Magnetic configurations of streamer structures in the solar atmosphere

We consider two types of streamer structures observed in the solar atmosphere. Structures of the first type are medium-scale configurations with scale lengths comparable to the scale height in the corona, kT/mg = 100 thousand km, which appear as characteristic plasma structures in the shape of a dome surrounding the active region with thin streamers emanating from its top. In configurations of this type, gravity plays no decisive role in the mass distribution. The plasma density is constant on magnetic surfaces. Accordingly, the structure of the configurations is defined by the condition ψ = const, where ψ is the flux function of the magnetic field. Structures of the second type are large-scale configurations (coronal helmets, loops, and streamers), which differ from the above structures in that their scale lengths exceed the scale height in the corona. For them, gravity plays a decisive role; as a result, instead of the magnetic surfaces, the determining surface is BgradΦ = 0. We constructed three-dimensional images of these structures. Some of the spatial curves called “visible contours” of the B_r = 0 surface are shown to be brightest in the corona. We assume that the helmet boundaries and polar plumes are such curves.     

On the stationary configuration of the heliospheric sheet

The expansion of solar coronal plasma is considered for the model described in Koutchmy et al. (1999). In addition to a spherical solar surface, the initial configuration represents a heliospheric sheet of dense plasma in the dipole equatorial plane. The heliospheric-sheet current decreases with distance as 1/r ², with its sign being opposite to the sign of the initial-dipole current. The latter follows from the fact that the plasma sheet is denser than the surrounding corona and that the equilibrium condition for the sheet in the gravitational and magnetic fields is satisfied. The field lines of this configuration are nearly straight. We have obtained a general solution of the steady-state MHD equations, which depends not only on distance r but also on latitude θ. Applicability of the solution to interpreting observational data, in particular, those obtained from the Ulysses spacecraft, is discussed.     

On asymptotics of low-frequency oscillations of the liquid core: 2. Frequency dependence of the inertial core-mantle coupling

New, unique information on the inertial and dissipative coupling of the liquid core and the mantle has been retrieved from modern high-precision (radiointerferometer and GPS) data on tidal variations in the rotation velocity and nutation of the Earth. Comparison of theoretical and observed data provided new estimates for the dynamic flattening of the outer liquid and the inner solid cores, mantle quality factor, viscosity of the liquid core, and electromagnetic coupling of the liquid core and the mantle [Molodensky, 2004, 2006]. As was shown in the first part of the paper [Molodensky, 2008] (further referred to as [I]), generation of eddy flows in Proudman-Taylor columns, whose orientation is controlled by the topography of the liquid core-mantle boundary, should be taken into account for correct estimation of the inertial coupling (see formulas (8) and (34) in [I]). The range of periods within which this effect plays a significant role is determined by the decay time of these flows. This time is estimated in the paper for the case where dissipation is related to viscous friction at the core-mantle boundary or with the electromagnetic coupling of the liquid core and the mantle. Because of significant uncertainties in modern data on the viscosity of the liquid core, the magnetic field intensity at the core-mantle boundary, and the electrical conductivity of the lower mantle, the dissipative coupling of the liquid core and the mantle cannot be calculated as yet. However, as shown in the paper, the decay time of eddy flows is connected with the attenuation time of subdiurnal free nutation and with the liquid core viscosity. This enables the estimation of the frequency dependence of the dissipative coupling in a fairly wide range. It is shown that the range of periods for which relations (8) and (34) in [I] are valid encompasses the best-studied length-of-day variations and, therefore, these relations are applicable to analysis of the majority of modern data.     

On the Upper Bound of the Liquid Core Viscosity

By using Molodensky and Sasao (1995a) and Molodensky and Groten (1998) an approach of expansion in powers of the small parameter =(+)/ (where + and are the frequencies of nutational motion in space and in a mantle-fixed reference frame, respectively, is tidal frequency) a theory of diurnal Earth tides and nutation for a realistic model of the Earth with an inhomogeneous, viscous liquid core and an anelastic mantle is constructed. It is shown that our approach is self-consistent for semi-annual, annual, and principal nutational components (when ||1/180). By comparing the results of modern VLBI-nutational data and the results of our calculations, we have found the region of possible values of the parameters which describe the anelastic properties of the Earth's lower mantle and the viscosity of the liquid core. It is shown that modern VLBI-data are about six orders of magnitude more sensitive to the liquid core viscosity than modern seismic data or Earth free oscillations data.     

