Cosmogonic aspects of the evolution of planetary systems

Adv. Space Res.

©COSPAR. 1981.

Vol. 1, pp. 21—36. Printed in Great Britain.

O273_1l77/8h/030l—002]~ $05.OOIO

COSMOGONIC ASPECTS OF THE EVOLUTION OF PLANETARY SYSTEMS H. Stiller,’ H.-J. Treder2 and D. Möhlmann’ ‘Akademie der Wissenschaften der DDR, Forschungsbereich Geo- und Kosmoswissenschaften, Potsdam, GDR 2Akademie der Wissenschaften der DDR, Zentral-institutfür Astrophysik, Potsdam, GDR

ABSTRACT The fundamental approaches to the problem of formation of planetary and satellite systems are discussed. Especially the hetegony principle and its proposed generalization to a formation principle including the central body, and a restricted actualistic principle are supposed to guide further approaches. Relevant characteristical parameters to identify the formation processes and possible future planetological tasks have been derived on this basis. INTRODUCTION Planetary and satellite systems are one step of the structuration of the cosmqs. One of the important challenges to cosmology is to explain this struoturation of the originally homogeneous cosmic matter into the structure—elements as we can observe them today. it is the generally accepted task of planetogony to understand the physical process forming from more or less homogeneously distribu-. ted matter the structure element: system of satellites (planets, moons) orbiting around a central body (star, planet). Here, Alfv~n and Arrhenius introduced the term “system of secondary bodies”, in formulating their hetegony—principle, postulating “that the formation of the regular systems of secondary bodies aroand a primary body depends in a unique way on only two parameters of the primary body, its mass and spin” /1/. It is the aim of this paper to discuss from our point of view the general (and very often controversial) ideas in the field of plane— togony, as it has been defined above. Especially, we investigate a possible generalization and modification of the basic principles, underlying the formation of systems of satellites orbiting around a central body and we discuss attempts for a further precision of the relevant criteria, parameters and conditions.

21

22

H. Stiller et al.

The differences in the fundamental approaches result mainly from different assumptions about ti’e origin and further evolution or the preplanetary matter. In principle this matter can result I) eitj’ier from e~ternelsources around the central body (also possibly in connection with its ovm formation) II) or from the central body (possibly in connection ~iith its own formation), or, of course, fro~i a co’io~netion of ootn elementary possibilities. As will be discussed later, the basic difference between models based on these two possibilities is the distribution of the angular momentum which plays an important role in formation and evolution of discs and rings Theories belonging to the category I (see Pig. 1) have their origin in ICants “nebular theory” of 1755 /2/. He assumed, that the formation of the planetary system was a direct consequence of formation and evolution of the sun from a gravitationally contracting primeval nebula. The accumulated matter around the sun then formed a preplanetary disc. The models, based on this “Kantian approach” differ in the processes forming this preplane— tary disc and in the evolution of planets from this matter.

I ~enticn

approach

Laplacian approach

(Matter accumulation)

(Matter ejection)

:.~attercapture theories

Rotation Instabilities

(Schmidt, Alfv~n)

(Laplace, Earwin, Poincare, Fessenkov, Lyttleton)

(~pisodical)matter capture of the evolved central body

Matter ejection from the rotational unstable central body

Primeval nebula theories (T~ant V ~eizsacker ter Rear

Collision theories (Chamberlin iioulton, Jeans

Kuiper)

Primary (central) and secondary bodies emerge from a contracting primeval nebula

Jeffreys)

Matter ejection as reoult of (an episodi— cal) close gravitational encounter Binary theories (Struve, Hoyle, Kopai) Binaries as predecessors of planetary syatems

