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Transits of exoplanets across cool stars contain blended information about structures on the stellar surface and about the planetary body and atmosphere. To advance understanding of how this information is entangled, a surface-flux transport code, based on observed properties of the Sun's magnetic field, is used to simulate the appearance of hypothetical stellar photospheres from the visible near 4000 Angstrom to the near-IR at 1.6 micron, by mapping intensities characteristic of faculae and spots onto stellar disks. Stellar appearances are computed for a Sun-like star of solar activity up to a star with mean magnetic flux density ~30 times higher. Simulated transit signals for a Jupiter-class planet are compared with observations. This (1) suggests that the solar paradigm is consistent with observations for stars throughout the activity range explored provided that infrequent large active regions with fluxes up to $\sim 3\times 10^{23}$ Mx are included in the emergence spectrum, (2) quantitatively confirms that for such a model, faculae brighten relatively inactive stars while starspots dim more active stars, (3) suggests that large starspots inferred from transits of active stars are consistent with clusters of more compact spots seen in the model runs, (4) that wavelength-dependent transit-depth effects caused by stellar magnetic activity for the range of activity and the planetary diameter studied here can introduce apparent changes in the inferred exoplanetary radii across wavelengths from a few hundred to a few thousand kilometers, increasing with activity, and (5) that activity-modulated distortions of broadband stellar radiance across the visible to near-IR spectrum can reach several percent., Comment: Accepted for publication in the Astrophysical Journal. Version corrected to match paper in print

Large solar flares and eruptions may influence remote regions through perturbations in the outer-atmospheric magnetic field, leading to causally related events outside of the primary or triggering eruptions that are referred to as "sympathetic events." We quantify the occurrence of sympathetic events using the full-disk observations by the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory associated with all flares of GOES class M5 or larger from 01 May 2010 through 31 December 2014. Using a superposed-epoch analysis, we find an increase in the rate of flares, filament eruptions, and substantial sprays and surges more than 20 degrees away from the primary flares within the first four hours at a significance of 1.8 standard deviations. We also find that the rate of distant events drops by two standard deviations, or a factor of 1.2, when comparing intervals between 4 hours and 24 hours before and after the start times of the primary large flares. We discuss the evidence for the concluding hypothesis that the gradual evolution leading to the large flare and the impulsive release of the energy in that flare both contribute to the destabilization of magnetic configurations in distant active regions and quiet-Sun areas. These effects appear to leave distant regions, in an ensemble sense, in a more stable state, so that fewer energetic events happen for at least a day following large energetic events., In press for Solar Physics. 9 pages, 3 figures

By rapidly evaporating as they fly through the Sun’s hot outer atmosphere, sungrazing comets reveal an otherwise invisible magnetic field that shapes the very beginnings of the solar wind.

We developed numerical codes designed for automated analysis of SDO/AIA image datasets in the six coronal filters, including: i) coalignment test between different wavelengths with measurements of the altitude of the EUV-absorbing chromosphere, ii) self-calibration by empirical correction of instrumental response functions, iii) automated generation of differential emission measure [DEM] distributions with peak-temperature maps [T p(x,y)] and emission measure maps [EM p(x,y)] of the full Sun or active region areas, iv) composite DEM distributions [dEM(T)/dT] of active regions or subareas, v) automated detection of coronal loops, and vi) automated background subtraction and thermal analysis of coronal loops, which yields statistics of loop temperatures [T e], temperature widths [σ T], emission measures [EM], electron densities [n e], and loop widths [w]. The combination of these numerical codes allows for automated and objective processing of numerous coronal loops. As an example, we present the results of an application to the active region NOAA 11158, observed on 15 February 2011, shortly before it produced the largest (X2.2) flare during the current solar cycle. We detect 570 loop segments at temperatures in the entire range of log(T e)=5.7 – 7.0 K and corroborate previous TRACE and AIA results on their near-isothermality and the validity of the Rosner–Tucker–Vaiana (RTV) law at soft X-ray temperatures (T≳2 MK) and its failure at lower EUV temperatures.

The Atmospheric Imaging Assembly (AIA) provides multiple simultaneous high-resolution full-disk images of the corona and transition region up to 0.5 R ⊙ above the solar limb with 1.5-arcsec spatial resolution and 12-second temporal resolution. The AIA consists of four telescopes that employ normal-incidence, multilayer-coated optics to provide narrow-band imaging of seven extreme ultraviolet (EUV) band passes centered on specific lines: Fe xviii (94 A), Fe viii, xxi (131 A), Fe ix (171 A), Fe xii, xxiv (193 A), Fe xiv (211 A), He ii (304 A), and Fe xvi (335 A). One telescope observes C iv (near 1600 A) and the nearby continuum (1700 A) and has a filter that observes in the visible to enable coalignment with images from other telescopes. The temperature diagnostics of the EUV emissions cover the range from 6×104 K to 2×107 K. The AIA was launched as a part of NASA’s Solar Dynamics Observatory (SDO) mission on 11 February 2010. AIA will advance our understanding of the mechanisms of solar variability and of how the Sun’s energy is stored and released into the heliosphere and geospace.

The Sun's outer atmosphere, or corona, is heated to millions of degrees, considerably hotter than its surface or photosphere. Explanations for this enigma typically invoke the deposition in the corona of nonthermal energy generated by magnetoconvection. However, the coronal heating mechanism remains unknown. We used observations from the Solar Dynamics Observatory and the Hinode solar physics mission to reveal a ubiquitous coronal mass supply in which chromospheric plasma in fountainlike jets or spicules is accelerated upward into the corona, with much of the plasma heated to temperatures between ~0.02 and 0.1 million kelvin (MK) and a small but sufficient fraction to temperatures above 1 MK. These observations provide constraints on the coronal heating mechanism(s) and highlight the importance of the interface region between photosphere and corona.

