A two-dimensional model for a solar prominence

A two-dimensional magnetohydrostatic model of a vertical prominence sheet is set up by allowing slow variations of the magnetic field and plasma properties with height. The width of the prominence is found to decrease with height and in many cases the field lines become less curved, while the strength of the horizontal magnetic field increases with height, in agreement with observations. Since we are only considering a local analysis, the model applies to a general prominence sheet, whether of Kippenhahn-Schlüter or Kuperus-Raadu type. The challenge in the future is to understand the detailed fine-scale microstructure which takes place in the mould formed by the present global macro-models.On leave from: Departament de Fisica, Universitat de les Illes Balears, E-07071, Palma de Mallorca, Spain.     

A two-dimensional solar spectrometer

A precise two-dimensional positioning device has been developed for use in conjunction with a resonant scattering spectrometer to study the spatial distribution of solar velocity fields. The principle of operation and constructional details are discussed and the experimental performance is evaluated. As an illustration of its use preliminary data obtained from a meridional scan are presented.Proceedings of the 14th ESLAB Symposium on Physics of Solar Variations, 16–19 September 1980, Scheveningen, The Netherlands.     

A two-dimensional model for a solar prominence: Effect of an external magnetic field

Using analytical approximations we study the effects of different external magnetic configurations on the half-width, mass, and internal magnetic structure of a quiescent solar prominence, modelled as a thin vertical sheet of cool plasma. Firstly, we build up a zeroth-order model and analyse the effects produced by a potential coronal field or a constant- force-free field. This model allows us to obtain the half-width and mass of the prominence for different values of the external field, pressure and shear angle. Secondly, the effects of these external magnetic configurations on a two-dimensional model proposed by Ballester and Priest (1987) are studied. The main effects are a change of the half-width with height, an increase of the mass, a decrease of the magnetic field strength with height and a change in the shape of the magnetic field lines.     

A simplified model solar atmosphere

A simplified representation of the temperature distribution in the solar photosphere is proposed: ( ₀) = ₀ - ₁ log ₀. An expression is derived for the emergent continuous spectrum from the simple model. The limitations and applications of the simple model are discussed.     

A nonlinear RLC solar cycle model

A simplified, monoparametric model, based on the Van der Pol nonlinear RLC electric oscillator, is found capable of describing the shape and related morphological properties (such as the Waldmeier effect) of the sunspot cycles. The model can also exhibit long periods of sunspot inactivity of the Maunder Minimum type. According to the model, the significant rise-to-fall time asymmetry of the most recent cycles suggests that it is unlikely that another cycle suppression will occur in the forthcoming decades. The complete sunspot record and the system's attractor are successfully emulated, given the sunspot number at cycle maxima.     

A model of solar differential rotation

An axisymmetric model for the Sun's differential rotation based upon a mechanism for angular momentum transport by compressible convection is developed. Convective heat transport is also considered. The model is simplified by the neglect of meridional circulation and radiative heat transport but is otherwise a self-consistent one because no adjustable parameters are used and the effective transport coefficients are expressed explicitly in terms of superadiabaticity of stratification rather than assigned externally. The model predictions agree satisfactorily with the observed rotation of the photosphere and with helioseismology data. The dependence of the rotation law, produced by the model, on rotation rate of a Sun-like star is discussed.     

A study of solar preflare activity using two-dimensional radio and SMM-XRP observations

We present a study of type III activity at meter- decameter wavelengths in the preflare phase of the 1986 February 3 flare using data obtained with the Clark Lake Multifrequency Radioheliograph. We compare this activity with similar type III burst activity during the impulsive phase and find that there is a displacement of burst sources between the onset and end times of the activity. A comparison of this displacement at three frequencies suggests that the type III emitting electrons gain access progressively to diverging and different field lines relative to the initial field lines. The energetics of the type III emitting electrons are inferred from observations and compared with those of the associated hard X-ray emitting electrons. The soft X-ray data from SMM-XRP shows enhanced emission measure, density and temperature in the region associated with the preflare type III activity.On leave from Indian Institute of Astrophysics, Kodaikanal, Tamil Nadu, India.     

A simple model for solar isorotational contours

The solar convective zone, or SCZ, is nearly adiabatic and marginally convectively unstable. But, the SCZ is also in a state of differential rotation, and its dynamical stability properties are those of a weakly magnetized gas. This renders it far more prone to rapidly growing rotational baroclinic instabilities than a hydrodynamical system would be. These instabilities should be treated on the same footing as convective instabilities. If isentropic and isorotational surfaces coincide in the SCZ, the gas is marginally (un)stable to both convective and rotational disturbances. This is a plausible resolution for the instabilities associated with these more general rotating convective systems. This motivates an analysis of the thermal wind equation in which isentropes and isorotational surfaces are identical. The characteristics of this partial differential equation correspond to isorotation contours, and their form may be deduced even without precise knowledge of how the entropy and rotation are functionally related. Although the exact solution of the global SCZ problem in principle requires this knowledge, even the simplest models produce striking results in broad agreement with helioseismology data. This includes horizontal (i.e. quasi-spherical) isorotational contours at the poles, axial contours at the equator and approximately radial contours at mid-latitudes. The theory does not apply directly to the tachocline, where a simple thermal wind balance is not expected to be valid. The work presented here is subject to tests of self-consistency, among them the prediction that there should be a good agreement between isentropes and isorotational contours in sufficiently well-resolved large-scale numerical magnetohydrodynamics simulations.     

