E. E. DeLuca

Evidence for Alfvén Waves in Solar X-ray Jets

Coronal magnetic fields are dynamic, and field lines may misalign, reassemble, and release energy by means of magnetic reconnection. Giant releases may generate solar flares and coronal mass ejections and, on a smaller scale, produce x-ray jets. Hinode observations of polar coronal holes reveal that x-ray jets have two distinct velocities: one near the Alfvén speed (∼800 kilometers per second) and another near the sound speed (200 kilometers per second). Many more jets were seen than have been reported previously; we detected an average of 10 events per hour up to these speeds, whereas previous observations documented only a handful per day with lower average speeds of 200 kilometers per second. The x-ray jets are about 2 × 103 to 2 × 104 kilometers wide and 1 × 105 kilometers long and last from 100 to 2500 seconds. The large number of events, coupled with the high velocities of the apparent outflows, indicates that the jets may contribute to the high-speed solar wind.

FORMATION OF TORUS-UNSTABLE FLUX ROPES AND ELECTRIC CURRENTS IN ERUPTING SIGMOIDS

We analyze the physical mechanisms that form a three-dimensional coronal flux rope and later cause its eruption. This is achieved by a zero-β magnetohydrodynamic (MHD) simulation of an initially potential, asymmetric bipolar field, which evolves by means of simultaneous slow magnetic field diffusion and sub-Alfvenic, line-tied shearing motions in the photosphere. As in similar models, flux-cancellation-driven photospheric reconnection in a bald-patch (BP) separatrix transforms the sheared arcades into a slowly rising and stable flux rope. A bifurcation from a BP to a quasi-separatrix layer (QSL) topology occurs later on in the evolution, while the flux rope keeps growing and slowly rising, now due to shear-driven coronal slip-running reconnection, which is of tether-cutting type and takes place in the QSL. As the flux rope reaches the altitude at which the decay index –∂ln B/∂ln z of the potential field exceeds ~3/2, it rapidly accelerates upward, while the overlying arcade eventually develops an inverse tear-drop shape, as observed in coronal mass ejections (CMEs). This transition to eruption is in accordance with the onset criterion of the torus instability. Thus, we find that photospheric flux-cancellation and tether-cutting coronal reconnection do not trigger CMEs in bipolar magnetic fields, but are key pre-eruptive mechanisms for flux ropes to build up and to rise to the critical height above the photosphere at which the torus instability causes the eruption. In order to interpret recent Hinode X-Ray Telescope observations of an erupting sigmoid, we produce simplified synthetic soft X-ray images from the distribution of the electric currents in the simulation. We find that a bright sigmoidal envelope is formed by pairs of -shaped field lines in the pre-eruptive stage. These field lines form through the BP reconnection and merge later on into -shaped loops through the tether-cutting reconnection. During the eruption, the central part of the sigmoid brightens due to the formation of a vertical current layer in the wake of the erupting flux rope. Slip-running reconnection in this layer yields the formation of flare loops. A rapid decrease of currents due to field line expansion, together with the increase of narrow currents in the reconnecting QSL, yields the sigmoid hooks to thin in the early stages of the eruption. Finally, a slightly rotating erupting loop-like feature (ELLF) detaches from the center of the sigmoid. Most of this ELLF is not associated with the erupting flux rope, but with a current shell that develops within expanding field lines above the rope. Only the short, curved end of the ELLF corresponds to a part of the flux rope. We argue that the features found in the simulation are generic for the formation and eruption of soft X-ray sigmoids.

HEATING OF THE SOLAR CHROMOSPHERE AND CORONA BY ALFVÉN WAVE TURBULENCE

A three-dimensional magnetohydrodynamic (MHD) model for the propagation and dissipation of Alfv?n waves in a coronal loop is developed. The model includes the lower atmospheres at the two ends of the loop. The waves originate on small spatial scales (less than 100?km) inside the kilogauss flux elements in the photosphere. The model describes the nonlinear interactions between Alfv?n waves using the reduced MHD approximation. The increase of Alfv?n speed with height in the chromosphere and transition region (TR) causes strong wave reflection, which leads to counter-propagating waves and turbulence in the photospheric and chromospheric parts of the flux tube. Part of the wave energy is transmitted through the TR and produces turbulence in the corona. We find that the hot coronal loops typically found in active regions can be explained in terms of Alfv?n wave turbulence, provided that the small-scale footpoint motions have velocities of 1-2?km?s?1 and timescales of 60-200?s. The heating rate per unit volume in the chromosphere is two to three orders of magnitude larger than that in the corona. We construct a series of models with different values of the model parameters, and find that the coronal heating rate increases with coronal field strength and decreases with loop length. We conclude that coronal loops and the underlying chromosphere may both be heated by Alfv?nic turbulence.

