Calculations of the evolution of the giant planets

Evolutionary calculations are presented for spherically symmetric protoplanetary configurations with a homogeneous solar composition and with masses of 10^?3, 1.5 × 10^?3, 2.85 × 10^?4, and 4.2 × 10^?4M_⊙. Recent improvements in equation-of-state and opacity calculations are incorporated. Sequences start as subcondensations in the solar nebula with densities of ～10^?10 to 10^?11 g cm^?3, evolve through a hydrostatic phase lasting 10⁵ to 10⁷ years, undergo dynamic collapse due to dissociation of molecular hydrogen, and regain hydrostatic equilibrium with densities ～1 g cm^?3. The nature of the objects at the onset of the final phase of cooling and contraction is discussed and compared with previous calculations.     

The equation of state for neutron stars

We present the results of an improved analysis of the equation of state of matter from metallic to nuclear density which takes into account: (a) in the region of low densities (?<10⁴ g cm^?3), the electron correlation energy in the lattice; (b) in the region of medium density (10⁴11 g cm^?3) a more refined discussion of the electron energy; (c) in the region of large densities (4.3×10¹¹ g cm^?3相似文献   

A limit for gravitational collapse

Earlier, under certain simplifying assumptions, on the basis of the General Theory of Relativity, it has been concluded by many authors that when the radius of a gravitationally collapsing spherical object of massM reaches the critical value of the Scharzschild radiusR _s=2GM/c ², then, in a co-moving frame, the object collapses catastrophically to a point. However, in drawing this conclusion due consideration has not been given to the nuclear forces between the nucleons. In particular, the very strong ‘hard-core’ repulsive interaction between the nucleons which has the range ～0.4×10^?13 cm has been totally ignored. On taking into account this ‘hard-core’ repulsive interaction, it is found that no spherical object of massM g can collapse to a volume of radius smaller thanR _min=(1.68×10^?6)M ^1/3 cm or to a density larger than ρ_max=5.0 × 10¹⁶ g cm^?3. It has also been pointed out that objects of mass smaller thanM _c～1.21×10³³ g can not cross the Schwarzschild barrier and gravitationally collapse. The only course left to the objects of mass less thanM _cis to reach the equilibrium as either a white dwarf or a neutron star.     

Equation of state under nuclear statistical equilibrium conditions

We investigate a three-parameter equation of state for stellar matter under nuclear statistical equilibrium conditions in the ranges of temperatures 3×10⁹–10¹¹ K and densities 10⁴–10¹³ g cm^?3 and for various ratios of the total number of neutrons to the total number of protons within the range 1–1.5. These conditions correspond to the initial stages of the gravitational collapse of iron stellar cores that are accompanied by nonequilibrium matter neutronization. We analyze the effect of the excited levels of atomic nuclei on the thermodynamic properties of the matter. We show that this effect is insignificant at low densities, ρ?10¹⁰ g cm^?3, but it leads to an expansion of the instability region, γ<4/3, at higher densities. The incorporated effects of the Fermi degeneracy of free nucleons prove to be insignificant, because their concentrations are low at low temperatures. In the future, we plan to investigate the effects of Coulomb interactions and neutron-rich nuclei on the thermodynamic properties of the matter.     

On the origin and initial temperature of Jupiter and Saturn

A two-stage growth of the giant planets, Jupiter and Saturn, is considered, which is different from the model of contraction of large gaseous protoplanets. In the first stage, within a time of ～3 × 10⁷ years in Jupiter's zone and ～2 × 10⁸ years in Saturn's zone, a nucleus forms from condensed (solid) material having the mass, ～10²⁸ g, necessary for the beginning of acceleration. The second stage may gravitating body, and a relatively slow accretion begins until the mass of the planet reaches ～10 m_⊕. Then a rapid accretion begins with the critical radius less than the radius of the Hill lobe, so that the classical formulae for the rate of accretion may be applied. At a mass m > m₁ ≈ 50 m_⊕ accretion proceeds slower than it would according to these formulae. When the planet sweeps out all the gas from its nearest zone of feeding (m = m₂ ≈ 130 m_⊕), the width of the exhausted zone being $\text{～}\text{built1}\text{3}$ of the whole zone of the planet) growth is provided the slow diffusion of gas from the rest of the zone (time scale increases to 10⁵?10⁶ years and more). The process is terminated by the dissipation of the remnants of gas. In Saturn's zone m₁ > m₂ ≈ 30 m_⊕. The initial mass of the gas in Jupiter's zone is estimated. Before the beginning of the rapid accretion about 90% of the gas should have been lost from the solar system, and in the planet's zone less than two Jupiter masses remain. The highest temperature of Jupiter's surface, ≈5000°K, is reached at the stage of rapid accretion, m < 100 m_⊕, when the luminosity of the planet reaches 3 × 10^?3 L_⊙. This favors an effective heating of the inner parts of the accretionary disk and the dissipation of gas from the disk. The accretion of Saturn produced a temperature rise up to 2000?2400° K (at m ≈ 20?25 m_⊕) and a luminosity up to 10^?4 L_⊙.     

