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1.
A.G.W. Cameron  M.R. Pine 《Icarus》1973,18(3):377-406
Numerical models have been constructed to represent probable conditions in the primitive solar nebula. A two solar mass fragment of a collapsing interstellar gas cloud has been represented by a uniformly rotating sphere. Two cases have been considered: one in which the internal density of the sphere is uniform and the other in which the density falls linearly from a central value to zero at the surface (the uniform and linear models). These assumptions served to define the distribution of angular momentum per unit mass with mass fraction. The spheres were flattened into disks, and models of the disks were found in which there was a force balance in the radial and vertical directions, subject to certain approximations, and with everywhere the assigned values of angular momentum per unit mass. The radial pressure gradient of the gas was included in the force balance. The energy transport in the vertical direction involved convection and radiative equilibrium; the principal contributors to opacity at lower temperatures were metallic iron grains and ice. The models contained two convection zones, an inner one due to the dissociation of hydrogen molecules, and an outer one in which there was a high opacity due to metallic iron grains. The characteristic semithickness of the disks ranged from about 0.1 astronomical units near the center to about one astronomical unit near the exterior. Characteristic angular momentum transport times and radiation lifetimes for these models of the initial solar nebula were estimated. Both types of characteristic lifetime were as short as a few years near the inner part of the models, and became about 104 years or longer at distances greater than ten astronomical units.  相似文献   

2.
Peter Bodenheimer 《Icarus》1977,31(3):356-368
The planet Jupiter is assumed to have formed as a subcondensation in the solar nebula. The initial phase of its evolution is one of hydrostatic contraction with radiative energy transport. Calculations of evolutionary sequences through this phase are presented, including the effects of angular momentum. The calculations are carried out in two space dimensions under the assumptions of axial symmetry, constancy of angular velocity on cylindrical surfaces about the rotation axis, a pressure-density relation given by the polytrope of index 3, conservation of angular momentum, and a homogeneous composition. The results show that under certain physically reasonable initial distributions of density and angular momentum the formation of a central planet and a rotating circumplanetary envelope is possible, while under assumptions a point of instability is reached that probably results in the breakup of the condensation by fission into two or more parts. The models are discussed with reference to the present angular momenta of Jupiter and its regular satellites.  相似文献   

3.
The formation of the solar nebula and the distribution of mass in its planetary system is studied. The underlying idea is that the protosun, fragmented out from an interstellar cloud as a result of cluster formation, gathered the planetary material and, hence, spin angular momentum by gravitational accretion during its orbital motion around the centre of the Galaxy. The study gives the initial angular momentum of the solar nebula nearly equal to the present value of the solar system.  相似文献   

4.
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.  相似文献   

5.
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6.
This paper considers the evolution of a flat svarm of cometary bodies (under the effect of the passage of stars), initially moving in one direction along the circular orbits with radii 1.4×104<r<2×104 AU and along elliptic orbits with semi-major axes 5×103<a<1×104 AU and with perihelia within 50<q<100 AU. Numerical simulation shows that the original flat belt of comets is thermalizing. Its root-mean-squarez-coordinate grows withr. A cometary cloud forms with a dense flattened inner core and a rarefied halo (the Oort cloud proper). The value =N core/N halo varies within a wide range (up to the order of magnitude) depending on the model used (N core andN halo are the numbers of comets in the core and the halo, respectively).The hypothesis of a massive Oort cloud (Marochniket al., 1988) implies that the Oort cloud should have a large angular momentum. This paper employs numerical simulation to calculate Oort cloud models to which the initially flat located at the periphery of the solar nebula rotating cometary swarms is evolving in time. The loss of the initial angular momentum over the time of the Oort cloud evolution is not large.  相似文献   