Prevalence of small-scale jets from the networks of the solar transition region and chromosphere

As the interface between the Sun’s photosphere and corona, the chromosphere and transition region play a key role in the formation and acceleration of the solar wind. Observations from the Interface Region Imaging Spectrograph reveal the prevalence of intermittent small-scale jets with speeds of 80 to 250 kilometers per second from the narrow bright network lanes of this interface region. These jets have lifetimes of 20 to 80 seconds and widths of ≤300 kilometers. They originate from small-scale bright regions, often preceded by footpoint brightenings and accompanied by transverse waves with amplitudes of ~20 kilometers per second. Many jets reach temperatures of at least ~105 kelvin and constitute an important element of the transition region structures. They are likely an intermittent but persistent source of mass and energy for the solar wind.

Sigmoidal Active Region on the Sun: Comparison of a Magnetohydrodynamical Simulation and a Nonlinear Force-free Field Model

In this paper we show that when accurate nonlinear force-free field (NLFFF) models are analyzed together with high-resolution magnetohydrodynamic (MHD) simulations, we can determine the physical causes for the coronal mass ejection (CME) eruption on 2007 February 12. We compare the geometrical and topological properties of the three-dimensional magnetic fields given by both methods in their pre-eruptive phases. We arrive at a consistent picture for the evolution and eruption of the sigmoid. Both the MHD simulation and the observed magnetic field evolution show that flux cancellation plays an important role in building the flux rope. We compute the squashing factor, Q, in different horizontal maps in the domains. The main shape of the quasi-separatrix layers (QSLs) is very similar between the NLFFF and MHD models. The main QSLs lie on the edge of the flux rope. While the QSLs in the NLFFF model are more complex due to the intrinsic large complexity in the field, the QSLs in the MHD model are smooth and possess lower maximum value of Q. In addition, we demonstrate the existence of hyperbolic flux tubes (HFTs) in both models in vertical cross sections of Q. The main HFT, located under the twisted flux rope in both models, is identified as the most probable site for reconnection. We also show that there are electric current concentrations coinciding with the main QSLs. Finally, we perform torus instability analysis and show that a combination between reconnection at the HFT and the resulting expansion of the flux rope into the torus instability domain is the cause of the CME in both models.

MODELING NONPOTENTIAL MAGNETIC FIELDS IN SOLAR ACTIVE REGIONS

Electric currents are present in the coronae above solar active regions, producing nonpotential magnetic fields that can be approximated as nonlinear force-free fields (NLFFFs). In this paper NLFFF models for two active regions observed in 2002 June are presented. The models are based on magnetograms from SOHO MDI and are constrained by nonpotential structures seen in BBSO Hα images and TRACE EUV images. The models are constructed using the flux rope insertion method. We find that the axial fluxes of the flux ropes are well constrained by the observations. The flux ropes are only weakly twisted, and electric currents flow mainly at the interface between the flux rope and its surroundings. In one case, the flux rope is anchored with both ends in the active region; in the other case, the flux rope extends to the neighboring quiet Sun. We find that the magnetic fields in these active regions are close to an eruptive state: the axial flux in the flux ropes is close to the upper limit for eruption. We also derive estimates for magnetic free energy and helicity in these regions.

HINODE X-RAY TELESCOPE DETECTION OF HOT EMISSION FROM QUIESCENT ACTIVE REGIONS: A NANOFLARE SIGNATURE?

The X-Ray Telescope (XRT) on the Japanese/USA/UK Hinode (Solar-B) spacecraft has detected emission from a quiescent active region core that is consistent with nanoflare heating. The fluxes from 10 broadband X-ray filters and filter combinations were used to construct differential emission measure (DEM) curves. In addition to the expected active region peak at log T = 6.3-6.5, we find a high-temperature component with significant emission measure at log T > 7.0. This emission measure is weak compared to the main peak—the DEM is down by almost three orders of magnitude—which accounts of the fact that it has not been observed with earlier instruments. It is also consistent with spectra of quiescent active regions: no Fe XIX lines are observed in a CHIANTI synthetic spectrum generated using the XRT DEM distribution. The DEM result is successfully reproduced with a simple two-component nanoflare model.

