SP-345 Evolution of the Solar System

 

16. MODEL OF THE HETEGONIC PLASMA

 

16.1. MAGNETIZED CENTRAL BODY

[265] The simplest assumption we could make about the nature of the magnetic field in the hetegonic nebula is that the field derives from a magnetized central body. This implies that the formation of satellites around a planet and the formation of planets around a star cannot take place unless the central body is magnetized. We know that the Sun and Jupiter are magnetized. Mars is not magnetized now. The magnetic states of Saturn and Uranus, which are also surrounded by secondary bodies, are not known. However, for our study, it is not essential that the central bodies be magnetized at present but only that they possessed sufficiently strong magnetic fields in the hetegonic era (see sec. 16.3 and table 16.3.1). This must necessarily be introduced as an ad hoc assumption. This assumption can in some cases be checked experimentally by analysis of remanent magnetization in preserved primordial ferromagnetic crystals in the way it has been done for crystals that now are gathered in meteorites (Brecher, 1971, 1972c; Brecher and Arrhenius, 1975).

A considerable amount of work has been done on theories of the magnetization of celestial bodies, but none of the theories is in such a state that it is possible to calculate the strength of the magnetic field. However, the theories give qualitative support to our assumption that the central bodies were magnetized during hetegonic times. It should also be noted that certain stars are known to possess magnetic fields of the order of several thousand G, and one (HD215441) even as high as 35 000 G (Gollnow, 1962).

To make a model of the state of the plasma surrounding such a body, we assume that the central body is uniformly magnetized parallel or antiparallel to the axis of rotation. In case there are no external currents, this is equivalent to assuming that the magnetic field outside the body is a dipole field with the dipole located at the center of the body and directed parallel or antiparallel to the spin axis.

As we shall find later, neither the strength nor the sign of the dipole appears explicitly in our treatment. The only requirement is that the strength of the magnetic field be sufficient to control the dynamics of the plasma.

[266] We shall also see later that only moderate field strengths of the planets are required to produce the necessary effect. The dipole moment of the Sun must have been much larger than it is now (table 16.3.1), but this does not necessarily mean that the surface field was correspondingly large, since the latter would depend on the solar radius and we know very little about the actual size of the Sun in the hetegonic era (ch. 25).

 

16.2. ANGULAR MOMENTUM

For understanding the evolutionary history of the solar system, it is important to examine the distribution of angular momentum in the system. Figures 2.3.1-2.3.4 show that the specific angular momenta of the respective secondary bodies exceed that of the spinning central body by one to three orders of magnitude.

This fact constitutes one of the main difficulties of all Laplacian-type theories; these theories claim that the secondary bodies as well as the central body derive from an initial massive nebula which, during its contraction, has left behind a series of rings that later form the secondary bodies. Each of these rings must have had essentially the same angular momentum as the orbital momentum of the secondary body formed from it, whereas the central body should have a specific angular momentum which is much less. No reasonable mechanism has been found by which such a distribution of angular momentum can be achieved during contraction. The only possibility one could think of is that the central body lost most of its angular momentum after it had separated from the rings.

In the case of the Sun, such a loss could perhaps be produced by the solar wind. Using the present conditions in the solar wind, an e-folding time for solar rotational braking has been claimed to be in the range 3-6 X 109 yr (Brandt, 1970). The currently accepted age of the Sun is about 5 X 109 yr. Thus, allowing for error in the estimate, it is not unlikely that solar wind emission may have been an efficient process for the loss of solar angular momentum. However, the above value is very uncertain since there is, as yet, no way of deciding whether the solar wind had its present properties at all times in the past. Emission of the solar wind depends on some hydromagnetic processes that are not very well understood.

It is possible that one or more links in this complicated causality chain has varied in such a way as to change the order of magnitude of the rate of loss of angular momentum. Hence, on the basis of the solar wind braking hypothesis, it is possible that the newborn Sun had about the same angular momentum as it has now, but it may have been larger by an order of magnitude or more.

There are speculations about an early period of intense "solar gale." These speculations are mainly based on an analogy with T-Tauri stars but [267] aside from the uncertainties in interpreting the T-Tauri observations the relation between such stars and the formation of planets is questionable. Furthermore, the record of irradiation of primordial grains gives no evidence of the steepness changes in the corpuscular energy spectrum, which ought to accompany a strong enhancement of solar wind emission (see also sec. 5.5).

