THE END OF THE IRON-CORE

AGE*

R. A. L Y T T L E T O N Institute of Astronomy, Cambridge, England

and Jet Populsion Laboratory, Pasadena, Calif., U.S.A.

(Received 1 December, 1972) Abstract The terrestrial planets aggregated essentially from small particles, to begin as solid cool bodies with the same general compositions, and there is no possibility of an iron-core developing within any of them at any stage. Their differing internal and surface properties receive ready explanation from their different masses which determine whether the pressures within are sufficient to bring about phase-changes. The claim that the terrestrial core can be identified by means of shockwave data as nickel-ironis based on theoretical misconception, whereas the actual seismic data establish an uncompressed-density value much lower than any such mixture could have. The onset of the Ramsey phase-change in the Earth takes the form of a rapid initial collapse to produce a large core in metallic state which thereafter continues to grow secularly as a result of radioactive heating and leads to reduction of surface-area at long last adequate to account for folded and thrusted mountain-building. The hypothesis implies a similar but retarded evolution for Venus. The Moon and Mars are too small in mass to have undergone the phase-change to a metallic core, and can have no resulting dipole field, nor can they develop terrestrial-typemountains. Effects resulting from a transition corresponding to the 20°-discontinuity will occur for Mars, including large-scale rifting at the surface, but will not occur on the Moon. Finally brief reference is made to subjective non-scientific factors associated with continued efforts to rely on the iron-core hypothesis despite its lack of any success in rendering the properties of the Earth explicable.

1. The Mechanism of Formation of Planets In recent years theories o f the origin o f the planets have m a i n l y t u r n e d a w a y f r o m the earlier so-called c a t a s t r o p h i c processes a n d have come to concentrate u p o n ideas o f the Sun acquiring the p l a n e t a r y m a t e r i a l b y o r d e r l y m e a n s t h a t m i g h t well occur to any star. One such n o t i o n relies on a p o s t u l a t e d stage in the d e v e l o p m e n t o f the Sun itself a c c o r d i n g to which, if the Sun condensed within a galactic gas-cloud, it might develop a s u r r o u n d i n g r o t a t i n g nebula, which as a result o f cooling w o u l d come to c o n t a i n dust-particles suitable for a c c u m u l a t i o n to small solid planets. However, a Sun so f o r m e d w o u l d r o t a t e rapidly, a n d a d d i t i o n a l mechanisms need to be i n t r o d u c e d (such as t h a t o f e n o r m o u s l y strong m a g n e t i c coupling o f the Sun to aggregations within the nebula) in o r d e r to rid the Sun o f its excessive r o t a t o r y m o m e n t u m . O n the other hand, i f the m a t e r i a l o f the n e b u l a were c a p t u r e d f r o m an interstellar g a s - a n d - d u s t c l o u d b y an already-existing slowly r o t a t i n g Sun, which capture could occur b y d y n a m i c a l interaction involving the cloud a n d a second a d j a c e n t star, or as a result o f accretion by the Sun simply passing t h r o u g h a cloud at sufficiently low relative speed, the necessary a n g u l a r m o n e n t u m to give the great range c o m p a r e d with the size o f the Sun c o u l d be acquired f r o m the outset, w i t h o u t m u c h affecting the solar r o t a t i o n , as a result o f the circumstances o f the m e c h a n i s m o f capture. Since the G a l a x y contains a great m a n y * Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973. The Moon 7 (1973) 422-439. All Rights Reserved Copyright © 1973 by D. Reidel Publishing Company, Dordrecht-Holland

THE END OF THE IRON-CORE AGE

423

such clouds, planetary systems if initiated in this way may be very numerous even if only a minute proportion of stars have chanced to undergo such an event. Yet another mechanism proposed is removal of material from a former companion-star to the Sun, either by grazing encounter with a third star, or by supernova explosion of the companion, the recoil of which removes the main mass but leaves a small wisp of suitably constituted material captured by the Sun. On any of these mechanisms, or simply by direct postulate, the initial solar nebula may be regarded as principally gaseous material, itself mainly hydrogen and helium in stellar proportions, but also essentially containing dust-particles, either from the outset or by subsequent cooling, amounting to about l~o of the total mass. But there can be no possibility of planets forming by self-gravitation within the gaseous component of such a nebula for the simple reason that the volume-density, which would be of the order of 10 -13 g cm -3, would be far and away too small, by several powers of 10, to counteract the strong field of the Sun. Even if a gaseous condensation were to start to form, the solar differential forces would immediately shear it apart and prevent it developing. On the other hand the presence of a considerable proportion of material in the form of dust-particles leads to an entirely different situation, as regards them, of the greatest importance to the growth of planets. For whereas volume-elements of the gas will describe small-circle orbits keeping always at the same distance from the general equatorial plane of the nebula, solid particles m u s t describe inclined orbits in planes through the centre of the Sun, since the gas can exert negligible force upon them. Accordingly, collisions between the particles will occur, and the ultimate effect will be to redistribute the whole of the dust-component into the form of an extremely thin disk, with its plane perpendicular to the angular momentum of the whole, and with each areal-element having circular motion with speed appropriate to its distance from the Sun. If the total quantity of dust is such that the nebula were optically opaque, or had anywhere near such an implied density, as will be shown to be the case, then because of its presence, the dust will settle to the disk-like form in a time of the order of the orbital period at the distance concerned. Once this configuration has been reached, if any extra particle were set moving out of the plane of the disk its orbit would necessarily intersect that plane twice per revolution, and so collisions would soon cause it to be absorbed into the disk. A kindly deity, recognizing our limited powers of intelligence, may well have decided to moderate the difficulty of the problem of the origin of the planets by providing a clue in the shape of the ring-system of Saturn, which there can be little doubt has its thin disk-shaped form for just this reason. Its particles evidently move too close to the planet for them to collect into larger particles, though gentle collisions must continually be taking place, as a result of perturbations from circular and coplanar orbits, thereby causing loss of energy and secular evolution of the rings, though in exactly what manner and at what rate are as yet quite unknown. The present paper is confined to discussion of the group of terrestrial planets, and although the great outer planets must start to form in the same manner by growthwithin a disk produced by solid particles, their later development to large mass will not be of further concern here.

