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THE ORIGIN OF THE SOLAR SYSTEM* A. G. W. Cameron Mount Wilson and Palomar Observatories** Pasadena, California With the growing astronomical evidence that the Galaxy is many billions of years older than the solar system, it becomes necessary to re- vise our ideas about the processes which enriched the interstellar medium in heavy elements. It is no longer very likely that the heavy elements of the solar system were built in the sort of enormous neutron fluxes which would be expected in supernovae of Type I if the light curves of these supernovae are due to the decay of Cf254 (Burbidge, Hoyle, Burbidge, Christy, and Fowler 1956). Between the time of formation of the Galaxy and the formation of the solar system enough of these super- novae would have occurred to produce heavy element concentrations in the interstellar medium at least a thousand times too large to be compatible with today's solar and meteoritic abundances. As soon as one is willing to accept less powerful neutron sources, a variety of possibilities suggest themselves, so that it becomes difficult to be sure which stellar sources have been mainly responsible for the synthesis of the heavy elements. We start with neutron capture on a slow time scale, in which heavy elements are slowly built up in a capture chain starting with the abundant elements of the iron peak. I now believe that the Ne^(a, n)Mg25 reaction is the principal source of these neutrons. Once the heavy elements have been synthesized on a slow time scale, sub- sequent reactions taking place on intermediate and fast time scales can add neutrons quickly and produce neutron-rich isobars. I believe that a variety of reactions associated with carbon thermonuclear reactions are responsible for producing these neutrons. It seems most likely that the products of the fast time scale will be ejected in Type I supernova explo- sions, although with very much smaller abundances than in the californium theory. *This research was supported by the Air Force Office of Scientific Re- search, ARDC, under contract AF 49(638)-21. **Permanent address: Atomic Energy of Canada, Ltd., Chalk River, Ontario.
Among the nuclei which are synthesized by neutron capture on a fast time scale is !**'⢠This has recently become a particularly interest- ing nuclide because Reynolds (1960a) found an excess amount of its decay product, Xe °, in the Richardton meteorite. At first it appeared that there was one part of excess Xe ^ per million parts of I . Since there is also about one part of lithium, beryllium, or boron isotope per million oxygen atoms, it seemed possible that the I129 might have been produced by spallation by high energy pro- tons from the Sun during the formation of the solar system. However, since the iodine content of Richardton is now found to be a factor "-25 lower than the first estimate (Goles 1960, Reynolds 1960b), this hypothe- sis becomes difficult to maintain. Instead, we must consider the I "to have survived the interval between the cessation of nucleogenesis in that part of the interstellar medium from which the Sun was formed, and the cooling of the meteorite parent bodies sufficiently to retain xenon. Assuming the galaxy to be 10 years older than the solar system, and rate of nucleogenesis 4. 6 billion years ago to be half the average rate of the preceding 10 years, then the above interval turns out to be 1. 0 x 10° years. This interval seems surprisingly small for many complex processes to take place. It therefore becomes of interest to estimate the time re- quired for the distribution of fresh radioactivity to the interstellar medium, for the formation of the star cluster of which the Sun was a member, for the contraction of the Sun, and for the formation and cooling of the planets (or at least of the meteorite parent bodies). The gas and dust in the plane of the galaxy form a disk 200 parsecs thick. This interstellar medium is composed of relatively dense clouds (about 10 hydrogen atoms per cm3) which move through the intercloud medium (of density 20 to 100 times smaller) with velocities of the order of 10 km/sec. The old Population I stars, of which Type I supernovae are probably members, form a layer with a thickness about four times that of the gas and dust. Hence about one Type I supernova in four ex- plodes in the interstellar medium, and about 90 percent of these will be located in the intercloud regions. The products of their explosions will expand to fill a sphere of about 40 parsecs diameter in about 10 million years. To be conservative we will neglect any further diffusion of the products into the interstellar medium. If the clouds were formed by an isotropic compression of the inter- stellar medium, the internal magnetic pressure would be very much greater than any likely external pressure, and the clouds would soon ex- pand again. To be stable, the clouds must have formed by compression of gas along the magnetic lines of force. A mechanism which seems to
