SP-345 Evolution of the Solar System





[473] Practically all other attempts to reconstruct the history of the solar system have been based on a more or less reasonable hypothesis about the properties of the early Sun. As has already been pointed out in the introduction, such a procedure is dangerous because in reality we know next to nothing about the early Sun. Theories about the formation of stars from interstellar clouds are speculative, and they seem to lack any observational confirmation. Such theories generally assume a basic process of gravitational collapse. This assumption is not necessarily correct; a "stellesimal" formation, in analogy with the "planetesimal" formation of planets and satellites, would be an interesting, and perhaps more attractive, alternative.

In the present study of the evolution of the solar system an attempt is made to avoid the uncertainties inherent in making assumptions about the early Sun. Our aim has not been to understand exclusively or preferentially the formation of planets around the Sun, but to develop a general theory of the formation of secondary bodies, planets or satellites, around a primary body, which may be either the Sun or a planet. The advantages of the method have been discussed in secs. 1.2 and 16.9, one of them being that the mechanism of formation of secondary bodies can be based largely on studies of the satellite systems without necessarily making any hypothesis about the primeval Sun (see fig. 16.9.1).

In this way it was possible to define the basic processes by which secondary bodies were formed. If we then make the plausible assumption that the planetary system has been formed by the same processes that have produced satellites, we are able to make important conclusions about the primeval Sun during the period the planets formed around it.

Using this method we shall here calculate the mass, magnetic field, and spin of the early Sun, and comment on its light and solar wind emission.


[474] 25.2. SOLAR MASS

As the empirical basis for our estimate we use:

(1) Diagram of the band structure of the secondary-body groups, fig.21.2.1.

The diagram has been plotted with the mass of the planet-forming Sun assumed to be equal to the present mass. If this is incorrect we should expect a systematic displacement of the bands in the planetary system.

There is no doubt that such a displacement does exist. The bands are not horizontal as expected theoretically according to ch. 21 but are sloping However, the bands in the different satellite systems also show a similar slope. An explanation of this phenomenon is given in sec. 23.9.2

Hence to conclude that the mass of the planet-producing Sun was different from the present mass does not seem justified.

(2) Table of normalized distances (table 23.6.1). The values for the planets are larger by about a factor of two than the values for the Jovian and Saturnian satellites. In principle this may be due to a mass loss by the Sun of a factor 21/2. However, the difference in the mathematical symbol
values are probably a sufficient cause for the difference.

We conclude that there are no certain indications of a change in the solar mass since the formation of the planetary system, but changes of perhaps 25 percent in either direction cannot be excluded.



The fact that the Sun has transferred angular momentum as far out as Neptune and Pluto makes it necessary to assume that, out to these distances, the solar magnetic field has been larger than the transplanetary field.

We do not know the strength of the transplanetary field, but it is not very likely that it was less than the present value of the "galactic field" which is believed to be of the order of 3 X 10-6 G. If a field deriving from a solar dipolemathematical symbol should exceed 3 X 10-6 G at a distance of 6 X 1014 cm we find from


µ = Br3 (25.3.1)




mathematical equation(25.3.2)


[475] This is a very high value but it is difficult to see how it could be avoided in any theory involving hydromagnetic transfer of angular momentum; in order to transfer angular momentum to a region in space the solar magnetic field must dominate in that region. Fields of this magnitude or larger are suggested by the magnetization phenomena in meteorites (Brecher, 1971, 1972a,c; Brecher and Arrhenius, 1974, 1975).

If the Sun during the hetegonic era had its present radius, its surface field would have been 2 X 106 G. If the radius of the Sun when Pluto formed were 1012 cm (Brownlee and Cox, 1961), the surface field would be > 650 G. This value is well within the range of observed stellar magnetic fields, whereas the value assuming the present radius of the Sun is higher than any observational value.

The solar magnetic field must also have been strong enough to bring the plasma around it into partial corotation and to support the plasma until this was achieved. The requirement for this is model-dependent and does not allow a very stringent derivation of the necessary magnetic field.



As an introductory remark it should be pointed out that there are a number of papers claiming that the Sun has a swiftly rotating core. There seems to be no convincing observational support of these speculations From a theoretical point of view, it has never been proven that such a situation is stable, and it seems indeed unlikely that it is. On the other hand the angular velocity of the Sun is a function of latitude, and, as isorotation is likely to prevail in the interior of the Sun, the angular velocity in the solar interior will depend on the interior structure of the solar magnetic field. Reasonable models of this have been discussed by Alfvén and Faltham mar (1963). We shall not discuss these problems further here but only state that the differential rotation is a small effect that we need not consider in this context. In the following we assume that the whole Sun rotates with roughly the same angular velocity.