424

R.A.LYTTLETON

For the inner regions of the disk, a numerical estimate can be made of its thickness by supposing the mass to equal the total mass of the terrestrial planets, which means about 1.2 x 102s g, and that it extends from inside the present distance of Mercury to beyond the present distance of Mars, say 2.4 x 1013 cm. Supposing the thickness to be uniform, the m a s s p e r unit area ~ would thus be about 7 g cm- 2. The volume-density of the material would of course be of order 1 g cm-3, and so the disk would be packed solid at first and just a few centimetres thick. The vital point where the formation of planets is concerned is that, precisely because of this high density, the disk provides conditions that are essentially different from those in the rarefied low-density nebula. If any slight aggregation should occur anywhere in the disk, and such a thing is bound to happen at a great many points, the local density would be entirely adequate to overcome the solar disruptive influence, and the increase would continue to develop. In other words, growth of larger bodies from the material of the disk would begin to occur at once anywhere that a slight local concentration happens, which means at first almost everywhere. Huge numbers would form, then develop and aggregate together to larger sizes, and so on, always of course remaining in the general form of a disk-distribution. If eventually as a result of this process there have formed n main identifiable bodies of density 0 and each of average linear dimensions r, then nr 30 will always be more or less equal to the total mass of the original disk, and so as r increases n will rapidly diminish, and separations will increase between the growing bodies. Assuming 0 ~ 3 and spherical shape, even when the radius had reached about 1 kin, there would nevertheless be as many as 1012 such bodies. As far as the whole area of the disk is concerned, these could be set out some 400 km apart, but as regards radial distance from the Sun, their successive orbits, if uniformly spaced, would have a mere 24 cm separation. Not until the bodies had become of order 100 km in radius, and about 106 in number, could they have adjacent orbits separated by their own diameters. The process would not be likely to happen in this uniform manner but instead at any stage there would be a range of individual masses. For a collision that resulted in two bodies combining into a single larger one, there could well be some escaping debris augmenting the so far uncollected dust and any much smaller masses, while collisions could also occur that brought about only some partial disruption of the bodies concerned, thus adding to the general mass of material still remaining in the disk and available for absorption into the growing bodies. But the largest masses would nevertheless continue to increase, for energy must steadily be lost as a result of the collisions, which requirement is met as the bodies grow larger and their number fewer. Meanwhile, however, angular momentum will be conserved, so the general scale of the system remains unaltered. By the time bodies approaching the size of the Moon had formed, say r ~ 108 cm, they would number about 103 , and these uniformly distributed as regards radial distance could have orbits separated by about 100 times their diameters, though their individual ranges of gravitational influence (in competition with the Sun) at 1 AU, for example, would be almost twice this in linear extent. Mutual perturbations would

THE END OF T H E I R O N - C O R E AGE

425

therefore still be of such strength as to make circular orbits quite impossible, with the consequence of further collisions, and hence formation of still larger bodies but again fewer of them. Not until the number of bodies had fallen to about 5 x 102 could the average separation of successive orbits round the Sun be greater than each of their diametral ranges of action, and by that stage the individual masses would average about 2.4 x 1025 g, on the present numerical values as adopted above, which is approaching the order of the lunar mass. It can be shown that growth by such means up to the size of the Moon would require only some 104 yr. Subsequent development to larger masses still would only finally cease when a stage had been reached that each of a few large bodies had swept up practically all elements of mass of whatever size in a general annular zone dominated by itself. Mathematically this would take infinite time, but 99~ clearance or even 99.9~ would require only a finite time, probably little more than 105 yr. An interesting feature of the later stages of the process, which can be interpreted as throwing some light on the origin of the Moon as a satellite of the Earth, is that even when large bodies were already developed there would remain, in the form of a disk, material both from the original dust and from the debris of collisions, but continually decreasing in areal-density as the incipient planets grew. This residuum would provide a mildly dissipative medium in which the larger bodies moved, though with velocities relative to it of smaller order than the orbital velocities themselves. These are precisely the conditions in which a body such as the Moon, at first moving as an independent small planet, could come to be permanently captured by another planet, in this case the Earth at some late stage of its growth. It can be shown rigorously that a Moon moving in an orbit near that of the Earth can become captured temporarily by purely conservative dynamical means under the combined action of the Sun and Earth (Lyttleton, 1967), but if in addition the slightest dissipation extracts energy from the relative motion of the Earth and Moon, as for instance capture of some of the medium by the Moon undoubtedly would, this will lock them together permanently. The process is extremely sensitive to the separation, and only a minute decrease will result in an indissoluble binary system. The foregoing brief account of the origin of the terrestrial planets and the Moon rests upon a detailed analysis of the mechanism of formation given in a recent paper (Lyttleton, 1972). It is of special interest here to recall that Urey himself has for many years maintained that the planets show every sign, from a chemical point of view, of having formed by aggregation of Moon-like masses, so that our Moon itself is to be regarded as a former independent small planet captured by the Earth. The discussion here summarised, however, shows that the growth of bodies to lunar size will have represented the development only up to a certain stage of the process of formation of planets from a dust-disk. It places the origin of the Moon as an individual body right back in the early stages after the first development of the disk, and its growth may have occupied less than 105 yr after the initial acquisition of the nebula by the Sun, with capture by the Earth occurring probably at a somewhat later stage when the Earth itself had neared completion of its own development yet sufficient of the disk'

426

R.A.LYTTLETON

dust-distribution still remained to enable the Earth-Moon system to become locked together gravitationally. 2. Internal Nature of Bodies so Formed

