The evolution of hydrogen-helium stars

According to the work of Truran and Cameron, and of others, on the chemical evolution of the Galaxy, the first generation of stars in the Galaxy contained principally massive objects. If big-bang nucleosynthesis was responsible for the formation of helium, the first generation of stars would contain about 80% hydrogen and 20% helium, to be consistent with the approximately 22% helium found in recent stellar evolutionary studies of the Sun. The present investigation has followed the pre-main sequence evolution and the main sequence evolution of stars of 5, 10, 20, 30, 100, and 200M . Normal stars in this entire mass range normally convert hydrogen into helium by the CN-cycle on the main sequence. the present hydrogen-helium stars of 5 and 10M must reach higher central temperatures in order to convert hydrogen to helium by the proton-proton chains. Consequently, the mean densities in the stars are greater, and the surface temperatures are higher than in normal stars. In the stars of 20M and larger, the proton-proton chains do not succed in supplying the necessary luminosity of the stars by the time the contraction has produced a central temperature near 10⁸K. At that point triple-alpha reactions generate small amounts of C¹², which then acts as a catalyst in the CN-cycle, the rate of which is then limited by the beta-decays occurring within the cycle. During the evolution of these more massive stars, the central temperature remains in the vicinity of 10⁸ K, and the surface temperature on the main sequence approaches 10⁵ K. The star of 200M becomes unstable against surface mass loss through radiation pressure in the later stages of its main sequence evolution, and these mass loss effects were not followed. Young galaxies containing these massive stars will have a very high luminosity, but if they have formed at one-tenth the present age of the universe or later, then the light from them will mainly reside in the visible or ultraviolet, rather than in the infrared as has been suggested by Partridge and Peebles.     

Evolution of giant gaseous protoplanets embedded in the primitive solar nebula

Evolutionary calculations are presented, in a spherically symmetric approximation, for a protoplanet of 1 Jovian mass with homogeneous solar composition during the early phase of quasi-static contraction prior to the dissociation of molecular hydrogen. In contrast to earlier calculations which assume that protoplanets are isolated, this study invokes a time-dependent surface boundary condition that simulates physical conditions in an evolving primitive solar nebula. In a first set of calculations the protoplanet is surrounded by a “thermal bath” whose temperature varies with time and whose pressure is small and constant in time. Under a wide range of parameters the result is evaporation and complete dispersal of the object. Conditions required for the protoplanet to survive are discussed. In a second set of calculations both the temperature and pressure at the surface vary with time according to models of the solar nebula. In this case the protoplanet is not dispersed, but the evolution is accelerated or retarded relative to that of an isolated protoplanet, depending upon whether the entropy in the nebula is lower than or higher than, respectively, the entropy in the outer layers of the protoplanet. Processes by which terrestrial planets can form in the cores of giant gaseous protoplanets are discussed.     

Hydrodynamic instability of the solar nebula in the presence of a planetary core

When a planetary core composed of condensed matter is accumulated in the primitive solar nebula, the gas of the nebula becomes gravitationally concentrated as an envelope surrounding the planetary core. Models of such gaseous envelopes have been constructed subject to the assumption that the gas everywhere is on the same adiabat as that in the surrounding nebula. The gaseous envelope extends from the surface of the core to the distance at which the gravitational attraction of core plus envelope becomes equal to the gradient of the gravitational potential in the solar nebula; at this point the pressure and temperature of the gas in the envelope are required to attain the background values characteristics of the solar nebula. In general, as the mass of the condensed core increases, increasing amounts of gas became concentrated in the envelope, and these envelopes are stable against hydrodynamic instabilities. However, the core mass then goes through a maximum and starts to decrease. In most of the models tested, the envelopes were hydrodynamically unstable beyond the peak in the core mass. An unstable situation was always created if it was insisted that the core mass contain a larger amount of matter than given by these solutions. For an initial adiabat characterized by a temperature of 450°K and a pressure of 5 × 10^?6 atm, the maximum core mass at which instability occurs is approximately 115 earth masses; this value is rather insensitive to the position in the solar nebula or to the background pressure of the solar nebula. However, if the adiabat is lowered, then the core mass corresponding to instability is decreased. Since the core masses found by Podolak and Cameron for the giant planets are significantly less than the critical core mass corresponding to the initial solar nebula adiabat, we conclude that the giant planets obtained their large amounts of hydrogen and helium by a hydrodynamic collapse process in the solar nebula only after the nebula had been subjected to a considerable period of cooling.     