The slope of the curves in fig. 23.6.1 depends on the value of mathematical symbol
From this slope we can calculate the spin period of the Sun when the terrestrial planets and the giant planets were produced.

The slope of the curve for the terrestrial planets is intermediate between the curves for the Uranian satellites (mathematical symbol
= 12) and the inner Saturnian satellites (mathematical symbol
= 8) so we may use the value mathematical symbol
= 10. This implies that the Sun had a spin period of 20 days when the terrestrial planets were formed. This is close to the present value (25 days).

Concerning the giant planets, the slope of the curve is intermediate between those for the Jovian satellites (mathematical symbol
= 29) and the outer Saturnian [476] satellites (mathematical symbol
=80). However, the latter group is highly irregular, and should not be given much weight. Hence the only conclusion we could draw is that the mathematical symbol
value should be much larger than 29, and hence that the solar spin period should be less than 1 yr. But we cannot exclude its having been very small, e.g., a few days, because the value of mathematical symbol
may take on any value up to infinity.



Comparing the planetary system and the satellite systems, we have found no reason to introduce parameters of the central bodies other than mass, magnetic moment, and spin. None of the observational facts we have analyzed here makes it necessary to conclude that the early Sun had any emission of light, ionizing radiation, heat, or solar wind. The early irradiation recorded by particle tracks and by surface-implanted gases (sec. 22.9) could as well be due to accelerated particles in the superprominences as to emission from the Sun. The former activity, associated with the angular momentum transfer, would presumably be large compared to the latter, which on the basis of preserved evidence could be negligible. A solar wind of the present type is excluded by the strong solar magnetic field and the high plasma densities in interplanetary space due to the infall of gas.

Whatever is the dominant source of the observed irradiation features they may provide an upper limit for the solar source. Although the total dose can be fairly accurately measured, the flux cannot yet be estimated for lack of a value for the time interval (which would be of the order of 103-104 yr at a flux corresponding to the present solar wind and flare activity at 1 AU (Lal, 1972b)). However, the energy spectrum, which can be approximated from the irradiation profiles, would be expected to be permuted by major enhancement of solar activity due to a hypothetical Hayashi phase or a "solar gale."

In spite of the many thousand measurements of irradiated grains carried out on the various groups of meteorites and in lunar rocks, no noticeable deviation in the steepness spectrum has been observed (Macdougall et al., 1974). This suggests that during the time period covered by the irradiation record no such dramatic changes in the properties of the Sun took place. This does not exclude their occurrence prior to the hetegonic era.

Violent solar events have been introduced ad hoc in other theories in order to avoid specific difficulties in the late part of the hetegonic era or to remove records that conflict with present evidence (sec. 26.10.1). Such difficulties do not occur in the present treatment.

Although we consequently see no need for assumptions of strongly [477] enhanced solar activity any time during or after the hetegonic era, no evidence seems to preclude a solar activity of the present kind throughout the development of the solar system. A solar thermal radiation of the same magnitude as the present one would, aside from the influence on condensation of volatiles, probably not produce very conspicuous effects. The high density of Mercury is sometimes attributed to its heating by the Sun. This may be correct, but does not necessarily follow. An analogous increase in density is found among the satellites of Jupiter (sec. 20.5.11) where it certainly has another cause.



Some time ago, Brownlee and Cox (1961) concluded that before the Sun reached its present state it must have spent about 200 Myr in a deuterium-burning state. According to their model the Sun had a radius of 1012 cm during this stage (fig. 25.6.1).

This model did not receive much attention when it was first proposed, probably because at about the same time it became "generally accepted" that there could be no deuterium in the galactic medium from which the Sun supposedly formed (because the big bang could not produce deuterium!).


FIGURE 25.6.1.- The Brownlee-Cox model of solar evolution through a deuterium-burning stage.

FIGURE 25.6.1.- The Brownlee-Cox model of solar evolution through a deuterium-burning stage. Under the assumptions that the initial content of deuterium corresponds to the deuterium/hydrogen ratio of the Earth and that the energy transport in the deuterium burning Sun is nonconvective, the radius of the Sun would have remained at about 16 times the present value during the deuterium burning. This stage would last about 108 yr before contraction to the present size. A different initial content of deuterium (which} is possible) would mainly change the duration of the deuterium-burning stage. (From Brownlee and Cox, 1961.)