It is of main interest here to consider what the foregoing mode of development of the planets and the Moon implies as regards their internal nature. It is plain that if the original material is interstellar dust, resulting presumably from supernova explosions, its composition would have been more or less uniform everywhere, and unlikely to lead to any great variation as regards composition over the range of the disk associated with the terrestrial planets. The temperature maintained by solar heating might well range from 200K to 400K from the outer to the inner parts of the disk, with the result that easily volatilisable substances could be solid at the outermost parts and gaseous nearer the Sun, but these temperatures are much smaller than the melting points of most heavy metals and certainly of rocks. It seems quite impossible that iron, which is of special concern here, could have had much greater relative abundance at the distance of the Earth from the Sun than at the distance at which Mars formed. The first difficulty of the iron-core interpretation of the present central region of the Earth is met up with at this point. The average content of iron in meteorites, which their properties show represent objects removed from already formed planets (and not original planet-building material), is in excess of 20% by mass, but even if it is supposed that the mantle and outer-shell of the Earth contain only 10% by mass of iron, in free form and in compounds, the total content would be 40% if the core is iron. On the same basis Mars, which is too large in radius to have any (non-negligible) iron core, could be allowed only 10% of iron. Using the higher figure of 20% by mass for meteoritic material in the mantle, the Earth would be almost 50% iron, and Mars then 20% iron. The attempt could be made to account for the great difference by postulating some comparable difference of relative abundance of iron in the original disk at appropriate distances, but such ad-hoc explanation would scarcely overcome the corresponding difficulty for the closely adjacent Moon, which can have no iron core and has uncompressed density the same as that of the outer-shell of the Earth. The difficulty does not arise at all on the phase-change interpretation of the core of the Earth (discussed in a later section of this paper), according to which a denser metallic phase of mantle material can be induced by subjecting it to pressure of about 1.5 x 1012 dyn cm -2, indeed quite the contrary, for it receives automatic explanation in terms of the differing central pressures in the planets. The central pressure in the Moon is less than a-~th of this value, and at the centre of Mars less than ½th of it, a value attained high up in the solid mantle of the Earth, whereas at the outer boundary of the terrestrial core it is now almost 1.4 × 10 la dyn cm -z. This is perhaps a suitable point to note that Mercury will present something of a puzzle on either basis if a close fly-past (projected for 1973-74) should confirm current values for its mass and radius. These imply mean-density 5.4 g cm- 3 almost that of the Earth, and it would require

T H E E N D OF T H E I R O N - C O R E AGE

427

about 60~o by mass of iron, but the central pressure remains far too low for the phasechange. This could be explained (away) by ascribing it to high iron-content in that part of the disk where Mercury developed, either original to the disk or as a consequence of greater proximity to the Sun (than for the Earth and Venus, which must be very similarly constituted to the Earth on either hypothesis concerning the core). Indeed, the latter explanation has been suggested already, but it may prove safer to postpone any speculation until definitive values become available for the mass and for the radius to which the mean-density is extremely sensitive. Another highly important consequence of the process of planetary formation results from the feature that the depth of the dust-disk perpendicular to its plane is bound to remain far smaller than the diameter of any planet that has developed to substantial mass. Even if any part of the disk were disturbed from coplanar motion by the developing planets, it will quickly be brought back to as thin a form as possible until the stage is reached at which the areal-density has become so low that collisions are no longer of importance, but by then of course almost the entire material of the disk will have aggregated into incipient planets. Similarly any growing planet will remain always in or near the plane of the disk and be brought back into it through the action of gathered in material. These considerations mean that captured material will reach the surface of the planet only in a very narrow great-circle band at any stage, and not uniformly all over the surface as discussions of planetary growth by accretion usually assume. In this process of formation, rotations of planets arise from the vorticity inherent in the disk as a result of its orbital motion, and so in the early stages while growth was from material moving in the plane of the disk, even if this had come to consist of a distribution of aggregations, as it would, the axes of rotation would be perpendicular to the plane of the disk. If through chance effects this came not to hold precisely, the impact band on the planet would not remain fixed relative to the surface, but nevertheless at any instant infall would be occurring only over a narrow great-circle strip. Not until the mass of a planet reached nearly that of the Moon would the kineticenergy per unit mass under free fall (from great distance) approach that needed to liquefy rocks. But such material in being brought to rest at the surface would necessarily share its energy with resident material. Thus at all stages of growth prior to reaching lunar mass, a forming planet would certainly remain in all-solid form. In fact however, not only would infalling disk-material jostle with adjacent material and prevent its speed reaching free-fall value, but for small particles a high proportion of the energy of impact would be radiated away. Even if, when a planet exceeded lunar mass, material were to melt both itself and the surface material along the narrow band where it fell, the resulting liquid would flow away polarwards under gravitational forces, now necessarily grown to considerable strength, to maintain an equipotential surface. Spread out laterally away from further incoming material, the liquid form would be ideally distributed to cool rapidly into a thin solid layer. Such flow would cease upon solidification, and if this occurred to any important extent before material had flowed to high latitudes away from the infall-band, equipotential form would be restored by