Solar extreme ultraviolet (EUV) images of quiescent active-region coronae are characterized by ensembles of bright 1-2 MK loops that fan out from select locations. We investigate the conditions associated with the formation of these persistent, relatively cool, loop fans within and surrounding the otherwise 3-5 MK coronal environment by combining EUV observations of active regions made with TRACE with global source-surface potential-field models based on the full-sphere photospheric field from the assimilation of magnetograms that are obtained by the Michelson Doppler Imager (MDI) on SOHO. We find that in the selected active regions with largely potential-field configurations these fans are associated with (quasi-)separatrix layers (QSLs) within the strong-field regions of magnetic plage. Based on the empirical evidence, we argue that persistent active-region cool-loop fans are primarily related to the pronounced change in connectivity across a QSL to widely separated clusters of magnetic flux, and confirm earlier work that suggested that neither a change in loop length nor in base field strengths across such topological features are of prime importance to the formation of the cool-loop fans. We discuss the hypothesis that a change in the distribution of coronal heating with height may be involved in the phenomenon of relatively cool coronal loop fans in quiescent active regions.

For main-sequence stars beyond spectral type M5 the characteristics of magnetic activity common to warmer solar-like stars change into the brown-dwarf domain: the surface magnetic field becomes more dipolar and the evolution of the field patterns slows, the photospheric plasma is increasingly neutral and decoupled from the magnetic field, chromospheric and coronal emissions weaken markedly, and the efficiency of rotational braking rapidly decreases. Yet, radio emission persists, and has been argued to be dominated by electron-cyclotron maser emission instead of the gyrosynchrotron emission from warmer stars. These properties may signal a transition in the stellar extended atmosphere. Stars warmer than about M5 have a solar-like corona and wind-sustained heliosphere in which the atmospheric activity is powered by convective motions that move the magnetic field. Stars cooler than early-L, in contrast, may have a jovian-like rotation-dominated magnetosphere powered by the star's rotation in a scaled-up analog of the magnetospheres of Jupiter and Saturn. A dimensional scaling relationship for rotation-dominated magnetospheres by Fan et al. (1982) is consistent with this hypothesis.

This review focuses on the processes that energize and trigger major solar flares and flux-rope destabilizations. Numerical modeling of specific solar regions is hampered by uncertain coronal-field reconstructions and by poorly understood magnetic re- connection; these limitations result in uncertain estimates of field topology, energy, and helicity. The primary advances in understanding field destabilizations therefore come from the combination of generic numerical experiments with interpretation of sets of observations. These suggest a critical role for the emergence of twisted flux ropes into pre-existing strong field for many, if not all, of the active regions that pro- duce M- or X-class flares. The flux and internal twist of the emerging ropes appear to play as important a role in determining whether an eruption will develop predom- inantly as flare, confined eruption, or CME, as do the properties of the embedding field. Based on reviewed literature, I outline a scenario for major flares and erup- tions that combines flux-rope emergence, mass draining, near-surface reconnection, and the interaction with the surrounding field. Whether deterministic forecasting is in principle possible remains to be seen: to date no reliable such forecasts can be made. Large-sample studies based on long-duration, comprehensive observations of active regions from their emergence through their flaring phase are needed to help us better understand these complex phenomena., Comment: in press for Advances in Space Research

A combination of heliospheric and solar data was used to identify open magnetic fields stretching from the lower corona to Earth orbit. 35 near-relativistic electron beams detected at the ACE spacecraft "labeled" the heliospheric segments of the open fields. An X-ray flare occurred

We investigate the distribution and evolution of existing and emerging magnetic network elements in the quiet-Sun photosphere. The ephemeral region emergence rate is found to depend primarily on the imbalance of magnetic flux in the area surrounding its emergence location, such that the rate of flux emergence is lower within strongly unipolar regions by at least a factor of 3 relative to flux-balanced quiet Sun. As coronal holes occur over unipolar regions, this also means that ephemeral regions occur less frequently there, but we show that this is an indirect effect-independent of whether the region is located within an open-field coronal hole or a closed-field quiet region. We discuss the implications of this finding for near-photospheric dynamo action and for the coupling between closed coronal and open heliospheric fields.

With the global view and high-cadence observations from SDO/AIA and STEREO, many spatially separated solar eruptive events appear to be coupled. However, the mechanisms for "sympathetic" events are still largely unknown. In this study, we investigate the impact of an erupting flux rope on surrounding solar structures through large-scale magnetic coupling. We build a realistic environment of the solar corona on 2011 February 15 using a global magnetohydrodynamics (MHD) model and initiate coronal mass ejections (CMEs) in active region (AR) 11158 by inserting Gibson-Low analytical flux ropes. We show that a CME's impact on the surrounding structures depends not only on the magnetic strength of these structures and their distance to the source region, but also on the interaction between the CME with the large-scale magnetic field. Within the CME expansion domain where the flux rope field directly interacts with the solar structures, expansion-induced reconnection often modifies the overlying field, thereby increasing the decay index. This effect may provide a primary coupling mechanism underlying the sympathetic eruptions. The magnitude of the impact is found to depend on the orientation of the erupting flux rope, with the largest impacts occurring when the flux rope is favorably oriented for reconnecting with the surrounding regions. Outside the CME expansion domain, the influence of the CME is mainly through field line compression or post-eruption relaxation. Based on our numerical experiments, we discuss a way to quantify the eruption impact, which could be useful for forecasting purposes., 38 pages, 13 figures