cause this has been suggested by Hoyle and Ireland (1960); if a section of the interstellar magnetic field loops up into the galactic halo, material will fall down the lines of force until it has sufficient kinetic energy to overpower magnetic restraints. The material thus compressed will con- tain products from supernovae which have exploded as much as 10^ years ago, but the probability is fairly high that some of the material is of recent origin. I estimate that, subject to a probable error of about a factor of five, the material collected will have an amount of I o equal to that which one would calculate for a continuous synthesis model with a decay time for uniform mixing of 10 million years. The time required to form the cloud by compression is about 20 million years. In order that such a cloud can condense further to form stars, the level of ionization in it must fall very low so that the gas becomes de- coupled from the magnetic field, and the temperature must become small enough so that Jeans' gravitational instability criterion is satisfied. According to this criterion, twice the thermal energy of the gas cloud plus the potential energy of gravitation must be less than zero. Therefore, for a uniform spherical gas cloud, contraction can take place only for temper- atures below .,2/3 1/3 T - n 30 which means that T must be less than about 7o K if the cloud has a typical mass M of about 1000 solar masses and a density n of about 10 particles per cm3. The principal heating mechanisms are collisions with other clouds, photoionization by starlight, and ionization by cosmic rays. The principal cooling mechanisms are electron-ion collisions, collisional excitation of H2 molecules, and molecule-grain collisions. It is likely that cosmic rays will be excluded if the clouds are magnetically isolated from the sur- rounding medium. Starlight can be excluded if there is a large effective grain density at the surface of the cloud. It may be that collisions with clouds will cause evaporation of some large grains and recondensation of small grains, and the optical activation of these and other small grains due to radiation damage. It is tempting to ascribe to these small grains the quantum mechanical properties suggested by Platt (1960), so that they can absorb radiation of wavelength ~400 times their diameters. Collisions between clouds will raise the gas kinetic temperature to a few thousand degrees, perhaps sufficient to dissociate H£ molecules. Reassociation will take place by collisions with grains, and hydrogen molecule cooling will quickly lower the temperature to about 40o K. Further cooling depends on molecule-grain collisions; we can only guess at the rate here because of our almost complete ignorance of the grain
properties. Temperatures as low as 7o K can probably be reached after total cooling times of 20 to 40 million years, but this is a highly uncertain estimate. However, collisions between clouds occur on the average about every 10 million years. Hence the clouds will be reheated usually before the temperature falls low enough for star formation to take place. Star formation thus requires a statistical fluctuation resulting in a somewhat greater than average interval between cloud collisions. This will add a variable time probably of the order of 30 million years to the I129 interval. When Jeans' instability criterion is satisfied, the cloud will contract at a rate which rapidly becomes a free fall. The reason for this is that cooling remains sufficiently rapid during the contraction, i. e., once Jeans' criterion becomes satisfied it stays well-satisfied. The free fall time is . t = 1. 11 (R3/GM)1/2 = 1.63 x 1015 n-1/2 sec, which is about 16 million years for n = 10. At the start, the effective gravity G is less owing to thermal pressures, so the effective free fall time may be taken as about 25 million years. Note that the above formula does not involve the mass of the cloud, so that subunits can condense out of the cloud as soon as they satisfy Jeans' criterion. The final subdivi- sions will have masses of solar order. The result of these considera- tions so far is to give a predicted Ii29 interval in the range 0.4 to 2. 2 x 108 years, with a probable value near 1.1 x 108 years. This would be decreased for more massive clouds than the one considered, and in- creased for less massive clouds. But it is already of the correct order of magnitude. We would thus begin to feel uncomfortable if the remaining stages of stellar contraction and planet formation should take a similar time. The free fall collapse stops when the protosun has a radius of about 3x10 astronomical units. At this point the medium becomes opaque to grain radiation. Further contraction is luminosity controlled, with den- sity in the protosun becoming a smooth function of the radius and with a substantial central condensation taking place. At this point also the re- quirement of the conservation of angular momentum will make the proto- sun gravitationally unstable at the equator, so that further contraction must be accompanied by mass loss. The contraction from 3 x 103 a. u. to 100 a. u. probably takes less than one million years. At this point a dynamical instability sets in owing to the operation of the following energy-absorbing processes: the disso- ciation of H2 molecules, the ionization of hydrogen, and the double ioniza- tion of helium. A free fall collapse takes place which causes the protosun
