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At least 127 records · Page 7

Virial theorem analysis of the structure and stability of magnetized clouds

The tensor virial theorem is used to analyze the structure and stability of self-gravitating, magnetized spheroids surrounded by a low-density medium with pressure and magnetic field. Analytical expressions are developed for the effect of a weak field and calculate critical states when the effect of the field is arbitrarily strong, comparing the results with full magnetohydrostatic calculations. This analysis suggests that a magnetic field may prevent gravitational collapse but may also be destabilizing, depending on its degree of concentration within the cloud.

Zweibel, Ellen G.↗

Recognition and characterization of hierarchical interstellar structure. I - Correlation function

The problem of the quantitative description of multiscale structure in interstellar cloud complexes and gravitational collapse calculations is considered, emphasizing the recognition and characterization of hierarchical fragmentation structure. The response of the two-point correlation function to a variety of analytical models for density structure is discussed for simple clustering of pointlike clouds to more complex models involving clouds with a distribution of sizes and densities and hierarchical substructure. By expressing the density distribution as the superposition of individual clouds, it is shown that the correlation function generates two types of terms: those involving each cloud's density convolved with itself and those involving pairs of different clouds. Major distortion of the correlation function are introduced by the presence of any image features with size scales a significant fraction of the image size.

Houlahan, Padraig↗

Virial theorem analysis of the structure and stability of magnetized clouds

The tensor virial theorem is used to analyze the structure and stability of self-gravitating, magnetized spheroids surrounded by a low-density medium with pressure and magnetic field. Analytical expressions are developed for the effect of a weak field and calculate critical states when the effect of the field is arbitrarily strong, comparing the results with full magnetohydrostatic calculations. This analysis suggests that a magnetic field may prevent gravitational collapse but may also be destabilizing, depending on its degree of concentration within the cloud.

Zweibel, Ellen G.↗

The intergalactic medium - Initial and boundary conditions for galaxy and primeval star formation

New detailed numerical calculations are presented of the evolution of the intergalactic medium (IGM) in a post recombination Friedmann universe, including a solution of the nonequilibrium rate equations for the ionization and recombination of H and He, the energy equation, and the equation of radiative transfer. The implications of this study for the characteristic mass scale and the epoch of gravitational collapse for the average 'first' star-forming clouds are discussed. The star-formation rate and associated metallicity generation implied if the IGM is fully ionized by starlight by redshift greater than 4 as suggested by recent interpretations of the Gunn-Peterson effect are examined. It is shown that the relative strengths of metal lines from a quasar absorption-line Lyman limit system cloud at z = 3 photoionized by the present intergalactic UV radiation background are compatible with the observations, at least for background sources of either AGN-type or star-forming galaxy spectra.

Giroux, Mark L.↗

New photoionization models of intergalactic clouds

New photoionization models of optically thin low-density intergalactic gas at constant pressure, photoionized by QSOs, are presented. All ion stages of H, He, C, N, O, Si, and Fe, plus H2 are modeled, and the column density ratios of clouds at specified values of the ionization parameter of n sub gamma/n sub H and cloud metallicity are predicted. If Ly-alpha clouds are much cooler than the previously assumed value, 30,000 K, the ionization parameter must be very low, even with the cooling contribution of a trace component of molecules. If the clouds cool below 6000 K, their final equilibrium must be below 3000 K, owing to the lack of a stable phase between 6000 and 3000 K. If it is assumed that the clouds are being irradiated by an EUV power-law continuum typical of WSOs, with J0 = 10 exp -21 ergs/s sq cm Hz, typical cloud thicknesses along the line of sight that are much smaller than would be expected from shocks, thermal instabilities, or gravitational collapse are derived.

Donahue, Megan↗

Stellar multiple systems - Constraints on the mechanism of origin

The discovery rate of premain-sequence binary and multiple systems has increased dramatically over the last few years, providing us with our first insights into the nature of such systems at young ages. The observational data derived from spectroscopic, occultation, speckle, visual, and other techniques are reviewed. Where possible, the premain-sequence binary population is compared with main-sequence systems. These results are interpreted in terms of binary formation mechanisms. While wide binaries (P is greater than 100 yr) are ordinarily explained by a fragmentation process during the collapse of a rotating protostar, the origin of some systems by capture is a possibility. The origin of close systems is not well understood: various processes, such as fragmentation during late stages of collapse, gravitational instabilities in disks, or orbital decay from a longer-period system are examined.