428

R.A.LYTTLE'I'ON

gravitation as soon as the weight of any equatorial excrescence so created came to exceed the strength of the underlying layers. With increasing general size of the developing planets, the areal-density in the dustdisk would diminish, and the later stages of development to the final individual planets would be by collection in of smaller aggregations which would be of lunar size or even far less. It is possible that some of the existing asteroids represent small planets that escaped from such gathering-in by larger ones but could increase no further in mass through exhaustion of the dust-disk. But even when an incipient planet fell to the surface of another larger one, the arresting of its motion must be dealt with locally, and though this might result in some melting and even vaporisation, it could not melt the whole body. For instance, if the whole present Moon fell onto the Earth, the energy brought in would be only a fraction of that needed to liquefy the entire planet, even if it could be distributed quickly through the whole mass, which of course it cannot. These considerations raise insuperable difficulties against the interpretation of the terrestrial core as constituted wholly or even largely of iron. For the original particles of interstellar dust, or solidified droplets within the cooling solar nebula, would be minute in size no larger than meteoric (not meteoritic) particles. Even if a fair proportion of these were pure iron, there is no possibility of their being as large as even of centimetric dimensions. Accordingly any planet accumulating within the dust-disk cannot be regarded as containing volume-elements of pure iron much larger in size than the original particles: there is just no way that these could first be sorted out and then assembled into large blocks of pure iron. Now in an all-solid planet, a large chunk of iron, supposing such came to exist, would be in hydrostatic imbalance owing its to higher than average density, and if surrounded by less-dense liquid would sink downwards. But there are two opposing views as to its possible behaviour within solid surrounding material. On the one hand, there may be a threshold of strength capable of keeping the iron where it is, just as ordinary objects of iron or of far higher density are seen to be able to rest indefinitely apparently on solid supports of lower density. On the other hand, the claim is made that under sufficiently long-sustained forces even solids must in reality be regarded as liquids - but of extremely high viscosity. On this basis, a mass of iron, of spherical form for example, would descend very gradually through a solid planet, with its motion resisted in accordance with the Stokes law. But under terrestrial gravity, descent through a distance comparable with the radius of the Earth even in a time of several aeons would require chunks of iron of kilometric dimensions. Since the velocity of descent varies inversely as the linear size, centimetric globules of iron would take some 1024 yr to be drawn into the core, while dust-particles of micron size would need 1028 yr! All this is on the supposition that the notion of viscosity would be applicable in such circumstances, whereas it seems certain that, for small particles at least, the idea that the threshold of strength would not be reached is more defensible physically, because of their relatively large surface areas. Thus if planets develop from dust, and start in all-solid form, there can be no possibility whatever of segregating the iron into a central core during the whole age of the Earth even if

THE END OF THE I R O N - C O R E AGE

429

it were present as pure iron in sufficient abundance to provide the known core-mass. The only line of escape from this would be to postulate that the Earth became sufficiently heated throughout by radioactivity more or less completely, thereby permitting the denser iron to drain down from a liquid magma to produce hydrostatic separation, and to postulate that such separation would occur within a reasonable period of time. But besides requiring impossibly great radioactivity, if total melting had ever occurred, re-solidification of the Earth could not yet have proceeded down through anything approaching the more than two-thirds of its mass that it has, and the hoped-for iron core would still be surrounded by a partly molten mantle at lower density. Having shown how the processes of planetary formation tell heavily against the notion of an iron core, if not alone entirely ruling out the possibility, it is proposed to turn next to known properties of the Earth and consider their bearing on the question. The first origins of the concept of high iron-abundance are probably lost in the mists of antiquity. One can well imagine, however, at a time when real knowledge was considered to be arrived at by authoritative apodictic assertion and thereafter to be confirmed by cunning casuistry, that the high mean-density was explained easily enough by claiming high content of heavy metals, and since iron would have been regarded as cosmically abundant, as evidenced by museum-specimens of meteorites, the narrowing down to high content of iron in particular would have been an understandable sequel. The notion must have persisted into comparatively recent times, for in his first researches on stellar structure even the normally argute Eddington adopted for the mean molecular weight of stellar material the value for iron. It has since emerged that no substantial proportion of the masses of the stars is so constituted. It would also have seemed hopeful to suppose that the existence of the terrestrial magnetic field could simultaneously be ascribed to ferromagnetic inclusions abundantly distributed in the interior. The discovery of the Curie-point, however, and of its insensitivity to pressure, has of course shown that ferromagnetism cannot persist at temperatures likely to prevail throughout most of the Earth. But the fact is that all scientific experience has shown that purely verbal guesses, unsupported by theory or experiment, as to the properties of complex natural systems and their causes, have vanishingly small probability of proving correct, and it cannot seriously be maintained that the guess over a century ago of high iron-content, will prove any exception to the rule, or even its not so antiquated modification, on discovery near the turn of the century of the liquid central core, that the bulk of the iron is concentrated therein. 3. Identification of the Core-Material

Although it has proved far beyond as-yet available resources to achieve in the laboratory static pressures of the order of those prevailing in the terrestrial core, and notwithstanding the high core-temperature (not known with much accuracy), the claim has been made that experiments in which shock-waves are passed through material initially unstressed and at standard temperature yield information that can be

430

R.A.LYTTLETON

directly compared with seismic data for the Earth. The procedure is considered to provide strong evidence that the terrestrial core is chemically different from the mantle and is composed predominantly of nickel-iron. The accounts leading up to such conclusions are mainly of a verbal kind supported by graphs showing the hydrodynamic velocity (OP/O~) 1/2 plotted against density as revealed by the shock-wave experiments, and the corresponding seismic curves of velocity against density for the core and mantle. The nature of the diagrams relied upon is somewhat remarkable for in the interval between their 1961-form and their 1963-form (which latter is shown in Figure 1), the curves representing the limits of the seismic data for the c o r e have not only shifted bodily towards and partially beyond the shock-wave curves for iron (unchanged in the two forms of diagram) which they did not reach in 1961, but have altered in slope too. On the basis of the Bullen (1963) models for the core, the seismic

12

I

I

10-

",~8-

I ~ 6l

l

3

4-

/

/12Mg

I 11 No

2 0

i 2

I 4

6 8 Density, gm/cm 3

I0

12

14

Fig. 1. Curves of shock-wave data for metals (from Birch, 1963). The dashed-curves show velocity against density for seismic waves for the mantle and core (at upper right) as given by Birch (1963). On Bullen's models for the core the curves fall to the left of these, as indicated. curves are found to lie even further away to the left than in the 1961 version of the diagram and do not anywhere reach the shock-wave curve for iron. However, leaving aside these curiosities, the seismic curve for the core which is shown as meeting that for iron intersects it at almost 30 ° , and this, assuming the comparison of the different velocity-curves to be meaningful, would seem to be capable of interpretation as

