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NASA NTRS1995

Hydrodynamics of binary coalescence. 2: Polytropes with gamma = 5/3

We present a new numerical study of the equilibrium and stability properties of close binary systems. We use the smoothed-particle hydrodynamics (SPH) technique both to construct accurate equilibrium configurations in three dimensions and to follow their hydrodynamic evolution. We adopt a simple polytropic equation of state p = K(sub rho)(exp gamma) with gamma = 5/3 and K = constant within each star, applicable to low-mass degenerate dwarfs as well as low-mass main-sequence stars. For degenerate configurations, we set the two polytropic constants equal, K = K prime, independent of the mass ratio. For main-sequence stars, we adjust K and K prime so as to obtain a simple mass-radius relation of the form R/R prime = M/M prime, where R prime and M prime are the radius and mass of the secondary. Along a sequence of binary equilibrium configurations for two identical stars, we demonstrate the existence of both secular and dynamical instabilities, confirming directly the results of recent analytic work. We use the SPH method to calculate the nonlinear development of the dynamical instability and to determine the final fate of the system. We find that the two stars merge together into a single, rapidly rotating object in just a few orbital periods. Equilibrium sequences are also constructed for systems containing two nonidentical stars. These sequences terminate at a Roche limit, which we can determine very accurately using SPH. For two low-mass main-sequence stars with mass ratio q approximately less than 0.4 we find that the (synchronized) Roche limit configuration is secularly unstable. We discuss the implications of our results for the evolution of double white-dwarf systems and W Ursae Majoris binaries.

Rasio, Frederic A.↗
NASA NTRS1992

Postcollapse hydrodynamics of SN 1987A - Two-dimensional simulations of the early evolution

The first few seconds of the explosion of SN 1987A are modeled here using a 2D cylindrical geometry smooth particle hydrodynamics code. The success of the explosion is determined to be sensitive to the duration of the infall, the timing of the bounce, and the subsequent neutrino heating. A semianalytical model for the initial structure of the collapsed object is used to present two simulations that differ by the mass that has been allowed to collapse into a neutron star prior to the bounce. In the case of a short initial infall, the explosion fails due to excessive cooling. For a longer initial infall, the cooling is less and the explosion is successful although relatively weak. It is shown that in this case, a successful explosion is brought about by the presence of an entropy gradient which, combined with the gravitational pull of the neutron star, leads to extremely strong instabilities. The critical importance of the global circulation for the success of the explosion is demonstrated.

Herant, Marc↗
NASA NTRS1991

Hydrodynamical instabilities and mixing in SN 1987A - Two-dimensional simulations of the first 3 months

Results are presented from numerical simulations of the early stages of the explosion of SN 1987A. Using a two-dimensional cylindrical geometry version of a smooth particle hydrodynamics code, the explosion is followed for three months to investigate both the early hydrodynamical instabilities and the effect of the subsequent radioactive decay of Ni-56 and Co-56 with half-lives of 6.1 and 77.8 days, respectively. It is shown that the mixing induced by hydrodynamical instabilities occurring during the first few hours is substantially modified at later time by the radioactive decay of Ni-56 and Co-56. The inner cavity of the expanding supernova remnant fills up with nickel, its decay products thus forming a giant 'nickel bubble'. The peak velocity of the nickel increases by approximately 30 percent after the decays. While these results adequately model the core of the observed Fe line profiles, they fail to reproduce the high velocity wings of the spectra.