Heated solar atmosphere: A one-fluid model

A one-fluid model of the solar atmosphere is considered. The corona is heated by waves propagating out from the Sun, and profiles for temperature, flow speed and number density are obtained. For a relatively quiet Sun the inwards heat flux in the inner corona is constant in T 5–6 × 10⁵ K and the temperature maximum is reached for r — R = 0.4 — 0.5 R where R is the solar radius. The number density in the inner corona decreases with an increasing particle flux.     

A model of the solar convection zone

A model of the convection zone is presented which matches an empirical model atmosphere (HSRA) and an interior model. A mixing length formalism containing four adjustable parameters is used. Thermodynamical considerations provide limits on two of these parameters. The average temperature-pressure relation depends on two or three combinations of the four parameters. Observational information on the structure of the outermost layers of the convection zone, and the value of the solar radius limit the range of possible parameter combinations. It is shown that in spite of the remaining freedom of choice of the parameters, the mean temperature-pressure relation is fixed well by these data.The reality of a small density inversion in the HSRA model is investigated. The discrepancy between the present model and a solar model by Mullan (1971) is discussed briefly.     

A model of solar flares and faculae

Theories of solar flares based on the storage of energy (usually as magnetic energy) in the solar atmosphere are shown to be incompatible with observational data.The sunspot energy deficit and the photospheric faculae both involve energy fluxes comparable with the flare requirement ( 3 × 10²⁹ erg s^–1). Both also require a subsurface system of waves or oscillations, perhaps those discussed by Danielson and Savage and by Wilson. The flare model proposed is based on a temporary diversion of this energy carried by Alfvén waves through spots and magnetic elements or micro-pores; the calculated plasma perturbation velocity in the umbra is about 6 km s^–1 for a major flare.In the atmosphere the wave energy divides into two parts to produce the cool, stationary optical flare and the particle flare. The first part is dissipated around flux tubes which are mainly horizontal in the chromosphere and which tend to concentrate along the magnetic neutral line (B = 0). Each tube vibrates individually as a taut wire in a viscous fluid, to excite the fluid just outside the tube. The second part of the energy emerges along tubes mainly vertical in the chromosphere and is converted to shock waves in the corona and then to particle energy for the radio and X-ray flare and the blast wave.The model includes white-light faculae, quasi-permanent X-ray and fast-particle emissions, sympathetic flares and surges. An unambiguous test would be provided by observations of plasma motions of a few kilometres per second in spots and micro-pores.     

A kinematic model of a solar flare

Hyder advocated the idea that the optical (H) flares can be identified with the response of the solar chromosphere to an infalling material stream resulting from the disparition brusque of a prominence. Since some flares are observed without any apparent association with infalling streams, in this paper we examine the possibility of identifying the optical flare with the response of the chromosphere to a supersonic disturbance, i.e., a shock, propagating downward. The undisturbed chromosphere is represented by the Harvard-Smithsonian Reference Atmosphere and the evolution of the shock is evaluated with the use of the CCW (Chisnell, Chester, Whitham) approximation based on the theory of characteristics. It is shown that the chromosphere is heated by the shock and that radiation is enhanced, and that the enhanced radiation terminates the shock around the height of the temperature minimum. Numerical results obtained and possible future improvements of this type of study are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A plasmoid model for the solar wind

A model describing magnetized plasmoids as a possible origin of the solar wind is discussed. The magnetized plasmoids are assumed to be created and accelerated to a very high speed through reconnection processes from small-scale magnetic loops. Afterward, the plasmoids are considered to be nearly in a relaxed state under magnetic helicity conservation and to expand freely and linearly. Characteristics of such plasmoids with finite are examined. The results show remarkable agreement between the model predictions and spacecraft observations including temperature characteristics such as the dependence on the heliocentric distance and ion mass. The validity of the assumptions and the applicability of the model are also discussed.     