Bodenheimer, Peter↗

Magnetohydrodynamic wave propagation in one-dimensional nonhomogeneous, self-gravitating clouds

We study the propagation of magnetohydrodynamic (MHD) waves through nonhomogeneous, selfgravitating, magnetic media representative of molecular cloud environments and focus on the issues of cloud support and line profiles. Since the general treatment of this topic is burdened by a complex mathematical formalism, we consider simplifying geometries which yield analytical solutions in the linear wave limit. In particular, we study both magnetoacoustic and Alfven wave propagation along the density gradient in a one-imensional slab. Of specific relevance to molecular clouds, we find that the back reaction of the Alfven waves can provide a pressure along the direction of the magnetic field lines; this pressure can help support a density enhancement against gravitational collapse. Furthermore, we find that the velocity amplitudes of these waves increase as the density decreases, in rough agreement with observational estimates of line width versus density relations.

Fatuzzo, Marco↗

Numerical simulation of three-dimensional self-gravitating flow

The three-dimensional flow of a self-gravitating fluid is numerically simulated using a Fourier pseudospectral method with a logarithmic variable formulation. Two cases with zero total angular momentum are studied in detail, a 323 simulation (Run B). Other than the grid size, the primary difference between the two cases are that Run A modeled atomic hydrogen and had considerably more compressible motion initially than Run B, which modeled molecular hydrogen. The numerical results indicate that gravitational collapse can proceed in a variety of ways. In the Run A, collapse led to an elongated tube-like structure, while in the Run B, collapse led to a flatter, disklike structure.

Shebalin, John V.↗

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.↗

A comparison of two algorithms for simulating collisionless systems

Two completely different simulation algorithms are compared by applying them to the same stellar dynamical problems: one is a self-consistent field (SCF) method for solving Poisson's equation and the other is a phase-space method for integrating the collisionless Boltzmann equation. We consider simulations of spherical stellar systems which are initially far from equilibrium and relax to their final states by gravitational collapse. The initial conditions consist of either uniform-density spheres or nonequilibrium models having Plummer density profiles, in which velocity dispersions are assigned according to given virial ratios. If a few tens of radial expansion terms with hundreds of thousands of particles are used in the SCF code, excellent agreement is found between the results it generates and those obtained with the phase-space solver, provided that a sufficiently large number of grid cells are employed with the latter. These findings imply that for simulating collisionless systmes over many dynamical times, the SCF approach based on sampling phase space is competitive with the approach treating phase space as a continuous fluid. The results of our tests make it possible to estimate the number of particles and basis functions required in situations like those modeled. Limitations of the SCF method and the choice of an optimal set of basis functions are also discussed.

Hozumi, Shunsuke↗

Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

Myhill, Elizabeth 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.↗

Numerical simulation of three-dimensional self-gravitating flow

The three-dimensional flow of a self-gravitating fluid is numerically simulated using a Fourier pseudospectral method with a logarithmic variable formulation. Two cases with zero total angular momentum are studied in detail, a 32(exp 3) simulation (Run A) and a 64(exp 3) simulation (Run B). Other than the grid size, the primary differences between the two cases are that Run A modeled atomic hydrogen and had considerably more compressible motion initially than Run B, which modeled molecular hydrogen. ('Compressible motion' is that part of the velocity which has zero curl, but non-zero divergence). The numerical results indicate that gravitational collapse can proceed in a variety of ways. In Run A, collapse led to an elongated tube-like structure, while in Run B, collapse led to a flatter, disk-like structure.

Shebalin, J. V.↗

Dynamics of Granular Materials

Granular materials exhibit a rich variety of dynamical behavior, much of which is poorly understood. Fractal-like stress chains, convection, a variety of wave dynamics, including waves which resemble capillary waves, l/f noise, and fractional Brownian motion provide examples. Work beginning at Duke will focus on gravity driven convection, mixing and gravitational collapse. Although granular materials consist of collections of interacting particles, there are important differences between the dynamics of a collections of grains and the dynamics of a collections of molecules. In particular, the ergodic hypothesis is generally invalid for granular materials, so that ordinary statistical physics does not apply. In the absence of a steady energy input, granular materials undergo a rapid collapse which is strongly influenced by the presence of gravity. Fluctuations on laboratory scales in such quantities as the stress can be very large-as much as an order of magnitude greater than the mean.