Herant, Marc↗
NASA NTRS2013

Constraints on Decreases in Eta Carinae's Mass-loss from 3D Hydrodynamic Simulations of Its Binary Colliding Winds

Recent work suggests that the mass-loss rate of the primary star Eta-A in the massive colliding wind binary Eta Carinae dropped by a factor of 2-3 between 1999 and 2010. We present result from large- (+/- 1545 au) and small- (+/- 155 au) domain, 3D smoothed particle hydrodynamics (SPH) simulations of Eta Car's colliding winds for three Eta-A mass-loss rates ( (dot-M(sub Eta-A) = 2.4, 4.8 and 8.5 × 10(exp −4) M(solar)/ yr), investigating the effects on the dynamics of the binary wind-wind collision (WWC). These simulations include orbital motion, optically thin radiative cooling and radiative forces. We find that dot-M Eta-A greatly affects the time-dependent hydrodynamics at all spatial scales investigated. The simulations also show that the post-shock wind of the companion star Eta-B switches from the adiabatic to the radiative-cooling regime during periastron passage (Phi approx.= 0.985-1.02). This switchover starts later and ends earlier the lower the value of dot-M Eta-A and is caused by the encroachment of the wind of Eta-A into the acceleration zone of Eta-B's wind, plus radiative inhibition of Eta-B's wind by Eta-A. The SPH simulations together with 1D radiative transfer models of Eta-A's spectra reveal that a factor of 2 or more drop in dot-M EtaA should lead to substantial changes in numerous multiwavelength observables. Recent observations are not fully consistent with the model predictions, indicating that any drop in dot- M Eta-A was likely by a factor of approx. < 2 and occurred after 2004. We speculate that most of the recent observed changes in Eta Car are due to a small increase in the WWC opening angle that produces significant effects because our line of sight to the system lies close to the dense walls of the WWC zone. A modest decrease in dot-M Eta-A may be responsible, but changes in the wind/stellar parameter of Eta-B, while less likely, cannot yet be fully ruled out. We suggest observations during Eta-Car's next periastron in 2014 to further test for decreases in dot-M Eta-A. If dot-M Eta-A is declining and continues to do so, the 2014 X-ray minimum should be even shorter than that of 2009.

Eta Carinae↗
NASA NTRS1993

The giant impact produced a precipitated Moon

The author's current simulations of Giant Impacts on the protoearth show the development of large hot rock vapor atmospheres. The Balbus-Hawley mechanism will pump mass and angular momentum outwards in the equatorial plane; upon cooling and expansion the rock vapor will condense refractory material beyond the Roche distance, where it is available for lunar formation. During the last seven years, the author together with several colleagues has carried out a series of numerical investigations of the Giant Impact theory for the origin of the Moon. These involved three-dimensional simulations of the impact and its aftermath using Smooth Particle Hydrodynamics (SPH), in which the matter in the system is divided into discrete particles whose motions and internal energies are determined as a result of the imposed initial conditions. Densities and pressures are determined from the combined overlaps of the particles, which have a bell-shaped density distribution characterized by a smoothing length. In the original series of runs all particle masses and smoothing lengths had the same values; the matter in the colliding bodies consisted of initial iron cores and rock (dunite) mantles. Each of 41 runs used 3,008 particles, took several weeks of continuous computation, and gave fairly good representations of the ultimate state of the post-collision body or bodies but at best crude and qualitative information about individual particles in orbit. During the last two years an improved SPH program was used in which the masses and smoothing lengths of the particles are variable, and the intent of the current series of computations is to investigate the behavior of the matter exterior to the main parts of the body or bodies subsequent to the collisions. These runs are taking times comparable to a year of continuous computation in each case; they use 10,000 particles with 5,000 particles in the target and 5,000 in the impactor, and the particles thus have variable masses and smoothing lengths (the latter are dynamically adjusted so that a particle typically overlaps a few tens of its neighbors). Since the matter in the impactor provides the majority of the mass left in orbit after the collision, and since the masses of the particles that originated in the impactor are smaller than those in the target, the mass resolution in the exterior parts of the problem is greatly improved and the exterior particles properly simulate atmospheres in hydrostatic equilibrium.