These uncertainties point out how difficult it is to draw any conclusions about the hetegonic process from the study of the formation of planets around the Sun. It is much safer to base our discussion on the formation of satellites around the planets.

In all the satellite systems we find that the specific angular momentum of the orbital motion of satellites is orders of magnitude higher than that of the spinning central planet. A braking of this spin by the same hypothetical process as suggested for the Sun is out of the question since this would require a mechanism that would give almost the same spin period to Jupiter, Saturn, and Uranus, in spite of the fact that these planets have very different satellite systems. From the spin isochronism discussed in secs. 9.7-9.8 we have concluded instead that the planets could not have lost very much angular momentum. We have also found that Giuli's theory of planetary spins (ch. 13) strongly supports the theory of planetesimal accretion which is fundamentally different from the picture of a contracting Laplacian nebula.

 

16.3. THE TRANSFER OF ANGULAR MOMENTUM

The transfer of angular momentum from a rotating central body is a ! problem that has attracted much interest over the years. It has been concluded that an astrophysically efficient transfer can only be produced by hydromagnetic effects. Hydromagnetic transfer was studied by Ferraro and led to his law of isorotation. Lüst and Schlüter (1955) demonstrated -that a hydromagnetic braking of stellar rotation could be achieved.

The Ferraro isorotation law assumes that not only the central body but also the surrounding medium has infinite electrical conductivity, which means that the magnetic field lines are frozen in. However, recent studies of the conditions in the terrestrial magnetosphere indicate the presence of components of electric field parallel to the magnetic field (E| |) over large distances in a few cases (Mozer and Fahleson, 1970; Kelley et al., 1971). Such electric fields may occur essentially in two different ways. As shown by Persson (1963, 1966), anisotropies in the velocity distribution of charged particles in the magnetosphere in combination with the magnetic field i gradient will result in parallel electric fields under very general conditions. However, E| | may also be associated with Birkeland currents in the magnetosphere, which are observed to have densities of the order of 10-6-10-4 amp/m2 . (Zmuda et al., 1967; Cloutier et al., 1970). Such currents have a tendency to [268] produce electrostatic double layers. A review by Block (1972) gives both theoretical and observational evidence for the existence of such layers, preferentially in the upper ionosphere and the lower magnetosphere.

The existence of an electric field parallel to the magnetic field violates the conditions for frozen-in field lines (see Alfvén and Falthammar, 1963, p. 191). it results in a decoupling of the plasma from the magnetic field lines. Hence the state of Ferraro isorotation is not necessarily established, and the outer regions of the medium surrounding the central body may rotate with a smaller angular velocity than does the central body itself.

 

16.3.1. A Simplified Model

We shall study an idealized, and in certain respects (see sec. 16.3.2) unrealistic, model of the hydromagnetic transfer of angular momentum from a central body with radius Rc, magnetic dipole moment µ, and spin angular velocity [Greek letter] capital omega (fig. 16.3.1).

Seen from a coordinate system fixed in space, the voltage difference between two points b1 and b2 at latitude [Greek letter] lambda subscript 1 and [Greek letter] lambda subscript 2
of a central body has a value

 

mathematical equation
(16.3.1)

 

Similarly, if there is a conducting plasma element between the points c1 and c2 situated on the lines of force through b1 and b2, but rotating around the axis with the angular velocity [Greek letter] omega, there will be a voltage difference induced between c1 and c2 given by

 

mathematical equation
(16.3.2)

 

If we have Ferraro isorotation (i.e., if the magnetic field lines are frozen into the medium), [Greek letter] omega
will be equal to [Greek letter] capital omega
, and hence bc = Vb. If, however, there....

 


[
269]

FIGURE 16.3.1.

FIGURE 16.3.1.- in the absence of Ferraro isorotation, the angular velocity [Greek letter] omega
in the outer regions of the magnetosphere is different from the angular velocity [Greek letter] capital omega
of the central body. This results in a current flow in the loop b1b2c2c1b1 (shown by broken lines) which may result in the electrostatic double layers L and L'. Along part of the paths b1c1 and b2 c2, the electric field has nonzero parallel components resulting in a decoupling of the plasma from the magnetic field lines.

