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We suggest a source for high-frequency Alfven waves invoked in coronal heating and acceleration of the solar wind. The source is associated with small-scale magnetic loops in the chromospheric network.
Recent theories of the solar cycle and of coronal heating strongly suggest that solar cycle variations of different quantities (i.e., sunspots, coronal green line, etc.) ought not to be expected to be in phase with one another. In agreement with this notion it is noted that the shape of the corona typical of a 'maximum' eclipse occurs 1.5 yr before sunspot maximum, compared with 2 yr as might be expected from Leighton's 'standard' model. Further, it is argued that the phase of the solar wind cycle can be determined from geomagnetic observations. Using this phase, a solar cycle variation of 100 km/sec in the solar wind velocity and 1 gamma in the magnetic field intensity becomes apparent. In general, the solar wind cycle lags behind the coronal-eclipse-form cycle by 3 yr, compared with the 2 yr that might be expected from model calculations.
This paper further develops the zero-dimensional (0D) hydrodynamic coronal loop model "Enthalpy-based Thermal Evolution of Loops" (EBTEL) originally proposed by Klimchuk et al (2008), which studies the plasma response to evolving coronal heating. It has typically been applied to impulsive heating events. The basis of EBTEL is the modelling of mass exchange between the corona and transition region and chromosphere in response to heating variations, with the key parameter being the ratio of transition region to coronal radiation. We develop new models for this parameter that now include gravitational stratification and a physically motivated approach to radiative cooling. A number of examples are presented, including nanoflares in short and long loops, and a small flare. It is found that while the evolution of the loop temperature is rather insensitive to the details of the model, accurate tracking of the density requires the inclusion of our new features. In particular, we are able to now obtain highly over-dense loops in the late cooling phase and decreases to the coronal density arising due to stratification. The 0D results are compared to a 1D hydro code (Hydrad). The agreement is acceptable, with the exception of the flare case where some versions of Hydrad can give significantly lower densities. This is attributed to the method used to model the chromosphere in a flare. EBTEL is suitable for general use as a tool for (a) quick-look results of loop evolution in response to a given heating function and (b) situations where the modelling of hundreds or thousands of elemental loops is needed. A single run takes a few seconds on a contemporary laptop.
Investigations of the physical processes responsible for the acceleration of the solar wind were pursued with the development of two new solar wind codes: a hybrid code and a 2-D MHD code. Hybrid simulations were performed to investigate the interaction between ions and parallel propagating low frequency ion cyclotron waves in a homogeneous plasma. In a low-beta plasma such as the solar wind plasma in the inner corona, the proton thermal speed is much smaller than the Alfven speed. Vlasov linear theory predicts that protons are not in resonance with low frequency ion cyclotron waves. However, non-linear effect makes it possible that these waves can strongly heat and accelerate protons. This study has important implications for study of the corona and the solar wind. Low frequency ion cyclotron waves or Alfven waves are commonly observed in the solar wind. Until now, it is believed that these waves are not able to heat the solar wind plasma unless some cascading processes transfer the energy of these waves to high frequency part. However, this study shows that these waves may directly heat and accelerate protons non-linearly. This process may play an important role in the coronal heating and the solar wind acceleration, at least in some parameter space.
The theoretical discussion of magnetic heating focuses on heating by dissipation of field-aligned electric currents. Several mechanisms are set forth to account for the very high current densities needed to generate the heat, but observed radiative losses do not justify the resultant Ohmic heating rate. Tearing modes, 'turbulent resistivity', and 'hyper-resistivity' are considered to resolve the implied inefficiency of coronal heating. Because the mechanisms are not readily applicable to the sun, transverse magnetic energy flows and magnetic flare release are considered to account for the magnitude of observed radiative loss. High-resolution observations of the sun are concluded to be an efficient way to examine the issues of magnetic heating in spite of the very small spatial scales of the heating processes.