Flares and eruptions from solar active regions are associated with atmospheric electrical currents accompanying distortions of the coronal field away from a lowest-energy potential state. In order to better understand the origin of these currents and their role in M- and X-class flares, I review all active-region observations made with SDO/HMI and SDO/AIA from 2010/05 through 2014/10 within approximately 40 degrees from disk center. I select the roughly 4% of all regions that display a distinctly nonpotential coronal configuration in loops with a length comparable to the scale of the active region, and all that emit GOES X-class flares. The data for 41 regions confirm, with a single exception, that strong-field, high-gradient polarity inversion lines (SHILs) created during emergence of magnetic flux into, and related displacement within, pre-existing active regions are associated with X-class flares. Obvious nonpotentiality in the active region-scale loops occurs in 6 of 10 selected regions with X-class flares, all with relatively long SHILs along their primary polarity inversion line, or with a long internal filament there. Nonpotentiality can exist in active regions well past the flux-emergence phase, often with reduced or absent flaring. I conclude that the dynamics of the flux involved in the compact SHILs is of preeminent importance for the large-flare potential of active regions within the next day, but that their associated currents may not reveal themselves in active region-scale nonpotentiality. In contrast, active region-scale nonpotentiality, which can persist for many days, may inform us about the eruption potential other than those from SHILs which is almost never associated with X-class flaring., Accepted for publication in the Astrophysical Journal. 17 pages, 8 figures, and on-line supporting materials

Solar flares and coronal mass ejections (CMEs), especially the larger ones, emanate from active regions (ARs). With the aim to understand the magnetic properties that govern such flares and eruptions, we systematically survey all flare events with GOES levels of >=M5.0 within 45 deg from disk center between May 2010 and April 2016. These criteria lead to a total of 51 flares from 29 ARs, for which we analyze the observational data obtained by the Solar Dynamics Observatory. More than 80% of the 29 ARs are found to exhibit delta-sunspots and at least three ARs violate Hale's polarity rule. The flare durations are approximately proportional to the distance between the two flare ribbons, to the total magnetic flux inside the ribbons, and to the ribbon area. From our study, one of the parameters that clearly determine whether a given flare event is CME-eruptive or not is the ribbon area normalized by the sunspot area, which may indicate that the structural relationship between the flaring region and the entire AR controls CME productivity. AR characterization show that even X-class events do not require delta-sunspots or strong-field, high-gradient polarity inversion lines. An investigation of historical observational data suggests the possibility that the largest solar ARs, with magnetic flux of 2x10^23 Mx, might be able to produce "superflares" with energies of order of 10^34 erg. The proportionality between the flare durations and magnetic energies is consistent with stellar flare observations, suggesting a common physical background for solar and stellar flares., 31 pages, 12 figures, 3 tables, accepted for publication in ApJ. A high-quality version can be found at http://www-space.eps.s.u-tokyo.ac.jp/~toriumi/toriumi2016apj.pdf

Solar flares result from some electromagnetic instability that occurs within regions of relatively strong magnetic field in the Sun's atmosphere. The processes that enable and trigger these flares remain topics of intense study and debate. I analyze observations of 289 X- and M-class flares and over 2500 active region magnetograms to discover (1) that large flares, without exception, are associated with pronounced high-gradient polarity-separation lines, while (2) the free energy that emerges with these fibrils is converted into flare energy in a broad spectrum of flare magnitudes that may well be selected at random from a power-law distribution up to a maximum value. This maximum is proportional to the total unsigned flux R within ~15 Mm of strong-field, high-gradient polarity-separation lines, which are a characteristic appearance of magnetic fibrils carrying electrical currents as they emerge through the photosphere. Measurement of R is readily automated, and R can therefore be used effectively for flare forecasting. The probability for major flares to occur within 24 hr of the measurement of R approaches unity for active regions with the highest values of R around 2 × 1021 Mx. For regions with R 1019 Mx, no M- or X-class flares occur within a day.

The X17 flare on 2003 October 28 was observed by high-resolution imaging or spectroscopic instruments on CORONAS, GOES, INTEGRAL, RHESSI, SOHO, and TRACE. These spacecraft observed the temporal evolution of the γ-ray positron-annihilation and nuclear de-excitation line spectra, imaged the hard X-ray bremsstrahlung and EUV and UV emission, and measured the surface magnetic field and subphotospheric pressure perturbations. In the usual pattern, the onset of the flare is dominated by particle acceleration and interaction, and by the filling of coronal magnetic structures with hot plasma. The associated positron-annihilation signatures early in the impulsive phase from 11:06 to 11:16 UT have a line-broadening temperature characteristic of a few hundred thousand kelvins. The most intense precipitation sites within the extended flare ribbons are very compact, with diameters of less than 1400 km, and a 195 A TRACE intensity that can exceed 7500 times the quiescent active-region value. These regions appear to move at speeds of up to 60 km s-1. The associated rapidly evolving, compact perturbations of the photosphere below these sites excite acoustic pulses that propagate into the solar interior. Less intense precipitation sites typically persist for several minutes behind the advancing flare ribbons. After ~1 ks, the flare enters a second phase, dominated by coronal plasma cooling and downflows and by annihilation-line radiation characteristic of a photospheric environment. We point out (1) that these detailed observations underscore that flare models need to explicitly incorporate the multitude of successively excited environments whose evolving signals differ at least in their temporal offsets and energy budgets, if not also in the exciting particle populations and penetration depths, and (2) that the spectral signatures of the positron annihilation do not fit conventional model assumptions.

We model a coronal volume over a quiet, mixed-polarity solar network as an ensemble of quasi-steady loop atmospheres. These are contained by an assumed potential field, including the associated variations in the loop cross section through the coronal volume and the loop flows induced by such asymmetries. The average temperature and density stratifications are close to those of the quiet-Sun corona for a coronal heating flux density into the corona of FH = 8 × 1014B/L (ergs cm-2 s-1) for loop-base field strengths B (G) and loop half-lengths L (cm). Earlier, that heating parameterization was shown to be consistent with the appearance and radiative losses of a solar corona in which active regions dominated the emission. This study thus supports the hypothesis that the same, likely braiding-driven, heating dominates throughout the quiescent corona. The average ratio β of gas to magnetic pressure lies close to unity throughout the modeled coronal height range of 22 Mm, with β > 1 in ~30% of the volume and β > 0.4 in ~90% of the volume, perhaps indicating that the quiet-Sun corona is driven to near its maximum heating capacity by the random walk of its footpoints. Our findings that the solar corona has β close to unity, and that our model corona exhibits insufficient fine structure and no significant spatially averaged Doppler shifts, imply that the quiet-Sun corona is often neither quasi-steady nor force free and thus that dynamic magnetohydrodynamics (MHD) models are essential to furthering our understanding of the quiet solar corona.