 

....is no isorotation, [Greek letter] omega
is not equal to[Greek letter] capital omega
and hence Vc- Vb will be nonzero, resulting in a current flow in the circuit b1c1c2b2b1 . In the sectors c1c2 and b1b2 this current together with the magnetic field gives rise to a force I X B which tends to accelerate [Greek letter] omega
and retard [Greek letter] capital omega
(in the case [Greek letter] omega
<[Greek letter] capital omega
), thus transferring angular momentum and tending to establish isorotation. The current I flows outward from the central body along the magnetic field line b1c1 and back again along the field line b2c2. In a time dt the current between c1 and c2 transfers the angular momentum

 

mathematical equation
(16.3.3)

 

where Q = I dt is the charge passing through the circuit b1c1c2b2b1 in time dt and [Greek letter] capital phi
is the magnetic flux enclosed between the latitude circles at [Greek letter] lambda subscript 1
and[Greek letter] lambda subscript 2
.

Suppose that the plasma is situated in the equatorial plane of a central body between r1 and r2 and condenses and forms a secondary body with mass Msc moving in a circular orbit of radius r and Kepler period TK. Its orbital momentum Csc is

[270] mathematical equation
(16.3.4)

 

where mathematical equation
and G and Mc represent the gravitational constant and the mass of the central body, respectively.

In an axisymmetric model with a constant current I flowing during a time tI we have

Q = ItI (16.3.5)

 

and

 

mathematical equation
(16.3.6)

 

The current I produces a tangential magnetic field B subscript phiwhich at r (r1< r < r2) is B subscript phi
= 2I/r. This cannot become too large in comparison to B. One of the reasons for this is that if the magnetic energy of B subscript phi
exceeds that of B by an order of magnitude, instabilities will develop (see sec. 15.3, especially the reference to Lindberg's experiment). For an order of magnitude estimate we may put

 

mathematical equation
(16.3.7)

 

which together with eqs. (16.3.3) and (16.3.5-16.3.6) gives

 

mathematical equation
(16.3.8)

 

where r is a distance intermediate between r1 and r2 and [Greek letter] alpha
and [Greek letter] beta constants of the order unity (which we put equal to unity in the following).

Putting C = Csc we obtain from eqs. (16.3.4) and (16.3.8) a lower limit mathematical symbol
= for µ:

 


[
271] TABLE 16.3.1. Minimum Values of Magnetic Fields and Currents for Transfer of Angular Momentum.

Central Body

Secondary Body

Mass of secondary body Msc (g)

Orbital radius of secondary body r (cm)

Orbital period of secondary body TK (sec)

Mscr5/TK

Dipole momentmathematical symbol

(G cm3)

Equatorial surface field B (G)

Current I (amp)

.

Sun

Jupiter

1.9 x 1030

0.778 x 1014

3.74 x 108

0.15 x 1092

0.97 x 1038

See table 16.3.2

1.6 x 1011

Sun

Neptune

1.03 x 1029

0.45 x 1015

5.2 x 109

3.6 x 1092

4.8 x 1038

0.23 x 1011

Jupiter

Callisto

0.95 x 1026

1.88 x 1011

1.44 x 106

1.5 x 1076

3.1 x 1030

9

9 x 108

Saturn

Titan

1.37 x 1026

1.22 x 1011

1.38 x 106

0.27 x 1076

1.3 x 1030

6

9 x 108

Uranus

Oberon

2.6 x 1024

0.586 x 1011

1.16 x 106

1.54 x 1072

3.1 x 1028

2

0.9 x 108

mathematical symbol
= minimum dipole moment of central body calculated from eq. (16.3.9).

B = minimum equatorial surface field.

I = current which transfers the momentum.

Note: If the angular momentum is transferred by filamentary currents (produced by pinch effect), the values of B and I become smaller, possibly by orders of magnitude.


 

[272] mathematical equation
(16.3.9)

 

with

 

mathematical equation
(16.3.10)

 

To estimate the necessary magnetic field we assume that tI is the same as the infall time tinf and introduce tI = 1016 sec (3 X 108 yr), a value we have used earlier (ch. 12), and obtain table 16.3.1.

From the study of spin isochronism (sec. 9.7) and planetesimal accretion we know that the size of the planets cannot have changed very much since their formation. As it is likely that the satellites were formed during a late phase of planet formation, it is legitimate to use the present value of the planetary radii in calculating the minimum surface magnetic field. From table 16.3.1 we find that surface fields of less than 10 G are required. There is no way to check these values until the remanent magnetism of small satellites can be measured, but with our present knowledge they seem to be acceptable. The value Jupiter must have had when it produced its satellites is of the same order of magnitude as its present field.