The Jovian spectrum in the 3-μm window

The spectral window of Jupiter at 3 μm is analyzed and compared with previously published spectra. The two components of the spectrum, the thermal and the solar reflected contributions, are calculated at low resolution (30 cm^?1) between 3300 and 3800 cm^?1 for preparing the interpretation of the Galileo Near Infrared Mapping Spectrometer experiment. The calculations yield to the following conclusions: (1) NH₃ is the main absorber between 3300 and 3600 cm^?1 for both the thermal spectrum and the solar reflected spectrum; H₂O appears only in the thermal component above 3600 cm^?1. (2) The thermal component can be seen only on the dark side of Jupiter; the atmosphere is sounded down to temperature levels of about 210°K. (3) The solar reflected component can be modelized by a reflecting layer between 135 and 140°K with an albedo of 0.3; high spatial resolution maps of Jupiter at 3 μm should give access to the NH₃ spatial distribution on Jupiter.     

For infrared spectrophotometry of Jupiter and Saturn

Infrared spectral observations of Mars, Jupiter, and Saturn were made from 100 to 470 cm^?1 using NASA's G. P. Kuiper Airborne Observatory. Taking Mars as a calibration source, we determined brightness temperatures of Jupiter and Saturn with approximately 5 cm^?1 resolution. The data are used to determine the internal luminosities of the giant planets, for which more than 75% of the thermally emitted power is estimated to be in the measured bandpass: for Jupiter L_J = (8.0 ± 2.0) × 10^?10L_⊙ and for Saturn L_S = (3.6 ± 0.9) × 10^?10. The ratio R of thermally emitted power to solar power absorbed was estimated to be R_J = 1.6 ± 0.2, and R_S = 2.7 ± 0.8 from the observations when both planets were near perihelion. The Jupiter spectrum clearly shows the presence of the rotational ammonia transitions which strongly influence the opacity at frequencies ?250 cm^?1. Comparison of the data with spectra predicted from current models of Jupiter and Saturn permits inferences regarding the structure of the planetary atmospheres below the temperature inversion. In particular, an opacity source in addition to gaseous hydrogen and ammonia, such as ammonia ice crystals as suggested by Orton, may be necessary to explain the observed Jupiter spectrum in the vicinity of 250 cm^?1.     

A Model of the Thermal Expansion of the Solar Corona with Allowance for Radiation

The Parker model is modified to describe a rapid temperature increase from the region of temperature minimum to the coronal base and to relate the electron density in the region of the temperature minimum (～0.85×10¹¹ cm^?3 according to the modified model) to that at the orbit of the Earth (～7.42 cm^?3 according to the model). The coronal temperature reaches its maximum (1.8×10⁶ K) at the Parker critical point; physical processes at this point are left beyond the scope of the model. It is suggested to consider the expanding solar corona as a self-heating system in which heating of the solar corona is related to the transonic regime of its expansion, which is maintained by the high coronal temperature.     

Three-dimensional calculations of the formation of the presolar nebula from a slowly rotating cloud

The presolar nebula may have formed from the collapse of a very slowly rotating interstellar cloud. The first three-dimensional, hydrodynamical calculations of the collapse of such clouds are presented. The models include radiative transfer in the Eddington approximation, as well as detailed equations of state appropriate for the nonisothermal regime of protostellar evolution. Very slowly rotating clouds, i.e., those with initial ratios of rotational energy to gravitational energy of 10^?3 or less, avoid fragmentation and instead collapse to form single central objects, containing quasistatic cores with densities of about 10^?10 g cm^?3. These cores are, however, surrounded by significantly nonaxisymmetric regions, such that the presolar nebula would have been bar-like over the scale of the present solar system. This nonaxisymmetry, coupled with differential rotation, results in gravitational torques that produce rapid outward transfer of angular momentum. The center of the presolar nebula should then be able to contract and collapse to pre-main-sequence densities without suffering fission or fragmentation.     