7.
Xun Zhu  Darrell F. Strobel 《Icarus》2005,176(2):331-350
Titan's atmospheric winds, like those on Venus, exhibit superrotation at high altitudes. Titan general circulation models have yielded conflicting results on whether prograde winds in excess of 100 m s−1 at the 1 mbar level are possible based on known physical processes that drive wind systems. A comprehensive two-dimensional (2D) model for Titan's stratosphere was constructed to systematically explore the physical mechanisms that produce and maintain stratospheric wind systems. To ensure conservation of angular momentum in the limit of no net exchange of atmospheric angular momentum with the solid satellite and no external sources and sinks, the zonal momentum equation was solved in flux form for total angular momentum. The relationships among thermal wind balance, meridional circulation, and zonal wind were examined with numerical experiments over a range of values for fundamental input parameters, including planetary rotation rate, radius, internal friction due to wave stresses, and net radiative drive. The magnitude of mid-latitude jets is most sensitive to a single parameter, the planetary rotation rate and results from the conversion of planetary angular momentum to relative angular momentum by the meridional circulation, whereas the strength of meridional circulation is mainly determined by the magnitude of the radiative drive. For Titan's slowly rotating atmosphere, the meridional temperature gradient is vanishingly small, even when the radiative drive is enhanced beyond reasonable magnitudes, and can be inferred from zonal winds in gradient/thermal wind balance. In our 2D model large equatorial superrotation in Titan's stratosphere can be only produced through internal drag forcing by eddy momentum fluxes, which redistribute angular momentum within the atmosphere, while still conserving the total angular momentum of the atmosphere with time. We cannot identify any waves, such as gravitational or thermal tides, that are sufficiently capable of generating the required eddy forcing of >50 m s−1 Titan-day−1 to maintain peak prograde winds in excess of 100 m s−1 at the 1 mbar level.  相似文献   

8.
The action of the solar corpuscular radiation on the rotational properties of small interplanetary dust particles is investigated. It is shown that the solar wind increases the angular momentum (spin) of the particle. Analytic solutions are presented for dominant terms in which quantities of the orders (v/u) n ,n 1, are neglected (v is the orbital velocity of dust particle around the Sun andu is the speed of the solar wind particles).  相似文献   

9.
The basic parameters describing the angular momentum distribution within the Uranus system and of its tidal evolution have been estimated. The nine satellites orbiting under the synchronous zone of Uranus is the maximum number in the solar system and it makes the Uranus system different compared with any other in the Solar system, however the satellites in question are relatively small and their contribution of the tidal dynamics of the system is small compared with that due to UI and UV. The time for existence of the nine satellites as integrated bodies can be estimated as 1.4 × 109 y (UVI) and more. The total tidal decrease in the Uranus angular velocity of rotation is estimated as 7 × 10–9s–1.  相似文献   

10.
In this paper the process of magnetic convection is studied. It is shown that outside of a radius of about 2 × 105 km, magnetic fields in the Sun may be buoyant. Outside this limit strong field regions tend to rise at the expense of weak field regions which tend to sink. Magnetic convection may be important in magnetic stars and even in the solar interior. A recent calculation of the angular velocity of the Sun provides a period of rotation for the solar core of from 0.5 to 5 days. This calculation requires that the magnetic field extract angular momentum from the solar interior. Magnetic convection thus seems to be required, if this calculation is correct. Furthermore, magnetic convection may transfer heat and thereby possibly change the internal temperature structure of the Sun from what would be expected solely by radiation transfer.  相似文献   

11.
A very significant problem in the modeling of disk-galaxy formation in the cold dark matter (CDM) cosmology is the so-called `angular momentum problem'. This problem arises when we numerically model the collapse of baryons within a dark halo in the CDM model. The formed baryonic disk has much less angular momentum than observed disk galaxies due to the considerable loss of angular momentum during the progressive merger of small clumps. As a result of efficient radiative cooling, the gas component collapses too deeply within the dark halo. When two such systems are merging, the angular momentum of the material near the center is effectively transported outwards by the tidal force. This is a physical reason for this problem, however, there may be a numerical origin due to the nature of the Smoothed Particle Hydrodynamics (SPH) method widely used in galaxy formation models. To address the numerical origin of the `angular momentum problem' with a much higher-resolution SPH model, we are developing our Parallel Tree-SPH code. After evolving four initial models with different mass and force resolution, we compare the angular momentum content of SPH particles. We find that both mass and force resolutions clearly affect the evolution of radiative cosmological SPH models. In most previous radiative cosmological SPH models, a mass ratio between SPH and dark matter particles is .However, we find that this mass ratio is a crucial parameter when we consider the angular momentum content of SPH particles and it is better to make the mass ratio ∼ 1.0 in such models. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

