Sixty Years in Solar Physics

I recount my career in solar physics beginning at Ondřejov Observatory in 1948 and ending with my ∼30 year stay at the Laboratory of Space Research in Utrecht.     

Spectral theory of electromagnetic induction in a radially and laterally inhomogeneous earth

Summary The partial differential equations of electromagnetic induction in a 3-D Earth of inhomogeneous conductivity are reduced to a system of ordinary differential equations of the 2nd order for the spectral coefficients of the field.

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au am nu¶rt; ¶rt; maum u¶rt;uu u m ¶rt;¶rt; n n¶rt;umu n¶rt; um ¶rt;uua au m n¶rt;a ¶rt; nma uum n.

     

Dynamical tides in close binary systems

The aim of the present paper will be to deduce the explicit form of differential equations which govern dynamical tides in close binary systems, with simplifications which are permissible for the mass-point model (Section 2), as well as for one exhibiting finite but high internal density concentration (Section 3). It is pointed out that, whereas the exact formulation of the problem leads to a simultaneous system of equations of sixth order (fourth in the inviscid case), this order reduces to four (or two for inviscid fluids) for the mass-point model; and to five (three for inviscid case) if the density concentration is high but finite.In the last section of this paper the coefficientsC _i,j which specify the amplitudes of the individual partial tides are explicitly formulated as functions of the time.     

Vibrational stability of double-star Roche model

The aim of the present paper will be to extend the methods of our previous investigations (Kopal, 1980, 1987) by employing the Clairaut coordinates (in which the radial component is identified with the total potential) to analyze the nature of small oscillations about the equilibrium form of Roche double-star model (identical, in fact, with zero-velocity surfaces of the restricted problem of three bodies).Linearized equations of this problem have been set up in Clairaut coordinates, and solved in a closed form. This solution turns out to be closely analogous to that obtained already for the rotating single-star Roche model, and discloses that (like in the preceding case) the terms secular in time appear already in the linear approximation. However, whether or not a retention of nonlinear terms in the equations of motion can regain secular stability of the respective configurations remains yet to be clarified by future investigations.     

Gravity-darkening in eclipsing binaries

A quantitative analysis of the ellipticity effect in close binary systems of the W Ursae Maioris type with spectroscopically known mass-ratios discloses that the photometric ellipticities of these variables are, in general, more than twice as large as the dynamical ellipticities (due to the geometrical distortion alone) computed for contact models of centrally condensed stars. If, moreover, this excess of the photometric over dynamical ellipticity is attributed to the phenomenon of gravity-darkening over distorted surfaces of the constituent components, this darkening must be present to a considerablylarger degree than that predicted by the theory of radiative transfer — a result difficult to reconcile with the existence of extensive sub-surface convection zones in late-type Main-Sequence stars. If, on the other hand, gravity-darkening is present in W UMa-type systems in the amount predicted by the theory (let alone in the presence of sub-surface convection), the only effective way of reconciling the theory with the observations would be to assume that the mean fractional radii of their constituent components are appreciablylarger than those appropriate for contact models in which the two components just fill the largestclosed Roche equipotentials capable of containing their mass. In other words, it would appear that the W UMa-type stars considered in this paper may constitute a single dumb-bell figure rather than two distinct components; and that the observed variations of light, colour or radial velocity are invoked by the axial rotation (and consequent variable cross-section) or this dumb-bell figure rather than to the contribution of individual stars.