Pig. 1

—

Basic planetolo,~ioalthe~r~

Cosmogonic Aspects of Planetary System Evolution

23

The first formulatjóñ of a theory of the categàry II (see Fig. 1) has been given gy Laplace in 1976 /31 with his model of an extended rotating hot atmosphere of the forming sun. He assumed, that as a result of the shrinkage of this atmosphere the increasing speed of the rotation flattened the central body into an at least unstable form. Then, rings should form around the sun, consisting of matter, ejected in the sun’s equatorial plane. The mass in the rings condensed to form the planets. Models, based on this “Laplacian approach” differ in the ejection—mechanisms and the process, forming the planets form this ejected matter. It should be noted that the models resulting from the described above approaches to the formation of planetary systems can be applied analogously to that of the satellite systems, and here we see analogies too, between formation and present state of the Galaxy and the early stages of systems of satellites orbiting around central bodies. Therefore, it seems to be possible to generalize the mentioned above hetegony—principle into a principle (see Pig. 2), postulating that satellites and central bodies (in the above given sense) have a common origin, and that predecessors of flat cosmic systems (galactic systems of stars, planetary and satellite systems) evolving from a more or less homogeneours distribution of matter are nearly coplanar discs of matter. Evolution and final structure of these discs depend on the involved distribution of angular momentum, mass density, composition, internal Interaction and total mass. This formation principle fulfills the hetegony—principle. As will be discussed later, astronomical evidence supports this more general principle.

Heterony principle (Alfvên, Arrhenius) Formation of regular secondary

generalization

systems in dependence of mass and spin of a primary body

Primary end secondary bodies (and more general—flat cosmic systems) evolve in dependence of the distribution and -transport of the angular momentum from common contracting masses.

~tctualistic principle (ii~lke, Alfv~en, Srrhenius)

-:o reconstract the formation processes one has to start

reduction

Common characteristico of the forma— tion processes, surviving peoulior evolutions end irreversibility. allowing reconstruction.

from the present state (ns the key to the past)

Pig. 2

—

Jasic principles

24

H. Stiller at al.

The formulated above principle and the discussed above resulting theoretical attempts need a further precision derivable from the properties of the four systems of secondary bodies in the solar system (planetary system; Jovian—, Saturnian— and Uranian—satel— lite systems). Nölke /9/ and nowadays Alfv~nand Arrhenius formulated the “actualistic principle”, postulating, that to reconstruct the increasingly older stages of the secondary systems one has to start from the present state. It is our feeling, that this actualistic principle has to be used with a great care, since the processes forming systems of secondary bodies seem to be rather general and, of course, partial irreversible and have a broad spectrum of peculiar (subsequent) evolutionary ways. Consequently, the “actualistic” (-sufficient general) parameters which survived peculiar evolutions and irreversibility, allow reconstruction. Therefore, and as will be discussed later an important task of planetology is to find out appropriated “actualistic” parameters. Insofar, we propose a “restricted actualistic principle”, applicable to those reconstructable parameters having their co~mnon origin in the general formation process of secondary bodies. Furthermore, it shall be noted that in addition to these informa— tions modern astronomy (on infrared— and microwave frequencies) gave and can give increasingly details about the properties of systems of satellites and. central bodies. There are two essential challenges in this field: —

—

to verify the existence of extrasolar planetary systems by astronomical methods. The proof of the existence of these systems would give further limitations to the basic theories as they have been mentioned above. to determine more precisely and by direct observations of pre— planetary discs, structure and properties of evolving systems of secondary bodies in their very early stages.

Results and further tasks of these astronomical contributions to the theory of the formation of systems of satellites and central bodies will be discussed later.COMPARATIVE STUDIES To reconstruct the common characteristica of the formation process of systems of satellites and central bodies it is necessary to determine, how these systems may have changed since their origin. Processes, that are able to cause essential changes are transfer of angular momentum by tidal action or resonance effects. The last mentioned possibility can be important only, when bodies with nearly commensurable orbits are locked into resonance. If exact resonance is established, the bodies will remain in resonance /4/. Therefore, resonances conserve rather than change the structure of satellite systems. Tidal effects, effective in spin—orbit coupling, may lead to a braking of the spin of satellites, making the spin periods equal to the orbital periods. As a result of their great masses the orbital characteristica o±~ the central bodies are not influenced essentially by these processes.