Attention is drawn to the implications of the high densities observed in flare plasmas in the wide temperature range from 10 to the 4th K to more than 10 to the 7th K. The chromospheric evaporation theory for the decay phase is discussed, and it is found that it is not consistent with the observations. It is pointed out that all the flare mechanisms proposed so far, e.g., magnetic field reconnection in various geometries, have entirely ignored the fundamental problem of how the high densities arise in the first place, and, in fact, they are unable to answer this question. It is suggested that compressional heatings of a flaring loop might be responsible for the density and emission measure (EM) increases observed in flare plasmas. Chromospheric evaporation associated with local heating in the initial rising phase of the flare, in distinction to the existing evaporation theory which assumes a coronal heating source, is also discussed. Possible observational tests, utilizing the newly launched Solar Maximum Mission (SMM) satellite, are presented.
Significant advances in our theoretical basis for understanding several physical processes related to dynamical phenomena on the sun were achieved. We have advanced a new model for spicules and fibrils. We have provided a simple physical view of resonance absorption of MHD surface waves; this allowed an approximate mathematical procedure for obtaining a wealth of new analytical results which we applied to coronal heating and p-mode absorption at magnetic regions. We provided the first comprehensive models for the heating and acceleration of the transition region, corona, and solar wind. We provided a new view of viscosity under coronal conditions. We provided new insights into Alfven wave propagation in the solar atmosphere. And recently we have begun work in a new direction: parametric instabilities of Alfven waves.
Any successful model of coronal loops must explain a number of observed properties. For warm (approx. 1 MK) loops, these include: 1. excess density, 2. flat temperature profile, 3. super-hydrostatic scale height, 4. unstructured intensity profile, and 5. 1000-5000 s lifetime. We examine whether thermal nonequilibrium can reproduce the observations by performing hydrodynamic simulations based on steady coronal heating that decreases exponentially with height. We consider both monolithic and multi-stranded loops. The simulations successfully reproduce certain aspects of the observations, including the excess density, but each of them fails in at least one critical way. -Xonolithic models have far too much intensity structure, while multi-strand models are either too structured or too long-lived. Storms of nanoflares remain the only viable explanation for warm loops that has been proposed so far. Our results appear to rule out the widespread existence of heating that is both highly concentrated low in the corona and steady or quasi-steady (slowly varying or impulsive with a rapid cadence). Active regions would have a very different appearance if the dominant heating mechanism had these properties. Thermal nonequilibrium may nonetheless play an important role in prominences and catastrophic cooling e(veen.gts..,coronal rain) that occupy a small fraction of the coronal volume. However, apparent inconsistencies between the models and observations of cooling events have yet to be understood.
A search for steady emission of the 2.223 MeV gamma-ray line arising from the direct capture reaction 1H(n, gamma)2H is presented on the basis of an analysis of SMM data. The upper limits for continuous 2.223 MeV gamma-ray line emission from the active and inactive sun, as established in the present work, are about two orders of magnitude less than previously published results. These findings for inactive periods also suggest that small flares (or a continuous acceleration mechanism) are unlikely to be the source of the heating of the quiet solar corona. It is concluded that the power in accelerated nuclei during inactive periods falls short of the coronal heating requirement by about four orders of magnitude unless there is a large and as yet unobserved population of nuclei at energies below 1 MeV. The energy release in other forms associated with the acceleration process falls short of the heating requirement by about two orders of magnitude if this energy release is in the same proportion to the power in accelerated nuclei as is estimated from observed flares.
Nanoflares are considered prime candidates for heating the non-flaring solar corona. However, direct detection of individual nanoflares with present-generation instruments remains challenging. Understanding the frequency and magnitude of nanoflares is crucial for comprehending their role in coronal heating. In this study, we employ field-aligned hydrodynamic model to simulate the emission from a non-flaring X-ray bright point (XBP) observed by the Marshall Grazing Incidence X-ray Spectrometer (MaGIXS). The length and magnetic field strength of the coronal loops associated with this XBP are derived from magnetic field extrapolation of observed photospheric magnetograms by SDO/HMI. Each loop is assumed to be heated by random nanoflares, whose frequency and magnitude are determined by the loop length and their field strength. The simulation results are then compared and matched against the observation to determine the nanoflare heating frequency. We will discuss the findings of this study. Furthermore, we will discuss the evolution of nanoflare heating frequency during the formation and decay of an active region (AR) on the solar disk.
