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Cassen, Patrick

Publications and source records attributed to Cassen, Patrick.

Evidence of Nebula Processes from Primitive Meteorites

Astronomical observations of T Tauri stars provide information about the masses, sizes, temperatures, and lifetimes of the solar-nebula-like disks surrounding these stars. Theoretical interpretations of these observations can be used to construct models of the evolution of the solar nebula, and to derive implications for the properties of meteoritic material. The consequences of nebular thermal history might have been retained in patterns of elemental fractionation, presolar grains abundances, and oxygen isotopes, among other meteorite properties. Thus, such data may be used in conjunction with models to constrain the parameters that describe the overall evolution of the solar nebula. On the other hand, major meteoritic components such as chondrules and CAIs apparently reflect localized processes that are not readily related to global thermal evolution. In several cases, the theoretical tools required for the evaluation of proposals for their mode of formation exist, but have yet to be applied. Proposals that meteoritic material was thermally and radiatively processed very close to the young Sun, based on the emerging picture of the interactions between young stars and their disks, have radical consequences for the distribution of solid material in the solar system and the formation of chondritic meteorites. Tests of these models may be provided by their predictions for irradiated material and the physical characteristics of primitive meteorites.

Cassen, Patrick↗

Theory of Planetary System Formation

Observations and theoretical considerations support the idea that the Solar System formed by the collapse of tenuous interstellar matter to a disk of gas and dust (the primitive solar nebula), from which the Sun and other components separated under the action of dissipative forces and by the coagulation of solid material. Thus, planets are understood to be contemporaneous byproducts of star formation. Because the circumstellar disks of new stars are easier to observe than mature planetary systems, the possibility arises that the nature and variety of planets might be studied from observations of the conditions of their birth. A useful theory of planetary system formation would therefore relate the properties of circumstellar disks both to the initial conditions of star formation and to the consequent properties of planets to those of the disk. Although the broad outlines of such a theory are in place, many aspects are either untested, controversial, or otherwise unresolved; even the degree to which such a comprehensive theory is possible remains unknown.

Cassen, Patrick↗

Dissipation of the Solar Nebula

We review the evidence that the lifetimes of circumstellar disks, and the solar nebula in particular, are of the order 107 years. Mechanisms of evolution and removal are examined and compared with observational evidence. The expected consequences for solar system material of different removal mechanisms are discussed, and promising avenues for future research are identified.

Cassen, Patrick↗

Utilitarian models of the solar nebula

Models of the primitive solar nebula based on a combination of theory, observations of T Tauri stars, and global conservation laws are presented. The models describe the motions of nebular gas, mixing of interstellar material during the formation of the nebula, and evolution of thermal structure in terms of several characteristic parameters. The parameters describe key aspects of the protosolar cloud (its rotation rate and collapse rate) and the nebula (its mass relative to the Sun, decay time, and density distribution). For most applications, the models are heuristic rather than predicted. Their purpose is to provide a realistic context for the interpretation of solar system data, and to distinquish those nebular characteristics that can be specified with confidence, independently of the assumtions of particular models, form those that are poorly constrained. It is demonstrated that nebular gas typically experienced large radial excursions during the evolution of the nebula and that both inward and outward mean radial velocities on the order of meters per second occured in the terrestrial planet region, with inward velocities predominant for most ofthe evolution. However, the time history of disk size, surface density, and radial velocities are sensitive to the total angular momentun of the protosolar cloud, which cannot be constrained by purely theoretical considerations.It is shown that a certain amount of 'formational' mixing of interstellar material was an inevitable consequenc of nebular mass and angular momentum transport during protostellar collapse, regardless of the specific transport mechanisms invloved. Even if the protosolar cloud was initially homogeneous, this mixing was important because it had the effect of mingling presolar material that had experienced different degrees of thermal processing during collapse and passage through the accertion shock. Nebular thermal structure is less sensitive to poorly constrained parameters than is dynamical history. A simple criterion is derived for the condition that silicate grains are evaporated at midplane, and it is argued that this condition was probably fulfilled early in nebular history. Cooling of a hot nebula due tocoagulation of dust and consequent local reduction of optical depth is examined, and it is shown how such a process leads naturally to an enrichment of rock-forming elements in the gas phase.

Cassen, Patrick↗

Further studies of gravitationally unstable protostellar disks

Models of the solar nebula reveal that it might have been gravitationally unstable, both early and later in its evolution. Such instabilities produce density waves and associated gravitational torques, which are potent agents of angular momentum transport. In previous work, we conducted a series of numerical simulations designed to quantify the effects of gravitational instabilities in a generalizable way (Tomley, Cassen, & Steiman-Cameron 1991). Here we present a second series of simulations in which we examine disks of greater size, increased star/disk mass ratio, and flatter surface density distribution than those in our initial study. The purpose is to represent disks at a later stage of evolution than those already studied, to test the quantitative relations derived in our earlier work and to explore the effects of mass ratio on the results. The new results indicate that the tendencies for unstable, uncooled disks to heat to stability and for dynamical evolution rates to be proportional to cooling rates are general characteristics of the behavior of gravitationally unstable disks. Nevertheless, there are quantitative, and (for strong cooling) even qualitative differences that are revealed in the new simulations, particularly with regard to the cooling rates at which clumping tends to occur.

