Radiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona

We present a series of numerical simulations of the quiet-Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun’s atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy.     

Observation of chromospheric evaporation during the solar maximum mission

A sample of flares detected in 1980 with the Bent Crystal Spectrometer and the Hard X-Ray Burst Spectrometer on the Solar Maximum Mission satellite has been analysed to study the upward motions of part of the soft X-ray emitting plasma. These motions are inferred from the presence of secondary blue-shifted lines in the Ca XIX and Fe XXV spectral regions during the impulsive phase of disk flares. Limb flares do not show such blue-shifted lines indicating that the direction of the plasma motion is mainly radial and outward. The temporal association of these upward motions with the rise of the thermal phase and with the impulsive hard X-ray burst, as well as considerations of the plasma energetics, favour the interpretation of this phenomenon in terms of chromospheric evaporation. The two measureable parameters of the evaporating plasma, emission measure and velocity, depend on parameters related to the energy deposition and to the thermal phase. The evaporation velocity is found to be correlated with the spectral index of the hard X-ray flux and with the rise time of the thermal emission measure of the coronal plasma. The emission measure of the rising plasma is found to be correlated with the total energy deposited by the fast electrons in the chromosphere by collisions during the impulsive phase and with the maximum emission measure of the coronal plasma.     

Interchange stability of a rapidly rotating magnetosphere

A rotation-dominated magnetosphere is unstable to magnetic flux-tube interchange motions if and only if the plasma content of a unit magnetic flux tube is a decreasing function of distance from the spin axis. For a spin-aligned dipole field the marginally stable distribution is approximately ρr^9/2 = constant, where ρ is the plasma mass density at the radial distance r in the equatorial plane. Plasma filling the Jovian magnetosphere from internal sources would initially violate this stability criterion so that interchange motions would act to establish the marginally stable distribution.     

The covariance of latitudinal and longitudinal motions of small magnetic features

We study the covariance of longitudinal and latitudinal motions of small magnetic features after subtracting long-term averages of differential rotation and meridional flow. The covariance is generally interpreted as Reynolds stress and linked to the equatorward transport of angular momentum. Using high-resolution magnetograms taken daily with the NSO Vacuum Telescope on Kitt Peak, we determine large-scale motions by a two-dimensional crosscorrelation analysis of pairs of consecutive daily observations from which active regions are excluded, i.e., we analyze the motions of small magnetic features. In the present work, we focus on 107 day pairs obtained during the year 1988 and on 472 day pairs taken in selected intervals from 1978 to 1990. We find that all covariance values are very small (below 250 m² s⁻²), which is about one to two orders of magnitude smaller than the values from sunspot measurements derived by other authors. At active region latitudes, the masking process increases the noise, which increases the chance that the covariances at these latitudes are not significantly different from zero. We find that the results depend strongly on the temporal averaging involved. Daily unaveraged crosscorrelations lead to no apparent correlation between the residual velocities, while in the monthly averages of the 1988 data, we find a covariance of −37 ± 15 m² s⁻² at 45° with a linear correlation of −0.59, which is significantly different from zero and has the right sign for an equatorial transport of angular momentum. When we average over longer time periods, the covariance values decrease again. The annual averages of the 1978–1990 data show both no significant covariances and the smallest errors. These small covariances imply that the motions of small magnetic features do not reflect the transport of angular momentum via the mechanism of Reynolds stress. Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.     

Periodic Motion Along Solar Filaments

We present observations of four filaments that exhibit large-amplitude periodic mass motion. Observations are obtained using the high resolution (2″) and high cadence (1 min) Hα telescope system at the Big Bear Solar Observatory (BBSO). The motions found in these events are along the axis of the filaments, and are associated with the activity of a nearby flare or filament. The most characteristic properties of these motions are long period (≥ q80 min), large distance (≥ q 4 × 10⁴ km) of mass transport at much higher velocity (≥ q 30 km s⁻¹) than ever detected from filament motions. The velocity, period, dimension and damping timescale measured for these motions are presented, and discussed to identify the most plausible restoring force and damping mechanism.     

