The magnetic field in the solar atmosphere

This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes.     

Vertically self-gravitating ADAFs in the presence of toroidal magnetic field

Force due to the self-gravity of the disc in the vertical direction is considered to study its possible effects on the structure of a magnetized advection-dominated accretion disc. We present steady-sate self similar solutions for the dynamical structure of such a type of the accretion flows. Our solutions imply reduced thickness of the disc because of the self-gravity. It also imply that the thickness of the disc will increase by adding the magnetic field strength.     

Simulating the generation of the solar toroidal magnetic field by differential rotation

Within the kinematic dynamo theory, we construct a mathematical model for the evolution of the solar toroidal magnetic field, excited by the differential rotation of the convective zone in the presence of a poloidal field of a relic origin. We use a velocity profile obtained by decoding the data of helioseismological experiments. For the model of ideal magnetic hydrodynamics, we calculate the latitudinal profiles of the increasing-with-time toroidal field at different depths in the solar convection zone. It is found that, in the region of differential rotation, the excited toroidal field shows substantial fluctuations in magnitude with depth. Based on the simulations results, we propose an explanation for the “incorrect polarity” of magnetic bipolar sunspot groups in solar cycles.     

Ion-acoustic waves in the solar atmosphere

A model for ion-acoustic waves in the solar atmosphere is presented. In the limit of strongly magnetized plasma this model leads to the Zakharov-Kuznetsov equation which possesses a flat solitary wave solution. An initial-value problem for this equation is solved numerically to show a transition of the flat solitary waves into spherical solitary waves. The paper suggests further developments of an ion-acoustic wave theory that may improve our knowledge of ion-acoustic waves and lead to the possibility of their being detected in the solar atmosphere.     

Temperature waves in the solar atmosphere

The properties of five-minute temperature waves in the photosphere are investigated. The phase and amplitude relations of temperature and acoustic waves are deduced. It is expected that the five-minute oscillations represent a mixture of acoustic and temperature waves. The temperature waves are generated due to linear interaction with acoustic waves.It is well known that concurrent with the acoustic waves, temperature or heat waves can appear in the case of nonadiabatic disturbances (Landau and Lifshitz, 1959). The temperature waves are dissipative damped waves. Propagation of nonadiabatic hydrodynamic waves in a stratified medium have been considered by Zhugzdha (1983). If stratification of heat exchange exists, a linear interaction of hydrodynamic and temperature waves arises. The temperature waves must be present in the solar atmosphere.     

Average photospheric poloidal and toroidal magnetic field components near solar minimum

Average (over longitude and time) photospheric magnetic field components are derived from 3 Stanford magnetograms made near the solar minimum of cycle 21. The average magnetograph signal is found to behave as the projection of a vector for measurements made across the disk. The poloidal field exhibits the familiar dipolar structure near the poles, with a measured signal in the line Fe i 5250 Å of 1 G. At low latitudes the poloidal field has the polarity of the poles, but is of reduced magnitude ( 0.1 G). A net photospheric toroidal field with a broad latitudinal extent is found. The polarity of the toroidal field is opposite in the nothern and southern hemispheres and has the same sense as subsurface flux tubes giving rise to active regions of solar cycle 21.These observations are used to discusse large-scale electric currents crossing the photosphere and angular momentum loss to the solar wind.Now at Kitt Peak National Observatory, Tucson, Ariz. 85726, U.S.A.     

Excitation of solar gravity waves

The interaction between convection and gravity waves are simulated numerically in a model closely corresponding to the physical conditions in the solar interior.The penetration of convective elements into the stably stratified interior is shown to generate gravity waves. The energy efficiency of this generation is less than 0.1 %. The simulations also show that the convective overshoot region is very shallow, 0.02–0.06 pressure scaleheights.     

On the energy release by magnetic field dissipation in the solar atmosphere

The energy release by Joule magnetic-field dissipation in the solar atmosphere is discussed. It is shown that the heating is unimportant in the case of granulation and intergranular space. In the case of spot features the additional temperatures T_r with the accounting of the radiation losses are no more than 30° for small new spots, 1° for the large umbrae and 300° for bright points in large umbrae. This effect gives the possibility to suggest a hypothesis on the source of temperature inhomogeneity in the spot umbra and the nature of bright points. In the chromosphere the dissipation is negligible.On leave from the Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), U.S.S.R., Moscow region, p/o Academgorodok.     

Acoustic waves in the lower solar atmosphere

The propagation and dissipation of acoustic waves in the lower solar atmosphere is studied. The level of shock formation is computed for various initial conditions. It is shown that shocks form rather low in the atmosphere and that this result does not depend critically on the assumed initial conditions.     