The magnetic field in the solar photosphere frequently carries strong electric currents, even though the global coronal configuration often resembles a potential field ringed by the heliospheric current sheet. To understand this, we compare TRACE EUV images of active-region coronae and potential-field source-surface extrapolations based on SOHO MDI magnetograms for 95 active regions. We conclude that significant nonpotentiality of the overall active-region coronal field occurs (1) when new flux has emerged within or very near a region within the last ~30 hr, resulting in complex polarity separation lines, or (2) when rapidly evolving, opposite-polarity concentrations are in contact at 4'' resolution. If these criteria are met by more than 15% of the region's flux, they correctly identify the (non) potentiality of active-region coronae in 88% of the cases. Flares are found to occur 2.4 times more frequently in active regions with nonpotential coronae than in near-potential regions, while their average X-ray peak flare brightness is 3.3 times higher. We suggest that the currents associated with coronal nonpotentiality have a characteristic growth and decay timescale of ~10-30 hr. We find that shear flows drive enhanced flaring or coronal nonpotentiality only if associated with complex and dynamic flux emergence within the above timescale. We discuss the implications of this finding for the modeling of the coronal-heliospheric coupling.

We simulate surface field patterns for cool dwarf stars of widely different levels of activity and estimate the associated global coronal radiative losses. We find that the integrated X-ray brightness of coronae of cool stars is relatively insensitive to the patterns of their surface magnetic fields, and that the X-ray flux is determined almost entirely by the magnetic flux through the stellar surfaces. This reconciles potentially inconsistent findings in the literature for the heating of solar and stellar coronae: solar studies suggested that the heating flux density entering coronal loops scales as FH = 0Bβ/Lλ (for a magnetic flux density B at the base of a loop of length L, with β = 1.0 ± 0.3 and λ = 1.0 ± 0.5), whereas combined solar and stellar data suggested that the X-ray flux density FX from entire cool-star coronae depends only on the average magnetic flux density || through the stellar photospheres. We find that the above two scalings are compatible because loop lengths and base magnetic flux densities are essentially uncorrelated for the global coronal loop ensemble and because the average loop lengths differ much less from star to star for Sun-like stars of different activity than the average base field strengths. We also explore the scaling properties of the constant of proportionality 0 for stars of significantly different surface gravity.

We constrain the properties of the mechanism(s) responsible for the bulk of the heating of the corona of the Sun by simulating, for the first time, the appearance of the entire solar corona. Starting from full-sphere magnetic field maps for 2000 December 1 and 8, when the Sun was moderately active, we populate nearly 50,000 coronal field lines with quasi-static loop atmospheres. These atmospheres are based on heating flux densities FH that depend in different ways on the loop half-length L, the field strength B at the chromospheric base, the loop expansion with height, and the heating scale height. The best match to X-ray and EUV observations of the corona over active regions and their environs is found for FH ≈ 4 × 1014B1.0±0.3/L1.0±0.5 (in ergs cm-2 s-1 for B in Mx cm-2 and L in cm), while allowing for substantial loop expansion with increasing height, and for a heating scale height that is at least a sizeable fraction of the loop length. This scaling for coronal heating points to DC reconnection at tangential discontinuities as the most likely coronal heating mechanism, provided that the reconnection progresses proportional to the Alfven velocity. The best-fit coronal filling factor equals unity, suggesting that most of the corona is heated most of the time. We find evidence that loops with half-lengths exceeding ~100,000 km are heated significantly more than suggested by the above scaling, possibly commensurate with the power deposited in the open field of coronal holes.

The solar magnetic field that extends through the chromosphere into the corona is envisioned to fan out from strong flux concentrations located within the supergranular downflow lanes. That so-called network field appears to be surrounded by a mixed-polarity magnetic field with a scale comparable to that of the granulation. We argue that for an internetwork field with a magnitude of a few tens of Mx cm-2, as suggested by both observations and models, the commonly held notion of a wineglass-shaped magnetic canopy of network flux that fully encloses weakly magnetic regions below it is fundamentally wrong. We estimate that in the presence of such a relatively strong internetwork field, as much as half of the coronal field over very quiet Sun may be rooted in that mixed-polarity internetwork field throughout the supergranules rather than in the network flux concentrations, as assumed until now. A corresponding amount of flux forms collars of closed loops around the network concentrations, connecting network flux back down onto the internetwork field over distances of several thousand kilometers. Within such a geometry, the rapid evolution of the internetwork field may substantially affect coronal heating and the acceleration of the solar wind. We discuss the potential consequences of these interacting network and internetwork fields for atmospheric heating, for wave propagation and the formation of acoustic shadows, and for the appearance of the near-surface solar outer atmosphere.

This study addresses the winds and magnetic fields in the inner asterospheres of Sun-like magnetically active stars by combining empirical relationships between rotation rate and mass loss, angular-momentum loss, and radiative losses with models of the magnetic fields at the surfaces of cool stars and in their inner asterospheres based on the solar example. Our models, for mean magnetic flux densities up to 10 times solar, suggest that the asterospheric fields of such stars are dominated by the large-scale dipole component of the surface field, as is the case for the Sun. Hence, most of the time a single current sheet is expected to separate domains of opposite magnetic polarity; the current sheets of more active stars generally have smaller latitudinal ripples. Magnetic braking requires that the total unsigned asterospheric magnetic flux increase linearly with the stellar angular velocity, which is a very much weaker increase than seen for the flux at the stellar surface. We show that this can be achieved by an increase in the radial distance at which the coronal field is forced open as surface activity increases. Combined with measured mass-loss rates and the assumption that the wind velocity is largely independent of activity, this requires the wind's Alfven radius to be nearly constant, decreasing with surface activity with a power of only -0.16 ± 0.13. We point out that the surface flux density of energy needed to drive a cool-star wind scales linearly with the unsigned surface magnetic flux density, as does that needed to heat the corona.