The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System

Starting from the four-body problem a generalization of both the restricted three-body problem and the Hill three-body problem is derived. The model is time periodic and contains two parameters: the mass ratio ν of the restricted three-body problem and the period parameter m of the Hill Variation orbit. In the proper coordinate frames the restricted three-body problem is recovered as m → 0 and the classical Hill three-body problem is recovered as ν → 0. This model also predicts motions described by earlier researchers using specific models of the Earth–Moon–Sun system. An application of the current model to the motion of a spacecraft in the Sun perturbed Earth–Moon system is made using Hill's Variation orbit for the motion of the Earth–Moon system. The model is general enough to apply to the motion of an infinitesimal mass under the influence of any two primaries which orbit a larger mass. Using the model, numerical investigations of the structure of motions around the geometric position of the triangular Lagrange points are performed. Values of the parameter ν range in the neighborhood of the Earth–Moon value as the parameter m increases from 0 to 0.195 at which point the Hill Variation orbit becomes unstable. Two families of planar periodic orbits are studied in detail as the parameters m and ν vary. These families contain stable and unstable members in the plane and all have the out-of-plane stability. The stable and unstable manifolds of the unstable periodic orbits are computed and found to be trapped in a geometric area of phase space over long periods of time for ranges of the parameter values including the Earth–Moon–Sun system. This model is derived from the general four-body problem by rigorous application of the Hill and restricted approximations. The validity of the Hill approximation is discussed in light of the actual geometry of the Earth–Moon–Sun system. This revised version was published online in July 2006 with corrections to the Cover Date.     

The role of plasma interchange motion for the formation of a plasmapause

Mcllwain's electric and magnetic field distributions (E3H and M2) have been used to calculate the drift path of plasma density irregularities taking into account plasma interchange motion driven by the gravitational and inertial forces acting on the whole mass of the plasma elements.It has been shown that there is a region in the magnetosphere which is unstable with respect to the interchange motion of the cold plasma element. Any plasma hole in the background density drifts ultimately toward an asymptotic trajectory. Along this trajectory the inward gravitational force is balanced by the outward inertial force averaged over one revolution around the Earth. This asymptotic trajectory, along which all plasma holes ultimately accumulate, is identified with the equatorial plasmapause. The maximum velocity for the interchange motion is proportional to the excess (or defect) of density in the plasma element, and inversely proportional to the integrated Pedersen conductivity. Plasma detachment is shown to occur preferentially in the post-midnight sector.     

A short wavelength instability in the neutral sheet of the earth's geomagnetic tail

In an earlier paper, Bowers (1973), ion plasma oscillations were found to be unstable in the steady state developed by Cowley (1972) for the neutral sheet in the Earth's geomagnetic tail. In this paper a similar stability analysis is carried out but for a different steady state, suggested by Dungey, with the result that unstable waves with frequencies near the electron plasma frequency are found. In the Dungey steady state the current necessary for magnetic field reversal is carried by plasma originating from both the magnetosheath and the lobes of the tail. This modifies the steady state proposed by Alfvén and subsequently developed by Cowley in which all the current is carried by plasma from the lobes of the tail thereby fixing the cross-tail potential Φ. With magnetosheath plasma present the value of Φ is no longer fixed solely by parameters in the lobes of the tail but the cross-tail electric field is still assumed localised in the dusk region of the sheet as in the Cowley model due to the balance of charge required in the neutral sheet. The value of Φ can be expected to increase as magnetic flux is transported to the tail which inflates and causes flux annihilation because the magneto-sheath plasma in the neutral sheet has insufficient pressure to keep the two lobes of the tail apart. The Vlasov-Maxwell set of equations is perturbed and linearised enabling a critical condition for instability to be found for modes propagating across the tail. Typically, this condition requireseΦ≳KT _m whereT _m is the temperature of magnetosheath electrons. The instability occurs in the presence of cold plasma which hasE×B drifted into the neutral sheet from the lobes of the tail. This contrasts with the usual two stream instability which is stabilised by the cold plasma. Once precipitated the instability may be explosive provided current disruption occurs, for then a further increase in Φ will result which drives a greater range of wave numbers unstable thereby causing even more turbulence and an even larger cross-tail electric field. Because of this behaviour the instability may be a trigger for a substorm.     

Conjecture about a hurricane system in the Jovian atmosphere

Kuiper (1972) had suggested that the Great Red Spot (GRS) of Jupiter is a giant hurricane. We present further arguments in support of this idea and propose that it may also apply to the smaller vortices such as the white and brown ovals (barges). Our estimates indicate that the spin-down time-constants for these Jovian vortices are significantly shorter than the observed lifetimes. Thus, the motions must be sustained through the continued release of internal energy. In analogy with the CISK mechanism for the terrestrial hurricane, transport of water vapor, which is observed on Jupiter, may provide the latent energy to fuel the motions. The energy the planet emits must be transported upwards; therefore its troposphere should be convectively unstable. In such an atmosphere, the proposed solar driven meridional circulation is multicellular, of the Ferrel-Thomson type. If the energy transport from the planetary interior is accelerated by the upward motions in the circulation, eastward zonal jets develop such as observed in the equatorial region. But if the upward flow of energy is impeded by the prevailing downward motions in the meridional circulation (which occur, for example, near 20 latitude), we propose that the convective instability is amplified. The conditions then are more favorable for the development of hurricanes which may appear in the form of the GRS and the white and brown ovals. The GRS with its large size and long life time (indicating that it is very deep) is unique, and we suggest that it may have been induced by meteor impact.     