Cosmogonic

Aspects

of Planetary

System Evolution

25

Therefore, we assume that the i~i~gd bodi~din the’ planetary system and the satellite systems of the planets are at present in an orbital state, that is not essentially different from that after their formation /1/, /5/. This gives the possibility to tackle the common aspects of the formation of systems of satellites and central bodies by comparative methods. Classical characteristic parameters To discuss more in detail the physics of systems of satellites and central bodies, the essential characteristica of these systems must be given. As is wellknown, the classical characteristica, basing to all the fundamental approaches, even of Kant and Laplace are a) stable and nearly coplanar orbits of the satellites b) nearly circular orbits of the satellites c) same sense of revolution of satellites and spin of the central body ci) same sense of revolution and spin of most of the satellites. As can be seen from Fig. 3 these characteristica are not sufficient to identify the formation process in a unique way, but the number of the possible approaches can be reduced.

________________

copIan~r orbit,

.Iatter cepture

x

circular orbits x

revol./ contr. srln B, L C?)

I

revel.!

see. zt,in possible

~rimeval nebula

I

x

Collision theories

x

?

theories

x

?

x

1

~otation Instabilities

x

x

x

possible

x

possible

3inary

Pig. 5

—

Classical (hetegonic) parameter

26

H. Stiller at al.

Energy levels of orbits One of the surprising discoveries of Alfv&ri is, that the bodies in the four different secondary systems of the Solar system move around their central bodies at distances which are comparable to those, where the amount of kinetic energy (or gravitational potential energy) of elements falling into the central body from far outside equals their ionization energy. It has been postulated by Alfv~n (1942) /6/ and proven experimentally that ionization of the infalling gas occurs at corresponding “critical velocities” if a magnetic field is present. This is an important argument for the essential-role that plasmaprocesses might have played during the formation processes of secondary systems. It is not necessary to describe here the resulting conclusions of Alfv~nand his coworkers. Prof. Alfv~nhas discussed this in the foregoing lecture. But it should be noted, that also from our point of view the advantages of this model are: —

—

a quite natural explanation of the remarkable coincidence of the order of magnitude of gravitational potential energy and ionization energy in such different systems a great number of properties of the secondary systems can be explained by taking into account the plasma—physical considerations of Alfv~n and Arrhenius /1/.

M 17

—

~IIJ~I I I

1

I

III 102 1O~10’ 1O~

I

~

S

Fig. 4

Energy Levels

Cosmogonic

Aspects

As can be seen from rig. magnitude condition of LI the orbital 0 const (

of Planetary

4, it can be that the fits order the of Of stated, ~ó~iddr~r bodies I~adiit’±~!’ = e Vion, withy—gravitational constant,

TI0 mass of the central body, a mass of the infalling e Vjo~ ionization energy of these elements). This is a general characteristic of secondary systems. Attempts to stand this on the basis of mechanical arguments, can not on first principles as plasma physics does. —

27

System Evolution

—

—

elements, further underbe based

Mass distribution in satellite systems A first rough estimation of the gross features of the mass distribution in satellite systems can be found by plotting a “distributed density” versus seinimajor axis of the secondary bodies, where the “distributed density” is determined by distributing the mass of a planet or satellite over a toroidal volume around the orbit of this body. The torus shall have a small diameter being the sum of half the distances to the orbits of the adjacent bodies /1/. It is well known, that the resulting distributed density diagrams for the four satellite systems in our Solar system3 differ and iO~ a~well g/cm3) as the character the distribution. Different in in magnitude (betweenof maximal values of 1011 g/cm groups of planets and satellites might be derived from these diagrams. It is interesting to note, as has been shown by Alfv~n, that there is a certain correlation between these groups and the separation of the above cited ionization energies into different bands. Furthermore, trends in the radial distribution of the masses of the sa— téllites within these groups have been discussed. We think that these distributions can be explained too with assuming that the preplanetary mass distribution increased with distance from the central body, having a maximum and decreased then at greater distances. A further and from our point of view, essential charac— teristioum follows from the radial distribution of the masses in satellite systems. In all four systems of our Solar system two groups of satellites can be derived from these distributions (Fig. 5 Pig. 8). —

—

—

a group “inner bodies” with smaller masses, and an averaged trend of slowly increasing and then decreasing masses (with increasing distance from the central body), a group of “outer bodies” with the greatest “individual” masses in the satellite system and an averaged trend of strongly decreasing masses with increasing distance from the central body.

