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An expansion of cross-sectional area directly impacts the mass flow along a coronal loop, and significantly alters the radiative and hydrodynamic evolution of that loop as a result. Previous studies have found that an area expansion from chromosphere to corona significantly lengthens the cooling time of the corona, and appears to suppress draining from the corona. In this work, we examine the fluid dynamics to understand how the mass flow rate, the energy balance, and the cooling and draining timescales are affected by a non-uniform area. We find that in loops with moderate or large expansion (cross-sectional area expansion factors of 2, 3, 10, 30, 100 from photosphere to apex), impulsive heating, for either direct thermal heating or electron beam heating, induces a steady flow into the corona, so that the coronal density continues to rise during the cooling phase, whereas a uniform loop drains during the cooling phase. The induced upflow carries energy into the corona, balancing the losses from thermal conduction, and continues until thermal conduction weakens enough so that it can no longer support the radiative losses of the transition region (TR). As a result, the plasma cools primarily radiatively until the onset of catastrophic collapse. The speed and duration of the induced upflow both increase in proportion to the rate of area expansion. We argue that observations of blue-shifted spectral lines, therefore, could place a constraint on a loop's area expansion., Comment: Resubmitted to ApJ. Comments and criticisms are welcomed!

The launches of Parker Solar Probe (Parker) and Solar Orbiter (SolO) are enabling a new era of solar wind studies that track the solar wind from its origin at the photosphere, through the corona, to multiple vantage points in the inner heliosphere. A key ingredient for these models is the input photospheric magnetic field map that provides the boundary condition for the coronal portion of many heliospheric models. In this paper, we perform steady-state, data-driven magnetohydrodynamic (MHD) simulations of the solar wind during Carrington rotation 2258 with the GAMERA model. We use the ADAPT and AFT flux transport models and quantitatively assess how well each model matches in-situ measurements from Parker, SolO, and Earth. We find that both models reproduce the magnetic field components at Parker quantitatively well. At SolO and Earth, the magnetic field is reproduced relatively well, though not as well as at Parker, and the density is reproduced extremely poorly. The velocity is overpredicted at Parker, but not at SolO or Earth, hinting that the Wang-Sheeley-Arge (WSA) relation, fine-tuned for Earth, misses the deceleration of the solar wind near the Sun. We conclude that AFT performs quantitatively similarly to ADAPT in all cases and that both models are comparable to a purely WSA heliospheric treatment with no MHD component. Finally, we trace field lines from SolO back to an active region outflow that was observed by Hinode/EIS, and which shows evidence of elevated charge state ratios.

It is extremely difficult to simulate the details of coronal heating and also make meaningful predictions of the emitted radiation. Thus, testing realistic models with observations is a major challenge. Observational signatures of coronal heating depend crucially on radiation, thermal conduction, and the exchange of mass and energy with the transition region and chromosphere below. Many magnetohydrodynamic simulation studies do not include these effects, opting instead to devote computational resources to the magnetic aspects of the problem. We have developed a simple method of accounting approximately for the missing effects. It is applied to the simulation output post facto and therefore may be a valuable tool for many studies. We have used it to predict the emission from a model corona that is driven by vortical boundary motions meant to represent photospheric convection. We find that individual magnetic strands experience short-term brightenings, both scattered throughout the computational volume and in localized clusters. The former may explain the diffuse component of the observed corona, while the latter may explain bright coronal loops. Several observed properties of loops are reproduced reasonably well: width, lifetime, and quasi-circular cross-section (aspect ratio not large). Our results lend support to the idea that loops are multi-stranded structures heated by "storms" of nanoflares., Comment: Accepted by the Astrophysical Journal; 25 pages, 15 figures, 2 movies