[478] Radio observations, however, have recently demonstrated that deuterium does exist in space (Solomon and Woolf, 1972), and Geiss and Reeves have suggested (1972) that the original deuterium content of the Sun can be reconstructed from the He3 content in the solar wind. Whether the Sun was produced by a gravitational collapse or by "stellesimal" accretion, it now seems unavoidable that the primeval Sun must have contained a reasonably large quantity of deuterium which must have been burned before the Sun could reach its present hydrogen-burning state.

It is beyond the scope of this treatise to analyze the evolution of the Sun in more detail. We shall only cite the results of a preliminary study (Alfvén, 1963) which indicate the following sequence of events:


FIGURE 25.6.2.- Below: Angular momentum transferred to the C cloud as a function of the mass processed through this cloud.

FIGURE 25.6.2.- Below: Angular momentum transferred to the C cloud as a function of the mass processed through this cloud. The transfer of momentum is proportional to the cumulative mass until a saturation is reached, when almost all the momentum is transferred. Above: Angular velocity of the Sun after the transfer. When saturation is reached, the solar angular velocity equals the Kepler velocity of Jupiter. If the transfer takes place when the Sun is in the deuterium-burning state with a moment of inertia 200 times the present value, the angular velocity increases by a factor of 200 as the Sun contracts, producing the present spin period (25 days) of the Sun when contraction is completed.


[479] (1) The Sun was formed as a D-burning star with R = 1.1 X 1012 cm and [Greek letter] tau= 20 days.

(2) Terrestrial planets were formed. This required a rather small change in spin.

(3) Giant planets were formed. The Sun transferred 99.4 percent of its spin angular momentum and was brought into isorotation with Jupiter: [Greek letter] tau
=12 yr (fig. 25.6.2).

(4) After consuming its deuterium the Sun contracted to its present size, thereby increasing its spin to the present value which is determined by this process.

(5) There has probably been no large change in the mass or the spin of the Sun since the completion of process (4) (fig. 25.6.3).


FIGURE 25.6.3.- Angular velocity of the Sun as a function of time.

FIGURE 25.6.3.- Angular velocity of the Sun as a function of time. It is assumed that the solar system does not lose any angular momentum to infinity (angular momentum is conserved within the solar system). As the Sun contracts, its moment of inertia decreases, so that its angular velocity increases. The contraction during deuterium burning is small and the angular velocity remains constant. The B cloud (forming the Earth, Venus, and Mercury) forms during this period but does not change the solar angular momentum appreciably. (The A cloud may have formed earlier). When the C cloud (from which the giant planets accrete) forms, the Sun loses most of its angular momentum and is brought into isorotation with Jupiter (period 12 yr). When the deuterium is totally consumed, the Sun contracts to its present state, with the moment of inertia decreasing by a factor of 200. The angular velocity increases by the same factor, accounting for the present angular velocity of the Sun.



There is a general belief that stars are forming by gravitational collapse; in spite of vigorous efforts no one has yet found any observational indication of confirmation. Thus the "generally accepted" theory of stellar formation may be one of a hundred unsupported dogmas which constitute a large part of present-day astrophysics.

As was demonstrated in secs. 9.7-9.8, the isochronism of spins gives good support for the view that celestial bodies as different as asteroids of mass ~1018 g and the giant planets of mass ~1030 g are formed by the accretional process of ch. 12. We can completely rule out gravitational collapse.

Now the question arises: If a certain accretional process is effective over 12 orders of magnitude in mass, why should it not be valid over 3 orders of magnitude more, so as to include a star like the Sun with mass 2 X 1033 g?

There are good reasons to believe that stars are forming in dark clouds. The development of radio and infrared astronomy is now supplying us with a richness of data about their properties. As has been pointed out in sec. 15.1 there is clear evidence that hydromagnetic and plasma processes are of decisive importance. In the present analysis we have looked at the star-formation problem using solar-system data as the empirical basis.

The properties of the source cloud which we have derived seems to be reconcilable with the observed properties of dark clouds. A further study of these phenomena may lead to a new understanding of how stars are formed. A hydromagnetic treatment combining dark cloud observations and solar system data may lead to the solution of this important problem.