emerged energy matches to better than one percent, the ratio of emerged to eruptive energy is $\approx2\%$, and the actual values of each energy term agree to within $10\%$ between the two cases. Crucially, the data injection cadence, when properly scaled, matches the cadence of synoptic observations of the Sun's surface magnetic field, and is three to four orders of magnitude longer than the inherent CFL time step of the simulations. The stability of the code and fidelity of the results over an entire active region lifetime, from emergence to eruption, strongly suggests that our method will produce reliable results when driven using solar synoptic observations from existing and anticipated ground and spaced based observatories.

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Self-Consistent Heating of the Magnetically Closed Solar Corona: Generation of Nanoflares, Thermodynamic Response of the Plasma and Observational Signatures

The energy that heats the magnetically closed solar corona originates in the complex motions of the massive photosphere. Turbulent photospheric convection slowly displaces the footpoints of coronal field lines, causing them to become twisted and tangled. Magnetic stresses gradually build until reaching a breaking point when the field reconnects and releases a sudden burst of energy. We simulate this basic picture of nanoflares using a high-fidelity, three-dimensional, multi-stranded magnetohydrodynamic simulation that starts with a fully stratified atmosphere. This simulation includes the effects of field-aligned thermal conduction and optically thin radiation and uses the state-of-the-art Transition Region Adaptive Conduction (TRAC) method to capture the response of the plasma to the nanoflare heating. We find that our physical model supports a unified explanation for both the diffuse emission observed in active regions and the bright coronal loops. Specifically, our results suggest that the diffuse emission originates from spatially and temporally uncorrelated nanoflares, whereas coherent clusters of nanoflares - nanoflare storms - are responsible for the formation of bright coronal loops. Quantitative comparisons between the simulated emission and observed characteristics of coronal loops show that key observed properties - such as loop widths, lifetimes and cross sections - are reasonably well reproduced by the model. The idea that avalanche spread naturally leads to circular cross sections in coronal loops is strongly supported. Our results also suggest that phase differences in heating and cooling events across neighboring magnetic flux strands are a plausible explanation for the anomalous cross-field motions of coronal loops that were recently reported in high-resolution observations.

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Filament Mass Losses Forced by Magnetic Reconnection in the Solar Corona

Recent observations of the solar atmosphere in cool extreme ultraviolet (EUV) lines have reported the prevalence of coronal rain falling from coronal cloud filaments that are associated with the magnetic dips of coronal X-point structures. These filaments mysteriously appear as clouds of mass in the corona that subsequently shrink and disappear due to mass losses that drain as coronal rain along arced field lines. Using a two and a half dimensional, magnetohydrodynamic model, we investigated evaporation-condensation as the formation mechanism of the subset of coronal cloud filaments that form above coronal X-points. Our simulation included the effects of field-aligned thermal conduction and optically thin radiation and used the state-of-the-art Transition Region Adaptive Conduction (TRAC) method to model the formation, maintenance, and mass loss of a filament above a coronal X-point. This paper presents a physical model that demonstrates magnetic reconnection as a filament loss mechanism, producing hybrid filament/coronal rain via mass losses through the X-point. A detailed analysis of how the mass of the filament forces the field to reconnect is also presented, revealing three phases that characterize the evolution of the reconnecting current sheet and associated mass losses. We conclude that the formation of certain coronal cloud filaments and subsequent mass losses via coronal rain can be explained by the evaporation-condensation model combined with filament mass losses forced by magnetic reconnection. We also report that rebound shocks generated by the impact of coronal rain condensations on the chromosphere together with retractive upflows can cause upward propagating condensations to form through a dynamic thermal runaway process.

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Simulating the photospheric to coronal plasma using magnetohydrodyanamic characteristics II: reflections on non-reflecting boundary conditions

We present our implementation of non-reflecting boundary conditions in the magnetohydrodynamics (MHD) code LaRe3D. This implementation couples a characteristics-based boundary condition with a Lagrangian remap code, demonstrating the generality and flexibility of such non-reflecting boundary conditions for use with arbitrary grid-based MHD schemes. To test this implementation for perturbations on a background state, we present simulations of a hot sphere in an angled magnetic field. We then examine a series of simulations where we advect a spheromak through a non-reflecting boundary condition at four speeds related to the fast and slow magnetosonic speeds and the Alfven speed. We compare the behavior of these simulations to ground truth simulations run from the same initial condition on an extended grid that keeps the spheromak in the simulation volume at all times. We find that the non-reflecting boundary condition can lead to severe, physical differences developing between a simulation using a non-reflecting boundary and a ground truth simulation using a larger simulation volume. We conclude by discussing the origins of these differences.