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., Comment: Accepted to ApJ

The nanoflare paradigm of coronal heating has proven extremely promising for explaining the presence of hot, multi-million degree loops in the solar corona. In this paradigm, localized heating events supply enough energy to heat the solar atmosphere to its observed temperatures. Rigorously modeling this process, however, has proven difficult, since it requires an accurate treatment of both the magnetic field dynamics and reconnection as well as the plasma's response to magnetic perturbations. In this paper, we combine fully 3D magnetohydrodynamic (MHD) simulations of coronal active region plasma driven by photospheric motions with spatially-averaged, time-dependent hydrodynamic (HD) modeling of coronal loops to obtain physically motivated observables that can be quantitatively compared with observational measurements of active region cores. We take the behavior of reconnected field lines from the MHD simulation and use them to populate the HD model to obtain the thermodynamic evolution of the plasma and subsequently the emission measure distribution. We find the that the photospheric driving of the MHD model produces only very low-frequency nanoflare heating which cannot account for the full range of active region core observations as measured by the low-temperature emission measure slope. Additionally, we calculate the spatial and temporal distributions of field lines exhibiting collective behavior, and argue that loops occur due to random energization occurring on clusters of adjacent field lines.

One of the greatest challenges in solar physics is understanding the heating of the Sun's corona. Most theories for coronal heating postulate that free energy in the form of magnetic twist/stress is injected by the photosphere into the corona where the free energy is converted into heat either through reconnection or wave dissipation. The magnetic helicity associated with the twist/stress, however, is expected to be conserved and appear in the corona. In previous work we showed that helicity associated with the small-scale twists undergoes an inverse cascade via stochastic reconnection in the corona, and ends up as the observed large-scale shear of filament channels. Our ``helicity condensation'' model accounts for both the formation of filament channels and the observed smooth, laminar structure of coronal loops. In this paper, we demonstrate, using helicity- and energy-conserving numerical simulations of a coronal system driven by photospheric motions, that the model also provides a natural mechanism for heating the corona. We show that the heat generated by the reconnection responsible for the helicity condensation process is sufficient to account for the observed coronal heating. We study the role that helicity injection plays in determining coronal heating and find that, crucially, the heating rate is only weakly dependent on the net helicity preference of the photospheric driving. Our calculations demonstrate that motions with 100\% helicity preference are least efficient at heating the corona; those with 0\% preference are most efficient. We discuss the physical origins of this result and its implications for the observed corona., Comment: Accepted by ApJ

Solar flares are observed and classified according to their intensity measured with the GOES X-ray Sensors. We show that the duration of a flare, as measured by the full width at half maximum (FWHM) in GOES is not related to the size of the flare as measured by GOES intensity. The durations of X-class flares range from a few minutes to a few hours, and the same is true of M- and C-class flares. In this work, we therefore examine the statistical relationships between the basic properties of flares -- temperature, emission measure, energy, etc. -- in comparison to both their size and duration. We find that the size of the flare is directly related to all of these basic properties, as previously found by many authors. The duration is not so clear. When examining the whole data set, the duration appears to be independent of all of these properties. In larger flares, however, there are direct correlations between the GOES FWHM and magnetic reconnection flux and ribbon area. We discuss the possible explanations, finding that this discrepancy may be due to large uncertainties in small flares, though we cannot rule out the possibility that the driving physical processes are different in smaller flares than larger ones. We discuss the implications of this result and how it relates to the magnetic reconnection process that releases energy in flares., Comment: ApJ, in press

It has been observationally well established that the magnetic configurations most favorable for producing energetic flaring events reside in delta-spots, a class of sunspots defined as having opposite polarity umbrae sharing a common penumbra. They are frequently characterized by extreme compactness, strong rotation and anti-Hale orientation. Numerous studies have shown that nearly all of the largest solar flares originate in delta-spots, making the understanding of these structures a fundamental step in predicting space weather. Despite their important influence on the space environment, surprisingly little is understood about the origin and behavior of delta-spots. In this paper, we perform a systematic study of the behavior of emerging flux ropes to test a theoretical model for the formation of delta-spots: the kink instability of emerging flux ropes. We simulated the emergence of highly twisted, kink-unstable flux ropes from the convection zone into the corona, and compared their photospheric properties to those of emerged weakly twisted, kink-stable flux ropes. We show that the photospheric manifestations of the emergence of highly twisted flux ropes closely match the observed properties of delta-spots, and we discuss the resulting implications for observations. Our results strongly support and extend previous theoretical work that suggested that the kink instability of emerging flux ropes is a promising candidate to explain delta-spot formation, as it reproduces their key characteristics very well., Comment: Accepted for publication in ApJ, but comments welcome