We find that bipolar active regions that emerge onto the Sun's surface are part of a smoothly decreasing frequency distribution that spans almost 4 orders of magnitude in flux and 8 orders of magnitude in frequency. Distributions of emergence latitude and dipole orientation narrow from nearly uniform for the smallest observed ephemeral regions (~5 × 1018 Mx) up to narrowly distributed about the mean for the largest active regions (close to 1022 Mx), while the emergence frequency increases smoothly and rapidly with decreasing flux. At the low end of the flux spectrum, the cycle variation in emergence frequency is at most a factor of 1.5, in antiphase with the cycle variation of close to an order of magnitude for the large active regions. We discuss a scenario in which the ephemeral regions with fluxes below ~30 × 1018 Mx have their origin in a turbulent dynamo, largely independent of the global sunspot cycle. Our empirical findings are based on a combination of previously published work on active regions and large ephemeral regions, complemented here with an analysis of the photospheric magnetic field outside active regions, as observed in SOHO/MDI full-disk magnetograms taken from the most recent sunspot minimum in 1996 to about 1 yr after sunspot maximum in 2001. We find that the spectrum of the emerging bipoles with fluxes (6-30) × 1018 Mx can be approximated throughout this period by a fixed exponential distribution with an e-folding scale of (5.3 ± 0.1) × 1018 Mx. We confirm that the ephemeral regions are an important source of flux for the quiet magnetic network, in particular for the smallest scales; the larger scale patterns are dominated by flux dispersing from decaying active regions. As the variation of these two sources is nearly in antiphase, the flux contained in the quiet-Sun network shows little overall variation: the flux spectrum and the total absolute flux for network concentrations with fluxes 20 × 1018 Mx are essentially independent of cycle phase. For network concentrations with fluxes 30 × 1018 Mx, mostly found in regions populated substantially by decayed active regions, the network flux distribution approaches an exponential for which the e-folding scale increases with sunspot activity from ~20 × 1018 Mx to ~33 × 1018 Mx, as the total flux in this component varies in phase with the sunspot cycle. A comparison of the flux-emergence rate with the network flux implies an overall mean replacement time for flux in quiet Sun of 8-19 hr.

Brown, D.S., Nightingale, R.W., Alexander, D., Schrijver, C.J., Metcalf, T.R., Shine, R.A., Title, A.M. and Wolfson, C.J., 2003, Observations of rotating sunspots from TRACE, Solar Physics, 216, 79-108.

We test the feasibility of 3D coronal-loop tracing in stereoscopic EUV image pairs, with the ultimate goal of enabling efficient 3D reconstruction of the coronal magnetic field that drives flares and coronal mass ejections (CMEs). We developed an automated code designed to perform triangulation of coronal loops in pairs (or triplets) of EUV images recorded from different perspectives. The automated (or blind) stereoscopy code includes three major tasks: (i) automated pattern recognition of coronal loops in EUV images, (ii) automated pairing of corresponding loop patterns from two different aspect angles, and (iii) stereoscopic triangulation of 3D loop coordinates. We perform tests with simulated stereoscopic EUV images and quantify the accuracy of all three procedures. In addition we test the performance of the blind stereoscopy code as a function of the spacecraft-separation angle and as a function of the spatial resolution. We also test the sensitivity to magnetic non-potentiality. The automated code developed here can be used for analysis of existing {\sl Solar TErrestrial RElationship Observatory (STEREO)} data, but primarily serves for a design study of a future mission with dedicated diagnostics of non-potential magnetic fields. For a pixel size of 0.6\arcsec (corresponding to the {\sl Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA)} spatial resolution of 1.4\arcsec), we find an optimum spacecraft-separation angle of $\alpha_s \approx 5^\circ$., Comment: Solar Physics (accepted 2015 June 15), in press

The dominant mechanism that heats the coronae of the Sun and of other cool stars remains to be identified, despite numerous solar and stellar studies. We address the problem from a statistical point of view, by approximating the emission expected from the ensemble of loops in stellar coronae. We develop a prototype of a global atmospheric, empirical model that employs (1) simulations of the surface magnetic field of the Sun and active stars throughout sunspot cycles, (2) potential field computations of the corresponding coronal field, and (3) an approximation of atmospheres for 2000 coronal loops for randomly selected field lines in each flux configuration, representative of all environments from very quiet to the interior of active regions. The latter requires specification of the flux density PH that passes through the base of the loops to heat the corona. We parameterize PH as a function of the base field strength Bbase (in G), loop half-length l (in Mm), and footpoint velocity v (in km s-1). We find a best fit for a heating flux density of PH ≈ 2 × 107(Bbase/100)1.0±0.5(l/24)-0.7±0.3(v/0.4)0.0±0.5 ergs cm-2 s-1 (the allowed ranges of the exponents are shown). This parameterization matches the observed soft X-ray losses from the coronae of the Sun and more active stars with rotation periods down to 5 days, throughout their activity cycles, as well as the characteristic coronal temperatures, and the relationships between disk-averaged radiative and magnetic flux densities. We compare this parameterization to models previously published in the literature and find that dissipation of current layers and turbulence are the most likely candidate heating mechanisms, for which both low-frequency driving and high-frequency driving meet the criteria comparably well. We find, moreover, that the heating scale length of ~20 Mm inferred from solar observations matches the characteristic e-folding height of the field strength over solar active regions, which suggests that coronal heating depends on the local field strength. Our modeling suggests that there is no need for a strong selection mechanism to determine which loops are heated and which are not, but that the sensitive dependence of the heating on the base field strength causes the appearance of a corona that consists of bright loops embedded in less bright environments. We compare the differential emission measures for the simulated coronae to those of the Sun and more active cool stars, and we also discuss the apparently weak velocity dependence of the best-fit parameterization for PH.