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Simulating the photospheric to coronal plasma using magnetohydrodyanamic characteristics I: data-driven boundary conditions

We develop a general description of how information propagates through a magnetohydrodynamic (MHD) system based on the method of characteristics and use that to formulate numerical boundary conditions (BCs) that are intrinsically consistent with the MHD equations. Our formulation includes two major advances for simulations of the Sun. First, we derive data-driven BCs that optimally match the state of the plasma inferred from a time series of observations of a boundary (e.g., the solar photosphere). Second, our method directly handles random noise and systematic bias in the observations, and finds a solution for the boundary evolution that is strictly consistent with MHD and maximally consistent with the observations. We validate the method against a Ground Truth (GT) simulation of an expanding spheromak. The data-driven simulation can reproduce the GT simulation above the photosphere with high fidelity when driven at high cadence. Errors progressively increase for lower driving cadence until a threshold cadence is reached and the driven simulation can no longer accurately reproduce the GT simulation. However, our characteristic formulation of the BCs still requires adherence of the boundary evolution to the MHD equations even when the driven solution departs from the true solution in the driving layer. That increasing departure clearly indicates when additional information at the boundary is needed to fully specify the correct evolution of the system. The method functions even when no information about the evolution of some variables on the lower boundary is available, albeit with a further decrease in fidelity.

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The Thickness of Electric Current Sheets and Implications for Coronal Heating

The thickness of current sheets is extremely important, especially as it relates to the onset of fast magnetic reconnection. Onset determines how much magnetic free energy can build up in a field before it is explosively released. This has implications for many phenomena on the Sun and throughout the universe, including the heating of the solar corona. Significant effort has been devoted to the question of whether equilibrium current sheets in realistic geometries have finite or zero thickness. Using a simple force balance analysis, we show why current sheets without a guide field (2D) and with a guide field that is invariant in the guide field direction (2.5D) cannot be in equilibrium if they have both finite thickness and finite length. We then estimate the conditions under which the tension of a curved line-tied guide field can facilitate equilibrium in 3D sheets that are finite in all dimensions. Finally, we argue that some quasi-statically evolving current sheets undergoing slow stressing (e.g., when the coronal magnetic field is subjected to photospheric boundary driving) may reach a critical shear, at which point they lose equilibrium, spontaneously collapse, and reconnect. The critical shear is generally consistent with the heating requirements of solar active regions.

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Impact of 3D Structure on Magnetic Reconnection

Results from 2.5D and 3D studies of the onset and development of the tearing instability are presented, using high fidelity resistive MHD simulations. A limited parameter study of the strength of the reconnecting field (or shear angle) was performed. An initially simple 1D equilibrium was used, consisting of a modified force-free current sheet, with periodic boundary conditions in all directions. In all cases, the linear and non-linear evolution led to a primary current sheet between two large flux ropes. The global reconnection rate during this later stage was analyzed in all simulations. It was found that in 2.5D the primary current sheet fragmented due to plasmoids, and as expected, the global reconnection rate, calculated using multiple methods, increases with the strength of the reconnecting field due to a stronger Alfvén speed. In 3D, the presence of interacting oblique modes of the tearing instability complicates the simple 2.5D picture, entangling the magnetic field of the inflow and introducing a negative effect on the reconnection rate. The two competing effects of stronger Alfvén speed and entangling, which both increase with the strength of the reconnecting field, resulted in a decrease in the reconnection rate with increasing reconnecting field. For all simulations, the 3D rates were less than in 2.5D, but suggest that as one goes to weak reconnecting field (or strong guide field), the system becomes more 2.5D like and the 2.5D and 3D rates converge. These results have relevance to situations like nano-flare heating and flare current sheets in the corona.