As we know next to nothing about the state of the Sun when the planets were formed, we cannot make a similar calculation for the solar surface field. We can be rather confident that the solar radius was not smaller than the present one, and the formation of Mercury at a distance of 5.8 X1012 cm places an upper limit on the solar radius. A dipole moment of 5 X 1038 G cm3 implies the values of the surface field shown in table 16.3.2.

In the absence of magnetic measurements from unmetamorphosed bodies in low-eccentricity orbits (such as asteroids), it is impossible to verify any of these values. If carbonaceous chondrites are assumed to be such samples, field strengths of the order of 0.1 to 1 G would be typical at a solar distance....

 


TABLE 16.3.2. Minimum Solar Equatorial Field for Different Radii of the Primeval Sun.

R =

1011

3 x 1011

1012

3 x 1012 cm

B =

5 x 105

18 000

500

18 G


 

[273] ....of 2-4 AU (Brecher, 1972a, c; Brecher and Arrhenius, 1974, 1975). If this field derived directly from the solar dipole, its value should be 1040-1041 G cm3; i.e., more than two orders of magnitude higher than the value in table 16.3.1. However, the field causing the magnetization of grains now in meteorites may also have been strengthened locally by currents as shown by De (1973) and Alfvén and Mendis (1973) and discussed further in ch. 17. As stars are known to possess surface fields as high as 35 000 G, at least the values in table 16.3.2 corresponding to R > 3 X 1011 cm do not seem unreasonable.

Table 16.3.1 also gives the value of the current I which transfers the angular momentum. It is calculated from

 

mathematical equation
(16.3.11)

 

which is obtained from eq. (16.3.7) by putting [Greek letter] alpha
= 1 and mathematical equation
. For the planets, I is only one or two orders of magnitude larger than the electric currents known to flow in the magnetosphere. For the Sun, it is of the order of the current in one single prominence. Hence the required currents are within our experience of actual cosmic plasmas.

 

16.3.2. Discussion of the Model

The model we have treated is a steady-state, homogeneous model and subject to the objections of secs. 15.2 and 15.3. It is likely that we can have a more efficient momentum transfer; e.g., through hydromagnetic waves or filamentary currents. This means that the magnetic dipole moments need not necessarily be as large as found here. It seems unlikely that we can decrease these values by more than one or two orders of magnitude but that can be decided only by further investigations. On the other hand, we have assumed that all the plasma condenses to grains and thus leaves the region of acceleration. This is not correct in the case where most ingredients in the plasma are noncondensable. If, for example, the plasma has a composition similar to the solar photosphere, only about 1 percent of its mass can form grains. As the behavior of volatile substances is not yet taken into account, some modification of our model may be necessary. We may guess that if the mass of volatile substances is 1000 times the mass of condensable substances, the magnetic fields and currents may have to be increased by a factor mathematical equation. Hence a detailed theory may change the figures of table 16.3.1 either downward or upward by one or two orders of magnitude.

 

[274] 16.4. SUPPORT OF THE PRIMORDIAL CLOUD

Closely connected with the problem of transfer of angular momentum is another basic difficulty in the Laplacian approach, namely, support of the cloud against the gravitation of the central body. As soon as the cloud has been brought into rotation with Kepler velocity, it is supported by the centrifugal force. In fact, this is what defines the Kepler motion. But the acceleration to Kepler velocity must necessarily take a considerable amount of time, during which the cloud must be supported in some other way.

Attempts have been made to avoid this difficulty by assuming that the Laplacian nebula had an initial rotation so that the Kepler velocities were established automatically. This results in an extremely high spin of the Sun, which then is supposed to be carried away by a "solar gale." This view could be theoretically possible when applied to the planetary system but lacks support in the observational record of early irradiation of grains (see secs. 5.5 and 16.2). When applied to the satellite systems the proposed mechanism fails also in principle. One of the reasons is that it is irreconcilable with the isochronism of spins.