THE END OF THE IRON-CORE AGE

431

evidence against the identification with iron. Possibly all that is being claimed is the weaker proposition that the core is composed of heavy materials 'like iron', but the high density of the core material is understandable at once on the Ramsey-hypothesis. However, if the comparison has validity, then the curves for the mantle would show at least equally that this is made of aluminium !, for the slopes of the two curves, seismic and shock-wave, are as near as possible the same, while the displacements from point to point at fixed velocity are if anything less than for the iron curves. But it is scarcely necessary to press this identification, for the simple direct comparison of the two sets of curves, seismic and shock-wave, appears to be without theoretical justification. In the seismic case, harmonic waves of small amplitude are propagated through material already under static pressures in excess of 1012 dyn cm -2 (and at high temperature), whereas in any experiments a shock-wave moves into hitherto unstressed material, and what is propagated through it is a non-oscillating disturbance in which the peak-pressure may attain to this same order. What might afford a proper basis for comparison would be, in the shock-wave case, the contriving of a secondary wave-motion within that portion of the material momentarily experiencing the highpressure peak, but even if the velocities were comparable the peak would have passed before a sound-wave could have travelled a distance of the order of the breadth of the shock-disturbance. Thus the attempts to save the iron-core hypothesis on any such basis are seen to be as yet highly unsatisfactory. Although the remarkable feature that the bulk-modulus k of the liquid-core material is a linear function of the pressure p does not lead to any specific identification, it does lead to making quite clear the 'mistaken identity' of the core as nickel-iron. The relation k = a + bp is so closely satisfied in the outer core that it is necessary in any diagram of k plotted against p and of reasonable page-size to leave gaps in the straight-line representation to display the data-points (k, p) if they are not almost all to be invisible on the line itself (Lyttleton, 1963, p. 3), indeed there can scarcely be a comparable instance in the whole of science where an empirical law has been found to be satisfied with such surpassing accuracy. Since also k=o(dp/dQ) in homogeneous material, an integral pressure-density relation exists of the form a+bp=a(o./~,) b, wherein ~u arises as a constant of integration, and clearly corresponds to the e(fective uncompressed density that the material would have if brought to zero pressure without change of form (which is always conceptually possible even if physically not so). Seismic data provide values of k, p, and ~ at all depths in the core, and the series of (k, p)-values imply a = 1.34 x 1012 dyn cm-2, for b = 3.5. The pressure-density relation then yields a value of .ou for each pair of values of (p, ~). The following Table I on page 432 shows the results of this latter calculation based on the Jeffreys-Bullen data for the core. The values of~u in the last column are as near a unique value as could be expected, since the data from which they are found contain for the most part, as seen, only 3 significant figures. This striking result not only confirms the accuracy of the linear law k = a + bp, but, which is the point of interest here, shows that whatever the core material may be its volume-density when uncompressed is only 6.1 g cm -3. It is

432

R. A. LYTTLETON

TABLE I a (g cm-3)

p (1012 dyn cm-2)

Qu(gcm-a) 4--

9.43 9.57 9.85 10.11 10.35 10.56 10.76 10.94 11.11 11.27 11.41 11.54

1.37 1.47 1.67 1.85 2.04 2.22 2.40 2.57 2.73 2.88 3.03 3.17

6.107 6.101 6.098 6.110 6.111 6.109 6.107 6.105 6.107 6.112 6.109 6.108

Mean va[ue."

Qu= 6.107 "0.004 gcm -a

manifest that there can be no possibility of interpreting this as some form of nickeliron mixture, for there can be no process resulting from pressure that could lead to a l o w e r effective density than material has in normal form at zero pressure. The mere numerical value could be accommodated by infusing the nickel-iron with a suitable proportion of lighter elements, such as silicon for example, but this would be no more than an ad-hoc further assumption introduced to save whatever percentage might be allowed to remain of the nickel-iron identification. Such a proposal has in a sense been considered in order to deal with a more subtle difficulty associated with the assumption of a sudden change of chemical composition across the core-mantle boundary. This difficulty is presented by the remarkable phenomenon that the velocities of P and S-waves, which throughout almost the entire mantle increase with depth, actually show slight anomalous relative decreases as the core-mantle boundary is approached (the S-velocity actually decreases, while the P-velocity undergoes a marked decrease of its rate of increase with depth). Efforts have been made as aforesaid, to account for this by postulating layers of different chemical composition contiguous to the interface, but any such attempts on the problem seem foredoomed to failure through the inevitable accompanying seismic effects of reflection and refraction that would be introduced at the boundaries of any such layer, effects that could not escape detection yet remain unobserved. On the other hand it is one of the most convincing triumphs of the phase-change hypothesis that it proves capable of accounting for precisely such a phenomenon even to the extent of showing that it must be confined to the low-pressure side of the interface, while at the same time the hypothesis accounts for the extreme sharpness in depth of the mantle-core boundary (Ramsey, 1949).

4. The Phase-Change Hypothesis The proposal that the terrestrial core has the s a m e composition as the mantle and outer-shell material, but represents a high-pressure metallic modification of it is associated most closely with the name of Ramsey (1948, 1949, 1950a, b, c), but was also