Airborne interferometric measurement of the infrared spectrum of Jupiter from 6 to 14 μm

A new spectrum of Jupiter from 700 to 1600 cm^?1 was obtained with an interferometric experiment using the 91.5 cm telescope of the NASA Airborne Infrared Observatory. The spectral resolution is 10 cm^?1 and the signal-to-noise ratio is 30 at 900 cm^?1. NH₃ absorption lines are observed between 820 and 1020 cm^?1. The 1306 cm^?1ν₄CH₄ band strongly appears in emission at a temperature of at least 145° K. The Jovian brightness temperature between 1400 and 1600 cm^?1, according to our measurement, is lower than 170° K.     

Composition and temperatures of the topside ionosphere over Arecibo

Results of analysis of about 150 autocorrelation functions are presented for the period from about 2300 hr on 5 October to about 1200 hr on 7 October 1967. A large percentage concentration of helium ions are observed. It reaches a value as high as 50 per cent with a maximum at around 800 km. Downward heat fluxes deduced from the temperature variations yield a value of about 2–2.5 × 10⁹ eV cm^?2 sec^?1 during the period 1200–1600 hr and a value of about 1.5 × 10⁸ eV cm^?2 sec^?1 during the period 0100–0400 hr at night. These agree well with other measurements. The O⁺ ions are found not to be in diffusive equilibrium, and from the O⁺ fluxes and the electron density profiles, the O⁺ drift velocity has been estimated. It is found that the speed can be as high as 1–5 × 10³ cm sec^?1 even at altitudes as high as 700 km.     

Tidal flows in binary systems

The expressions of the tidal velocity in not very close binaries (double stars, the Sun and a planet, a planet and a satellite) are derived and applied in particular to white dwarfs and the giant planets of the solar system. The magnitude of the velocity on the surface of Jupiter is estimated to be about 0.5 cm s^?1. In white dwarfs the velocities of the order of tens m s^?1 may be encountered, and they can influence their evolution. The symmetry of the tidal flows is noted to be suitable for the magnetic field generation.     

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.     

Mariner 10 observations of hydrogen Lyman alpha emission from the venus exosphere: Evidence of complex structure

The Ultraviolet Spectrometer Experiment on the MARINER 10 spacecraft measured the hydrogen Lyman α emmission resonantly scattered in the Venus exosphere at several viewing aspects during the encounter period. Venus encounter occurred at 17:01 GMT on 5 February 1974. Exospheric emissions above the planet's limb were measured and were analyzed with a spherically symmetric, single scattering, two-temperature model. On the sunlit hemisphere the emission profile was represented by an exospheric hydrogen atmosphere with T_c = 275±50 K and n_c = 1.5 × 10⁵ cm^?3 and a non-thermal contribution represented by T_H = 1250±100 K with n_H = 500±100 cm^?3. The observations of the dark limb showed that the spherically symmetric model used for the sunlit hemisphere was inappropriate for the analysis of the antisolar hemisphere. The density of the non-thermal component had increased at low altitudes, < 12,000 km, and decreased at high altitudes, > 20,000 km, by comparison. We conclude that the non-thermal source is on the sunward side of the planet. Analysis of the dark limb crossing suggests that the exospheric temperature on the dark side is <125 K if the exospheric density remains constant over the planet; upper limits are discussed. An additional source of Lyman α emission, 70 ± 15 R, was detected on the dark side of the planet and is believed to be a planetary albedo in contrast to multiple scattering from the sunlit side. Our analysis of the MARINER 10 data is consistent when applied to the MARINER 5 data.     

The Galilean satellites as a source of CO in the Jovian upper atmosphere

Material from the Galilean satellites of Jupiter ejected by energetic particles in the Jovian magnetosphere may provide large sources of oxygen to the parent planet. Formation of a CO molecule is the ultimate fate of an oxygen atom in the upper Jovian atmosphere. This high altitude source of CO supports Beer and Taylor's (1978, Astrophys. J.221) observations and analysis, provided that the globally averaged O atom input flux is ～10⁷ cm^?2 sec^?1 and the eddy diffusion coefficient at the tropopause is ～10³ cm² sec^?1. Implications for the possible presence of other atoms and molecules derived from the satellites are discussed.     

Vertical distribution of water vapor and mars model lower and middle atmosphere

Observations and model calculations of water vapor diffusion suggest that about half the amount of water vapor is distributed with constant mixing ratio in the Martian atmosphere, the other half is the excess water vapor in the lower troposphere. During 24 hr the total content of water vapor may vary by a factor of two. The eddy diffusion coefficient providing agreement between calculations and observations is K = (3–10) × 10⁶ cm² sec^?1 in the troposphere. An analytical expression is derived for condensate density in the stratosphere in terms of the temperature profile, the particle radius r, and K. The calculations agree with the Mars 5 measurements for r = 1.5 μm, condensate density 5 × 10^?12 g/cm³ in the layer maximum at 30 to 35 km, condensate column density 7 × 10^?6 cm^?2, K = (1?3) × 10⁶ cm² sec^?1, and the temperature profile T = 185 ? 0.05z ? 0.01z² at 20 to 40 km. Condensation conditions yield a temperature of 160°K at 60 km in the evening; the scale height for scattered radiation yields T = 110°k at 80 to 90 km. The Mars model atmosphere has been developed up to 125 km.     