A plasma may be supported by a magnetic field against gravitation if a toroidal current mathematical symbol
is flowing in the plasma so that the force mathematical symbolbalances the gravitational force (GMcMB)/r2, where MB is the total mass of plasma magnetically suspended at any particular time. Let us assume for the sake of simplicity that the plasma to be supported is distributed over a toroidal volume with large radius r and small radius r/2. If N and m are the number density and the mean mass of a plasma particle in this volume, the condition for balance is expressed by

 

mathematical equation
(16.4.1)

or

 

mathematical equation
(16.4.2)

 

The magnetic field produced by this current is approximately homogeneous within the toroidal volume and has a value

mathematical equation
(16.4.3)

 

[275] Once again we note that, if this field mathematical symbol
becomes too large compared to the B, dipole field will be seriously disturbed and instabilities will develop. For stability, mathematical symbol
must be of the same order of or less than, B. Let us put mathematical equation
, withmathematical symbol
. If for B we use its equatorial value at a distance r (i.e., B = µ/r3), we obtain from eq. (16.4.3)

 

mathematical equation
(16.4.4)

 

which gives the value of the dipole moment µ necessary for the support of the plasma. If [Greek letter] delta = 1, we get a lower limit to µ. Comparing mathematical symbol
with mathematical symbol
as given by eq. (16.3.9) we find that Msc and MB in these two equations are equal if mathematical symbol
is larger than mathematical symbol
by a factormathematical symbol
. In the case of Sun-Jupiter, this is (3 X 108/1016)-1/2approximately5500; for the satellite systems this factor is of the order of 105. Hence the magnetic fields required to suspend the entire distributed mass of the planetary and satellite systems together with a complement of hydrogen and helium during transfer of angular momentum are unreasonably large. (This conclusion is not affected by the uncertainty discussed at the end of sec. 16.3 which is applicable here.) Consequently there is no way to suspend the total mass of the plasma until it is accelerated to Kepler velocity.

 

16.5. THE PLASMA AS A TRANSIENT STATE

We have found that only a small fraction MB of the final mass Msc of a planet or satellite cam be supported by the magnetic field at any particular time. This means that the plasma density [Greek letter] rho
at any time can only be a small fraction mathematical symbol
of the distributed density [Greek letter] rho subscript dst
(mass of the final secondary body divided by the space volume from which it derives; see sec. 2.4)

 

mathematical equation
(16.5.1)

 

This cam be explained if matter is falling in during a long time tinf but resides in the plasma state only during a time tres<< tinf. This is possible if tres is the time needed for the plasma to condense to grains. Since during each time interval tres an amount of matter MB condenses to grains, we have

[276] mathematical equation
(16.5.2)

so that

 

mathematical equation
(16.5.3)

 

It is reasonable that the characteristic time for the production of grains in Kepler orbit is the Kepler period TK. Hence we put tres = TK which together with eqs. (16.3.10) and (16.5.3) gives

 

mathematical equation
(16.5.4)

 

This means that the instantaneous densities are less than the distributed densities by 10-7 for the giant planets to 10-11 for the satellite systems. Hence from figs. 2.4.1-2.4.4 we find that the plasma densities we should consider (compare sec. 2.4) are of the same order of magnitude as the present number densities in the solar corona (102-108 cm-3).

It should be observed that these values refer to the average densities. Since the plasma is necessarily strongly inhomogeneous, the local densities at some places are likely to be several orders of magnitude higher. Indeed the differences between the local and average densities should be of the same order as (or even larger than) the density differences between solar prominences and the solar corona in which they are embedded.

This is important because both the time of condensation of a grain and its chemical and structural properties depend upon local conditions. Assuming that the primordial components of meteorites were formed in the hetegonic nebula, one can place some limits on the properties of the medium from which they formed. The densities suggested in this way, mainly from the vapor pressures of the grain components (Arrhenius, 1972; De, 1973), are much higher than [Greek letter] rho
but still lower than[Greek letter] rho subscript dst
.

 

16.6. CONCLUSIONS ABOUT THE MODEL

We can now restate the requirements of our model in the following way:

(1) Gas should be falling into the environment of the central body in [277] such a way as to account for the density distribution in the solar system. This is satisfied by the infall mechanism we are going to study in ch. 21. In short, this implies that neutral gas falling under gravitation toward the central body becomes ionized when it has reached the critical velocity for ionization. The ionization prevents a closer approach to the central body and the plasma is suspended in the magnetic field.

(2) Angular momentum is transferred from the central body to this plasma. A state of partial corotation is produced. This will be studied in ch. 17.