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The Rise and Emergence of Untwisted Toroidal Flux Ropes on the Sun

Magnetic flux ropes (MFRs) rising buoyantly through the Sun's convection zone are thought to be subject to viscous forces preventing them from rising coherently. Numerous studies have suggested that MFRs require a minimum twist in order to remain coherent during their rise. Furthermore, even MFRs that get to the photosphere may be unable to successfully emerge into the corona unless they are at least moderately twisted, since the magnetic pressure gradient needs to overcome the weight of the photospheric plasma. To date, however, no lower limit has been placed on the critical minimum twist required for an MFR to rise coherently through the convection zone or emerge through the photosphere. In this paper, we simulate an untwisted toroidal MFR which is able to rise from the convection zone and emerge through the photosphere as an active region that resembles those observed on the Sun. We show that untwisted MFRs can remain coherent during their rise and then pile-up near the photosphere, triggering the undular instability, allowing the MFR to emerge through the photosphere. We propose that the toroidal geometry of our MFR is critical for its coherent rise. Upon emerging, a pair of lobes rises into the corona which interact and reconnect, resulting in a localized high speed jet. The resulting photospheric magnetogram displays the characteristic salt-and-pepper structure often seen in observations. Our major result is that MFRs need not be twisted to rise coherently through the convection zone and emerge through the photosphere.

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Time variations of the non-potential and volume-threading magnetic helicities

Relative magnetic helicity is a gauge invariant quantity suitable for the study of the magnetic helicity content of heliospheric plasmas. Relative magnetic helicity can be decomposed uniquely into two gauge invariant quantities, the magnetic helicity of the non-potential component of the field, and a complementary volume-threading helicity. Recent analysis of numerical experiments simulating the generation of solar eruptions have shown that the ratio of the non-potential helicity to the total relative helicity is a clear marker of the eruptivity of the magnetic system, and that the high value of that quantity could be a sufficient condition for the onset of the instability generating the eruptions. The present study introduces the first analytical examination of the time variations of these non-potential and volume-threading helicities. The validity of the analytical formulas derived are confirmed with analysis of three-dimensional (3D) magnetohydrodynamics (MHD) simulations of solar coronal dynamics. Both the analytical investigation, and the numerical application show that, unlike magnetic helicity, the non-potential and the volume-threading helicities are not conserved quantities, even in the ideal MHD regime. A term corresponding to the transformation between the non-potential and volume-threading helicities frequently dominates their dynamics. This finding has an important consequence for their estimation in the solar corona: unlike with relative helicity, their volume coronal evolution cannot be ascertained by the flux of these quantities through the volume's boundaries. Only techniques extrapolating the 3D coronal field will enable both the proper study of the non-potential and volume-threading helicities, and the observational analysis of helicity-based solar-eruptivity proxies.

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A Hydrodynamic Model of Alfvénic Wave Heating in a Coronal Loop and its Chromospheric Footpoints

Alfvénic waves have been proposed as an important energy transport mechanism in coronal loops, capable of delivering energy to both the corona and chromosphere and giving rise to many observed features, of flaring and quiescent regions. In previous work, we established that resistive dissipation of waves (ambipolar diffusion) can drive strong chromospheric heating and evaporation, capable of producing flaring signatures. However, that model was based on a simplified assumption that the waves propagate instantly to the chromosphere, an assumption which the current work removes. Via a ray tracing method, we have implemented traveling waves in a field-aligned hydrodynamic simulation that dissipate locally as they propagate along the field line. We compare this method to and validate against the magnetohydrodynamics code Lare3D. We then examine the importance of travel times to the dynamics of the loop evolution, finding that (1) the ionization level of the plasma plays a critical role in determining the location and rate at which waves dissipate; (2) long duration waves effectively bore a hole into the chromosphere, allowing subsequent waves to penetrate deeper than previously expected, unlike an electron beam whose energy deposition rises in height as evaporation reduces the mean-free paths of the electrons; (3) the dissipation of these waves drives a pressure front that propagates to deeper depths, unlike energy deposition by an electron beam.