Tomley, Leslie↗

Theoretical, observational, and isotopic estimates of the lifetime of the solar nebula

There are a variety of isotopic data for meteorites which suggest that the protostellar nebula existed and was involved in making planetary materials for some 10(exp 7) yr or more. Many cosmochemists, however, advocate alternative interpretations of such data in order to comply with a perceived constraint, from theoretical considerations, that the nebula existed only for a much shorter time, usually stated as less than or = 10(exp 6) yr. In this paper, we review evidence relevant to solar nebula duration which is available through three different disciplines: theoretical modelling of star formation, isotopic data from meteorites, and astronomical observations of T Tauri stars. Theoretical models based on observations of present star-forming regions indicate that stars like the Sun form by dynamical gravitational collapse of dense cores of cold molecular clouds in the interstellar medium. The collapse to a star and disk occurs rapidly on a time scale of the order 10(exp 5) yr. Disks evolve by dissipating energy while redistributing angular momentum, but it is difficult to predict the rate of evolution, particularly for low mass (compared to the star) disks which nonetheless still contain enough material to account for the observed planetary system. There is no compelling evidence, from available theories of disk structure and evolution, that the solar nebula must have evolved rapidly and could not have persisted for more than 1 Ma. In considering chronologically relevant isotopic data for meteorites, we focus on three methodologies: absolute ages by U-Pb/Pb-Pb, and relative ages by short-lived radionuclides (especially Al-26) and by evolution of Sr-87/Sr-86. Two kinds of meteoritic materials-refractory inclusions such as CAIs and differentiated meteorites (eucrites and angrites) - appear to have experience potentially dateable nebular events. In both case, the most straightforward interpretations of the available data indicate nebular events spanning several Ma. We also consider alternative interpretations, particularly the hypothesis of radically heterogeneous distribution of Al-26, which would avoid these chronological interpretations. The principal impetus for such alternative interpretations seems to be precisely the obviation of the chronological interpretation (i.e., the presumption rather than the inference of a short (less than or = Ma) lifetime of the nebula). Astronomical observations of T Tauri stars indicate that the presence of dusty disks is a common if not universal feature, that the disks are massive enough to accomodate a planetary system such as ours, and that at least some persist for 10(exp 7) yr or more. The results are consistent with the time scales inferred from the meteorite isotopic data. They cannot be considered conclusive with regard to solar nebula time scales, however,in part because it is difficult to relate disk observations to processes that affect meteorites, and in part because the ages assigned for these stars could be wrong by a factor of several in either direction. We conclude that the balance of available evidence favors the view that the nebula existed and was active for at least several Ma. However, because the evidence is not definitive, it is important that the issue be perceived to be an open question, whose answer should be sought rather than presumed.

Podosek, Frank A.↗

Theoretical, observational, and isotopic estimates of the lifetime of the solar nebula

There are a variety of isotopic data for meteorites which suggest that the protostellar nebula existed and was involved in making planetary materials for some 10(exp 7) yr or more. Many cosmochemists, however, advocate alternative interpretations of such data in order to comply with a perceived constraint, from theoretical considerations, that the nebula existed only for a much shorter time, usually stated as less than or equal to 10(exp 6) yr. In this paper, we review evidence relevant to solar nebula duration which is available through three different disciplines: theoretical modeling of star formation, isotopic data from meteorites, and astronomical observations of T Tauri stars. Theoretical models based on observations of present star-forming regions indicate that stars like the Sun form by dynamical gravitational collapse of dense cores of cold molcular clouds in the interstellar clouds in the interstellar medium. The collapse to a star and disk occurs rapidly, on a time scale of the order 10(exp 5) yr. Disks evolve by dissipating energy while redistributing angular momentum, but it is difficult to predict the rate of evolution, particularly for low mass (compared to the star) disks which nonetheless still contain enough material to account for the observed planetary system. There is no compelling evidence, from available theories of disk structure and evolution, that the solar nebula must have evolved rapidly and could not have persisted for more than 1 Ma. In considering chronoloically relevant isotopic data for meteorites, we focus on three methodologies: absolute ages by U-Pb/Pb-Pb, and relative ages by short-lived radionuclides (especially Al-26) and by evolution of Sr-87/Sr-86. Two kinds of meteoritic materials-refractory inclusions such as CAIs and differential meteorites (eucrites and augrites) -- appear to have experienced potentially dateable nebular events. In both cases, the most straightforward interpretations of the available data indicate nebular events spanning several Ma. We also consider alternative interpretations, particularly the hypothesis of radically heterogeneous distribution of Al-26, which would avoid these chronological interpretations. The principal impetus for such alternative interpretations seems to be precisely the obviation of the chronological interpretation (i.e., the presumption rather than the inference of a short (less than or equal to 1 Ma) lifetime of the nebula). Astronomical observations of T Tauri stars indicate that the presence of dusty disks is a common if not universal feature, that the disks are massive enough to accomodate a planetary system such as ours, and that at least some persist for 110(exp 7) yr or more. The results are consistent with the time scales inferred from the meteoritic isotopic data. They cannot be considered conclusive with regard to solar nebula time scales, however, in part because it is difficult to relate disk observations to processes that affect meteorites, and in part because the ages assigned for these stars could be wrong by a factor of several in either direction. We conclude that the balance of available evidence favors the view that the nebula existed and was active for at least several Ma. However, because the evidence is not definitive, it is important that the issue be perceived to be an open question, whose answer should be sought rather than presumed.