Transport of angular momentum and chemical species by anisotropic mixing in stellar radiative interiors

Small levels of turbulence can be present in stellar radiative interiors due to, e.g., the instability of rotational shear. In this paper we estimate turbulent transport coefficients for stably stratified rotating stellar radiation zones. Stable stratification induces strong anisotropy with a very small ratio of radial‐to‐horizontal turbulence intensities. Angular momentum is transported mainly due to the correlation between azimuthal and radial turbulent motions induced by the Coriolis force. This non‐diffusive transport known as the Λ‐effect has outward direction in radius and is much more efficient compared to the effect of radial eddy viscosity. Chemical species are transported by small radial diffusion only. This result is confirmed using direct numerical simulations combined with the test‐scalar method. As a consequence of the non‐diffusive transport of angular momentum, the estimated characteristic time of rotational coupling (≲100 Myr) between radiative core and convective envelope in young solar‐type stars is much shorter compared to the time‐scale of Lithium depletion (∼1 Gyr) (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of the motions of fast stars based on observations with the Pulkovo normal astrograph

Astrometric CCD observations of 1123 stars with large proper motions (μ > 300 mas yr⁻¹) from the LSPM (I/298) catalog in the declination zone +30°–+70° have been carried out with the Pulkovo normal astrograph since 2006. The observational program includes mostly stars that previously have not entered into high-accuracy projects to determine the proper motions. Our studies are aimed at determining new proper motions of fast stars in the HCRF/UCAC3 system and searching for stars with invisible companions in the immediate Galactic neighborhoods of the Sun. Having analyzed about 10 000 CCD frames, we have obtained the equatorial coordinates of 414 program stars in the HCRF/UCAC3 system at an accuracy level of 10–50 mas and determined their new proper motions. To derive the proper motions, we have used the data from several star catalogs and surveys (M2000, CMC14, 2MASS, SDSS) as early epochs. The epoch differences range from 5 to 13 years (on average, about 10 years); the mean accuracy of the derived proper motions is 4–5 mas yr⁻¹. For 70 stars, we have revealed significant differences between the derived proper motions and those from the LSPM and I/306A catalogs (these proper motions characterize the mean motion of the photocenter in 50 years or more). Apart from systematic errors, these differences can result from the existence of invisible components of the program stars.     

Two-dimensional transport of solids in viscous protoplanetary disks

Large-scale radial transport of solids appears to be a fundamental consequence of protoplanetary disk evolution based on the presence of high temperature minerals in comets and the outer regions of protoplanetary disks around other stars. Further, inward transport of solids from the outer regions of the solar nebula has been postulated to be the manner in which short-lived radionuclides were introduced to the terrestrial planet region and the cause of the variations in oxygen isotope ratios in the primitive materials. Here, both outward and inward transport of solids are investigated in the context of a two-dimensional, viscously evolving protoplanetary disk. The dynamics of solids are investigated to determine how they depend on particle size and the particular stage of protoplanetary disk evolution, corresponding to different rates of mass transport. It is found that the outward flows that arise around the disk midplane of a protoplanetary disk aid in the outward transport of solids up to the size of CAIs s and can increase the crystallinity fraction of silicate dust at 10 AU around a solar mass star to as much as ∼40% in the case of rapidly evolving disks, decreasing as the accretion rate onto the star slows. High velocity, inward flows along the disk surface aid in the rapid transport of solids from the outer disk to the inner disk, particularly for small dust. Despite the diffusion that occurs throughout the disk, the large-scale, meridonal flows associated with mass transport prevent complete homogenization of the disk, allowing compositional gradients to develop that vary in intensity for a timescale of one million of years. The variations in the rates and the preferred direction of radial transport with height above the disk midplane thus have important implications for the dynamics and chemical evolution of primitive materials.     