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Electric-Current Neutralization, Magnetic Shear, and Eruptive Activity in Solar Active Regions

The physical conditions that determine whether or not solar active regions (ARs) produce strong flares and coronal mass ejections (CMEs) are not yet well understood. Here we investigate the association between electric-current neutralization, magnetic shear along polarity inversion lines (PILs), and eruptive activity in four ARs; two emerging and two well-developed ones. We find that the CME-producing ARs are characterized by a strongly non-neutralized total current, while the total current in the ARs that did not produce CMEs is almost perfectly neutralized. The difference in the PIL-shear between these two groups is much less pronounced, which suggests that the degree of current-neutralization may serve as a better proxy for assessing the ability of ARs to produce CMEs.

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Testing predictors of eruptivity using parametric flux emergence simulations

Solar flares and coronal mass ejections (CMEs) are among the most energetic events in the solar system, impacting the near-Earth environment. Flare productivity is empirically known to be correlated with the size and complexity of active regions. Several indicators, based on magnetic-field data from active regions, have been tested for flare forecasting in recent years. None of these indicators, or combinations thereof, have yet demonstrated an unambiguous eruption or flare criterion. Furthermore, numerical simulations have been only barely used to test the predictability of these parameters. In this context, we used the 3D parametric MHD numerical simulations of the self-consistent formation of the flux emergence of a twisted flux tube, inducing the formation of stable and unstable magnetic flux ropes of Leake (2013, 2014). We use these numerical simulations to investigate the eruptive signatures observable in various magnetic scalar parameters and provide highlights on data analysis processing. Time series of 2D photospheric-like magnetograms are used from parametric simulations of stable and unstable flux emergence, to compute a list of about 100 different indicators. This list includes parameters previously used for operational forecasting, physical parameters used for the first time, as well as new quantities specifically developed for this purpose. Our results indicate that only parameters measuring the total non-potentiality of active regions associated with magnetic inversion line properties, such as the Falconer parameters $L_{ss}$, $WL_{ss}$, $L_{sg}$ and $WL_{sg}$, as well as the new current integral $WL_{sc}$ and length $L_{sc}$ parameters, present a significant ability to distinguish the eruptive cases of the model from the non-eruptive cases, possibly indicating that they are promising flare and eruption predictors.

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Testing the Accuracy of Data Driven MHD Simulations of Active Region Evolution

Models for the evolution of the solar coronal magnetic field are vital for understanding solar activity, yet the best measurements of magnetic field lie at the photosphere, necessitating the development of coronal models which are \textit{"data-driven"} at the photosphere. We present an investigation to determine the feasibility and accuracy of such methods. Our validation framework uses a simulation of active region (AR) formation, modeling the emergence of magnetic flux from the convection zone to the corona, as a ground-truth dataset, to supply both the photospheric information, and to perform the validation of the data-driven method. We focus our investigation on how the data-driven model accuracy depends on the temporal frequency of the driving data. The Helioseismic and Magnetic Imager on NASA's Solar {\jl Dynamics} Observatory produces full-disk vector magnetic field measurements at a 12 minute cadence. Using our framework we show that ARs that emerge over 25 hours can be modeled by the data-driving method with only $\sim$1\% error in the free magnetic energy, assuming the photospheric information is specified every 12 minutes. However, for rapidly evolving features, under-sampling of the dynamics at this cadence leads to a strobe effect, generating large electric currents and incorrect coronal morphology and energies. We derive a sampling condition for the driving cadence based on the evolution of these small-scale features, and show that higher-cadence driving can lead to acceptable errors. Future work will investigate the source of errors associated with deriving plasma variables from the photospheric magnetograms as well as other sources of errors such as reduced resolution and instrument bias and noise.

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Science Objective: Understanding Energy Transport by Alfvénic Waves in Solar Flares

Solar flares are driven by the release of magnetic energy from reconnection events in the solar corona, whereafter energy is transported to the chromosphere, heating the plasma and causing the characteristic radiative losses. In the collisional thick-target model, electrons accelerated to energies exceeding 10 keV traverse the corona and impact the chromosphere, where they deposit their energy through collisions with the much denser plasma in the lower atmosphere. While there are undoubtedly high energy non-thermal electrons accelerated in flares, it is unclear whether these electron beams are the sole mechanism of energy transport, or whether they only dominate in certain phases of the flare's evolution. Alfvénic waves are generated during the post-reconnection relaxation of magnetic field lines, so it is important to examine their role in energy transport.