A possible interpretation- of the characteristical radius, separating these two groups will be given later by the paper ci’ Möhlmann within this workshop.

JASA 1:7-C

28

H. Stiller et al.

In M (1024kg)

10

—

.8— \

64— 2

II 1

\

t

i

i

42 4

6

8

I

I

10 12

I

I

14 16

18

r/r 0

Fig. 5

Mass distribution in the planetary system

21kg) In M(10 6— ft

4r~

‘S.’ “~

23Fig. 6

I. 2

I 4

I 6

I 8

Mass distribution

I 10

I 12

~ 14

r/r~

in the Jovian system

Cosmogonic

Aspects

of

Planetary

System Evolution

En M(1020kg)

\

6-

N N

A

2-f? ‘

I

I

I

I

2

4

6

8 r/r

0 Fig. 7 Mass distribution in the Saturnian system

20kg) Ln M (10

4

-—

N 2’

2

IS” ‘

2

I

Fig. 8

I

I 2

I

I 4

r/r

0 Mass distribution in the IJranian system

29

30

H. Stiller et al.

Summarizing we conclude: —

—

the comparative study of “individual” masses of satellites shows, that the formation process of systems of satellites and central bodies is not strong enough to fix their single masses. The final mass of a satellite seems to depend on many processes and conditions, as composition, state, local dynamics and spezific interaction properties of the preplanetary matter Therefore, single masses of satellites are no characteristics in the above given sense for the identification of the processes forming these systems. Groups of satellites, derived from their radial mass distribution have similarities in all the four satellite systems in our Solar system. Therefore, the separation of the satellite systems in two (an inner and an outer) groups with a different radial dependence shall assumed to be a characteristicum for the conmion formation process of these systems. It should be noted here it was especially 0. Yu. Sciinu.dt who advocated this separation of the planetary system (into terrestrial and outer planets) as a significant physical characteristicum. We think that this separation is an essential property of satellite systems. It is interesting to note, that the inner group is connected with bodies of rocky planetary matter, while the outer bodies a consist mainly of the icy and gaseous component. Physical properties of these three different components of planetary matter will be discussed more in detail in the introducing lecture o±~ Stiller and Rranck at this workshop.

Angular momentum It has been supposed that angular momentum of systems of satellites and central bodies must be an essential parameter since the energy of angular momentum can not be dissipated by collisions within the preplanetary matter. Therefore, the total angular momentum must be conserved. Only its distribution might have been changed by transport caused by viscous—like interactions or by the action of magnetic fields. Especially the different distribution of angular momentum in the planetary system and the satellite systems (compared with their central bodies) seems to indicate the adequacy of the Kantian approach for the formation of the planetary system and that of the Laplacian approach for the satellite systems But the peculiar role of individual masses, as described above, restricts this possible importance of the angular momentum of the planets and satellites. Indeed, the radial distribution of angular momentum of the planets and satellites in the solar system has no more information than the mass distribution has, identifying the same two groups of planets and satellites as the mass distribution does (Fig. 9) Therefore, “specific angular momentum” (angular momentum divided by the individual mass) could be a more appropriated sub3ect for comparative studies.

Cosmogonic Aspects of Planetary System Evolution

31

tnL 10-

IiIiIIii~

2

4

6

8

10

12

14

16

r/r0

Fig. 9 Angular momentum distribution in the planetary system

On the other side, as a result of the conservation of the total angular momentum, serious constraints are given for models of the formation of satellite systems. Especially models of common origin of the satellites and the central bodies from a contracting cloud have to explain where that angular momentum is deposited, involved in the original contracting matter. As is well—known, all the four discussed satellite systems have a considerable less total angular momentum than had a hypothetical sphere of the total mass of the system and a radius equal to the semimajor axis of the outermost body in the system. We assume, that transport of angular momentum outwards is an essential and characterizing phenomenon during the contraction stages in prestellar and. preplanetary matter. Such a transport, caused by viscous interactions must be expected as result of the increasing orbital velocity of the collapsing disc— shaped matter towards the center of gravity. The effectivity of this outward transport of angular momentum could be enhanced by turbulence—amplified viscosity. Also, magnetic fields could give an essential contribution to these transport processes. Prom our point of view, these angular momentum transport processes by shearing stresses during the contraction phase may have led to the observed general characteristics of angular momentum distribution. Two arguments supporting this shall be given here. At first, we refer to the work of Lynden—Bell and Pringle /7/ about the evolution of viscous discs, stating “thus the minimum energy configuration is a limit in which one particle of infinitesimal mass carries all the angular momentum in a circular orbit at