Numerous observations have revealed that power-law distributions are ubiquitous in energetic solar processes. Hard X-rays, soft X-rays, extreme ultraviolet radiation, and radio waves all display power-law frequency distributions. Since magnetic reconnection is the driving mechanism for many energetic solar phenomena, it is likely that reconnection events themselves display such power-law distributions. In this work, we perform numerical simulations of the solar corona driven by simple convective motions at the photospheric level. Using temperature changes, current distributions, and Poynting fluxes as proxies for heating, we demonstrate that energetic events occurring in our simulation display power-law frequency distributions, with slopes in good agreement with observations. We suggest that the braiding-associated reconnection in the corona can be understood in terms of a self-organized criticality model driven by convective rotational motions similar to those observed at the photosphere., Comment: Accepted by ApJ

The underlying origin of solar eruptive events (SEEs), ranging from giant coronal mass ejections to small coronal-hole jets, is that the lowest-lying magnetic flux in the Sun's corona undergoes the continual buildup of stress and free energy. This magnetic stress has long been observed as the phenomenon of "filament channels:" strongly sheared magnetic field localized around photospheric polarity inversion lines. However, the mechanism for the stress buildup - the formation of filament channels - is still debated. We present magnetohydrodynamic simulations of a coronal volume that is driven by transient, cellular boundary flows designed to model the processes by which the photosphere drives the corona. The key feature of our simulations is that they accurately preserve magnetic helicity, the topological quantity that is conserved even in the presence of ubiquitous magnetic reconnection. Although small-scale random stress is injected everywhere at the photosphere, driving stochastic reconnection throughout the corona, the net result of the magnetic evolution is a coherent shearing of the lowest-lying field lines. This highly counter-intuitive result - magnetic stress builds up locally rather than spreading out to attain a minimum energy state - explains the formation of filament channels and is the fundamental mechanism underlying SEEs. Furthermore, this mechanism may be relevant to other astrophysical or laboratory plasmas., Comment: 14 pages + 4 figures. Submitted to ApJL

Two of the most widely observed and yet most puzzling features of the Sun's magnetic field are coronal loops that are smooth and laminar and prominences/filaments that are strongly sheared. These two features would seem to be quite unrelated in that the loops are near their minimum-energy current-free state, whereas filaments are regions of high magnetic stress and intense electric currents. We argue that, in fact, these two features are inextricably linked in that both are due to a single process: the injection of magnetic helicity into the corona by photospheric motions and the subsequent evolution of this helicity by coronal reconnection. In this paper, we present numerical simulations of the response of a \citet{Parker72} corona to photospheric driving motions that have varying degrees of helicity preference. We obtain four main conclusions: 1) in agreement with the helicity condensation model of \citet{Antiochos13}, the inverse cascade of helicity by magnetic reconnection results in the formation of prominences/filaments localized about polarity inversion lines (PILs); 2) this same process removes most structure from the rest of the corona, resulting in smooth and laminar coronal loops; 3) the amount of remnant tangling in coronal loops is inversely dependent on the net helicity injected by the driving motions; and 4) the structure of the solar corona depends only on the helicity preference of the driving motions and not on their detailed time dependence. We discuss the implications of our results for high-resolution observations of the corona., Comment: 19 pages; 13 figures; submitted to ApJ