THE END OF THE IRON-CORE AGE

433

considered by Bullen about the same time. The hypothesis can be regarded as based upon the inescapable fact that matter cannot have infinite strength. If subjected to increasing pressure its volume will decrease, but at certain stages this will happen suddenly: first there will occur a collapse to a metallic phase, then it will at intervals undergo further sudden decreases as its successive electron-shells collapse until ionisation is complete, and it would then in principle proceed on to that state of neutron-star material with electrons forced back into the nuclei themselves, though these latter stages would require pressures far higher than planetary values. It is the great merit and interest of the Ramsey hypothesis that the Earth, and also Venus, are of sufficient mass (and internal temperature) to have undergone at least the first of these phasechanges, thereby providing examples of planets with metallic cores. By theoretical means, it had been shown some years before Ramsey's work that for hydrogen a phase-change to metallic form would be induced by pressure of 0.7 x 1012 dyn cm -2, at which the density would double suddenly from 0.4 g cm -3 to 0.8 g cm -3. Similar investigations of more complex substances are beyond present resources, while in addition it is not yet possible to produce static pressures of this order experimentally, but the fact that this pressure for hydrogen is only half that at the present core-mantle interface suggests that 1012 dyn cm-2 may represent the order of magnitude of pressures at which most if not all substances undergo this transition to metallic form, accompanied by a sudden large increase of density, and Ramsey adduced general theoretical arguments rendering this conclusion highly plausible. In default of rigorous theoretical demonstration or direct experimental verification, it is nevertheless entirely valid procedure scientifically to test a hypothesis by investigating its consequences to find to what extent the conclusions are in agreement with known results. It will in fact be shown that many more properties of the terrestrial planets and the Moon fall readily into explicable order on the phase-change hypothesis than on the iron-core hypothesis, quite apart from the considerations already advanced that most would regard as disposing of the latter anyway. The remarkable result was established by Ramsey (1950a) that, if the phase-change is such that the associated increase of density is by a factor in excess of 1.5, there would occur with gradually increasing mass a sudden catastrophic collapse, affecting the whole planet, and resulting in the formation within a matter of minutes of a core of 'large' radius consisting of material in the new phase. The critical pressure Pc (T) for the phase-change decreases as temperature increases, but if for the present the dependence on T is ignored, then as the mass m of a planet increases, its central pressure also does so. Above a certain mass MI (see Figure 2) considerably before the critical pressure has been reached at the centre, if the factor of density-increase (2 say) exceeds 1.5, then as well as the distribution that the planet will be in, configuration A, as we may term it, there will exist two other possible equilibrium configurations, B and C say, but with central cores of material in the new phase. Of these, state B with smaller core, is always unstable, while C with 'large' core is always stable. The planet will as yet remain in state A without any core because that is a thorouglhy stable equilibrium configuration. However, with further increase of mass, the core

434

R.A.LYTTLETON

associated with B gets smaller (and that of C larger), until for a certain mass M 2 ( > m 1) a stage is reached when B reaches coincidence with A. Then, upon the slightest addition of mass to the planet, configurations A and B cease to exist at all (it is not a matter of their becoming unstable), and there remains state C as the only possible configuration available. The planet thereupon collapses rapidly to this configuration and in doing so immediately develops a 'large' core of radius (depending on 2) that is in general a sizable fraction of the radius of the planet. The associated linear series o f configurations are illustrated schematically in Figure 2 in which the mass as ordinate is plotted against

M2

m

S

y/~ rapicd~al pse A ~ j~ble

series

MI

X' stable

unstable

central pressure

Fig. 2. The three linear series of configurations associated with the phase-change to higher density. For 2 < 1.5: evolution proceeds along O Y before core-formation starts and then along YP with steadily growing core. Both series are of stable forms. For Z > 1.5: evolution is steady by stable forms along O Y, but immediately beyond, for m > Me, the representative point leaps to Y', the motion YY' corresponding to the rapid collapse to a configuration with 'large' core. Thereafter the planet evolves stably along Y'Q with steadily growing core. the central pressure. The critical situation is reached at the point Y, where m = M o, and beyond which configurations A and B no longer exist. The effect of temperature-increase, which would in any event be produced by long-lived radioactive elements in the deep interior, is to lower the value of the critical mass M 2 (T). The resulting evolution for a planet of fixed mass can still be represented by Figure 2 by regarding the point Y, corresponding to mass M2 (T), as moving down in the direction along the curve YA towards the point X, and to lower values of po of course, at the same time carrying the curve Y X ' Y ' Q bodily with it (these are only schematic curves). This leaves the evolutionary situation unchanged in that when Y passes below the level of the (fixed) mass of the planet, only state C can exist, and then as before rapid collapse immediately sets in accompanied by formation of a'large' core. A close estimate can be placed on the original critical pressure from consideration

THE END OF THE IRON-CORE AGE

435

of internal pressures for the Earth and Venus. For Venus in all-solid form, the central pressure would be 1.42 × 1012 dyn cm-2, which is only slightly greater than the present value at the core-mantle interface in the Earth, 1.37 x 1012 dyn cm -2. But the temperature in the central regions of the Earth (which remain practically isothermal) will be much higher now than in the centre of a cool Venus when first formed, and it may thus be inferred that Venus could have grown to its present mass as an all-solid stable planet without any metallic-liquid core. (In this form its overall radius would have been about 6300 kin, compared with the present solid-surface radius of 6056 km.) Development of a core in Venus would be deferred until radioactive-energy release raised the temperature sufficiently to reduce the critical pressure for the phase-change to 1.42 x 10 t2 dyn cm -2, and the all-solid form may have prevailed for a period as long as 109 yr to permit adequate release of energy by long-lived radioactive elements. But for an all-solid Earth equal to the present mass, in which the central pressure would be 1.63 x 1012 dyn c m - z , the early history would obviously depend on whether the critical pressure for the phase-change at low temperature were less or greater than this. If less, the planet would pass the crucial mass Mo while still growing, and a core would first form at that instant. Increasing mass would then cause evolution along the stable C-series Y'Q with the core growing in unison, its size at each stage depending on the precise value of the critical pressure. On the other hand, if pc (T) were initially greater than 1.63 × 10a2 dyn cm -2, the Earth could attain its full mass as a cool body in all-solid form, and then, as for Venus, remain solid until rising temperature brought p~(T) down to this central value, at which point the sudden collapse would come about. The radius of the resulting core would be 2042 km, and its mass just over 6% of the total Earth-mass. Even so, this 'large' core is much smaller than the present core, which has radius 3473 km and is just over 31% of the whole mass. But in either case, the important conclusion emerges that development of a core within the Earth, together with its various consequences, would occur much earlier in the history of the solar system than for Venus, which on this basis must be regarded as lagging considerably behind the Earth as regards internal evolution by an extent dependent on the effect of radioactivity on the critical pressure but possibly of the order 109 yr. The collapse is accompanied by enormous release of gravitational energy, 5.94 x 10 sv erg for the Earth - enough to provide for about 1013 of the largest recorded earthquakes and so would scarcely have gone unnoticed! - and 3.17 x 1037 erg for Venus. About 80% of this energy goes into work done on the core material, and according to Ramsey about half would be taken up by the phase-change, and the very considerable remainder to heating the core, which incidentally would bring it to liquid form, and also to producing wave-motions throughout the planet. Even if only onetenth went into heat, the temperature of the core would be raised several hundred degrees above its existing higher-than-original value, and some effect of this in Venus still extant owing to the later core-formation, is suggested by the feature that the pressure at the core-mantle interface is as low as 1.23 x 1022 dyn cm -2 at present, slightly less than the terrestrial value, suggesting that the deep interior of Venus is at somewhat higher temperature than is that of the Earth.

