On the Mechanism of the Magnetic Dynamo of the Planets Sh. Sh. Dolginov Academy of Sciences, Moscow, U.S.S.R. Results of testing the effectiveness of the theory of precessional dynamos in the genera- tion of the magnetic fields of the planets are presented. It is shown that the magnetic state of Earth and of the planets Mars, Jupiter, and Venus can be satisfactorily described by the formula 17 — IT v I J 3 "i fli — fl3 -^j- -fff — sin«3 where H, v, T, 0, and a are the dipole fields, volumes of liquid cores, periods of rotation, rates of precession, and angles between precession vector and angular rotation, respec- tively, for the planets and Earth. The v, corresponds to known models of the internal structure. It is shown that the magnetic state of Mercury satisfies this formula if the dynamic flattening of the planet t = 5.7 x 10~3 - 8.3 x 10s. The idea that the magnetic field of the With a model of a purely iron-nickel core, Earth is related to the operation of some the radioactive elements U and Th are forced sort of dynamo mechanism in its highly con- out because of their chemical and physical ductive liquid core has now been largely con- incompatibility with iron at the pressures firmed. present in the core. Thermal sources in the Modern kinematic models of the terrestrial core have been related to processes of con- magnetic dynamo have been found capable tinuing differentiation of matter in the of describing the basic peculiarities of the Earth: the settling of heated iron, melted terrestrial magnetic field (refs. 1 and 2). At from the mantle (ref. 3) and the latent heat the same time, no physical theory of the ter- of melting, liberated upon crystallization of restrial field as yet presented considers the the outer core at the boundary with the inner actual parameters and processes in the core solid core (ref. 4). of the Earth. This is particularly true con- In order for thermal convection to occur in cerning the uncertainty of the mechanism the liquid core of the Earth, the temperature generating the terrestrial dynamo. Three gradient must exceed the adiabatic gradient. mechanisms are known: In a number of publications during 1971- 1973 (ref. 8), concepts of the isothermal 1. Convection in the core under the in- state of the core were discussed. A stable fluence of thermal sources (refs. 3 and thermal state is incompatible with thermal 4). convection in the core, to which the genera- 2. Convection under the influences of tion of the magnetic field is related. Ideas of forces of gravity (ref. 5). the thermal conditions of the Earth's core 3. Convection in the core caused by pre- have changed, on the basis of assumptions of cession of the axis of rotation of the the presence of radioactive potassium K40 in Earth (refs. 6 and 7). the core (ref. 9). 493 494 COSMOCHEMISTRY OF THE MOON AND PLANETS The effectiveness of thermal sources in any liquid in the core, leading to the motion nec- mechanism of generation of the magnetic essary for the operation of the dynamo. In field has been assumed to be low, because of the final analysis, the energy of the magnetic the low efficiency of thermal machines. Ac- dynamo is taken from the kinetic energy in cording to one hypothesis (ref. 5), the pro- the Earth's rotation. cesses of differentiation of material indicated The details of the precessional mechanism by Urey and Verhoogen are actually in- generating the magnetic field have not been volved in the generation of the magnetic field, worked out. There are contradictory opinions but only because of the gravitational energy concerning its effectiveness. Braginskiy (ref. released during these processes. Convection 12) turned his attention to the fact that the in the core is caused by direct upwelling of speed of the liquid under the influence of the impurities of light silicon, accompanying the Poincare force fluctuates with the frequency process of crystallization and sinking of of the main rotation <,> and therefore cannot heavy iron. directly influence slow processes in the dy- The hypothesis of the gravitational nature namo. On the other hand Dolginov (ref. 13) of the "motor" driving the Earth's dynamo notes that the precession of a liquid in a encounters great difficulties in light of cur- nonspherical envelope results in the appear- rent hypotheses of the nonhomogeneous for- ance of flows of a spiral nature that are sim- mation of the planets (refs. 10 and 11). As ilar to tidal flows. Flows of a spiral nature concerns thermal sources, their role is at facilitate the generation of magnetic fields least as great in the creation of the necessaiy (ref. 14). conductivity and viscosity in the core. At the present time, the magnetic fields of Malkus suggested that the precession of the Earth, Venus, Mars, Jupiter, and Mer- the Earth was the motive force of the mag- cury have been studied. For the first four netic dynamo. The precession of the planets planets, certain models of the internal struc- is caused by the action of the gravitational ture are known (refs. 15-20), as well as the fields of the Sun and other celestial bodies on parameters of rotation and dynamic flatten- the equatorial bulge of the rotating planets. ing (refs. 21 and 22), and magnetic fields The presence of precession, at an angular (refs. 23-27). velocity n, results in an additional angular This paper presents a model and results of acceleration n = [0 X «] and an additional a test of the effectiveness of the mechanism inertial force Fr, — — />[n X «] X f. Malkus of the precessional dynamo in the generation called this the Poincare force, after the man of the magnetic fields of the Earth, Mars, and who first solved analytically the problem of Jupiter. Furthermore, conditions are studied the motion of a fluid in a precessing spheroi- under which the magnetic states of Venus dal container. The experiments performed by and Mercury can be explained, on the basis Malkus showed that with certain relation- of the hypothesis of precession as the motive ships of w and n in the precessing liquid, tur- force of the planetary dynamo. bulent flow arises, which is not predicted by The approach is based on the following as- classical theory. sumptions : The rate of precession of the planet is di- rectly proportional to its dynamic flattening, 1. The processes of generation of the field and independent of its radius and mass. Since in the planets are similar in terms of model- the core and mantle of the Earth have some- ing and are determined by a number of di- what differing dynamic flattening, the grav- mensionless parameters. ity fields of the Sun and the Moon create 2. The magnetic fields are proportional to different torques on the core and mantle, the volumes of the liquid cores of the planets causing stress both in the core and in the (ref. 28). mantle, which tend to equalize the rates of 3. The rates of convection of matter are the two precessions. These stresses act on the proportional to the Poincare force Frj MAGNETIC DYNAMO OF THE PLANETS 495 —' [<o X n] X r, where o> is the angular veloc- the metallic state. According to Zharkov et ity of rotation, and n is the angular velocity al. (ref. 19), this occurs at depths of of precession. r/Rj = 0.8. The magnetically active-area ap- 4. Under these conditions, a simple depen- parently begins at a point ranging from dence between the dipole fields of two planets r/Rj = 0.7 to r/Rj = 0.15. The volume of the 1 and 2 is assumed to exist: magnetically active area of Jupiter, with V, T2 a sin these dimensions, exceeds the volume of the Yl-2 sin , (1) liquid core of the Earth by some 1600 times. Now, formula (1) and the data of table 1 where y is the ratio of the dipole fields -~- lead to the following values of calculated and on the surface at the magnetic equator; « is measured field strength ratios between the the angle between vectors <o and n; V is the Earth and Mars (ye-m using the various volume of the liquid core, and T the rotation models), Jupiter and Earth (jj-e) ; ye-m = period. Volume Vi is the liquid core of the 315,180,140,110, and 130, respectively, while Earth, and is assumed known (ref. 19). measured ye-m = 470. Calculated yt-e = 22, while measured •/,-„ = 13. We note the moderately good degree to Earth, Mars, Jupiter which the measured and calculated values of dipole field ratios of the three rapidly rotat- We present below the values of the param- ing planets agree with this tremendous differ- eters T, n, a, and H0 of three rapidly rotating ence in volumes and fields. planets. Formula (1) has one unknown, V->, the volume of the liquid core of the second Venus planet. The dimensions of the core of Mars The planet Venus apparently does not have have been very approximately determined. a magnetic field of its own which exceeds 10 The measured values of radius, mass, and gammas (refs. 24 and 27). It is natural to moment of inertia are satisfied in various expect that formula (1) will take note of models with significantly differing core di- this fact with some accuracy. According to mensions Rc. In the model of Kozlovskaya the data from the trajectory measurements (ref. 15), Rc = 960 km; in the model of Ring- on Mariner 5 and radar studies of the wood (ref.