Podosek, Frank A.↗

Meteoritic Constraints on Models of the Solar Nebula: The Abundances of Moderately Volatile Elements

The "moderately volatile" elements are those which condense (or evaporate) in the temperature range 650 - 1350 K, as a mix of material with solar abundances is cooled (or heated) tinder equilibrium conditions. Their relative abundances in chondritic meteorites are solar (or "cosmic", as defined by the composition of Cl meteorites) to within a factor of several, but vary within that range in a way that correlates remarkably well with condensation temperature, independent of chemical affinity. It has been argued that this correlation reflects a systematically selective process which favored the accretion of refractory material over volatile material from a cooling nebula. Wasson and Chou (Meteoritics 9, 69-94, 1974, and Wasson and co-authors in subsequent papers) suggested that condensation and settling of solids contemporaneously with the cooling and removal of nebular gas could produce the observed abundance patterns, but a quantitative model has been lacking. We show that the abundance patterns of the moderately volatile elements in chondritic meteorites can be produced, in some degree of quantitative detail, by models of the solar nebula that are designed to conform to observations of T Tauri stars and the global conservation laws. For example, even if the local surface density of the nebula is not decreasing, condensation and accretion of solids from radially inflowing gas in a cooling nebula can result in depletions of volatiles, relative to refractories, like those observed, The details of the calculated abundance patterns depend on (but are not especially sensitive to) model parameters, and can exhibit the variations that distinguish the meteorite classes. Thus it appears that nebula characteristics such as cooling rates, radial flow velocities, and particle accumulation rates can be quantitatively constrained by demanding that they conform to meteoritic data; and the models, in turn, can produce testable hypotheses regarding the time and location of the formation of the chondrite parent bodies and the planets.

Cassen, Patrick↗

On the evolution of gravitationally unstable protostellar disks

2D, N-body simulations of the nonlinear development of long-wavelength instabilities predicted to occur early in the formation stage of protostellar disks forming single stars are presented under conditions of controlled energy loss. It is found that the thermodynamics and long-term evolution of gravitationally unstable disks are intimately coupled: the global evolution rate is linearly proportional to the rate at which dissipated energy reaches and escapes from the surfaces of the disk. An upper limit is obtained to the rate at which energy is lost if it is assumed that the disk maintains vertical isothermality.

Tomley, Leslie↗

Equilibrium models of self-gravitating inviscid disks resulting from the collapse of rotating clouds

A method is presented for the construction of velocity and surface density profiles of infinitely thin, self-gravitating disks formed from the collapse of spherical clouds, under the condition that the angular momentum of each material parcel is conserved. Results are presented for initially uniformly rotating clouds with density distributions varying as R exp -n and n = 0, 1, 2. The resulting disk surface density distributions are well represented by power laws in the cylindrical radius over most of their extent. The form of the zeroth-order approximation provides a useful representation of the final surface density function near the center for all three cases, and for n = 2 this result holds throughout the disk. This result is not generally true for the velocity functions, however.

Stemwedel, Sally W.↗

Numerical models of rotating protostars

The effects of rotation on the internal structure of protostars are examined and the consequences of these effects for evolution are examined using rotating protostar models with various choices of the angular speed of the initial cloud and the mass accretion rate. The temporal order of the onset of convective deuterium burning, attainment of sufficient angular momentum for critical uniform rotation, development of a nearly Keplerian disk through direct infall, and the onset of nonaxisymmetric instability is determined. It is shown that the latter three events always occur in the stated order. Different evolutionary scenarios result depending on when deuterium ignition occurs relative to the other three events.

Durisen, Richard H.↗

Protostellar collapse, dust grains and solar system formation

Attempts to understand the origin of the solar system come from two perspectives. The first is that of the insider looking out; the system components beyond the earth are examined in detail, their properties categorized, and explanations are sought that make sense of the patterns and relations among them. The primitive meteorites are prime objects of study from this perspective. The other perspective is that of the outsider looking in, considering other stars that are now in their formative stages and trying to understand the physical processes that govern all such events, under the assumption that the solar system is not unique. A compelling theory of the origin of the solar system must, of course, merge the fruits of both perspectives.

Cassen, Patrick↗