436

R.A.LYTTLETON

5. Consequences of the Phase-Change Mechanism One of the most impressive of the numerous succesful consequences of the Ramsey hypothesis is that is leads directly to an extent of contraction of the Earth at last fully sufficient to satisfy the requirements long since demanded by geologists the world over for the purpose of mountain-buiding. Here is what Leet and Judson (1961) have to say in their celebrated treatise on physical geology: "One generalization on which all geologists agree is that mountain-building involves a reduction in the surface area of the globe - a shortening ot the distance between points on the surface - and that all mountain-building is the product of a single mechanism - squeezing by horizontal compression. But when it comes to what causes the squezing, there is no general agreement." Well, there need be no disagreement continued now: it results simply from the large decrease of volume associated with the Ramsey phase-change. The radius of the Earth, when in all-solid form, would be 6741 kin, but on collapse would decrease to 6671 km, to bring the planet to the stable series C, with core-radius 2042 km on the basis of static models and neglecting temperature-increase. At the boundary of this core the pressure would be 1.63 × 1012 dyn cm -2, the same as the original central value, while beyond this in the solid mantle pressure decreases steadily outwards. Subsequent evolution now proceeds secularly along the stable C-series as radioactive heating further lowers the critical pressurepc (T). Over a period of possibly between 3 and 4 aeons, the core has grown to its existing size, while the accompanying decrease of overall radius to the present 6371 km has been just about 300 kin. In terms of surface-area, this means a diminution by the prodigious amount of 50 million km zabout 10% of the total a r e a - and this vast reduction would have to be accommodated by folding and thrusting. The wonder is that there are any large areas free from mountains ! No other hypothesis yet proposed succeeds in yielding anywhere near such an amount of contraction. Even supposing the core were iron somehow separated downwards from a primeval initial mixture with rock, the resulting theoretical decrease of radius and surface-area would be at most little more than a tenth of these values, while the thermal-contraction hypothesis, which postulates a molten Earth, produces even less. The consequences of the catastrophic collapse almost defy imagination as to the details of what may happen at the surface, but gravitation would necessarily maintain this an equipotential, apart from comparatively small surviving irregularities, possibly of the order of those exhibited now as mountains and ocean-depths, that could be maintained by the strengths of the outermost materials at that stage. But thereafter minutely slow contraction would proceed, on average at the surface by no more than I0 -z cm per year, though it would occur there only intermittently at long intervals awaiting the build-up of sufficient stresses. That a core so formed can no longer be regarded as of iron will in no way remove the possibility that the main magnetic field may be generated therein, for its material having undergone the Ramsey phase-change will now be in the metallic state anyway.

THE END OF THE IRON-CORE AGE

437

The course of evolution indicated for Venus is similar to that for the Earth, though as yet contraction will have taken place to somewhat less an extent of about 250 km in radius and nearly 40 x 106 km 2 decrease of surface area (which at present is about 460 x 106 km2). Thus it can be predicted that mountain ranges resulting from folding and thrusting will be found on Venus, and this planet will have experienced eras of mountain-buiding just as has the Earth. There is already some evidence of this in that radar measures claim to detect large-scale surface features of altitudes some 6 km in the equatorial regions of the planet, which however awaits detailed mapping or its whole surface (cf. Rogers et al., 1972). Where the question of a magnetic field is concerned, the core-material, as for the Earth, will be in equally suitable form, but here the extremely slow rotation of Venus, assuming the cause to be related to this, may mean an extremely weak field. Turning next to Mars, its central pressure cannot be as great as 0.3 x 1012 dyn cm -2, and moreover the temperature of the central region is unlikely to be even as high as for the Earth or Venus in view of the much smaller size. Thus there can be no possibility whatever of the phase-change having come about, and Mars must therefore be without any metallic core. That this is so is confirmed most directly by the overall radius of the planet, which would fall substantially short of the observed value if there were any sizable core, iron or phase-change, indeed the deficiency would be as large as 150 km if the proportion by mass were the same as in the Earth. Second, close-up photography from spacecraft has now confirmed what had long been conjectured from telescopic observation, that there are no mountain ranges of terrestrial type. (Volcanic mountains on Mars are by no means ruled out.) Third, there has been found no detectable magnetic field for Mars, a result that was firmly predicted on the basis of the phase-change hypothesis before the Mariner IV magnetometer measures of July 1965, (which set an upper limit to the moment of about 3 x 10 . 4 that of the Earth). As the period and inclination associated with the Martian rotation are just about the same as for the Earth, a comparable magnetic field was widely expected. But clearly the absence of any field, which may rank as one of the greatest discoveries to date of the spaceprogram, tells strongly against the existence of any metallic core, and the low central pressure supplies the explanation without special assumption. The pressure at the 20°-discontinuity in the Earth, 0.14 x 1012 dyn cm -2, is reached in Mars, and the existence of a similar level of discontinuity in Mars can be predicted. This phase-change, which involves compression to only slightly higher density crystal-structure, requires with increasing temperature higher pressure to produce it, and as temperature rises through radioactive heating the effect is to cause the planet to expand ( n o t mere thermal expansion but a phase-change expansion), though seismic data for the Earth show that it is only to about one-tenth the extent of volumedecrease associated with the Ramsey phase-change. Thus there may well be expected riftings at the Martian surface, which over the whole lifetime of the planet may have increased in area by nearly 2 x 106 km 2. Some signs of long broad rifts on the planet have already been seen in spacecraft photographs. However, it is a matter for conjecture what effect erosion might have on such riftings and at what rate this may proceed.