32

H. Stiller et al.

infinity while all the remaining mass aggregats at the centre”. Second, the cometary belt, suggested by Oort, being at orbital distances at some 1o4 AU from the sun, could represent this “particle of infinitesimal mass” and carry an essential part of the angular momentum of the “initial state”. The corresponding angular momentum carrying masses of the satellite systems should have been captured by the suns gravity. Regular schemes for orbital

parameters

The best known example for regular schemes of orbital parameters of planets is the so called Titius—Bode law for the planetary orbital radii. As is also well known, there exist a lot of similar schemes. It is not our aim to discuss them in detail, but we think it would be valuable, to characterize some conditions for a sense— ful application of such schemes in comparative planetology. It is known from mathematics, that every finite distribution of discrete elements can be approximated by an appropriated series. Arguments, justifying attempts for an eventually cal interpretation of such series are: —

—

—

simplicity

possible

physi-

and accuracy of the structure of the series

no “missing links” (gaps) or verification of the existence of predicted yet “missing links” applicability to physically similar systems

At least, such schemes are valuable only, if they can be derived from physical models. To find this physics, they can be an appropriated tool. ASTRONOMICAL RESULTSOur understanding of star formation is still far from complete, but some of the principal characteristica of the collapse processes are understood now with reasonable confidence. As a result of modern astronomical observations at radio— and infrared wavelengths some stages of these collapse processes became identifiable with certain typs of observable objects. On the other side, succesful theoretical attempts clarified the importance of the relevant physical processes in connection with the collapse. It is not our aim to review here the actual state of astronomical research on this field, but we will summarize the generally accepted actual results which seem to be relevant for planetogonic processes too. As a result of the non—vanishing angular momentum of a collapsing cloud of dust and gas, the collapse is not sherical, as it has been assumed originally for mathematical simplicity in the first numerical computations of these collapse processes. .The matter concentrates not only in the center of gravity but also in the equatorial plane. After thermonuclear ignition of the protostar the resulting radiative pressure accelerates the infalling matter predominantly near to the axis of rotation to high velocities away from the star.

Cosmogonic Aspects of Planetary System Evolution

33

The more intense dust belt in the .~quatorialplan~can not be moved away so fast. Therefore, a preplanetary disc evolves. A group of observed bipolar nebula, described by Elsi~tsser, Staude, Eiora and others /8/ seems to represent this evolutionary stage. A well— known exemple is the bipolar nebula S 106. Fig. 10 gives a schematical picture of such a bipolar nebula. Summarizing, the following characteristica of bipolar nebula in connection with very young stars have been derived: —

—

—

—

the axis of rotation of the circunstellar matter coincides with that of the connected molecular cloud, wherefrom the newborn star evolved the young star it yet obscured at optical wavelengths by the equatorial dust shell At infrared wavelengths the star becomes observable Following a model of Liora~1979) /8/ the dust shell o~S 106 has a diameter of 2.2 x 10 m, a thickness of 0.6 x 10’~m. Assuming a particle density of 2~rf3 and particles with an averaged density of 3 x 10.i k~n , the mass of the dust shell is of the order of 0.1 solar masses Ilear to the axis of rotation observed

a steady outflux of matter can be

axis of rotation central body

I

(young star) — ——

— —

— ____~~~\.‘__~__

mass flow of rarefied optically emitting matter Fig. 10

— —

——

preptanetary disc

Schematic structure of a bipolar nebula

34

H. Stiller et al..

These observations are an essential argument for theories, basing on the assumption, that the preplanetary matter results from the formation process of the central star. The supposed analogue formation of planets and their satellite systems has to be understand then as a result of further condensation processes in this prepla— netary matter. Further astronomical observations seem to be necessary to clarify more in detail dynamics and energetics of observable preplanetary discs and the possible role of magnetic fields. A further challenge for astronomy is the investigation of extraso— lar planetary systems by astrometrical methods. SU1~1MA.RY -