Cameron, A. G. W.↗
NASA NTRS1998

Three-Dimensional Hydrodynamic Simulations of the Postimpact Proto-Earth

Astrophysical fluid configurations are susceptible to a variety of nonaxisymmetric instabilities under the combined effects of rotation, self-gravity, and thermal pressure. When strong enough, they can induce rapid transport of mass and angular momentum. Our own previous studies of nonaxisymmetric instabilities in model protostars and protostellar disks show that significant transport can occur on orbital timescales and that material can be ejected to large distances. In this contribution, we present three-dimensional simulations of the circumterrestrial debris belt that may have resulted from a giant impact. Our three-dimensional hydrodynamics code with self-gravity and artificial viscosity is fully second-order in space and time; the equations of hydrodynamics and the Poisson equation are solved on an Eulerian cylindrical grid. In the preliminary calculations presented here, we use a simplified EOS where the central proto-Earth is treated as an n = 1/2 polytropic fluid, surrounded by a more compressible, rapidly rotating, fluid disk that represents silicate vapor. Our initial disk parameters are generated from the endstate data of recent smoothed particle hydrodynamics giant-impact calculations. Ultimately, we wish to detennine under what conditions nonaxisymmetric instabilities grow in the postimpact disk and whether they facilitate the transport of material outside the proto-Earth's Roche Limit, leading to the formation of the Moon. In future work, we hope to include a more realistic EOS and the consequences of heating, cooling, and phase transitions.

Pickett, B. K.↗
NASA NTRS1994

A comparison of cosmological hydrodynamic codes

We present a detailed comparison of the simulation results of various hydrodynamic codes. Starting with identical initial conditions based on the cold dark matter scenario for the growth of structure, with parameters h = 0.5 Omega = Omega(sub b) = 1, and sigma(sub 8) = 1, we integrate from redshift z = 20 to z = O to determine the physical state within a representative volume of size L(exp 3) where L = 64 h(exp -1) Mpc. Five indenpendent codes are compared: three of them Eulerian mesh-based and two variants of the smooth particle hydrodynamics 'SPH' Lagrangian approach. The Eulerian codes were run at N(exp 3) = (32(exp 3), 64(exp 3), 128(exp 3), and 256(exp 3)) cells, the SPH codes at N(exp 3) = 32(exp 3) and 64(exp 3) particles. Results were then rebinned to a 16(exp 3) grid with the exception that the rebinned data should converge, by all techniques, to a common and correct result as N approaches infinity. We find that global averages of various physical quantities do, as expected, tend to converge in the rebinned model, but that uncertainites in even primitive quantities such as (T), (rho(exp 2))(exp 1/2) persists at the 3%-17% level achieve comparable and satisfactory accuracy for comparable computer time in their treatment of the high-density, high-temeprature regions as measured in the rebinned data; the variance among the five codes (at highest resolution) for the mean temperature (as weighted by rho(exp 2) is only 4.5%. Examined at high resolution we suspect that the density resolution is better in the SPH codes and the thermal accuracy in low-density regions better in the Eulerian codes. In the low-density, low-temperature regions the SPH codes have poor accuracy due to statiscal effects, and the Jameson code gives the temperatures which are too high, due to overuse of artificial viscosity in these high Mach number regions. Overall the comparison allows us to better estimate errors; it points to ways of improving this current generation ofhydrodynamic codes and of suiting their use to problems which exploit their best individual features.

Kang, Hyesung↗
NASA NTRS2013

Effects of the LBV Primary's Mass-loss Rate on the 3D Hydrodynamics of eta Carinae's Colliding Winds