(3) The condensation of the nonvolatile substances of the plasma produces grains with chemical and structural properties exemplified by primordial components in meteorites. This condensation should take place in an environment permeated by a magnetic field of the order of 0.1-1 G in the case of the planetary system (Brecher, 1972a,c; Brecher and Arrhenius, 1974, 1975). It is, however, also possible that a major portion of the primordial grains are of interstellar origin and became electromagnetically trapped in the circumsolar plasma.

(4) The grains should acquire such a dynamic state that they move in eccentric Kepler orbits thus satisfying the prerequisites for planetesimal accretion. Many-particle systems in this state are termed jet streams; the characteristic energy and mass balance in such systems are described in chs. 6 and 12.

The plasma state necessarily coexists with the jet streams. In fact, the grains and the plasma out of which they condense will interact mutually. As a population of orbiting grains has a "negative diffusion coefficient" (Baxter and Thompson, 1971, 1973), the grains originally distributed through a given volume will tend to form a number of separate jet streams. Once a jet stream is formed it will collect new grains as they condense in its environment. Inside the jet streams, the grains accrete to larger bodies and eventually to planets and satellites. A perspective of the various processes is represented by fig. 16.6.1. There are a number of jet streams in the equatorial plane, and these are joined with the central body by plasma regions somewhat similar to the present-day solar prominences but having much greater dimensions if the central body is the Sun. We shall refer to these regions as superprominences.

 

16.7 THE HETEGONIC NEBULAE

In Laplacian-type theories, the medium surrounding the primordial Sun is called the "solar nebula" or "circumsolar nebula" and forms the precursor for the planets. In contrast to Laplacian theories, we are not developing a theory of the formation of planets alone, but a general hetegonic...

 


[
278]

FIGURE 16.6.1.- A sketch of the series of hetegonic processes leading to formation of secondary bodies around a spinning magnetized central body (not drawn to scale).

FIGURE 16.6.1.- A sketch of the series of hetegonic processes leading to formation of secondary bodies around a spinning magnetized central body (not drawn to scale). The dipole magnet is located at the center of the central body and is aligned with the spin axis. The gas falling from "infinity" into the environment of the central body becomes ionized by collision with the magnetized plasma when its free-fall velocity exceeds the critical velocity for ionization, and the ionized gas then remains suspended in the magnetic field. The rotation and magnetic field together with the conducting plasma surrounding the central body give rise to a homopolar emf which causes a current flow in the plasma This current I together with the magnetic field B give rise to a force I x B which transfers angular motion from the central body to the surrounding plasma. The current also produces prominence -like regions of gas (by pinch effect) which are denser and cooler than the surrounding regions and in these regions the condensation of grains takes place Through viscous effects, the population of grains evolves into a number of jet streams while the noncondensable gases form a thin disc in the equatorial plane.

 

....theory applicable both to the formation of planets around the Sun and the formation of satellites around planets. Since the term "solar nebula" only refers to one of these systems, "hetegonic nebulae" is a preferable term where reference is made to the entire system.

In retaining the term "nebula" it is important to definitely disassociate it from the 19th-century concept; i.e., a homogeneous disc of nonionized gas with uniform chemical composition described by prehydromagnetic dynamics. For a number of reasons that we have discussed earlier this concept is obsolete. In terms of modern theory and observation we need instead [279] to consider the central bodies to be surrounded by a structured medium of plasma and grains throughout the period of formation of the secondary bodies. The results of the preceding analysis combined with some of the results discussed in subsequent chapters lead to a rather complex patter which we shall now describe.

The space around the central body may be called a supercorona, characterized by a medium that is similar to the present solar corona but much larger in extent due to the flux of gas from outside into the system during the formative era. It is magnetized, primarily by the magnetic field of the central body. Its average density, to show the proper behavior, would be of the same order as that of the solar corona (102-108 cm-3). This supercorona consists of four regions of widely differing properties (fig. 16.6.1). Note that the central body may be either the Sun or a planet.

(1) Jet streams: The theory of these is given in ch. 6. They fill up a very small part of this space. The small diameter of the toroid is only a few percent of the large diameter and hence they occupy 10-3-10-4 of the volume. They are fed by injection of grains condensed in large regions around them. The accretion of satellites or planets takes place in the jet streams (see chs. 11-12).