to shrink from 100 a. u. to about 0. 34 a. u. in a period of ~200 years. About half a solar mass is shed in the form of a nebula during this time. The sun will require about another 70 million years to reach the main sequence, but as we shall see this time is not to be added to the I ^ interval. The important stages in the evolution of the planets will take place while the Sun has a radius of ~0. 34 a. u. and a surface temperature of about 410o K. The nebula probably does not form gaseous "protoplanets" directly, as Kuiper (1951) has suggested, because even protoplanets stable against tidal disruption (Roche criterion) would still suffer thermal disruption (Jeans' criterion) unless the radius of the protoplanets was at least six times greater than the "homogeneous" height of the nebula. Detailed calculations show that in the portion of the nebula shed between 0. 3 and 30 a.u., part of the gas has been heated in excess of 1000o K. This is sufficient to destroy all traces of the original interstel- lar grains. Cooling is a relatively slow process, and the vaporized gases will recondense on a relatively small number of centers, as in a cloud chamber in very slow expansion. It is to be expected that solid bodies the size of boulders will be formed. These will tend to fall toward the plane of the ecliptic and to accumulate into larger bodies. The terrestrial planets represent a very inefficient collection of the total amount of solid material available. The time scale for this planet accumulation is probably very small compared to 10 years, and therefore it probably does not add appreciably to the I129 interval. There are three stages in the development of the protosun at which magnetic forces are very important. These are: (a) in the early stages of luminosity-controlled contraction when a unified rate of angular velocity is being produced, (b) the escape of strong magnetic fields from the nebula which is shed during the dynamical collapse, and (c) following the dynam- ical collapse when an outer solar convection zone can build an external dipole field which can interact with the nebula to brake the Sun's rotation. At each stage an intense acceleration of charged particles may take place, thus producing extensive nuclear spallation throughout the nebula (support for this view is found in the lithium-rich spectrum of T Tauri type proto- stars--Herbig 1956). It might be possible to produce by spallation some 10-° atoms of Al per Si atom and 10-6 Be10 atoms per oxygen atom. According to the calculations of Fish, Goles, and Anders (1960) these abundances of short-lived radioactivities could have melted the asteroids, which is one of the steps in their model for the synthesis of the meteorites.
Arnold: How can we interpret the fact that some meteorites show essen- tially no excess Xe °, even though they may have iodine abundances as high or higher than in Richardton (e.g., Beardsley: Goles 1960, Reynolds 1960b)? The different xenon results could reflect different time scales for the formation of the meteorites, different diffusive properties of the meteorites, or differences in the thermal histories. Cameron: In my model all the time scales for formation of the meteorite parent bodies are the same; the subsequent history may be different. Anders: Some calculations by Goles and Fish reveal that the cooling times for melted asteroids containing the complement of K " which would have been present 4. 5 x 10^ years ago are already comparable with the Richardton I-Xe age, so that the amount of time elapsed between nucleosynthesis and the formation of solid objects in the solar system is very uncertain on the short end. Therefore, differences in the Xel29 content are likely to reflect principally the position of the meteorites in their parent object. Arnold: Then in your model the I-Xe "age" refers to an event which took place later than any of the events discussed by Cameron, and so the interpretation of these ages is still quite uncertain. REFERENCES Burbidge, G. R., Hoyle, F., Burbidge, E. M., Christy, R. F., and Fowler, W. A. (1956) Phys. Rev. 103, 1145. Fish, R. A., Goles, G. G., and Anders, E. (1960) Astrophys. J., 132, 243. Goles, G. G. (1960) J. Geophys. Res., in press. Herbig, G. (1956) in STELLAR POPULATIONS, ed. O'Connell (Inter- science, New York). Hoyle, F., and Ireland, J. G. (1960) Mon. Not. Roy. Astronom. Soc. 120, 173. Kuiper, G. P. (1951) in ASTROPHYSICS, A TOPICAL SYMPOSIUM, ed. Hynek (McGraw-Hill Book Co., Inc., New York). Platt, J. R. (1960) Lowell Obs. Bulletin 105. 278 - Proceedings of a Con- ference on the "Polarization of Starlight in the Interstellar Medium. " Reynolds, J. R. (1960a) Phys. Rev. Letters, 4, 8. Reynolds, J. R. (1960b) unpublished work. 6