At the heart of eta Carinae's spectacular "Homunculus" nebula lies an extremely luminous (L(sub Total) greater than approximately 5 × 10(exp 6) solar luminosity) colliding wind binary with a highly eccentric (e approximately 0.9), 5.54-year orbit (Figure 1). The primary of the system, a Luminous Blue Variable (LBV), is our closest (D approximately 2.3 kpc) and best example of a pre-hypernova or pre-gamma ray burst environment. The remarkably consistent and periodic RXTE X-ray light curve surprisingly showed a major change during the system's last periastron in 2009, with the X-ray minimum being approximately 50% shorter than the minima of the previous two cycles1. Between 1998 and 2011, the strengths of various broad stellar wind emission lines (e.g. Halpha, Fe II) in line-of-sight (l.o.s.) also decreased by factors of 1.5 - 3 relative to the continuum2. The current interpretation for these changes is that they are due to a gradual factor of 2 - 4 drop in the primary's mass-loss rate over the last approximately 15 years1, 2. However, while a secular change is seen for a direct view of the central source, little to no change is seen in profiles at high stellar latitudes or reflected off of the dense, circumbinary material known as the "Weigelt blobs"2, 3. Moreover, model spectra generated with CMFGEN predict that a factor of 2 - 4 drop in the primary's mass-loss rate should lead to huge changes in the observed spectrum, which thus far have not been seen. Here we present results from large- (plus or minus 1620 AU) and small- (plus or minus 162 AU) domain, full 3D smoothed particle hydrodynamics (SPH) simulations of eta Car's massive binary colliding winds for three different primary-star mass-loss rates (2.4, 4.8, and 8.5 × 10(exp -4) solar mass/yr). The goal is to investigate how the mass-loss rate affects the 3D geometry and dynamics of eta Car's optically-thick wind and spatially-extended wind-wind collision (WWC) regions, both of which are known sources of observed X-ray, optical, UV, and near-IR emission and absorption. We use two domain sizes in order to better understand how the primary's mass-loss rate influences the various observables that form at different length scales. The 3D simulations provide information important for helping constrain η Car's recent mass-loss history and future state.

lavestigate↗
NASA NTRS1994

Nonaxisymmetric evolution in protostellar disks

We present a two-dimensional, multigridded hydrodynamical simulation of the collapse of an axisymmetric, rotating, 1 solar mass protostellar cloud, which forms a resolved, hydrotastic disk. The code includes the effects of physical viscosity, radiative transfer and radiative acceleration but not magnetic fields. We examine how the disk is affected by the inclusion of turbulent viscosity by comparing a viscous simulation with an inviscid model evolved from the same initial conditions, and we derive a disk evolutionary timescale on the order of 300,000 years if alpha = 0.01. Effects arising from non-axisymmetric gravitational instabilities in the protostellar disk are followed with a three-dimensional SPH code, starting from the two-dimensional structure. We find that the disk is prone to a series of spiral instabilities with primary azimulthal mode number m = 1 and m = 2. The torques induced by these nonaxisymmetric structures elicit material transport of angular momentum and mass through the disk, readjusting the surface density profile toward more stable configurations. We present a series of analyses which characterize both the development and the likely source of the instabilities. We speculate that an evolving disk which maintains a minimum Toomre Q-value approximately 1.4 will have a total evolutionary span of several times 10(exp 5) years, comparable to, but somewhat shorter than the evolutionary timescale resulting from viscous turbulence alone. We compare the evolution resulting from nonaxisymmetric instabilities with solutions of a one-dimensional viscous diffusion equation applied to the initial surface density and temperature profile. We find that an effective alpha-value of 0.03 is a good fit to the results of the simulation. However, the effective alpha will depend on the minimum Q in the disk at the time the instability is activated. We argue that the major fraction of the transport characterized by the value of alpha is due to the action of gravitational torques, and does not arise from inherent viscosity within the smoothed particle hydrodynamics method.