Behringer, Robert P.↗

Singular Isothermal Disks and the Formation of Multiple Stars

A crucial missing ingredient in previous theoretical studies of fragmentation is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore consider the equilibrium configuration of isopedically magnetized, scale-free, singular isothermal disks, without the assumption of axial symmetry. We find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into separate bodies. We advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

Galli, Daniele↗

Singular Isothermal Disks: Nonaxiymmetric Bifurcations and Equilibria - Paper 2

We review the difficulties of the classical fission and fragmentation hypotheses for the formation of binary and multiple stars. A crucial missing ingredient in previous theoretical studies is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore formulate and solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable analytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance omega from the rotation axis of the system. In agreement with earlier analysis by Syer and Tremaine, we find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into M = 2, 3, 4, ... separate bodies. On the basis of our experience in this paper, we advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

Galli, Danielle↗

The Investigation of the Effects of Gravity on Single Bubble Sonoluminescence

In single bubble following it's rapid collapse each cycle of oscillation of an ultrasonic field. Since widely varying length and time scales affect the bubble dynamics and optical emission processes, it is difficult to anticipate the importance of the effects of gravity present for observations on earth. Our bubble is driven in an acoustically resonating cavity at it's first harmonic mode. The acoustical radiation pressure (Bjerknes force) will then keep it suspended in the center near the pressure antinode. When driven in a region where the diffusive processes balance the bubble it acts in a nonlinear but regular way, emitting a short (approx. 200ps) burst of light each acoustic cycle. Balancing the Bjerknes force with buoyancy, as in, we can see that the bubble should be displaced from the velocity node approximately 20m at normal gravity. Therefore, water flows past the bubble at the time of collapse. Gravitation also changes the ambient pressure at the bubble's location, as Delta.P = rho.g.h this gives a change of approximately -0.5% in our experiment when going from 1.8g to 0g. Studies of ambient pressure changes were also done in order to assess these effects. Inside a pressure sealed chamber a spherical glass cell is filled with distilled water which has been degassed to 120mmHg. A bubble is then trapped in the center and driven by a piezoelectric transducer at 32.2kHz attached to the side of the cell. An optical system is then set up to take strobbed video images along and light emission data simultaneously. Temperature, pressure, drive voltage, and listener voltage are also monitored. PMT output in Volts The radii of the bubbles for both experiment s are fit using the Rayleigh-Plesset equation and the acoustic drive amplitude and the ambient bubble radius are found. There is little change in the acoustic drive amplitude as we expect, since we are not varying the drive voltage. However. the ambient bubble radius goes up considerably. These changes (increased light output, increased maximum bubble radius, and increased ambient bubble radius) are also observed when the ambient pressure is varied in the laboratory by an amount similar to that due to gravitation. The changes in the ambient bubble radius and light output with a change in ambient pressure are predicted by the "dissociation hypothesis" and have been observed by other groups in the laboratory. It seems clear that buoyancy's effect on light output and bubble radius, are at best on the same order as the effects of ambient pressure.

Dzikowicz, Ben↗

Perspectives: Black Holes

When asked to discuss Cyg XR-1, E. E. Salpeter once concluded, 'A black hole in Cyg X(R)-1 is the most conservative hypothesis.' Recent observations now make it likely that a black hole in Cyg XR-1 is the only hypothesis tenable. Chandrasekhar first showed that compact stars - those with the inward force of gravity on their outer layers balanced by the pressure generated by the Pauli exclusion principle acting on its electrons (in white dwarfs) or nucleons (in neutron stars) - have a maximum mass. Equilibrium is achieved at a minimum of the total energy of the star, which is the sum of the positive Fermi energy and the negative gravitational energy. The maximum mass attainable in equilibrium is found by setting E = 0: M(max) = 1.5 M(Sun). If the mass of the star is larger than this, then E can be decreased without bound by decreasing the star's radius and increasing its (negative) gravitational energy. No equilibrium value of the radius exist, and general relativity predicts that gravitational collapse to a point occurs. This point singularity is a black hole.

Dolan, Joseph F.↗