438

R . A . LYTTLETON

On the same basis, it can also be predicted that marsquakes occur for the planet, as also even more certainly can venusquakes be predicted for Venus. In the Moon, the Central pressure is only 0.047 × 1011 dyn cm -2, which is reached in the Earth at about 150 km depth. Thus neither phase-change can occur for the Moon, and its geometrical size is entirely consistent with this. For the same reason, neither terrestrial-type mountains, surface-rifting of Martian type nor intrinsic moonquakes would be expected to be found on the Moon. 6. Conclusion We come finally to a different type of problem arising from the notion of an iron core, and ask how it is that so questionable and unsuccessful a hypothesis can continue to be revered by enthusiastic adherents, while on the other hand the hypothesis proposed by Ramsey, which at once strikes order into the properties of the terrestrial planets, is largely ignored or dismissed without adequate consideration. There are well-known reasons of an unscientific but obvious kind for this, not least that noted by Medawar (1972) to the effect that even amongst scientists there are many who unconsciously resent the prospect of resolution of long-standing problems, for they have come to love the related ideas they have grown up with even though landed in confusion by them. They consider the idea to be self-evident in its own right; and to such an extent has the iron entered their soul that they are blinded to any criticisms and receive them resignedly much as a doting mother reacts to criticisms of a wayward son. Indeed they seem able even to extract some mystical joy from the confused state of the subject, which can be interpreted as implying an impenetrable profundity that is its principal glory. The rationalisation usually put forward to account for lack of progress is that 'more observations are needed', as if it were known somehow that when the millennium comes all will be revealed thereby, without the need of giving real thought to the matter meanwhile. It seems not adequately recognised, when it comes to assessing the tenability of any hypothesis, that purely verbal accounts and assertions contribute nothing to science unless they can at least supply some testable predictions or suggest some crucial experiments. Apart from the iterative claim that if a sample could be got from the Earth's core it would prove to be iron (a not very hopeful experiment), the hypothesis of an iron core has done none of these things, but introduces only difficulty into the theory of the terrestrial planets. On the other hand the theory takes on a ready coherence of intelligibility once these planets and the Moon (with Mercury to some extent excepted at present) are discussed together in terms of the phase-change hypothesis, which can be done in detailed mathematical and numerical manner that provides a proper basis for scientific discussion. Moreover the resulting theory leads to testable predictions, some of which have already proved correct while others await verification, as has been seen in the foregoing sections. It would take us too far into questions ousidet the scope of this paper to discuss more fully the meaning of the attachment exhibited for outmoded and invalid hypotheses.

THE END OF THE IRON-CORE AGE

439

B u t the r e a d e r who m a y be stirred by the i r o n - c o r e p h e n o m e n o n to an interest in this aspect o f the subject o f the N a t u r e o f K n o w l e d g e will find m u c h o f relevance in a discussion b y I r v i n g L a n g m u i r (1968) entitled Pathological Science, which concerns itself a c c o r d i n g to its a u t h o r with 'the science o f things t h a t a r e n ' t so'. Besides rec o u n t i n g in detail n u m e r o u s specific examples, as for instance mitogenetic rays, the Allison-effect, extrasensory perception, a n d flying saucers, L a n g m u i r catalogues the s y m p t o m s b y which such kinds o f science can be recognised a n d diagnosed, a n d he also lists the s t a n d a r d reactions o f their p r o p o n e n t s to criticisms a n d to results n o t f a v o u r i n g their ideas. M a n y o f these are only t o o clearly the s y m p t o m s a n d reactions t h a t are f o u n d to be associated with the iron-core theory.

References Birch, F.: 1961, Geophys. J. Roy. Astron. Soc. 4, 309. Birch, F. : 1963, Solids under Pressure, McGraw-Hill, p. 146. Bullen, K. E. : 1963, Introduction to Seismology, 3rd edn., Ch. 13, Cambr. Univ. Press. Langmuir, I. : 1968, Pathological Science, Gen. Elec. Report No. 68-C-035. Leet, L. D. and Judson, S.: 1961, Physical Geology, Prentice-Hall, p. 358. Lyttleton, R. A.: 1963, Proc. Roy. Soc. A275, 3, 8. Lyttleton, R. A.: 1965, Proe. Roy. Soc. A287, 471. Lyttleton, R. A. : 1967, Proe. Roy. Soe. A296, 285. Lyttleton, R. A.: 1969, Astrophys. Space Sci. 5, 18. Lyttleton, R. A. : 1972, Monthly Notices Roy. Astron. Soe. 158, 463. Medawar, P. B. : 1972, The Hope of Progress, 102 Methuen. Ramsey, W. H. : 1948, Monthly Notices Roy. Astron. Soc. 108, 406. Ramsey, W. H. : 1949, Monthly Notices Geophys. Suppl. 5, 409. Ramsey, W. H. : 1950a, Monthly Notices Geophys. Suppl. 6, 42. Ramsey, W. H. : 1950b, Monthly Notices Roy. Astron. Soe. 110, 325. Ramsey, W. H. : 1950c, Monthly Notices Roy. Astron. Soc. 110, 444. Ramsey, W. H.: 1951, Monthly Notices Roy. Astron. Soe. 111,427. Ramsey, W. H. : 1954, Occas. Notes Roy. Astron. Soe. 3, 87. Rogers, A. E. E., Ingalls, R. P., and Rainville, L. P.: 1972, Astron. J. 77, 100.