Engineering topics

Hut, Piet

Publications and source records attributed to Hut, Piet.

12 records

NASA NTRS1995

Building a better leapfrog

In stellar dynamical computer simulations, as well as other types of simulations using particles, time step size is often held constant in order to guarantee a high degree of energy conservation. In many applications, allowing the time step size to change in time can offer a great saving in computational cost, but variable-size time steps usually imply a substantial degradation in energy conservation. We present a meta-algorithm' for choosing time steps in such a way as to guarantee time symmetry in any integration scheme, thus allowing vastly improved energy conservation for orbital calculations with variable time steps. We apply the algorithm to the familiar leapfrog scheme, and generalize to higher order integration schemes, showing how the stability properties of the fixed-step leapfrog scheme can be extended to higher order, variable-step integrators such as the Hermite method. We illustrate the remarkable properties of these time-symmetric integrators for the case of a highly eccentric elliptical Kepler orbit and discuss applications to more complex problems.

Hut, Piet↗

NASA NTRS1995

Binary-binary interactions and the formation of the PSR B1620-26 triple system in M4

The hierarchical triple system containing the millisecond pulsar PSR B1620-26 in M4 is the first star system ever detected in a globular cluster. Such systems should form in globular clusters as a result of dynamical interactions between binaries. We propose that the triple system containing PSR B1620-26 formed through an exchange interaction between a wide primordial binary and a pre-existing binary millisecond pulsar. This scenario would have the advantage of reconciling the approximately 10(exp 9) yr timing age of the pulsar with the much shorter lifetime of the triple system in the core of M4.

Rasio, Frederic A.↗

NASA NTRS1994

Star cluster evolution with primordial binaries. 3: Effect of the Galactic tidal field

We present the results of N-body simulations of tidally limited star clusters with an initial population of 0%-20% binaries. We find that (1) if enough binaries are initially present, the binary fraction may fall to a minimum value, then increase at late times; (2) the cluster evaporation timescale is quite insensitive to the details of the initial binary distribution; (3) the cluster core radius stabilizes at a few percent of the half-mass radius when binaries are present, just as in the case of isolated clusters; and (4) there may be a marked difference between the spatial distribution of low-energy and high-energy binaries as the cluster evolves. Specifically, the spatial distribution of the lower energy systems is often substantially more extended than that of the more tightly bound pairs. At no time are our simulated clusters well described by simple dynamical models that neglect the close coupling between the binding energies and the center-of-mass energies of the binaries they contain.

Mcmillan, Steve↗

NASA NTRS1994

The onset of gravothermal oscillations in globular cluster evolution

We have carried out an extensive set of Fokker-Planck simulations of the evolution of globular clusters on very long timescales, up to 600 times the initial core collapse time t(sub cc). We consider an idealized equal mass star cluster, with a wide range of values for the total number of stars, 7000 less than N less than 2 x 10(exp 6). Our models include the heating effect of compact binaries formed in three-body encounters, which halts the initial core collapse and drives a core reexpansion. Postcollapse gravothermal oscillations of the cluster core are found to occur for all N approximately greater than or equal to 8000. For 8000 approximately less than or equal to N approximately less than or equal to 11,000, the oscillation has a simple, regular waveform with a single, well-defined period. For N approximately equals 12,000, the oscillations become nonlinear in a process resembling a period doubling. For N approximately greater than or equal to 14,000, the waveform of the oscillations becomes increasingly more irregular with increasing N, resembling chaotic behavior for N approximately greater than or equal to 15,000. During the oscillations, the core radius and core mass vary dramatically: by more than a factor of 10 for N greater than 15,000, by more than a factor of 100 for N greater than 5 x 10(exp 4), and by more than a factor of 1000 for N greater than 5 x 10(exp 5). However, even during the times of maximum expansion, the core contains only a small fraction of the cluster mass. For most N values, the maximum core mass at any time after core collapse is less than 1% of the cluster mass. The exceptions lie in the range 5 x 10(exp 4) approximately less than or equal to N approximately equal to or less than 2 x 10(exp 5), where the maximum post-collapse core mass reaches approximately 2% of the cluster mass. We discuss the observational implications of these predictions.

Breeden, Joseph L.↗

NASA NTRS1993

Stellar black holes in globular clusters

The recent discovery of large populations of millisec pulsars associated with neutron stars in globular clusters indicates that several hundred stellar black holes of about 10 solar masses each can form within a typical cluster. While, in clusters of high central density, the rapid dynamical evolution of the black-hole population leads to an ejection of nearly all holes on a short timescale, systems of intermediate density may involve a normal star's capture by one of the surviving holes to form a low-mass X-ray binary. One or more such binaries may be found in the globular clusters surrounding our galaxy.

