K. Schwartz

The melting of asteroidal-sized bodies by unipolar dynamo induction from a primordial T Tauri sun

This paper examines the heating of asteroidal parent bodies by electrical induction during early solar evolution and prior to positioning of the sun onto the main sequence. Under the conditions assumed, which include a high initial solar spin rate, interplanetary electric fields of order 1 V/m would have existed in frames of reference comoving with the planets, leading to electrical heating from joule losses in the asteroidal interiors. The mechanism additionally requires the high plasma efflux characteristic of T Tauri objects and the presence of a circumstellar obscuration of the type commonly associated with early stellar objects. The proper combination of circumstellar obscuration, solar spin, solar wind flow, and starting planetary temperatures is shown to lead to asteroidal heating competitive with that found for a class of fossil radioactive species. The time dependence of the solar spin and plasma flow are shaped so as to be consistent with current views on the evolution to T Tauri objects and of the spin down of stars. Calculations also include cases of joint heating by fossil radionuclides and electrical induction, and show a complicated relationship due to the intrinsic nonlinearity of the electrical heating mechanism. Implications regarding the pre-main sequence dynamics of the sun are contained in the hypothesis of electrical heating if the contribution from radionuclides and gravitational accretion can be shown to be insufficient to account for the heating episode. Finally, some consequences of the mechanism applied to planets in the presence of an intense solar wind are considered.

A theory for the interpretation of lunar surface magnetometer data

The solution to the problem of the motion of the Moon relative to spatial irregularities in the interplanetary magnetic field is found. The lunar electrical conductivity is modeled by a two-layer conductivity profile. For the interaction of the Moon with the corotating sector structure of the interplanetary magnetic field it is found that the magnetic field in the lunar shell is the superposition of an oscillatory uniform field, an oscillatory dipole field and anoscillatory field that is toroidal about the axis of the motional electric field. With various lunar conductivity models and the theory of this paper, lunar surface magnetometer data can be quantitatively interpreted to yield information on the conductivity and consequently the temperature of the lunar core.

UNIPOLAR INDUCTION IN THE MOON AND A LUNAR LIMB SHOCK MECHANISM.

The unipolar induction mechanism is employed to calculate electric field profiles in the interior of a chemically homogeneous Moon possessing a steep radial thermal gradient characteristic of long-term radioactive heating. The thermal models used are those of Fricker, Reynolds, and Summers. From the magnetic field, the magnetic back pressure upon the solar wind is found. The electric field profile is shown to depend only upon the activation energy,Eo, of the geological material and the radial gradient of the reciprocal temperature. The current is additionally dependent upon the coefficient of the electrical conductivity function but only by a scale factor. Since the Moon is experimentally known to correspond to the case of weak interaction with the solar wind, the magnetic back pressure is calculated without the need for an iterative procedure. The results indicate that a hot Moon can yield sufficient current flow so that the magnetic back pressure is observable as a vestigial limb shock wave using an activation energy of about 2/3 eV together with a conductivity coefficient of about 103 mhos/m. Such matter is approximated by diabase-like composition, although the result that both the activation energy and coefficient enter into the current determination does not rule out the possibility of a match with other similar substances. The calculations are entirely consistent with earlier results which indicated a model where the unipolar current density is dominated by a high impedance surface layer and a strong shock wave is inhibited. In addition to the magnetic back pressure, the integration of the current continuity equation permits current densities and joule heating rates to be calculated, though the magnitude of the latter for present solar wind conditions is not thermally important.

Polarized magnetic field fluctuations at the apollo 15 site: possible regional influence on lunar induction.

High-frequency (5 to 40 millihertz) induced lunar magnetic fields, observed at the Apollo 15 site near the southeastern boundary of Mare Imbrium and the southwestern boundary of Mare Serenitatis, show a strong tendency toward linear polarization in a direction radial to the Imbrium basin and circumferential to the Serenitatis basin, a property that could be indicative of a possible regional influence on the induction.

Electromagnetic induction in spherical cap current layers under lunar and terrestrial conditions

Abstract We present the theory of electromagnetic induction in spherical cap current sheets of arbitrary angular size, with arbitrary axisymmetric integrated electrical conductivity variations and located at any radial position with respect to the surface of observation. The external time-varying magnetic field may be arbitrarily oriented with respect to the current layer cap and the induced fields are derived for vacuum boundary conditions appropriate to terrestrial induction and plasma confinement boundary conditions relevant to lunar induction in the solar wind or magnetosheath plasmas. Numerical evaluations show the induced magnetic field as a function of position over the current sheet cap, depth to the current layer, size of the cap, integrated electrical conductivity of the current sheet, and frequency of the fluctuating external field. The local vertical magnetic field component and the horizontal field component which is normal to the periphery of the cap exhibit peak inductive responses above the edge of the current sheet for external magnetic fields perpendicular to the axis of the cap. Thus, induced magnetic field fluctuations observed over the edge of a conductivity anomaly may exhibit a highly directional, or polarized behavior. This may provide an explanation for the asymmetric character of induced magnetic field fluctuations observed on the lunar surface.

Topology of induced lunar magnetic fields

Using the asymmetric theory of lunar induction derived by Schubertet al. (1973a), we have obtained the total and induced magnetic field line structure within the Moon and the diamagnetic cavity. Total field distributions are shown for orientations of the oscillating interplanetary field parallel, perpendicular and at 45° to the cavity axis. Induced field lines are shown only for the orientations of the interplanetary field parallel and orthogonal to the cavity axis. When compared with the field lines derived using the long wavelength limit of spherically symmetric vacuum induction theory, the configurations obtained using the asymmetric theory exhibit significant distortion. For all orientations of the interplanetary field, the field lines are strongly compressed on the sunlit hemisphere because of the confining solar wind pressure at the lunar surface and the exclusion of the field by the lunar ‘core’. Field line compression is also observed in the antisolar region in agreement with the experimental observations of Schubertet al. (1973b). and Smithet al. (1973). For the parallel orientation of the interplanetary field, antisolar compression is caused by cavity confinement of the induced field. For the interplanetary field perpendicular to the cavity axis there is, in addition to compression by the cavity boundary, redistribution of field lines from the sunlit to the night side. In this case field lines entering the Moon just forward of the limb pass through the lunar ‘crust’ on the night side and then exit forward of the limb. This phenomenon manifests itself as a displacement of the null in the induced magnetic field at the surface sunward of the limb, in striking similarity to the magnetospheric field lines of the Earth.

The early despinning of the Sun

It is shown that if the Sun passed through a T Tauri stage, then a mass loss of only 15% would be sufficient to despin the Sun to an angular velocity of 0 (10−5 rad/sec) at 107 years without the additional braking effect of an enhanced magnetic field. Thus the present Sun could have a core rotating at most ten times faster than its surface.