12.
We investigate the rotation profile of solar-like stars with magnetic fields. A diffu-sion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 σ level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 M⊙, there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.  相似文献   

13.
In the present paper, a general evolutionary scheme for axisymmetrical rotationally supported equilibrium models for galaxies is considered. Its main phases are: an expansion phase of the initial protogalaxy, assumed to consist into an homogeneous gas sphere structured into clouds, from recombination to maximum expansion, during which it is surmized that angular momentum is acquired by tidal interactions by the expanding configuration; then a violent relaxation collapse phase, following maximum expansion and ending into a virialized deformed polytropic configuration; the reaching of virialization is considered as an adequate initial state for the new phase of virialized contraction of the gaseous component, due to the collisions of the constituent gas clouds, while the stellar component, due to the stars already formed according to a generalized Schmidt-type law during the early expansion and violent relaxation phases, is assumed to have reached a stabilized situation.The initial mean density and radius for both galaxy and component clouds expressed as functions of the density fluctuation spectrum at recombination, act as physical parameters determining the characteristics of the system at maximum expansion, together with the total amount of angular momentum acquired during the expansion phase. The main physical parameters at virialization are then completely specified when the initial distribution of the clouds inside the galaxy is assigned and the constants appearing in it are derived by normalization with the observed data.We find for systems of given mass that the larger the angular momentum per unit mass is: (1) the larger are the equatorial semiaxis at maximum expansion and at virialization and the lower the mean density; (2) the larger is the time elapsed up the maximum expansion and to virialization; while for systems of different mass, we obtain that to the larger mass correspond the larger time elapsed up to maximum expansion and to virialization, and the lower mean density.For the contraction phase following virialization, two limiting cases are considered: (A) either the star component already present at virialization is entirely neglected; (B) or it is thought to contract as the gas component. In such cases, it is found for systems of equal mass that lower angular momenta lead to final configurations characterized by no or small flat gaseous components (which may correspond to lenticulars and early type spirals) while the contrary is true for large angular momenta (corresponding to late type spirals and irregulars). As mass and angular momentum per unit mass decrease, according to an assumed lawj M, the allowed configurations on the late type side of the morphological sequence tend towards earlier and earlier types, until for masses low enough (1010 m ), only halo type configurations seem to exist. According to this view, the observed lack of spirals with masses below 1010 m and the wide mass range exibited by the stellar halo type galaxies might be interpreted. In general, it appears that in the limit of the approximations made, a morphological sequence of galaxies can be described by two parameters, mass and angular momentum.  相似文献   

14.
F.J. Ciesla 《Icarus》2010,208(1):455-467
Refractory objects such as Calcium, Aluminum-rich Inclusions, Amoeboid Olivine Aggregates, and crystalline silicates, are found in primitive bodies throughout our Solar System. It is believed that these objects formed in the hot, inner solar nebula and were redistributed during the mass and angular momentum transport that took place during its early evolution. The ages of these objects thus offer possible clues about the timing and duration of this transport. Here we study how the dynamics of these refractory objects in the evolving solar nebula affected the age distribution of the grains that were available to be incorporated into planetesimals throughout the Solar System. It is found that while the high temperatures and conditions needed to form these refractory objects may have persisted for millions of years, it is those objects that formed in the first 105 years that dominate (make up over 90%) those that survive throughout most of the nebula. This is due to two effects: (1) the largest numbers of refractory grains are formed at this time period, as the disk is rapidly drained of mass during subsequent evolution and (2) the initially rapid spreading of the disk due to angular momentum transport helps preserve this early generation of grains as opposed to later generations. This implies that most refractory objects found in meteorites and comets formed in the first 105 years after the nebula formed. As these objects contained live 26Al, this constrains the time when short-lived radionuclides were introduced to the Solar System to no later than 105 years after the nebula formed. Further, this implies that the t=0 as defined by meteoritic materials represents at most, the instant when the solar nebula finished accreting significant amounts of materials from its parent molecular cloud.  相似文献   