Anelastic parameters of the mantle and Love numbers consistent with modern VLBI data

Summary The domain of the possible values of the mantle's anelasticity parameters and Love numbers based on modern VLBI-data is found. A new method of the joint analysis of VLBI- and tidal data is suggested, which gives possibility to obtain better estimations of the Q-factor of the free core nutation.     

On the effect of oceanic tides on the inertial coupling between the liquid core and the mantle

The amplitudes and phases of forced nutation and diurnal earth tides depend significantly on the moment of forces between the liquid core and mantle of the Earth, resulting from the differential rotation of the core. The solution to the dynamic problem of rotation of an imperfectly elastic mantle with an imperfectly liquid core and an ocean indicates that the predominant role is played by the so-called core-mantle inertial coupling (related to the effect of hydrodynamic pressure in the liquid core on the ellipsoidal core-mantle boundary). The magnitude of this coupling depends significantly not only on the dynamic flattening of the liquid core but also on the elastic and inelastic properties of the mantle, as well as on the amplitudes and phases of oceanic tides. In this paper, the effects of oceanic tides on the magnitude of inertial coupling between the liquid core and the mantle and on the period and damping decrement of free nearly diurnal nutation are estimated.     

On the Dynamical Effects of the Mantle in the Theory of Nutations

The influence of inerial forces in the mantle on its tidal deformations is considered. It is shown that the main role is played the corrections, described by spheroidal deformations, which result in corrections of nutational amplitudes of about –0.076 mas for the prograde semi-annual component, –0.056 mas for the retrograde annual component, 0.099 mas for the retrograde 19-year component, and –0.024 mas for the prograde 14-day component. These values exceed the errors of modem VLBI-measurements significantly (being of the order of 0.02-0.03 mas with the exception of the main nutational component); the effect of toroidal deformations is negligibly smalt in comparison with the accuracy of the VLBI-measurements, and for any practical purposes need not be considered.     

On the Mechanism of the Secular Tidal Acceleration of the Solid Inner Core and the Viscosity of the Liquid Core

As is known, the secular deceleration of the Earth's diurnal rotation is explained mainly by the tidal friction in the ocean. Below we consider this mechanism in some detail, taking into account also elastic deformations of the mantle under the action of ocean loading and the interaction between the tide-generating body, ocean tidal wave, liquid outer core, and solid inner core. It is shown that elastic displacements of the core-mantle boundary under the action of ocean loading are of about the same amplitude and phase as the elastic loading displacements of the Earth's outer surface. As a result, side by side with the mechanism of secular deceleration of diurnal rotation of the mantle, there are also (1) the opposite mechanism of secular acceleration of diurnal rotation of the outer liquid core and of the solid inner core and (2) the mechanism of excitation of differential rotation in the liquid core. Taking these effects into account, we compare theoretical and modern observed data on the eastward drift of the solid inner core. It is shown that the best agreement may be obtained if the turbulent viscosity of the liquid core is about 2 × 10 ³ Poise     

Temporal variations in the tidal response of the medium in the vicinities of the sources of catastrophic earthquakes

The idea of predicting earthquakes by continuously monitoring temporal variations in the tidal response of the medium was suggested by Beaumont and Berger in 1974. However, it became possible to implement the idea only recently. This possibility has arisen due to the deployment of Global Seismic Network (GSN), which collects the data on tidal tilts and gravity in the epicenters of strong earthquakes before and after the strongest events. In this paper, we present the results of model analytical and numerical calculations of the elastic displacements of the Earth’s surface caused by the earthquakes and their preparatory processes. The analytical calculations are limited to the model of a uniform elastic halfspace; the numerical calculations, in addition to this model, also cover the models with radially heterogeneous distributions of elastic moduli in the crust and in the upper mantle, which are determined by the PREM model. We describe the results of modeling temporal variations in the tidal response of the medium in the vicinity of the source of a catastrophic earthquake. The model of seismic source is specified by the length and the orientations of the fault plane and by the value of the discontinuity in the tangential component of the displacement vector on the opposite sides of the fault. The model is based on the GPS data on the horizontal and vertical displacements of the Earth’s surface. We suggest the method for determining temporal changes in the tidal response of the medium in the seismically active regions. This method improves the sensitivity and time resolution of the standard techniques of sliding-window analysis by more than an order of magnitude. The comparative analysis of temporal variations in the tidal response of the medium in the zones of the magnitude 9 earthquake in Japan (March 9, 2011) illustrates the described approach.