We study the statistical properties of the connectivity of the corona over the quiet Sun by analyzing the potential magnetic field above the central area of source planes sprinkled randomly with some 300 magnetic monopoles each. We find that the field is generally more complex than one might infer from a study of the field within the source plane alone, or from a study of the 3D field around a small number of sources. Whereas a given source most commonly connects to only its nearest neighbors, it may connect to up to several dozen sources; only a weak trend relates the source strength and the number of connections. The connections between pairs of sources define volumes, or domains, of connectivity. Domains that have a finite cross section with the source plane are enclosed by surfaces that contain a pair of null points. In contrast, most of the bounding surfaces of domains that lie above the source plane appear not to contain null points. We argue that the above findings imply (i) that we should expect at best a weak correlation between coronal brightness and the flux in an underlying flux concentration, and (ii) that the low-lying chromospheric field lines (such as are observable in Hα) provide information on source connections that are largely complementary to those traced by the higher-reaching coronal field lines (observable in the extreme ultraviolet). We compare sample TRACE and SOHO/MDI observations of the quiet corona and photosphere with our finding that the number density of null points within the source plane closely matches that of the sources; because we find essentially no foci of coronal brightening away from significant photospheric magnetic flux concentrations, we conclude that coronal heating at such null points does not contribute significantly to the overall heating. We argue that the divergence of field lines towards multiple sources restricts the propagation of braids and twists, so that any coronal heating that is associated with the dissipation of braids induced by footpoint shuffling in mixed-polarity network is likely (a) to occur predominantly low in the corona, and (b) to be relatively more efficient in quiet Sun than in active regions for a given field strength and loop length.

We study transverse loop oscillations triggered by 17flares and filament destabilizations; only 2 such cases have been reported in the literature until now. Oscillation periods are estimated to range over a factor of ∼15, with most values between 2 and 7 min. The oscillations are excited by filament destabilizations or flares (in 6% of the 255 flares inspected, ranging from about C3 to X2). There is no clear dependence of oscillation amplitude on flare magnitude. Oscillations occur in loops that close within an active region, or in loops that connect an active region to a neighboring region or to a patch of strong flux in the quiet Sun. Some magnetic configurations are particularly prone to exhibit oscillations: two active regions showed two, and one region even three, distinct intervals with loop oscillations. The loop oscillations are not a resonance that builds up: oscillations in loops that are excited along their entire length are likely to be near the fundamental resonance mode because of that excitation profile, but asymmetrically excited oscillations clearly show propagating waves that are damped too quickly to build up a resonance, and some cases show multiple frequencies. We discuss evidence that all oscillating loops lie near magnetic separatrices that outline the large-scale topology of the field. All magnetic configurations are more complicated than a simple bipolar region, involving mixed-polarities in the interior or vicinity of the region; this may reflect that the exciting eruptions occur only in such environments, but this polarity mixing likely also introduces the large-scale separatrices that are involved. Often the oscillations occur in conjunction with gradual adjustments in loop positions in response to the triggering event. We discuss the observations in the context of two models: (a) transverse waves in coronal loops that act as wave guides and (b) strong sensitivity to changes in the field sources for field lines near separatrices. Properties that favor model b are (1) the involvement of loops at or near separatrices that outline the large-scale topology of the field, (2) the combined occurrence of oscillations and loop translations, (3) the small period spread and similar decay time scale in a set of oscillating loops in one well-observed event, and (4) the existence of loops oscillating in antiphase with footpoints close together in two cases. All other properties are compatible with either model, except the fact that almost all of the oscillations start away from the triggering event, suggestive of an outward-pushing exciting wave more in line with model a. The spread in periods from event to event suggests that the oscillations may reflect the properties of some driver mechanism that is related to the flare or mass ejection.

We simulate the photospheric magnetic field on very active cool stars using a flux injection and surface distribution model with strictly solar parameters, including an 11 yr sunspot cycle and associated butterfly pattern. The only free parameter is the magnitude of the cycle. We demonstrate that the combination of supergranulation-driven dispersal and meridional advection of the field on a very active Sun-like star leads to a strong polar cap field. The polar caps contain so much flux that in comparable environments on the Sun convection is suppressed; it appears inevitable that this leads to the formation of (clusters of) starspots within large unipolar areas that form at high latitudes. The model exhibits a peak total flux in the polar cap regions that is roughly proportional to the cycle amplitude for active regions, 0, whereas the total absolute flux covering the stellar surface has a significantly weaker than linear dependence on 0. We find, for example, that for a star with a rotation period of P ~ 6 days, the total absolute flux on the star is ~10 times that characteristic of the active Sun, while the peak polar cap flux is stronger by a factor of ~30. Within the polar caps of such active stars, flux concentrations coagulate to form relatively large clusters. The tendency for larger flux concentrations to disperse more slowly causes the polar cap flux to be concentrated in a more restricted latitude range with increasing activity; the corresponding longitudinally averaged flux density in the polar caps of the simulated star with P ~ 6 days reaches ~300-500 Mx cm-2. The polar cap field in these simulations displays a ring of one polarity at high latitudes around a polar patch of the opposite polarity during much of the spot cycle. This bipolar pattern forms a persistent flux reservoir, so that the cycle modulation of the polar cap flux of an active star is relatively weak, consistent with observations of polar cap spot coverage on active cool stars. Based on these model results, we propose that polar spots are consistent with a dynamo like that of the Sun for a sufficiently enhanced emergence frequency of active regions.