15.
3He is an intermediate product in the proton-proton chain, and standard models of the Sun predict a large bulge of enhanced 3He abundance near M r /M 0 = 0.6 in the contemporary Sun. The relatively low abundance of 3He at the solar surface, which is derived from solar wind observations, poses severe constraints to non-standard solar models.Direct measurements of the 3He abundance in the solar atmosphere are extremely difficult, whereas indirect measurements, e.g., in the solar wind, have been performed with considerable precision. The interpretation of solar wind observations with respect to solar surface abundances has been greatly improved in recent years. Abundance measurements have been performed under a large variety of solar wind conditions and refined models have been developed for the transport processes in the chromosphere and the transition region and for the processes occurring in the solar corona. From these measurements we estimate the present isotopic number ratio 3He/4He to be (4.1 ± 1.0) × 10–4 at the solar surface, corresponding to the weight abundance X 3 = (9.0 ± 2.4) × 10–5. The zero-age Main-Sequence abundance of 3He (after burning of D) might have been slightly lower (by about 10 to 20%) than the present-day value.Non-standard solar models involving mild turbulent diffusion (Lebreton and Maeder, 1987) could account for a slow secular increase of the 3He/4He ratio in the solar atmosphere. On the other hand it is difficult to reconcile models with severe mass loss as proposed by Guzik, Willson, and Brunish (1987) with this constraint. The slowing down of the solar rotation during the early Main-Sequence evolution was accompanied by stronger differential rotation probably implying a more effective mixing of the inner parts. Again, the surface abundance of 3He imposes severe limits on the evolution of the distribution of momentum within the early Sun.  相似文献   

16.
In an attempt to explain the observed rotation profile in the solar radiative zone and the tachocline, Spiegel & Zahn proposed a model based on anisotropic turbulent angular momentum transport. Although very successful in reproducing some of the features of the solar tachocline, their model assumes without verification that the origin of the turbulence could be caused by latitudinal shear instability. This paper studies the weakly non-linear evolution of two-dimensional shear instability, in which the interaction between the global rotation profile and the Reynolds stresses can be described self-consistently. Provided that the initial rotation profile is sufficiently close to marginal stability (which is the case of the solar tachocline), the instability is shown to saturate and to relax to a marginally stable state, which differs very little from the observed rotation profile. It is therefore likely that the tachocline is in a state of marginal stability with respect to latitudinal shear instability, and shows that angular momentum transport in the tachocline is unlikely to be caused by shear-induced turbulence.  相似文献   

17.
We investigate the dynamical evolution of 100 000 rotating triple systems with equal-mass components. The system rotation is specified by the parameter ω=?c2E, where c and E are the angular momentum and total energy of the triple system, respectively. We consider ω=0.1,1, 2, 4, 6 and study 20 000 triple systems with randomly specified coordinates and velocities of the bodies for each ω. We consider two methods for specifying initial conditions: with and without a hierarchical structure at the beginning of the evolution. The evolution of each system is traced until the escape of one of the bodies or until the critical time equal to 1000 mean system crossing times. For each set of initial conditions, we computed parameters of the final motions: orbital parameters for the final binary and the escaping body. We analyze variations in the statistical characteristics of the distributions of these parameters with ω. The mean disruption time of triple systems and the fraction of the systems that have not been disrupted in 1000 mean crossing times increase with ω. The final binaries become, on average, wider at larger angular momenta. The distribution of their eccentricities does not depend on ω and generally agrees with the theoretical law f(e)=2e. The velocities of the escaping bodies, on average, decrease with increasing angular momentum of the triple system. The fraction of the angles between the escaping-body velocity vector and the triple-system angular momentum close to 90° increases with ω. Escapes in the directions opposite to rotation and prograde motions dominate at small and large angular momenta, respectively. For slowly rotating systems, the angular momentum during their disruption is, on average, evenly divided between the escaping body and the final binary, whereas in rapidly rotating systems, about 80% of the angular momentum is carried away by the escaping component. We compare our numerical simulations with the statistical theory of triple-system disruption.  相似文献   