Lorentz Force: A Possible Driving Force for Sunspot Rotation

Zhao and Kosovichev (Astrophys. J. 591, 446, 2003) found two opposite sub-photospheric vortical flows in the depth range of 0 – 12 Mm around a fast rotating sunspot. So far there is no theoretical model explaining such flow motions. In this paper, we try to explain this phenomenon from the point of view of magnetic flux tubes interacting with large-scale vortical motions of plasma. In the deeper zone under the photosphere, the magnetic force may be less than the nonmagnetic force of plasma. The vortical flow located there twists the flux tube and magnetic free energy is built up in the tube. In the shallower zone under the photosphere, the magnetic force may be greater than the nonmagnetic force. Thus, part of the stored magnetic free energy is released to drive the plasma to rotate in two opposite directions, e.g., in the depth ranges of 0 – 3(5) and 9 – 12 Mm. In addition, we also define a vector of nonpotential magnetic stress τ, which can be related to flare occurrence. It is calculated for the active region NOAA 10930 on 11 December 2006. We find that: i) the integral of its line-of-sight (LOS) stress successively increases around the magnetic neutral line (MNL) prior to and during the flare and decreases to a minimum after the flare; ii) the integral of its transverse stress exceeds the integral of its LOS component by one order of magnitude over the whole field of view; iii) the transverse stress first points toward the MNL, then along it, and finally it points away from it. We need other data to verify whether or not the magnetic energy is transported in the horizontal direction to the neutral line, and then partly changes into the energy in LOS direction before and during the flare.     

Gamma-ray bursts from unstable Poynting-dominated outflows

Poynting-flux driven outflows from magnetized rotators are a plausible explanation for gamma-ray burst engines. We suggest a new possibility for how such outflows might transfer energy into radiating particles. We argue that, in a region near the rotation axis, the Poynting flux drives non-linearly unstable large-amplitude electromagnetic waves (LAEMW) that 'break' at radii     where the MHD approximation becomes inapplicable. In the 'foaming' (relativistically reconnecting) regions formed during the wave breaks, the random electric fields stochastically accelerate particles to ultrarelativistic energies which then radiate in turbulent electromagnetic fields. The typical energy of the emitted photons is a fraction of the fundamental Compton energy     with     plus additional boosting due to the bulk motion of the medium. The emission properties are similar to synchrotron radiation, with a typical cooling time ∼10⁻³ s. During the wave break, the plasma is also bulk accelerated in the outward radial direction and at larger radii can produce afterglows due to interactions with the external medium. The near equipartition fields required by afterglow models may be due to magnetic field regeneration in the outflowing plasma (similar to field generation by LAEMW in laser–plasma interactions) and mixing with the upstream plasma.     

Two-dimensional observations of the velocity field in and around sunspots

Doppler spectroheliograms of sunspots and their surroundings have been obtained with a spatial resolution approaching one second of arc and a time resolution of 20 s per frame. Observations of 5 sunspots, located 18°, 45°, 56°, 60° and 72° from the disk center respectively, showed considerable long-lived fine structure and, in particular, indicated the following:

1. The Evershed outflow terminated in spoke-like structures that constitute the ragged outer boundary of the penumbra. Some of these spokes extended more than 8000 km beyond the average outer boundary.
2. Although there was considerable long-lived fine structure of both Doppler polarities in the extra-penumbral photosphere, the spatially-averaged horizontal flow was outward for roughly 10000 km beyond the outer boundary of the penumbra. This extra-penumbral velocity field was distinct from the Evershed flow, and, in particular, did not represent its extension beyond the end of the penumbral spokes.

Although these results are based on observations of relatively few sunspots, they do suggest that if magnetic fields are carried outward from sunspots by material motions, then these motions are more like the supergranulation than an extension of the Evershed velocity.     

On the formation of coronal cavities

We present a theoretical study of the formation of a coronal cavity and its relation to a quiescent prominence. We argue that the formation of a coronal cavity is initiated by the condensation of plasma which is trapped by the coronal magnetic field in a closed streamer and which then flows down to the chromosphere along the field lines due to lack of stable magnetic support against gravity. The existence of a coronal cavity depends on the coronal magnetic field strength; with low strength, the plasma density is not high enough for condensation to occur. Furthermore, we suggest that prominence and cavity material is supplied from the chromospheric level. Whether a coronal cavity and a prominence coexist depends on the magnetic field configuration; a prominence requires stable magnetic support.We initiate the study by considering the stability of condensation modes of a plasma in the coronal streamer model obtained by Steinolfson et al. (1982) using a 2-D, time dependent, ideal MHD computer simulation; they calculated the dynamic interaction between outward flowing solar wind plasma and a global coronal magnetic field. In the final steady state, they found a density enhancement in the closed field region with the enhancement increasing with increasing strength of the magnetic field. Our stability calculation shows that if the density enhancement is higher than a critical value, the plasma is unstable to condensation modes. We describe how, depending on the magnetic field configuration, the condensation may produce a coronal cavity and/or initiate the formation of a prominence.NRC Research Associate.     