Recent observations of coronal loops in EUV wavelengths with the Transition Region and Coronal Explorer (TRACE) and the Extreme-Ultraviolet Imaging Telescope (EIT) on the Solar and Heliospheric Observatory (SOHO) demonstrated three new results that cannot be explained by most of the existing loop models: (1) EUV loops are near-isothermal along their coronal segments, (2) they show an overpressure or overdensity compared with the requirements of steady state loops with uniform heating, and (3) the brightest EUV loops exhibit extended scale heights up to 4 times the hydrostatic scale height. These observations cannot be reconciled with the classical RTV (Rosner, Tucker, & Vaiana) model, they do not support models with uniform heating, and they even partially violate the requirements of hydrostatic equilibrium. In this study we are fitting for the first time steady state solutions of the hydrodynamic equations to observed intensity profiles, permitting a detailed consistency test of the observed temperature T(s) and density profiles ne(s) with steady state models, which was not possible in previous studies based on scaling laws. We calculate some 500 hydrostatic solutions, which cover a large parameter space of loop lengths (L ? 4-300 Mm), of nonuniform heating functions (with heating scale heights in the range of ?H ? 1-300 Mm), approaching also the limit of uniform heating (?H L). The parameter space can be subdivided into three regimes, which contain (1) solutions of stably stratified loops, (2) solutions of unstably stratified loops (in the case of short heating scale heights, ?H,Mm ? ), and (3) a regime in which we find no numerical solutions (when ?H,Mm ). Fitting the hydrostatic solutions to 41 EUV loops observed with TRACE (selected by the criterion of detectability over their entire length), we find that only 30% of the loops are consistent with hydrostatic steady state solutions. None of the observed EUV loops is consistent with a uniform heating function while in quasi-steady state. Those loops compatible with a steady state are found to be heated near the footpoints, with a heating scale height of ?H = 12 ? 5 Mm, covering a fraction ?H/L = 0.2 ? 0.1 of the loop length. These results support coronal heating mechanisms operating in or near the chromosphere and transition region.

The Extreme Ultraviolet Imaging Telescope (EIT) and the Michelsen Doppler Imager (MDI) instruments on the Solar and Heliospheric Observatory (SOHO) ran a coordinated observing campaign over the dates 1997 August 10-14. MDI generated 12 resolution magnetograms (06 pixels) of the solar photosphere at a nominal cadence of one minute while EIT observed Fe XII (195 A) (5'' resolution; 25 pixels) in the MDI high-resolution field of view at a cadence of ~17 minutes. We investigate the relationship between the quiet-Sun photospheric magnetic field and the quiet solar corona by first removing instrumental effects from the EIT data, time-averaging the MDI data for improved statistics, and coaligning the two data sets and applying solar rotation tracking. At the time of the observation, this was the longest continuous run of its kind. We conduct a detailed investigation of the processes of evolution in the photospheric magnetic field and look for sympathetic effects in the solar corona. We measure the lifetimes, dimensions, and orientations of small-scale coronal brightenings and reconcile these processes against the evolution of the underlying photospheric magnetic field. Using statistics collected from this study, we find that emerging bipoles in quiet Sun reach a typical length of ≈14 Mm before fading or reconnecting to other flux concentrations in a time period of ≈5-12 hr, and the quiet solar corona completely decorrelates in approximately 15 hr. We find that the majority of large coronal loops in quiet Sun are the products of numerous smaller magnetic flux concentrations coalescing in the photosphere rather than the product of a single large emerging bipole. This continuous process of emergence and coalescence leads to the observation that there is no preferred orientation to small-scale coronal brightenings in the solar corona.

The observed disk-integrated radiative losses from the outer atmospheres of stars with convective envelopes are determined by the distribution of magnetic field over their surfaces. Earlier modeling of the random walk transport of the solar photospheric magnetic field with the classical Leighton model has given us insight into how field patterns form and evolve on large scales. This paper presents the first comprehensive simulations of the dynamic photospheric magnetic field of the Sun down to the scale of the mixed polarity network, thus incorporating all flux involved in outer atmospheric heating. The algorithm incorporates the classical diffusion model but includes ephemeral regions (which populate the network that contributes significantly to the disk-integrated chromospheric emission) and the early phase of decay of active regions (which is important for the field patterns in very active stars). Moreover, individual flux concentrations are tracked and subjected to collisions and fragmentation, and the flux dispersal is made dependent on the flux contained in the concentrations, as observed on the Sun. The latter modification causes the model to be nonlinear. Tests demonstrate that the new model successfully describes the solar magnetic field. The model is then used to simulate the field on other cool stars covering several orders of magnitude in activity and to estimate the surface-averaged radiative losses associated with that field. The stellar extrapolations are based on the statistical properties of solar bipolar regions throughout the cycle. Simulations in which only the frequency of flux emergence is changed to simulate stars of different activity are shown to be consistent with the observed nonlinear relationships between disk-averaged radiative losses from chromospheres and coronae of cool stars. Consequently, the properties of the solar magnetic field from small ephemeral regions up to large active regions are compatible with stellar observations. Stellar observations suggest that those field properties are not the only ones that can explain the flux-flux relationships, however, because also stars with polar spots or persistent active longitudes obey these same flux-flux relationships. The model is also used to understand how rapidly flux is processed in stellar photospheres in stars with activity patterns like the Sun: the average total absolute magnetic flux Φ* (Mx) at the stellar surface is found to be proportional to the mean rate of flux emergence and cancellation E* (Mx s-1) within the range from E☉ up to 10E☉, where E☉ is the flux injection rate for the active Sun. This linearity is primarily a consequence of an activity-dependent change in the shape of the flux histogram for emerging bipoles. This change reflects that active regions and ephemeral regions have a different dependence on dynamo strength. The implications of the results of the simulations for the dynamo and for the relationship between activity and stellar rotation are discussed.