(2) Low-density plasma regions: Most of the space outside the jet streams is filled with a low-density plasma. This region with a density perhaps in the range 10-105 cm-3 occupies most of the volume of the supercorona. The supercorona is fed by infall of matter from a source at large distance ("infinity"). The transfer of angular momentum from the central body is achieved through processes in this plasma; there is a system of strong electric currents flowing in the plasma which results in filamentary structures (superprominences ).

(3) Filamentary structures or superprominences: The plasma structurally resembles the solar corona with embedded prominences produced by strong currents. These stretch from the surface of the central body out to the most distant regions to which angular momentum is transferred by the currents. As in the solar corona, the filaments have a density that is orders of magnitude larger and a temperature that is much lower than those of the surrounding medium. As high plasma density favors condensation, most of the condensation takes place in the filaments. When condensed grains leave the filaments, they possess a tangential velocity which determines their Kepler orbits; their interaction leads to the formation of jet streams. At the same time, plasma from the low-density regions is drawn into the filaments by the pinch effect.

(4) Noncondensable gas clouds: As the injected matter contains a large fraction of noncondensable gases presumably they form the main constituent- there is an increasing supply of such gases in the filaments and in the interfilamentary plasma. When partial corotation is established, [280] this gas is accumulated close to the equatorial plane. Part of the gas is retained in the jet streams where the apparent attraction accumulates it (ch. 6). Hence accretion in the jet streams may take place in a cloud of noncondensable gases. When an embryo has become so large that its gravitation becomes appreciable, it may capture an atmosphere from the gas supply of the jet stream.

It is likely that the jet streams cannot keep all the gas. Some of it may diffuse away, possibly forming a thin disc of gas that may leak into the central body or transfer gas from one jet stream to another. In fig. 16.6.1 the gas is assumed to form toruses around the jet streams which flatten out to discs. It is doubtful whether any appreciable quantity of gas can leak out to infinity because of momentum considerations.

The behavior of the noncondensable gases is necessarily the most hypothetical element in the model because we have very little, essentially indirect, information about it.

 


FIGURE 16.7.1.Sequence of processes leading to the formation of secondary bodies around a central body.

FIGURE 16.7.1.Sequence of processes leading to the formation of secondary bodies around a central body.

 

[281] The diagram in fig. 16.7.1 outlines the sequence of processes leading to the formation of secondary bodies around a central body. These processes will be discussed in detail in the following chapters.

 

16.8. IRRADIATION EFFECTS

Analyses of particle tracks and surface-related gases in meteorites demonstrate that individual crystals and rock fragments become individually irradiated with accelerated particles (ch. 22). This irradiation evidently took place before material was permanently locked into the parent bodies of the meteorites of which they are now a part. Considerable fluxes of corpuscular radiation with approximately solar photospheric composition must have existed during that period of formation of meteorite parent bodies when individual crystals and rock fragments were free to move relative to each other; that is, during the time of embryonic accretion. This process may still be going on as, for example, in the asteroidal and cometary jet streams.

With present information it is not possible to fix the point in time when this irradiation began or to decide whether it was present during or soon after the era of gas infall and condensation of primordial matter. Hence the specific irradiation phenomena are not a critical part of our treatment of these early phases. On the other hand, the properties of our model are such that particle acceleration into the keV ("solar wind") and MeV or GeV ("solar flare") ranges in general is expected.

In sec. 15.4 our model is characterized as a synthesis of phenomena now observed in the Earth's magnetosphere and in the solar corona. This implies that we should expect the model to exhibit to a certain extent other related properties of these regions. It is well known that in the magnetosphere there are processes by which particles are accelerated to keV energies (as shown by the aurora and by direct space measurements). In the van Allen belts there are also particles accelerated by magnetospheric processes to MeV energies. Furthermore, it is well known that solar activity, especially in connection with flares, produces MeV-GeV particles ("solar cosmic rays" ).

Our superprominences should produce similar effects in the whole region where transfer of angular momentum takes place and grains are condensing. Hence in our model grains necessarily are irradiated in various ways. Even nuclear reactions may be produced. All these effects will occur independently of whether the Sun was hot or cool or had an activity of the present type. In fact, the only required properties of the central body, be it the Sun or a planet, are gravitating mass, spin, and magnetization.

A detailed theory of irradiation effects is difficult and cannot be worked out until the theory of both the magnetosphere and solar activity is much [282] more advanced than today. When this stage is reached the irradiation effects will probably allow specific conclusions. Already, present studies of the irradiation record in the constituent grains of meteorites make it possible to place limits on total dosage and energy spectra of the primordial grain irradiation (see, e.g., Macdougall et al., 1974).