Laughlin, Gregory↗
NASA NTRS1982

The passage of a star by a massive black hole

The gridless, smoothed particle hydrodynamic method of Lucy (1977) and Gingold and Monaghan (1977, 1980, a, b, 1981) is used to solve the three-dimensional problem posed by the effects on a 1.0 solar mass star of a 10,000 solar mass black hole's passage, in an initially parabolic orbit with a variety of pericenter distances. It is found that the tidal forces induce rotation and radial and nonradial pulsations in the star, and that the loss of orbital energy to these internal motions leads to the star's capture by the black hole. While the outer layers of the star are disrupted at small pericenter distances, the entire star is destroyed at even smaller distances. These results are applicable to X-ray sources, active galactic nuclei, and quasars

Nolthenius, R. A.↗
NASA NTRS1989

The origin of the moon and the single impact hypothesis. III

Calculations of the single-impact hypothesis for the origin of the moon were performed using the smoothed particle hydrodynamics (SPH) code developed by Benz et al. (1986). Results are presented from calculations of a relatively low-level collision with an impactor mass in the range 6-8 x 10 to the 26th g. Several runs of the calculations are conducted for this mass range with variations in the SPH code, the equation of state, and the initial planetary models. The effects of these variations are compared. It is found that the orbiting mass is injected by gravitational torques.

Benz, W.↗
NASA NTRS1991

Effects of a giant impact on Uranus

The effects of a giant impact on Uranus with respect to the axis tilt of Uranus and its satellites are discussed. The simulations of possible giant impacts were carried out using Cray supercomputers. The technique used is called smooth particle hydrodynamics (SPH). In this technique, the material in the proto-Uranus planet and in the impactor is divided into a large number of particles which can overlap one another so that local averages over these particles determine density and pressure in the problem, and the particles themselves have their own temperatures and internal energies. During the course of the simulation, these particles move around under the influence of the forces acting on them: gravity and pressure gradients. The results of model simulations are presented.

Slattery, W. L.↗
NASA NTRS1991

A simulation of the collapse and fragmentation of cooling molecular clouds

The application of the Smoothed Particle Hydrodynamics method to the fragmentation of rotating cloud and disk systems is described, allowing for molecular cooling due to H2 and CO. A novel approach to solving Poisson's equation for disklike structures which exploits the multigrid algorithm is also described. Numerical studies are presented which investigate the evolution of both rotating clouds and Maclaurin disks, in each case with both an isothermal equation of state and with molecular cooling. The results establish the influence of molecular cooling on the fragmentation of molecular clouds. The isothermal sequences, if they fragment at all, do so into far fewer lumps than the cooling sequences. This is not due to a cooling instability as such, but rather to the reduced thermal support. One of the sequences shows a remarkable similarity to the W49A star-forming region.

Monaghan, Joe J.↗
NASA NTRS1991

Tidal disruption of inviscid planetesimals

In view of previous efforts' demonstration that strongly dissipative planetesimals are immune to tidal disruption, an examination is presently conducted of the complementary case of inviscid planetesimals arising from collisions that are sufficiently energetic to entirely melt the resulting planetesimal and debris. The tidal disruption is numerically simulated by means of the smoothed particle hydrodynamics (SPH) code of Cameron and Benz (1991), concentrating on the tidal disruption of 0.01 earth-mass planetesimals passing by the earth with variations in the impact parameter at perigee and velocity at infinity. The SPH models show that tidal forces during a close encounter can efficiently convert orbital angular momentum into spin angular momentum, thereby initiating equatorial mass-shedding to inviscid planetesimals that have been spun up beyond the limit of rotational stability.

Boss, A. P.↗
NASA NTRS1991

The origin of the moon and the single impact hypothesis. IV

The smoothed-particle hydrodynamics method developed to simulate the conditions under which a major planetary collision may have led to the formation of the moon is presently used in 41 simulations exploring the relevant parameter space. Two possible scenarios emerge: one in which the moon is formed directly in the collision or only after dissipation and evolution of the disk. Attention is given to the Giant Blowoff hypothesis, in which not only the primitive atmosphere but large amounts of mantle material flow over the surface of the orbiting disk and blow off in the forward direction. Large amounts of angular momentum can also be lost.