The collapse of self-gravitating clouds of pure hydrogen

Exploratory models of the collapse of spherical self-gravitating clouds are studied in relation to the problem of the formation of first generation star-systems. The masses which were considered are in the range of 83 to 5.2×10¹⁰ M _⊙. For simplicity, the assumed composition includes hydrogen only, which could be in the form of H, H₂, H⁺ or H^?. Since the physical conditions that might have prevailed in a primeval nebula are not well known, rather simple initial conditions were chosen: The gas starts from rest and has initially a uniform temperature. We consider the case of rather cool (T ₀～100 K) neutral clouds with different initial ionization degrees. Some of the initial density-distributions here considered are uniform while others are decreasing from the center outwards. The assumed initial values for the densities are ～10^?24 g cm^?3, except for one of the models, for which it is ～10^?26 g cm^?3. Several atomic processes within the gas, including physical-chemical reactions and the evaluation of radiative emission coefficients are considered. A system of differential equations is set up in order to evaluate the concentrationsn _H,n _{H 2},n _H ⁺,n _H ^? andn _e as a function of time. The treatment makes possible the study of the cooling and heating properties of the gas. Furthermore, the dynamical, thermal and chemical evolution of the cloud can be followed during the collapse. The computations apply only to the optically thin stages. The models show the importance of a correct evaluation of the chemical reactions and dissipative mechanisms, which cannot be ignored in a realistic treatment of the collapse of self-gravitating clouds. The influence of the initial conditions on the dynamical and thermal properties during evolution are also analysed.     

Existence and amount of intergalactic dust

The existence of intergalactic dust has been proved by the following observational facts: the decrease of the numbers of distant galaxies and clusters of galaxies behind the central regions of near clusters of galaxies; the different distributions of RR Lyrae stars and galaxies near ι Microscopii (Hoffmeister's cloud); the dependence of colour excesses of galaxies on supergalactic coordinates as well as on the surface density of bright galaxies; the colour index vs redshift correlation of quasistellar objects. The densities of intergalactic dust are estimated to be between 5×10^?30 g cm^?3 (near the centers of clusters of galaxies) and 2×10^?34 g cm^?3 (in general intergalactic space). The grains may be formed either in the early phases of the Universe (25相似文献   

Rapid neutron capture process in supernovae and chemical element formation

The rapid neutron capture process (r-process) is one of the major nucleosynthesis processes responsible for the synthesis of heavy nuclei beyond iron. Isotopes beyond Fe are most exclusively formed in neutron capture processes and more heavier ones are produced by the r-process. Approximately half of the heavy elements with mass number A > 70 and all of the actinides in the solar system are believed to have been produced in the r-process. We have studied the r-process in supernovae for the production of heavy elements beyond A = 40 with the newest mass values available. The supernova envelopes at a temperature >109 K and neutron density of 10²⁴ cm^?3 are considered to be one of the most potential sites for the r-process. The primary goal of the r-process calculations is to fit the global abundance curve for solar system r-process isotopes by varying time dependent parameters such as temperature and neutron density. This method aims at comparing the calculated abundances of the stable isotopes with observation. We have studied the r-process path corresponding to temperatures ranging from 1.0 × 10⁹ K to 3.0 × 10⁹ K and neutron density ranging from 10²⁰ cm^?3 to 10³⁰ cm^?3. With temperature and density conditions of 3.0 × 10⁹ K and 10²⁰ cm^?3 a nucleus of mass 273 was theoretically found corresponding to atomic number 115. The elements obtained along the r-process path are compared with the observed data at all the above temperature and density range.     

Models of Saturn's interior: Evidence for phase separation

Models of Saturn's interior have been constructed based on an accumulation picture of planet formation. It was found that central pressures were ～90 Mb, and central temperatures ～10^4°K. In sharp contrast to Jupiter, which requires large amounts of heavy material in the envelope to match the observed gravitational quadrupole moment, Saturn requires an almost solar envelope. Indeed, the ratio of enhanced material in the envelope to material in the core is less than ～0.1, while the corresponding value for Jupiter is ～2.