Vlasov – Maxwell,Self-consistent Electromagnetic Wave Emission Simulations in the Solar Corona

1.5D Vlasov – Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the context of solar physics. The simulations mimic the plasma emission mechanism and Larmor-drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that a 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to the Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. The generated perturbations consist of two parts: i) non-escaping (trapped) Langmuir type oscillations, which are localised in the regions of density inhomogeneity, and are highly filamentary, with the period of appearance of the filaments close to electron plasma frequency in the dense regions; and ii) escaping electromagnetic radiation with phase speeds close to the speed of light. When the density gradient is removed (i.e. when plasma becomes stable to the Larmor-drift instability) and a low density super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, the plasma emission mechanism generates non-escaping Langmuir type oscillations, which in turn generate escaping electromagnetic radiation. It is found that in the spatial location where the beam is injected, standing waves, oscillating at the plasma frequency, are excited. These can be used to interpret the horizontal strips (the narrow-band line emission) observed in some dynamical spectra. Predictions of quasilinear theory are: i) the electron free streaming and ii) the long relaxation time of the beam, in accord with the analytic expressions. These are corroborated via direct, fully-kinetic simulation. Finally, the interplay of the Larmor-drift instability and plasma emission mechanism is studied by considering a dense electron beam in the Larmor-drift unstable (inhomogeneous) plasma. The latter case enables one to study the deviations from the quasilinear theory.     

The cooling of a sunspot

A mechanism is proposed to explain the cooling of a sunspot in terms of the detailed interactions between the magnetic field and the convective motions. The mechanism provides that an axially symmetric concentration of magnetic field deforms the normal supergranule cell pattern below the sunspot into a radial outflow of plasma over a region of diameter 60 Mm.The flow occurs at depths where the magnetic and kinetic energy densities are approximately equal ( 5 Mm) and is described in terms of a Carnot refrigeration cycle. Application of the hydromagnetic equations to a very simple model shows that, because the magnetic field concentration causes the outflow, the field will itself decay in a time short compared with the lifetime of a spot. However, a slightly more sophisticated model does suggest conditions under which this decay is considerably reduced.Observations of the outward drift of magnetic knots around sunspots and of supergranule-type surface motions extending radially outwards from the penumbra of a spot to the nearest faculae are discussed in relation to the mechanism.     

Latitudinal transport by barotropic waves in Titan's stratosphere.: I. General properties from a horizontal shallow-water model

We present a numerical study of barotropic waves in Titan's stratosphere based on a shallow-water model. The forcing of the zonal flow by the mean meridional circulation is represented by a relaxation towards a barotropically unstable wind profile. The relaxation profile is consistent with observations and with previous results from a 3D general circulation model. The time constant of the forcing that best matches the northward eddy-transport of zonal momentum from the 3D model is τ∼5 Titan days. The eddy wind field is a zonal wavenumber-2 wave with a peak amplitude about 10% of the mean wind speed. The latitudinal transport of angular momentum by the wave tends to keep the flow close to marginal stability by carrying momentum upgradient, from the core of the jets into the low latitudes. Although the strongest eddy motions occur at the latitudes of the wind maxima, the strongest mixing takes place at the barotropically unstable regions, close to ±30° and spanning about 30° in latitude. An eddy-mixing time constant of the order of 1 Titan day is inferred within these regions, and of a few tens of days within regions of stable flow. Horizontal gradients in transient tracer fields are less than 10% of the latitudinal gradient of the meridional tracer profile. Cassini's detection of such waves could provide a direct observation of wind speeds at stratospheric levels.     

Magnetic Field Line Transport in Anisotropic Magnetic Turbulence: Anomalous, Quasilinear, and Percolative Regimes Versus the Kubo Number

The transport of plasma and of energetic particles because of magnetic turbulence is relevant to many space plasmas, ranging from the planetary magnetospheres to the solar corona and to the heliosphere. Various transport regimes for magnetic field lines can be obtained depending on the Kubo number. Here we show, by means of a numerical simulation, that the Kubo number also determines the level of chaos of the field lines. Weak chaos, closed magnetic surfaces, and anomalous transport regimes are obtained for R≪ 1; widespread chaos, destroyed magnetic surfaces, and quasilinear scaling of the diffusion coefficient for R ≳ 0.3; and global stochasticity as well as percolation scaling of the diffusion coefficient for R≫ 1. This revised version was published online in July 2006 with corrections to the Cover Date.