Recent high-resolution imaging and spectroscopic observations have generated renewed interest in spicules' role in explaining the hot corona. Some studies suggest that some spicules, often classified as type II, may provide significant mass and energy to the corona. Here we use numerical simulations to investigate whether such spicules can produce the observed coronal emission without any additional coronal heating agent. Model spicules consisting of a cold body and hot tip are injected into the base of a warm (0.5 MK) equilibrium loop with different tip temperatures and injection velocities. Both piston- and pressure-driven shocks are produced. We find that the hot tip cools rapidly and disappears from coronal emission lines such as Fe xii 195 and Fe xiv 274. Prolonged hot emission is produced by preexisting loop material heated by the shock and by thermal conduction from the shock. However, the shapes and Doppler shifts of synthetic line profiles show significant discrepancies with observations. Furthermore, spatially and temporally averaged intensities are extremely low, suggesting that if the observed intensities from the quiet Sun and active regions were solely due to type II spicules, one to several orders of magnitude more spicules would be required than have been reported in the literature. This conclusion applies strictly to the ejected spicular material. We make no claims about emissions connected with waves or coronal currents that may be generated during the ejection process and heat the surrounding area.
The physics of solar wind flow in the acceleration region and impulsive phenomena in the solar corona is studied. The study of magnetohydrodynamic wave propagation in the corona and the solutions for steady state and time dependent solar wind equations gives insights concerning the physics of the solar wind acceleration region, plasma heating and plasma acceleration processes and the formation of shocks. Also studied is the development of techniques for placing constraints on the mechanisms responsible for coronal heating.
The behavior of velocity, magnetic field, and pressure perturbations about a continuously varying interface in pressure equilibrium is investigated in detail within ideal incompressible magnetohydrodynamics. A specific initial value problem is solved in quadrature for a thin interface and compared with the solution for a discontinuous interface. The unattenuated surface wave about a discontinuous interface is replaced at a thin interface by a collective surface disturbance which decays, with the associated energy density flowing into local oscillations within the interface. At long times the envelope of the local oscillations is concentrated within a small fraction of the thin interface (gradients within the envelope increase linearly with time, eventually resulting in a breakdown of the linearized ideal theory). Thus, the derived decay rate of the surface disturbance gives a mode-conversion rate rather than a heating rate. In applications to the propagation and dissipation of surface waves in the solar corona, this rate cannot in general be interpreted as a coronal heating rate.
One hundred fifty-six large-scale enhancements of X-ray emission from solar active regions were studied on full-disk filterheliograms to determine characteristic morphology and expansion rates for heated coronal plasma. The X-ray photographs were compared with H-alpha observations of flares, sudden filament disappearances, sprays, and loop prominence systems (LPS). Eighty-one percent of the X-ray events were correlated with H-alpha filament activity, but only 44% were correlated with reported H-alpha flares. The X-ray enhancements took the form of loops or arcades of loops ranging in length from 60,000 km to 520,000 km and averaging 15,000 km in width. Lifetimes ranged from at least 3 hr to more than 24 hr. The event frequency was approximately 1.4 per day. X-ray loop arcades evolved from sharp-edged clouds in cavities vacated by rising H-alpha filaments. Expansion velocities of the loops were about 50 km/s immediately after excitation and 1-10 km/s several hours later. These long-lived loop arcades are identified with LPS, and it is suggested that the loops outlined magnetic fields which were reconnecting after filament eruptions. Another class of X-ray-enhanced loops stretched outside active regions and accompanied sprays or lateral filament ejections. It is suggested that these loops outlined closed magnetic fields guiding slow-mode shocks from flares and filament eruptions.
On 2008 May 2, Chandra observed the X-ray spectrum of xi Boo (G8 V+K4 V), resolving the binary for the first time in X-rays and allowing the coronae of the two stars to be studied separately. With the contributions of ξ Boo A and B to the system's total X-ray emission now observationally established (88.5% and 11.5% respectively), consideration of mass loss measurements for GK dwarfs of various activity levels (including one for xi Boo) leads to the surprising conclusion that xi Boo B may dominate the wind from the binary, with xi Boo A's wind being very weak despite its active corona. Emission measure (EM) distributions and coronal abundances are computed for both stars and compared with Chandra measurements of other moderately active stars with G8-K5 spectral types, all of which exhibit a narrow peak in EM near log T = 6.6, indicating that the coronal heating process in these stars has a strong preference for this temperature. As is the case for the Sun and many other stars, our sample of stars shows coronal abundance anomalies dependent on the first ionization potential (FIP) of the element. We see no dependence of the degree of FIP effect on activity, but there is a dependence on spectral type, a correlation that becomes more convincing when moderately active main-sequence stars with a broader range of spectral types are considered. This clear dependence of coronal abundances on spectral type weakens if the stellar sample is allowed to be contaminated by evolved stars, interacting binaries or extremely active stars with logLX 29, explaining why this correlation has not been recognized in the past.