 

16.9. THE MODEL AND THE HETEGONIC PRINCIPLE

In ch. 1 it was pointed out that, because the general structure of the satellite systems is so similar to that of the planetary system, one should aim at a general hetegonic theory of formation of secondary bodies around a central body. This is a principle that has been pronounced repeatedly over the centuries and no one seems to have denied it explicitly. It is an extremely powerful principle because of the severe constraints it puts on every model. In spite of this it has usually been neglected in the formulation of solar system theories.

 


FIGURE 16.9.1.- Diagram showing how the speculative character of a theory is reduced by the hetegonic principle which implies that all theories should be applicable to both planetary and satellite systems.

FIGURE 16.9.1.- Diagram showing how the speculative character of a theory is reduced by the hetegonic principle which implies that all theories should be applicable to both planetary and satellite systems. This eliminates the need to rely on hypotheses about the early Sun and ties the theory closer to observations.

 

[283] Earlier we used the hetegonic principle for a choice between alternative explanations of the resonances in the satellite systems (sec. 9.6). The diagram in fig. 16.9.1 shows how the principle is applied to the two similar series of processes leading to the formation of secondary bodies from a primeval dispersed medium. The chain of processes leading to the formation of planets around the Sun is repeated in the case of formation of satellites around the planets, but in the latter case a small part (close to the planet) of the planetary jet stream provides the primeval cloud out of which the satellites form. Hence there is only one basic chain of processes, as summed up in fig. 16.7.1, which applies to the formation of both planets and satellites. This means that a complete theory of jet streams (including not only grains but also the gas component) must give the initial conditions for satellite formation.

Hence we can explore the hetegonic process without making detailed assumptions about the properties of the early Sun. This is advantageous because these properties are poorly understood. Indeed, the current theories of stellar formation are speculative and possibly unrelated to reality. For example, the Sun may have been formed by a "stellesimal" accretion process analogous to the planetesimal process. The planetesimal process works over a mass range from 1018 g (or less) up to 1030 g (see secs. 9.7-9.8). One may ask whether to these 12 orders of magnitude one could not add 3 more so as to reach stellar masses (1033 g). Observations give no real support to any of the conventional theories of stellar formation and may agree just as well with a stellesimal accretion. As was pointed out in sec. 15.3, it is now obvious that many homogeneous models are misleading and have to be replaced by inhomogeneous models. The introduction of stellesimal accretion would be in conformity with the latter approach.

From fig. 16.9.1 and the discussion above, we conclude that we need not concern ourselves with the hypothetical question of whether the Sun has passed through a high-luminosity Hayashi phase or whether the solar wind at some early time was stronger than it is now. Neither of these phenomena could have influenced the formation of satellites (e.g., around Uranus) very much. The similarity between the planetary system and satellite systems shows that such phenomena have not played a major dynamic role.

Instead of basing our theory on some hypothesis about the properties of the early Sun, we can draw conclusions about solar evolution from the results of our theory based on observation of the four well-developed systems of orbiting bodies (the planetary system and the satellite systems of Jupiter, Saturn, and Uranus). This will be done in ch. 25.

What has been said so far stresses the importance of studying jet streams (see ch. 6). The theoretical analysis should be expanded to include the gas (or plasma) which is trapped by the apparent attraction. One should also investigate to what extent meteor streams and asteroidal jet streams are [284] similar to those jet streams in which planets and satellites were formed. The formation of short-period comets is one of the crucial problems (see ch. 14).

As a final remark: Although the hetegonic principle is important and useful it should not be interpreted too rigidly. There are obviously certain differences between the planetary system and the satellite systems. The most conspicuous one is that the planets have transferred only a small fraction of their spin to satellite orbital momenta, whereas the Sun appears to have transferred most of its spin to planetary orbital momenta. The principle should preferably be used in such a way that the theory of formation of secondary bodies is developed with the primary aim of explaining the properties of the satellite systems. We then investigate the extent to which this theory is applicable to the formation of planets. If there are reasons to introduce new effects to explain the formation of planets, we should not hesitate to do this. As we shall see, there seems to be no compelling reason to assume that the general structure is different but there are local effects which may be produced by solar radiation.


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