A model of the quiet solar atmosphere

The solar atmosphere may be divided into a number of isolated active components and a quiet residue. On the largest scale the latter is dominated by a general dipole magnetic field of strength 1–2 G; its observable components are flux concentrations in supergranule boundary regions (SBRs), spicules, mottles and polar plumes. The velocity field in the SBRs is discussed. There are continuous gas streaming motions up and down between the photosphere and the corona; spicules may be mainly downward moving gas.A unifying model is developed of these various components, as well as the heating mechanism of the whole quiet atmosphere. Highly ordered velocity fields of the cell, together with a gravitational wave, cause a vertical magnetic force tube to collapse below a critical level; the result is an upward eruption of a vortex ring at the Alfvén velocity. The complex mass velocity pattern may explain spicules, mottles and plumes, as well as unobservable streaming motions.The quiet atmosphere is divided into regions above SBRs and those above the inner parts of the cells. Hydromagnetic eruptions from the former may account for the entire heat requirement of the atmosphere. The model atmosphere has a chromosphere-corona transition layer which bulges upwards above the SBRs and so conforms with EUV data. The energy and mass balances in this solar atmosphere are considered, and it is also shown to be consistent with the radio data.     

A model of the magnetized solar wind

A steady state, inviscid, single fluid model of the solar win d in the equatorial plane is developed using magneto-hydrodynamics and including the heat equation wit h thermal conduction but no non-thermal heating (i.e. a conduction model). The effects of solar rotation and magnetic field are included enabling both radial and azimuthal components of the velocity and magnetic fields to be found in a conduction model for the first time.The magnetic field cuts off the thermal conduction far from the sun and leads to an increased temperature at 1 AU and relatively small changes to the radial velocity and density. Models have been found which fit the experimental electron densities in 2 R < r < 16 R . These models predict at 1 AU a radial velocity of 300–380 km·sec^-1 and a density of 8 protons·cm^-3. The latter velocity corresponds to a density profile obtained by Blackwell and Petford (1966) during the last sunspot minimum, and is about 100 km·sec^-1 above that found in previous conduction models which fit the coronal electron densities. The radial velocities are now consistent with the mean quiet solar wind, as are the densities when the experimental values are averaged over a magnetic sector. However, the azimuthal velocity at 1 AU is only 1–2 km·sec^-1 which is low compared to the experimental values, as found by previous authors.     

A nonlinear model of the solar dynamo

The role of nonlinearity is explored in a mean-field dynamo model. Magnetic fields are amplified by the combined action of the and-effects, and as the field's intensity increases the Lorentz force becomes important. Torsional oscillations and meridional circulations are driven by the Lorentz force, and the oscillations are consistent with those measured on the surface of the Sun. The torsional oscillations feedback in the induction equation and saturate the magnetic field's growth by quenching differential rotation. This model can also help us understand the processes responsible for the range of periods seen in the activity cycles of other stars like the Sun.     

A preliminary theoretical line-blanketed model solar photosphere

Solar Physics - A preliminary theoretical solar model is presented that produces closer agreement with observation than has been heretofore possible. The qualitative advantages and shortcomings of...     

A model exciter for type III solar radiobursts

In an earlier paper (Harvey and Aubier, 1973) the large scale radial electron density gradient in the corona and solar wind was shown to cause the phase velocity of plasma waves to decrease as they propagate away from the Sun, thus leading to appreciable Landau damping of the plasma waves. It is proposed here that this same phase velocity decrease creates conditions which facilitate the stabilisation of a beam of exciter electrons of finite duration, provided that three conditions are fulfilled. Two of these conditions concern the velocity-time distribution of the exciter electrons at their point of ejection from the Sun, while the third is simply that, above a certain altitude, the coronal electron density decreases with altitude r faster than r ^?2. The plasma wave source is then associated with the leading edge of the electron stream. The spatial density of the power converted into plasma waves is calculated as a function of position and time, and is shown to be independent of the nature of the stabilisation mechanism. The maximum of this power density is found to move outwards from the Sun at a uniform speed when a simple electron injection model with a Maxwellian velocity distribution is introduced.     

A torsional wave model for solar radio pulsations

One of the widely accepted models for solar radio pulsations invokes radial oscillations of a magnetic flux tube. Due to acoustic, radiative damping, this theory does not easily explain the long length of the pulse trains, the large modulation depths or the great stability of the pulse repetition rate often observed. Torsional waves efficiently modulate synchrotron emission, and since they do not undergo radiative damping, can produce stable pulse repetition rates and long pulse trains.     

A bimodal model of the solar wind speed

Until the ULYSSES spacecraft reached high latitude, the only means for measuring the solar wind velocity in the polar regions was from radio scattering observations (IPS), and these remain the only way to measure the velocity near the sun. However, IPS, like many remote sensing observations, is a line-of-sight integrated measurement. This integration is particularly troublesome when the line-of-sight passes through a fast stream but that stream does not occupy the entire scattering region. Observations from the HELIOS spacecraft have shown that the solar wind has a bimodal character which becomes more pronounced near the sun. Recent observations from ULYSSES have confirmed that this structure is clear at high latitudes even at relatively large solar distances. We have developed a method of separating the fast and slow contributions to an IPS observation which takes advantage of this bimodal structure. In this paper I will describe the technique and its application to IPS observations made using the receiving antennas of the EISCAT incoherent backscatter radar observatory in northern Scandinavia.