The two general classes of models that deal with the required heating of stellar chromospheres and coronae assume that outer stellar atmospheres are heated by hydrodynamic or by magnetohydrodynamic (MHD) waves and that these waves are generated by turbulent motions in the stellar convection zones. This paper considers the types of MHD waves and the source of these waves in stars like sun, the efficiency of the generation of MHD waves, and the manner of propagation and energy dissipation of MHD waves. It is shown that the basic criteria for the validity of any theory of MHD wave heating must account for the mean level of heating observed in stellar chromospheres and coronae, and for the range of radiative losses observed for a given spectral type. It is also required that the MHD wave heating theory accounts for the existence of inhomogeneities in stellar atmospheres. The results obtained indicate that magnetic tube waves might supply enough energy for the chromospheric and coronal heating and might also account for the observed range of variations of stellar radiative losses for a given spectral type.
We present detailed three-dimensional simulations of active regions resulting from numerical models of sunspots coupled to coronal excitation and emission. The models incorporate a fully three-dimensional magnetoconvection calculation, described in a poster by Hurlburt and Rucklidge, potential field extrapolations from the sunspot model boundary conditions, steady-state coronal loops powered by the convective motions at the surface, EUV and X-ray instrument response functions, and a full voxel rendering. The result is a simulated dynamical active region in three dimensions which enables us to explore coronal heating and its relationship to the dynamics of the photosphere and convection zone. The 3D rendering of the resulting EUV emission allows us to investigate the expected coronal signatures of the EUVI instruments on board the twin STEREO spacecraft to be launched in 2004. The hybrid model developed here also provides a simulation testbed for the development of future STEREO image reconstruction tools: an integral component in the access to STEREO data by the solar physics community.
In this paper we study the three-dimensional (3D) structure of hot (T(sub e) approximately equals 1.5 - 2.5 MK) loops in solar active region NOAA 7986, observed on 1996 August 30 with the Extreme-ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SoHO). This complements a first study on cooler (T(sub e) approximately equals 1.0 - 1.5 MK) loops of the same active region, using the same method of Dynamic Stereoscopy to reconstruct the 3D geometry. We reconstruct the 3D-coordinates x(s), y(s), z(s), the density n(sub e)(s), and temperature profile T(sub e)(s) of 35 individual loop segments (as function of the loop coordinate s) using EIT 195 A and 284 A images. The major findings are: (1) All loops are found to be in hydrostatic equilibrium, in the entire temperature regime of T(sub e) = 1.0 - 2.5 MK; (2) The analyzed loops have a height of 2-3 scale heights, and thus only segments extending over about one vertical scale height have sufficient emission measure contrast for detection; (3) The temperature gradient over the lowest scale height is of order dT/ds is approximately 1 - 4 K/km; (4) The radiative loss rate is found to exceed the conductive loss rate by about two orders or magnitude, making thermal conduction negligible to explain the temperature structure of the loops; (5) A steady-state can only be achieved when the heating rate E(sub H) matches the radiative loss rate in hydrostatic equilibrium, requiring a heat deposition length lambda(sub H) of the half density scale height lambda, predicting a scaling law with the loop base pressure, EH varies as p(sub 0 exp 2). This favors coronal heating mechanisms that operate near the loop footpoints; (6) We find a reciprocal correlation between the loop pressure p(sub 0) and loop length L, i.e. p(sub 0) varies as 1/L, implying a scaling law of the steady-state requirement with loop length, i.e. E(sub H ) varies as 1/L(exp 2). The heating rate shows no correlation with the loop-aligned magnetic field component B(sub z) at the footpoints, but is correlated with the azimuthal field B(sub phi) = Bz(RDelta Phi/L) of a twisted loop, and is thus consistent with heating mechanisms based on field-aligned currents.