Generation of waves by the solar magnetic field polarity reversal

In this paper an excitation of waves is considered during the time interval in which the undisturbed magnetic field changes its direction. If this interval is taken to be 2 years, which is shorter than the 11-year cycle, then the undisturbed components of the magnetic field may be linearly dependent on time and independent of the coordinates. The excitation of waves is due to the undisturbed stationaryV ₀ flow with divV ₀ = 0 and with (V ₀ rot₀) = constant.We use the local Cartesian coordinate system, which is immovable towards the solar centre, and consider the case when the toroidal component of the undisturbed magnetic field changes its sign simultaneously with one of the axial components. The third component does not change its direction.The efficiency of the enhancement of the magnetic field and velocity disturbances depends on the Alfvén wave frequency, _A. When _A = 0, the component of the disturbed velocity, which is directed along the constant component of the undisturbed magnetic field, increases. In this case the shear waves excite the carrier (high) frequency (KV ₀), whereK is the wave vector. Due to the shear instability the amplitude of the velocity increases during 1 year before the moment of reversal of the global magnetic field polarity (RGMFP) for an arbitrary latitude. It reaches a maximum at RGMFP and decreases in the next year. When _A > 0, then the amplitudes of the disturbed values reach maxima before the moment of RGMFP, and when _A < 0, they reach maxima after it.We argue that the shear waves propagate from middle latitudes to the pole and equator. Using the results of the analytical solutions and leaning on the evidence of the observational data (Gigolashvili and Japaridze, 1992), we derive the result that the component of the undisturbed magnetic field, which is perpendicular to the solar surface, changes its sign simultaneously with the toroidal component.     

Thermal-convective-instability of a stellar atmosphere in the presence of a nonlinear magnetic field

Thermal-convective-instability of a stellar atmosphere is investigated in the presences of a nonlinear magnetic field. A model proposed by Roberts (1981) in the context of neutron stars is used. The simultaneous effect of both nonlinear magnetic field and rotation is also considered. The criteria obtained for monotonic instability generalize the criterion derived by Defouw (1970) in the absence of magnetic field and rotation.     

Alfvén waves in the solar atmosphere

The nonlinear propagation of Alfvén waves on open solar magnetic flux tubes is considered. The flux tubes are taken to be vertical and axisymmetric, and they are initially untwisted. The Alfvén waves are time-dependent axisymmetric twists. Their propagation into the chromosphere and corona is investigated by solving numerically a set of nonlinear time-dependent equations, which couple the Alfvén waves into motions parallel to the initial magnetic field (motion in the third coordinate direction is artificially suppressed). The principal conclusions are: (1) Alfvén waves can steepen into fast shocks in the chromosphere. These shocks can pass through the transition region into the corona, and heat the corona. (2) As the fast shocks pass through the transition region, they produce large-velocity pulses in the direction transverse to B _o. The pulses typically have amplitudes of 60 km s^–1 or so and durations of a few tens of seconds. Such features may have been observed, suggesting that the corona is in fact heated by fast shocks. (3) Alfvén waves exhibit a strong tendency to drive upward flows, with many of the properties of spicules. Spicules, and the observed corrugated nature of the transition region, may therefore be by-products of magnetic heating of the corona. (4) It is qualitatively suggested that Alfvén waves may heat the upper chromosphere indirectly by exerting time-dependent forces on the plasma, rather than by directly depositing heat into the plasma.     

Force-free magnetic fields in the solar atmosphere

Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reflectionless propagation of acoustic waves in the solar atmosphere

The possibility that vertical acoustic waves with frequencies lower than the cutoff frequency corresponding to the temperature minimum pass this minimum is investigated. It is shown that the averaged temperature profile in the solar atmosphere can be approximated by several so-called reflectionless profiles on which the acoustic waves propagate without internal reflection. The possibility of the penetration of vertical acoustic waves, including low-frequency ones, into the solar corona is explained in this way.     

Parametric generation of acoustic-gravity waves in the solar atmosphere

Based on a plane isothermal solar-atmosphere model, we investigate the parametric generation of acoustic-gravity waves (AGWs) in the approximation of a fixed field for vertically propagating disturbances. Both nonpropagating and propagating AGWs are shown to be generated at the difference frequency via the nonlinear interaction of primary waves in the frequency range “forbidden” for the propagation of AGWs during their linear generation. An acoustic wind has been found to be formed in the solar atmosphere at zero difference frequency; its velocity increases with height in inverse proportion to the decreasing ambient density. We study the nonlinear generation of AGWs at the second harmonic during the interaction of disturbances from the forbidden frequency range.     

Reflection of acoustic waves in the real solar atmosphere

We use space-time variations of velocity restored from observations to isolate acoustic waves propagating into upper layers of the atmosphere. At reflection, acoustic ten-minute waves penetrate into the evanescent layers of the photosphere up to the temperature-minimum layers, and five-minute waves reach the layers of the lower chromosphere.     

Parametric generation of magnetoacoustic-gravity waves in the solar atmosphere

Based on a plane-parallel isothermal solar model atmosphere permeated by a horizontal magnetic field whose strength is proportional to the square root of the plasma density and in the approximation of a specified field for vertically propagating and nonpropagating magnetoacoustic-gravity waves, we consider the nonlinear interaction between the corresponding disturbances, to within quantities of the second order of smallness. We investigate the efficiency of the nonlinear generation of waves at difference and sum frequencies and of an acoustic flow (wind) as a function of the magnetic-field strength and the excitation frequency of the initial disturbances at the lower atmospheric boundary.     

Propagation of cylindrical relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of cylindrical relativistic shock waves in the presence of a constant azimuthal magnetic field or in its absence for the medium, where the nucleon number density is uniform. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.     

Propagation of plane relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of plane relativistic shock waves in the presence of a transverse magnetic field for the medium, where the nucleon number density obeys a power law of distance from the plane of explosion. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.