Kulkarni, S. R.↗

NASA NTRS1993

Discreteness noise versus force errors in N-body simulations

A low accuracy in the force calculation per time step of a few percent for each particle pair is sufficient for collisionless N-body simulations. Higher accuracy is made meaningless by the dominant discreteness noise in the form of two-body relaxation, which can be reduced only by increasing the number of particles. Since an N-body simulation is a Monte Carlo procedure in which each particle-particle force is essentially random, i.e., carries an error of about 1000 percent, the only requirement is a systematic averaging-out of these intrinsic errors. We illustrate these assertions with two specific examples in which individual pairwise forces are deliberately allowed to carry significant errors: tree-codes on supercomputers and algorithms on special-purpose machines with low-precision hardware.

Hernquist, Lars↗

NASA NTRS1992

Binaries in globular clusters

Recent observations have shown that globular clusters contain a substantial number of binaries most of which are believed to be primordial. We discuss different successful optical search techniques, based on radial-velocity variables, photometric variables, and the positions of stars in the color-magnitude diagram. In addition, we review searches in other wavelengths, which have turned up low-mass X-ray binaries and more recently a variety of radio pulsars. On the theoretical side, we give an overview of the different physical mechanisms through which individual binaries evolve. We discuss the various simulation techniques which recently have been employed to study the effects of a primordial binary population, and the fascinating interplay between stellar evolution and stellar dynamics which drives globular-cluster evolution.

Hut, Piet↗

NASA NTRS1992

Rates of collapse and evaporation of globular clusters

Observational estimates of the dynamical relaxation times of Galactic globular clusters are used here to estimate the present rate at which core collapse and evaporation are occurring in them. A core collapse rate of 2 +/- 1 per Gyr is found, which for a Galactic age of about 12 Gyr agrees well with the fact that 27 clusters have surface brightness profiles with the morphology expected for the postcollapse phase. A destruction and evaporation rate of 5 +/- 3 per Gyr is found, suggesting that a significant fraction of the Galaxy's original complement of globular clusters have perished through the combined effects of mechanisms such as relaxation-driven evaporation and shocking due to interaction with the Galactic disk and bulge.

Hut, Piet↗

NASA NTRS1992

The evolution of a primordial binary population in a globular cluster

A simple model is presented for the evolution of a primordial binary population in a globular cluster. Monte Carlo simulations are given for an initial population of 50,000 binaries against a fixed background population of 500,000 single stars in a tidally truncated cluster model. Individual histories of all binaries are followed through mass segregation, scattering recoil, escape from the cluster, or coalescence. It is found that most binaries are destroyed by binary-binary interactions, with the rest escaping in the point-mass approximation. In a more realistic model, the majority of the rest merge. At any instant, most of the remaining binaries are drifting in toward the center before their first strong encounter. A typical binary spends most of its active life in or near the cluster core. The few binaries which receive a recoil sufficient to place them in the halo past the half-mass radius remain there long enough to make a significant contribution to the radial binary distribution.

Hut, Piet↗

NASA NTRS1991

A post-core-collapse model for the nucleus of M33

A model for the post-collapse core of M33 is proposed. By analogy with globular clusters, the formation of tight binary systems powers the reexpansion of the core, and it is expected that low-mass X-ray binaries form at a rate about equal to that of all galactic globular clusters combined. About a dozen such binaries should be present, and their combined emission may explain the large and enigmatic unresolved X-ray emission from the nucleus of M33. In addition, tidal formation of cataclysmic binaries may lead to a nova rate of more than about one per century. Numerous blue stragglers have probably formed through mergers caused by stellar collisions, but their density is probably too low to explain the blue color of the nucleus. Young stars are the likely cause for the color, and their presence may complicate the simple dynamical picture presented here.

Hernquist, Lars↗

NASA NTRS1988

On the evolution of globular cluster systems. I - Present characteristics and rate of destruction in our Galaxy

The current dynamic state and rate of destruction for the system of globular clusters in the Galaxy are modeled. It is found that gravitational shocks due to the central bulge of the Galaxy are very efficient in destroying clusters on highly radial orbits. This effect, extrapolated at the present unweighted destruction rate over 10 to the 10th yr, can account for the observed difference between the velocity distribution of globular clusters and other tracers of the halo population.

Aguilar, Luis↗

NASA NTRS1987

Comet showers as a cause of mass extinction

Three independent pieces of evidence supporting a connection between comet showers and clustering in terrestrial cratering and mass extinctions are presented. The temporal profile of a comet shower triggered by a star passing through the Oort cloud is calculated. Four weak peaks are found in the age of distribution of impact craters over the past 100 Myr, as well as two compact clusters of ages of impact glass broadly coincident with crater-age peaks. Recent paleontological observations are reviewed that indicate a stepwise character for some well-documented mass extinctions in the past 100 Myr which roughly coincide with three of the four peaks in crater ages and which have a duration compatible with comet shower predictions.

Hut, Piet↗