Two of the most important features of the solar atmosphere are its hot, smooth coronal loops and the concentrations of magnetic shear, known as filament channels, that reside above photospheric polarity inversion lines (PILs). The shear observed in filament channels represents magnetic helicity, while the smoothness of the coronal loops indicates an apparent lack of magnetic helicity in the rest of the corona. At the same time, models that attempt to explain the high temperatures observed in these coronal loops require magnetic energy, in the form of twist, to be injected at the photosphere. In addition to magnetic energy, this twist also represents magnetic helicity. Unlike magnetic energy, magnetic helicity is conserved under reconnection, and is consequently expected to accumulate and be observed in the corona. However, filament channels, rather than the coronal loops, are the locations in the corona where magnetic helicity is observed, and it manifests itself in the form of shear, rather than twist. This naturally raises the question: if magnetic helicity needs to be injected to heat coronal loops, why is it only observed in filament channels, while coronal loops are observed to be laminar and smooth? This thesis addresses this question using a series of numerical simulations that demonstrate that magnetic helicity is transported throughout the solar corona by magnetic reconnection in such a way that it accumulates above PILs, forming filament channels, and leaving the rest of the corona generally smooth. In the process, it converts magnetic energy into heat, accounting for the large observed temperatures. This thesis presents a model for the formation of filament channels in the solar corona and the presence of smooth, hot coronal loops, and shows how the transport of magnetic helicity throughout the solar corona by magnetic reconnection is responsible for both of these phenomena., Comment: Ph.D Thesis - The Johns Hopkins University

It is extremely difficult to simulate the details of coronal heating and also make meaningful predictions of the emitted radiation. Thus, testing realistic models with observations is a major challenge. Observational signatures of coronal heating depend crucially on radiation, thermal conduction, and the exchange of mass and energy with the transition region and chromosphere below. Many magnetohydrodynamic simulation studies do not include these effects, opting instead to devote computational resources to the magnetic aspects of the problem. We have developed a simple method of accounting approximately for the missing effects. It is applied to the simulation output ex post facto and therefore may be a valuable tool for many studies. We have used it to predict the emission from a model corona that is driven by vortical boundary motions meant to represent photospheric convection. We find that individual magnetic strands experience short-term brightenings, both scattered throughout the computational volume and in localized clusters. The former may explain the diffuse component of the observed corona, while the latter may explain bright coronal loops. Several observed properties of loops are reproduced reasonably well: width, lifetime, and quasi-circular cross section (aspect ratio not high). Our results lend support to the idea that loops are multistranded structures heated by "storms" of nanoflares.

A major unexplained feature of the solar atmosphere is the accumulation of magnetic shear, in the form of filament channels, at photospheric polarity inversion lines (PILs). In addition to free energy, this shear also represents magnetic helicity, which is conserved under reconnection. In this paper, we address the problem of filament channel formation and show how they acquire their shear and magnetic helicity. The results of 3D simulations using the Adaptively Refined Magnetohydrodynamics Solver (ARMS) are presented that support the model of filament channel formation by magnetic helicity condensation developed by \citet{Antiochos13}. We consider the supergranular twisting of a quasi-potential flux system that is bounded by a PIL and contains a coronal hole (CH). The magnetic helicity injected by the small-scale photospheric motions is shown to inverse-cascade up to the largest allowable scales that define the closed flux system: the PIL and the CH. This process produces field lines that are both sheared and smooth, and are sheared in opposite senses at the PIL and the CH. The accumulated helicity and shear flux are shown to be in excellent quantitative agreement with the helicity-condensation model. We present a detailed analysis of the simulations, including comparisons of our analytical and numerical results, and discuss their implications for observations., Comment: Submitted to ApJ

This article presents results that challenge the paradigms that (1) the convection zone is the source of the radial magnetic field in the photosphere and (2) that coronal currents are neutralized from the perspective of the photosphere. We demonstrate, using a new analysis tool applied to simulations and observations, that bare or partially dressed current channels are supported by the solar corona and that fingerprints of these coronal current systems can be detected in the photosphere. These coronal current channels can be a significant source of the radial component of the magnetic field in the photosphere. The roots of these coronal current channels in the photosphere are the source of the magnetic field component parallel to the polarity inversion line in active region NOAA 12673. These analyses and observations transform our theoretical understanding of coronal evolution and argue for a reexamination of the present paradigm in which the convection zone is the sole source of the photospheric magnetic field.