18.
If the Sun loses angular momentum from its core, due to core contraction, into the solar wind at the observed rate, then an 0.7 day rotational period for the core of the Sun is required for temporal equilibrium. The rotational power released in the core contraction process can equal the observed magnetic energy released in the solar activity cycle if the Sun's core rotates with a period near 1.4 to 4 days. The rotational power released from a rotating object is , where is the torque on the object and is its angular velocity. Fitting this to the solar wind torque and core rotation rate provides an 0.5 to 5 day rotation period for the Sun's core. A gravitational Pannekoek-Rosseland electric field in the Sun makes the Ferraro theorem inapplicable in such a way that rather than a constant angular velocity with radius, an inverse square radial dependence occurs. This results in a two day rotational period for the region in the Sun where most of the angular momentum resides. The consistency of the above four methods suggests that the Sun's observed oblateness is due to a rapidly rotating solar core. The oblateness of the photosphere is estimated to be near 3.4×10–5.  相似文献   

19.
Patrick Cassen  Ann Moosman 《Icarus》1981,48(3):353-376
An analysis is presented of the hydrodynamic aspects of the growth of protostellar disks from the accretion (or collapse) of a rotating gas cloud. The size, mass, and radiative properties of protostellar disks are determined by the distribution of mass and angular momentum in the clouds from which they are formed, as well as from the dissipative processes within the disks themselves. The angular momentum of the infalling cloud is redistributed by the action of turbulent viscosity on a shear layer near the surface of the disk (downstream of the accretion shock) and on the radial shear across cylindrical surfaces parallel to the rotation axis. The fraction of gas that is fed into a central core (protostar) during accretion depends on the ratio of the rate of viscous diffusion of angular momentum to the accretion rate; rapid viscous diffusion (or a low accretion rate) promotes a large core-to-disk mass ratio. The continuum radiation spectrum of a highly viscous disk is similar to that of a steady-state accretion disk without mass addition. It is possible to construct models of the primitive solar nebula as an accretion disk, formed by the collapse of a slowly rotating protostellar cloud, and containing the minimum mass required to account for the planets. Other models with more massive disks are also possible.  相似文献   

20.
A periodic long-term modulation of the solar surface rotation with a time scale on the order of 100 years is found in the sunspot data from 1874 to 1992 obtained by combinig the Greenwich Photoheliographic Results from cycle 11 to cycle 20 analysed by Balthasar, Vázquez, and Wöhl and the Mitaka sunspot sketch data from cycle 18 to 22 of the National Astronomical Observatory of Japan which was the Tokyo Astronomical Observatory of the University of Tokyo until 1988. A new index of the solar rotation M defined by integrating the angular momentum density over the whole surface, which we call the angular momentum surface layer density, reached a maximum at solar cycle 14, decreased to a minimum at cycle 17, and then increased to reach another maximum at cycle 21. The increase of M means acceleration of the surface layer as a whole by transport of angular momentum from the deeper layer. This implies an decrease (increase) of the radial gradient of the differential rotation if the basic radial gradient of the differential rotation increases (decreaes) inward. The decrease of M means deceleration of the surface layer and implies an increase (decrease) of the radial gradient. The degree of the equatorial acceleration of the surface differential rotation is also found to have undergone the same 100 year periodic modulation during the same interval, reaching a minimum at cycle 14, a maximum at cycle 17, and a minimum at cycle 21 in antiphase with the modulation of M. Thus both radial and latitudinal gradients of the differential rotation increased and decreased in phase (in anti-phase) if the basic radial gradient increases (decreases) inward.  相似文献   

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