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Bodenheimer, P.

Publications and source records attributed to Bodenheimer, P..

30 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

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 1000, 1500, 28,500 and 42,000 solar masses. Recent improvements in equation-of-state and opacity calculations are incorporated. Sequences start as subcondensations in the solar nebula with densities of 10 to the -10th to 10 to the -11th g/cu cm, evolve through a hydrostatic phase lasting 100 thousand to 10 million years, undergo dynamic collapse due to dissociation of molecular hydrogen, and regain hydrostatic equilibrium with densities of about 1 g/cu cm. The nature of the objects at the onset of the final phase of cooling and contraction is discussed and compared with previous calculations.

Bodenheimer, P.↗
NASA NTRS1979

Fragmentation in a rotating protostar - A comparison of two three-dimensional computer codes

The collapse of an isothermal protostellar cloud with pressure, gravity, and rotation included is followed with two independent computer codes. For the initial condition, a nonaxisymmetric perturbation of mode m = 2 and 50% amplitude is introduced into a cloud of 1 solar mass with a mean density of 1.44 x 10 to the -17g/cu cm and a uniform angular velocity of 1.6 x 10 to the -12 rad/sec. The collapse is followed through an increase in density of over four orders of magnitude to the point where a binary protostar forms. The agreement between the results of the two calculations is good.

Boss, A. P.↗
NASA NTRS1978

Evolution of rotating interstellar clouds. III - On the formation of multiple star systems

The evolution of a rotating massive cloud, starting at interstellar densities, continuing through a series of intermediate fragmentation stages, and ending with stellar multiple systems with components near the main sequence, is outlined. The scenario is based on results of two- and three-dimensional numerical hydrodynamical calculations of collapsing clouds. Transfer of spin angular momentum primarily into orbital motion is assumed to occur at each fragmentation stage. Expected initial conditions in the cloud lead to final fragments which have in many cases the masses and angular momenta appropriate to observed main-sequence systems. Other points of comparison with observations are briefly noted.

Bodenheimer, P.↗
NASA NTRS1978

Ortho- and para-hydrogen in dense clouds, protoplanets, and planetary atmospheres

If ortho- and para-hydrogen achieve a thermal ratio on dynamical time scales in a molecular hydrogen cloud, then the specific heat is high enough in the temperature range 35-70 K to possibly induce hydrodynamic collapse. The ortho-para ratio in many interstellar cloud fragments is expected to meet this condition. The same may have been true for the primitive solar nebula. Detailed hydrodynamic and hydrostatic calculations are presented that show the effects of the assumed ortho-para ratio on the evolution of Jupiter during its protoplanetary phase. Some possible consequences of a thermalized ortho-para ratio in the atmospheres of the giant planets are also discussed.

Decampli, W. M.↗
NASA NTRS1978

Numerical calculations of protostellar hydrodynamic collapse

Although 1-D (spherically symmetric) experiments of protostar collapse are highly idealized, they are the only ones which have been carried to a stage where a 'stellar' object is formed. Experiments have shown that the parameters (e.g., radius and luminosity) of the visible stellar core are sensitive to the assumed initial conditions, particularly the initial density. One of the major findings of 2-D numerical experiments is the formation of rings. Three-dimensional hydrodynamical calculations indicate that a collapsing cloud will break up into two or more orbiting subcondensations with the possible subsequent development of a stellar multiple system.

Bodenheimer, P.↗
NASA NTRS1977

Calculations of the effects of angular momentum on the early evolution of Jupiter

Early phases in the evolutionary development of a rotating cloud of gas and dust are investigated to determine whether physically reasonable initial conditions are likely to produce a planet-satellite system with the values of specific orbital angular momentum currently observed for Jupiter and its inner satellites. Spherically symmetric computations of Jupiter's evolutionary history are reviewed, and transport of angular momentum is considered along with evolutionary sequences of individual differentially rotating models with decreasing values of equatorial radius. The problem of accounting for the present specific orbital angular momenta of Jupiter and its regular satellites is examined qualitatively, and a range of possible angular-momentum distributions in an initially tidally unstable cloud is assessed. The results show that particular physically plausible angular-momentum distributions, which could either be established as initial conditions or be caused by angular-momentum transport, will lead to favorable situations for the formation of a central planet and a surrounding rotating cloud with specific angular momentum comparable to that of the regular satellites.

Bodenheimer, P.↗
NASA NTRS1976

Evolution of rotating interstellar clouds. II - The collapse of protostars of 1, 2, and 5 solar masses

Numerical calculations have been made for the early stages of collapse of axisymmetric rotating protostars of 1, 2, and 5 solar masses. The calculations employ a range of values of total angular momentum, as well as two types of initial density distribution. The effects of boundary conditions are tested by using constant volume and constant surface pressure with identical initial conditions. The principal result of the calculations is that, in all cases tried, the collapse leads to the formation of a ring structure in the interior of the cloud, with a local density minimum at the center of the cloud. The rings approach equilibrium with a structure consistent with that of previous analytic determinations, after which they undergo further gravitational collapse. The collapse of a two-solar-mass cloud, similar to that assumed by Cameron and Pine (1973), does not appear to lead to the equilibrium nebula these authors construct.

Black, D. C.↗
NASA NTRS1975

Evolution of rotating interstellar clouds. I - Numerical techniques

A method is described for the numerical calculation of the hydrodynamic evolution of a self-gravitating configuration in two space dimensions with assumed axial symmetry. The calculation is formulated in cylindrical coordinates with respect to a moving Eulerian grid and is solved using explicit hydrodynamics combined with implicit radiative transfer. The physics included is appropriate for calculation of the collapse of a rotating protostellar cloud. The gravitational field is obtained by means of an alternating-direction iterative technique. Numerical tests to demonstrate the correctness of the method are presented for special cases.

Black, D. C.↗
NASA NTRS1974

Calculations of the early evolution of Jupiter

The evolution of the protoplanet Jupiter is followed, using a hydrodynamic computer code with radiative energy transport. Jupiter is assumed to have formed as a subcondensation in the primitive solar nebula at a density just high enough for gravitational collapse to occur. The initial state has a density of 0.0015 nanograms per cu cm and a temperature of 43 K; the calculations are carried to an equilibrium state where the central density reaches 0.5 g per cu cm and the central temperature reaches 25,000 K. During the early part of the evolution the object contracts in quasi-hydrostatic equilibrium; later on hydrodynamic collapse occurs, induced by the dissociation of hydrogen molecules. After dissociation is complete, the planet regains hydrostatic equilibrium with a radius of a few times the present value. Further evolution beyond this point is not treated here; however the results are consistent with the existence of a high-luminosity phase shortly after the planet settles into its final quasi-static contraction.-

Bodenheimer, P.↗