Observations with the Transition Region and Coronal Explorer, TRACE, show frequent catastrophic cooling and evacuation of quiescent solar coronal loops over active regions. We analyze this process using image sequences taken in passbands showing plasma from a few million degrees down to less than 100 000 K, taken at a cadence of 90 s. The loop evacuation often occurs after plasma high in the corona has cooled to transition-region or even chromospheric temperatures. The cooling loops frequently show Lyman-α and C iv emission developing initially near the loop tops; later, that cool plasma usually slides down on both sides of the loop. The relatively cool material often forms clumps that move at speeds of up to 100 km s−1. The downward acceleration is no more than 80 m s−2, less than $$\frac{1}{3}{\text{rd}}$$ of the surface gravity. Cooling appears to progress with delays of the order of up to 103 s between thin, neighboring strands within flux bundles with cross-sections of at least 1–2 Mm, so that hot and cool loops are transiently outlined at essentially the same location. The falling material at temperatures of ≲ 0.1 MK shows no evidence of loop braiding on scales above the resolution of ∼1 Mm; loop cross-sections appear independent of height. Existing numerical models suggest that the observed catastrophic loop-top cooling in non-flaring conditions can occur if the loop heating precipitously drops by 1.5 orders of magnitude or more, first and most strongly high in the corona. Using order-of-magnitude geometrical arguments, we estimate that loop bundles in the interior of an active region undergo catastrophic cooling on average once every 2 days, while in a decayed bipolar region that time interval is approximately a week.

The magnetic field in the outer solar atmosphere is frequently distorted by flares. In some cases, a fraction of the field exhibits a rapidly damped oscillation (Schrijver et al.; Aschwanden et al.). If this is a resonating wave trapped in the field, then the rapid damping requires a viscosity or resistivity that is at least 108 times larger than expected (Nakariakov et al.). We propose instead that some of the field lines are so sensitive to the source positions that rocking motions of the photospheric plasma associated with some solar flares (Kosovichev & Zharkova) cause a few loops to oscillate in (anti)phase in the fundamental mode, with a period and decay rate that are determined largely by the characteristics of the photosphere, saying little about the high atmosphere.

We present a detailed analysis of the geometric and physical parameters of 281 EUV nanoflares, simultaneously detected with the TRACE telescope in the 171 and 195 A wavelengths. The detection and discrimination of these flarelike events is detailed in the first paper in this series. We determine the loop length l, loop width w, emission measure EM, the evolution of the electron density ne(t) and temperature Te(t), the flare decay time τdecay, and calculate the radiative loss time τloss, the conductive loss time τcond, and the thermal energy Eth. The findings are as follows: (1) EUV nanoflares in the energy range of 1024-1026 ergs represent miniature versions of larger flares observed in soft X-rays (SXR) and hard X-rays (HXR), scaled to lower temperatures (Te 2 MK), lower densities (ne 109 cm-3), and somewhat smaller spatial scales (l ≈ 2-20 Mm). (2) The cooling time τdecay is compatible with the radiative cooling time τrad, but the conductive cooling timescale τcond is about an order of magnitude shorter, suggesting repetitive heating cycles in time intervals of a few minutes. (3) The frequency distribution of thermal energies of EUV nanoflares, N(E) ≈ 10-46(E/1024)-1.8 (s-1 cm-2 ergs-1) matches that of SXR microflares in the energy range of 1026-1029, and exceeds that of nonthermal energies of larger flares observed in HXR by a factor of 3-10 (in the energy range of 1029-1032 ergs). Discrepancies of the power-law slope with other studies, which report higher values in the range of a = 2.0-2.6 (Krucker & Benz; Parnell & Jupp), are attributed to methodical differences in the detection and discrimination of EUV microflares, as well as to different model assumptions in the calculation of the electron density. Besides the insufficient power of nanoflares to heat the corona, we find also other physical limits for nanoflares at energies 1024 ergs, such as the area coverage limit, the heating temperature limit, the lower coronal density limit, and the chromospheric loop height limit. Based on these quantitative physical limitations, it appears that coronal heating requires other energy carriers that are not luminous in EUV, SXR, and HXR.

Observations of the quiet off-limb corona in most EUV lines and in white light are compatible with a (nearly) hydrostatic stratification of the density at a temperature of 1.2-1.5 MK. We show that, in contrast, the quiet solar corona in the 171 and 195 A passbands of the SOHO/EIT has an effective emission scale height that significantly exceeds that for hydrostatic stratification at the observed characteristic temperature. We conclude that this different behavior is caused primarily by resonant scattering that occurs in the EUV lines of Fe IX, Fe X, and Fe XII as a result of their exceptionally high oscillator strengths. A fit to an approximate model suggests that roughly 1/10 to possibly more than half of the detected photons in EIT (and in TRACE) images in the 195 and 171 A passbands, respectively, of the quiet solar corona have been subjected to scattering. This scattering is responsible for much of the background haze that is seen in high-resolution TRACE images of the quiet corona; the hotter active-region corona is subject to much less scattering. We discuss these results in view of stellar coronal studies and future solar instrumentation.

We report here, for the —rst time, on spatial oscillations of coronal loops, which were detected in extreme-ultraviolet wavelengths (171 with the T ransition Region and Coronal Explorer, in the tem- Ae ) perature range of MK. The observed loop oscillations occurred during a —are that began at T e B 1.0¨1.5 1998 July 14, 12:55 UT and are most prominent during the —rst 20 minutes. The oscillating loops connect the penumbra of the leading sunspot to the —are site in the trailing portion. We identi—ed —ve oscillating loops with an average length of L \ 130,000 ^ 30,000 km. The transverse amplitude of the oscillations is A \ 4100 ^ 1300 km, and the mean period is T \ 280 ^ 30 s. The oscillation mode appears to be a standing wave mode (with —xed nodes at the footpoints). We investigate diUerent MHD wave modes and —nd that the fast kink mode with a period q \ 205(L /1010 cm~3)1@2 cm)(n e /109 (B/10 G)~1 s provides the best agreement with the observed period. We propose that the onset of loop oscillations in distant locations is triggered by a signal or disturbance that propagates from the central —are site with a radial speed of B700 km s~1. Because the observed loop oscillation periods are compa- rable to photospheric 5 minute oscillations, a resonant coupling between the two systems is possible. We further —nd evidence for global extreme-UV dimming in the entire active region possibly associated with a coronal mass ejection. Subject headings: Sun: coronaSun: —aresSun: oscillationsSun: UV radiation