Constraints on Active Region Coronal Heating

We derive constraints on the time variability of coronal heating from observations of the so-called active region moss by the Transition Region and Coronal Explorer (TRACE). The moss is believed to be due to million-degree emission from the transition regions at the footpoints of coronal loops whose maximum temperatures are several million degrees. The two key results from the TRACE observations discussed in this paper are that in the moss regions one generally sees only moss, not million-degree loops, and that the moss emission exhibits only weak intensity variations, � 10% over periods of hours. TRACE movies showing these results are presented. We demonstrate, using both analytic and numerical calculations, that the lack of observable million-degree loops in the moss regions places severe constraints on the possible time variability of coronal heating in the loops overlying the moss. In particular, the heating in the hot moss loops cannot be truly flarelike with a sharp cutoff, but instead must be quasi-steady to an excellent approximation. Furthermore, the lack of significant variations in the moss intensity implies that the heating magnitude is only weakly varying. The implications of these conclusions for coronal heating models will be discussed. Subject headings: Sun: corona — Sun: transition region — Sun: UV radiation On-line material: mpg animation

MAGNETOHYDRODYNAMIC MODELING OF THE SOLAR ERUPTION ON 2010 APRIL 8

The structure of the coronal magnetic field prior to eruptive processes and the conditions for the onset of eruption are important issues that can be addressed through studying the magnetohydrodynamic (MHD) stability and evolution of nonlinear force-free field (NLFFF) models. This paper uses data-constrained NLFFF models of a solar active region (AR) that erupted on 2010 April 8 as initial conditions in MHD simulations. These models, constructed with the techniques of flux rope insertion and magnetofrictional relaxation (MFR), include a stable, an approximately marginally stable, and an unstable configuration. The simulations confirm previous related results of MFR runs, particularly that stable flux rope equilibria represent key features of the observed pre-eruption coronal structure very well, and that there is a limiting value of the axial flux in the rope for the existence of stable NLFFF equilibria. The specific limiting value is located within a tighter range, due to the sharper discrimination between stability and instability by the MHD description. The MHD treatment of the eruptive configuration yields a very good agreement with a number of observed features, like the strongly inclined initial rise path and the close temporal association between the coronal mass ejection and the onset of flare reconnection. Minor differences occur in the velocity of flare ribbon expansion and in the further evolution of the inclination; these can be eliminated through refined simulations. We suggest that the slingshot effect of horizontally bent flux in the source region of eruptions can contribute significantly to the inclination of the rise direction. Finally, we demonstrate that the onset criterion, formulated in terms of a threshold value for the axial flux in the rope, corresponds very well to the threshold of the torus instability in the considered AR.

Photospheric Flux Cancellation and the Build-up of Sigmoidal Flux Ropes on the Sun

In this study we explore the scenario of photospheric flux cancellation being the primary formation mechanism of sigmoidal flux ropes in decaying active regions. We analyze magnetogram and X-ray observations together with data-driven non-linear force-free field (NLFFF) models of observed sigmoidal regions to test this idea. We measure the total and canceled fluxes in the regions from MDI magnetograms, as well as the axial and poloidal flux content of the modeled NLFFF flux ropes for three sigmoids—2007 February, 2007 December, and 2010 February. We infer that the sum of the poloidal and axial flux in the flux ropes for most models amounts to about 60%-70% of the canceled flux and 30%-50% of the total flux in the regions. The flux measurements and the analysis of the magnetic field structure show that the sigmoids first develop a strong axial field manifested as a sheared arcade and then, as flux cancellation proceeds, form long S-shaped field lines that contribute to the poloidal flux. In addition, the dips in the S-shaped field lines are located at the sites of flux cancellation that have been identified from the MDI magnetograms. We find that the line-of-sight-integrated free energy is also concentrated at these locations for all three regions, which can be liberated in the process of eruption. Flare-associated brightenings and flare loops coincide with the location of the X-line topology that develops at the site of most vigorous flux cancellation.