Following our above outlined suggestions, (see Pig. ii) the formation processes of systems with satellites orbiting around a central body can be characterized by

and

Ce.neral fornation ~rir.ciple:

Connon origin of catellite, central bodjea

I~edu~edactualistic

Applicability of characteristic parameters of the aomaon forma-

principle:

tion processes, which survived peculiar processes and allow reconstruction Characteristic

Flatness or coplanarity, circu-

parameters:

lar orbits, sense of revolution and spins, distribution Future tasks;

energy levels,

mass

in two groups,

a) Comparative studies of secondary systems, md. missions and astrometrical methods (extrasolar planet, cyst.) b) Astronomical investigations of the physical properties of preplanetary discs (t~amica, magaetie fields, structur, •.,)

composition,

-

c) Theoretical investigations (Syolution of pre~lanetary discs, planetesimal and planetary matter)

~jg.

11

—

Suensary

-

Cosmogonic Aspects of Planetary System Evolution —

—

—

a common contraction of a fra~:~ehtØf-:an interstellar cloud, leading to a central mass (star) and an equatorial circumstellar shell (Kantian approach) the evolution of characterized by inward transport the evolution of

this cjrcuns-tellar shell (preplanetary disc) is an outward transport of angular momentum and an of mass, leading to appropriated conditions for larger bodies (planets)

the satellite systems around the planets have been evolved analogously

To understand these processes —

—

—

35

more in detail

it is necessary to

investigate theoretically the characteristica and evolutionary processes leading to a structuration of preplanetary discs perform astronomical observations, including extraterrestrial experiments to observe more in detail the characteristics of preplanetary discs initiate comparative studies, to find out the common features in satellite systems. Such investigations can be carried out by astrometrical techniques, to get a more representative group of satellite systems by including extrasolar planetary systems, and by comparative planetology. A special task is to find further ar— gunlents supporting the existence of a common formation principle. At present, the following common characteristica of stable satellite systems seam to be generally accepted:

1) nearly coplanar orbits 2) nearly circular orbits 3) common sense of revolution of satellites and spin of the central body 4) common sense of’ revolution and spin of’ most of the satellites 5) energy level of orbits 6) two different groups in the mass distribution (and analogously in the distribution of angular momentum) Further characteristic analoga possibly exist as a result of similar evolutions in dynamics and. kinematics of the preplanetary (or presatellite) discs in the distribution of orbital parameters, in the differences in composition between the two groups of satellites. It is- the task of such comparative studies to find further common characteristics of satellite systems. They can give then the basis to apply the “actualistic principle” to identify the processes more in detail, leading to the formation of regular systems with satellites orbiting around central bodies.

36

H. Stiller -

et al.

References 1.

H. Alfvên and G. Arrhenius, Evolution of the Solar ~ NASA SF 345, Washington, 1976. —

2.

I. Kant, All~emeine Naturgeschiçhte und Theorie des Himmels, 1755, Kants Werke (Insel—Ausgabe) B. II, Naturwissenschaftli— che Schriften, 1912.

3.

P. S. de Laplace, ~osition P. 5. de Laplace,

du Systeme du Monde, 1976 (in Oeuvres Complete, VI, 1884).

4.

P. Goidreich,

Mon. Not. Astron.

Soc. 130,

(3),

159 (1965).

5.

D. Brouwer and G. Clemence, in:- The Solar System, Vol. III, p. 31 (1961).

6.

H. Alfvên, On the cosmo~oriy of the solar system, Stockholms Observatoriwn Ann. 14 (2), 3.

7.

D. Lyn.den—Bell and J. E. Pringle, Mon. Not. R. A~tr. Soc. 168, 603 (1974).

8.

H. Els~sser and H. J. Staude, stron. Astrophys. 70, L 3, (1978) and C. Diora, H Elsasser and 3. P Lahull~ Astron. Astrophys. 74, 89 (1979).

9.

F. Nölke, Der Entwicklungsgang unseres Planetensystems, P. Dunimlers Verl., Berlin u. Bonn, 1930.