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Sunquake Generation by Coronal Magnetic Restructuring

Sunquakes are the surface signatures of acoustic waves in the Sun's interior that are produced by some but not all flares and coronal mass ejections (CMEs). This paper explores a mechanism for sunquake generation by the magnetic field changes that occur during flares and CMEs, using MHD simulations with a semiempirical FAL-C atmosphere to demonstrate the generation of acoustic waves in the interior in response to changing magnetic tilt in the corona. We find that Alfven-sound resonance combined with the ponderomotive force produces acoustic waves in the interior with sufficient energy to match sunquake observations when the magnetic field angle changes by the order of 10 degrees in a region where the coronal field strength is a few hundred gauss or more. The most energetic sunquakes are produced when the coronal field is strong, while the variation of magnetic field strength with height and the time scale of the tilt change are of secondary importance.

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Distribution of Electric Currents in Solar Active Regions

There has been a long-lasting debate on the question of whether or not electric currents in solar active regions are neutralized. That is, whether or not the main (or direct) coronal currents connecting the active region polarities are surrounded by shielding (or return) currents of equal total value and opposite direction. Both theory and observations are not yet fully conclusive regarding this question, and numerical simulations have, surprisingly, barely been used to address it. Here we quantify the evolution of electric currents during the formation of a bipolar active region by considering a three-dimensional magnetohydrodynamic simulation of the emergence of a sub-photospheric, current-neutralized magnetic flux rope into the solar atmosphere. We find that a strong deviation from current neutralization develops simultaneously with the onset of significant flux emergence into the corona, accompanied by the development of substantial magnetic shear along the active region's polarity inversion line. After the region has formed and flux emergence has ceased, the strong magnetic fields in the region's center are connected solely by direct currents, and the total direct current is several times larger than the total return current. These results suggest that active regions, the main sources of coronal mass ejections and flares, are born with substantial net currents, in agreement with recent observations. Furthermore, they support eruption models that employ pre-eruption magnetic fields containing such currents.

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Simulations of Emerging Magnetic Flux. I: The Formation of Stable Coronal Flux Ropes

We present results from 3D visco-resistive magnetohydrodynamic (MHD) simulations of the emergence of a convection zone magnetic flux tube into a solar atmosphere containing a pre-existing dipole coronal field, which is orientated to minimize reconnection with the emerging field. We observe that the emergence process is capable of producing a coronal flux rope by the transfer of twist from the convection zone as found in previous simulations. We find that this flux rope is stable, with no evidence of a fast rise, and that its ultimate height in the corona is determined by the strength of the pre-existing dipole field. We also find that although the electric currents in the initial convection zone flux tube are almost perfectly neutralized, the resultant coronal flux rope carries a significant net current. These results suggest that flux tube emergence is capable of creating non-current-neutralized stable flux ropes in the corona, tethered by overlying potential fields, a magnetic configuration that is believed to be the source of coronal mass ejections.

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Effect of ion-neutral collisions in simulations of emerging active regions

We present results of 2.5D numerical simulations of the emergence of sub-surface magnetic flux into the solar atmosphere, with emerging flux regions ranging from $10^{18}$ to $10^{21}$ Mx, representing both ephemeral and active regions. We include the presence of neutral Hydrogen in the governing equations, improve upon previous models by including the ionization in the equation of state, and use a more realistic convection zone model. We find that ionization and recombination of plasma during the rise of a convection zone flux tube reduces the rise speed of the tube's axis. The presence of neutral Hydrogen allows the effective flow of mass across fieldlines, by the addition of a Pedersen resistivity to the generalized Ohm's law, which dissipates current perpendicular to the magnetic field. This causes an increase of up to 10% in the amount of magnetic in-plane flux supplied to the corona and a reduction of up to 89% in the amount of sub-surface plasma brought up into the corona. However, it also reduces the amount of free magnetic energy supplied to the corona, and thus does not positively affect the likelihood of creating unstable coronal structures.

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