Models of the giant planets

Models of the giant planets were constructed based on the assumption that the hydrogen to helium ratio is solar in these planets. This assumption, together with arguments about the condensation sequence in the primitive solar nebula, yields models with a central core of rock and possibly ice surrounded by an envelope of hydrogen, helium, methane, ammonia, and water. These last three volatiles may be individually enhanced due to condensation at the period of core formation. Jupiter was found to have a core of about 40 earth masses and a water enhancement in the atmosphere of about 7.5 times the solar value. Saturn was found to have a core of 20 earth masses and a water enhancement in the atmosphere of about 25 times the solar value. Rock plus ice constitute 75–85% of the mass of Uranus and Neptune. Temperatures in the interiors of these planets are probably above the melting points, if there is an adiabatic relation throughout the interiors. Some aspects of the sensitivities of these results to uncertainties in rotational flattening are discussed.     

Cosmological considerations regarding Uranus

The cosmogony of Uranus is discussed within the context of a picture in which solid condensed materials accumulate to form a large body, which then acquires significant amounts of gas from the primitive solar nebula. Of prime cosmogonical importance is the tilt of the equatorial plane of the planet and of the plane of tilt of the planet can easily occur as a result of a major collision during the formation process; it seems most likely that the tilt of the satellite orbits requires that they were formed from a gaseous disc rotating about the planet after the tilt of the planetary rotational axis had occurred. Possible methods for tilting this gaseous disc are discussed. A strong early magnetic field may have helped in this and may have played an essential role in showing down the spin of the planet to the present observed value. These processes may have produced significant compositional differences between the satellites of Uranus and those of Jupiter and Saturn.     

Clumping of Interstellar grains during formation of the primitive solar nebula

The author has previously shown that a considerable amount of clumping of interstellar grains is likely to take place during the free-fall collapse phase of an interstellar cloud which is forming the primitive solar nebula, with the assumption of sonic turbulence in the gas. The original estimate involved the crude assumption of hierarchal amalgamation of the grains upon collision. A Monte Carlo simulation of this process confirmed the general features of the results, but it was further found that the introduction of a low sticking probability reduced the size of the lumps quite significantly. A more realistic calculation was therefore carried out in which it was assumed that clumps of grains would tend to stick together if their collisions were approximately head-on, but that they would tend to fragment into smaller pieces if the collisions were more tangential. For typical values of the amalgamation parameter, this tends to spread the mass of the interstellar grains over a wide range of clump sizes, ranging from individual grains to objects in the millimeter or centimeter size.     

Treatment of pulsating white dwarfs including general relativistic effects

In this paper, pulsating white dwarfs are treated via general relativity. Numerical integration of Einstein's equations was used to find equilibrium white dwarfs models and the fundamental periods of small oscillations about these equilibrium models. In these calculations account was taken of coulomb, Thomas-Fermi, and exchange interactions as well as ion zero point energies. It is shown that general relativity makes not just a quantitative difference in the results but a qualitative differences; pure C¹² models which are stable in Newtonian mechanics can be unstable against collapse (at a central density of 3×10¹⁰ g/cm³) when general relativity is taken into account. The collapsing model may become a neutron star or may continue towards the Schwarzschild radius.More realistic white dwarf models with carbon burning products at the center, also were studied. For these models, the density at which the star becomes unstable against collapse due to electron capture (3×10⁹ g/cm³) was found to be lower than the density at which general relativistic instability occurs.