Cameron, A. G. W.↗
NASA NTRS1991

Tidal disruption of inviscid protoplanets

Roche showed that equilibrium is impossible for a small fluid body synchronously orbiting a primary within a critical radius now termed the Roche limit. Tidal disruption of orbitally unbound bodies is a potentially important process for planetary formation through collisional accumulation, because the area of the Roche limit is considerably larger then the physical cross section of a protoplanet. Several previous studies were made of dynamical tidal disruption and different models of disruption were proposed. Because of the limitation of these analytical models, we have used a smoothed particle hydrodynamics (SPH) code to model the tidal disruption process. The code is basically the same as the one used to model giant impacts; we simply choose impact parameters large enough to avoid collisions. The primary and secondary both have iron cores and silicate mantles, and are initially isothermal at a molten temperature. The conclusions based on the analytical and numerical models are summarized.

Boss, Alan P.↗
NASA NTRS1991

Impact cratering calculations

In the course of carrying out finite difference calculations, it was discovered that for large craters, a previously unrecognized type of crater (diameter) growth occurred which was called lip wave propagation. This type of growth is illustrated for an impact of a 1000 km (2a) silicate bolide at 12 km/sec (U) onto a silicate half-space at earth gravity (1 g). The von Misses crustal strength is 2.4 kbar. The motion at the crater lip associated with this wave type phenomena is up, outward, and then down, similar to the particle motion of a surface wave. It is shown that the crater diameter has grown d/a of approximately 25 to d/a of approximately 4 via lip propagation from Ut/a = 5.56 to 17.0 during the time when rebound occurs. A new code is being used to study partitioning of energy and momentum and cratering efficiency with self gravity for finite-sized objects rather than the previously discussed planetary half-space problems. These are important and fundamental subjects which can be addressed with smoothed particle hydrodynamic (SPH) codes. The SPH method was used to model various problems in astrophysics and planetary physics. The initial work demonstrates that the energy budget for normal and oblique impacts are distinctly different than earlier calculations for silicate projectile impact on a silicate half space. Motivated by the first striking radar images of Venus obtained by Magellan, the effect of the atmosphere on impact cratering was studied. In order the further quantify the processes of meteor break-up and trajectory scattering upon break-up, the reentry physics of meteors striking Venus' atmosphere versus that of the Earth were studied.

Ahrens, Thomas J.↗
NASA NTRS1991

Terrestrial production vs. extraterrestrial delivery of prebiotic organics to the early Earth

A comprehensive treatment of comet/asteroid interaction with the atmosphere, ensuring surface impact, and resulting organic pyrolysis is required to determine whether more than a negligible fraction of the organics in incident comets and asteroids actually survived collision with Earth. Results of such an investigation, using a smoothed particle hydrodynamic simulation of cometary and asteroidal impacts into both oceans and rock, demonstrate that organics will not survive impacts at velocities approx. greater than 10 km s(exp -1), and that even comets and asteroids as small as 100m in radius cannot be aerobraked to below this velocity in 1 bar atmospheres. However, for plausible dense (10 bar CO2) early atmospheres, there will be sufficient aerobraking during atmospheric passage for some organics to survive the ensuing impact. Combining these results with analytical fits to the lunar impact record shows that 4.5 Gyr ago Earth was accreting at least approx. 10(exp 6) kg yr(exp 1) of intact cometary organics, a flux which thereafter declined with a approx. 100 Myr half-life. The extent to which this influx was augmented by asteroid impacts, as well as the effect of more careful modelling of a variety of conservative approximations, is currently being quantified. These results may be placed in context by comparison with in situ organic production from a variety of terrestrial energy sources, as well as organic delivery by interplanetary dust. Which source dominated the early terrestrial prebiotic inventory is found to depend on the nature of the early terrestrial atmosphere. However, there is an intriguing symmetry: it is exactly those dense CO2 atmospheres where in situ atmospheric production of organic molecules should be the most difficult, in which intact cometary organics would be delivered in large amounts.

Chyba, C. F.↗