Engineering topics

Laughlin, Gregory

Publications and source records attributed to Laughlin, Gregory.

7 records

NASA NTRS2001

Short-Term Dynamical Interactions Among Extrasolar Planets

We show that short-term perturbations among massive planets in multiple planet systems can result in radial velocity variations of the central star which differ substantially from velocity variations derived assuming the planets are executing independent Keplerian motions. We discuss two alternate fitting methods which can lead to an improved dynamical description of multiple planet systems. In the first method, the osculating orbital elements are determined via a Levenberg-Marquardt minimization scheme driving an N-body integrator. The second method is an improved analytic model in which orbital elements such as the periods and longitudes of periastron are allowed to vary according to a simple model for resonant interactions between the planets. Both of these methods can potentially determine the true masses for the planets by eliminating the sin(i) degeneracy inherent in fits that assume independent Keplerian motions. As more radial velocity data is accumulated from stars such as GJ876, these methods should allow for unambiguous determination of the planetary masses and relative inclinations.

Laughlin, Gregory↗

NASA NTRS2000

The Evolution and Disruption of Planetary Systems

Planetary systems that encounter passing stars can experience severe orbital disruption, and the efficiency of this process is greatly enhanced when the impinging systems are binary pairs rather than single stars. Using a Monte Carlo approach, we have performed nearly half a million numerical experiments to examine the long term ramifications of planetary scattering on planetary systems. We have concluded that systems which form in dense environments such as Orion's Trapezium cluster have roughly a ten percent chance of being seriously disrupted. We have also used our programs to explore the long-term prospects for our own Solar system. Given the current interstellar environment, we have computed the odds that Earth will find its orbit seriously disrupted prior to the emergence of a runaway greenhouse effect driven by the Sun's increasing luminosity. This estimate includes both direct disruption events and scattering processes that seriously alter the orbits of the Jovian planets, which then force severe changes upon the Earth's orbit. We then explore the consequences of the Earth being thrown into deep space. The surface biosphere would rapidly shut down under conditions of zero insolation, but the Earth's radioactive heat is capable of maintaining life deep underground, and perhaps in hydrothermal vent communities, for some time to come. Although unlikely for the Earth, this scenario may be common throughout the universe, since many environments where liquid water could exist (e.g., Europa and Callisto) must derive their energy from internal (rather than external) heating.

Laughlin, Gregory↗

NASA NTRS2000

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↗

NASA NTRS2000

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↗

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 NTRS1993

The formation of protostellar disks. I - 1 M(solar)

Hydrodynamical calculations of the collapse of an axisymmetric, rotating one solar mass protostellar cloud, including the effects of radiative transfer and radiative acceleration but without magnetic fields, are presented. The results include calculations of infrared protostellar spectra as a function of time and viewing angle. A numerical algorithm involving explicit nested grids is used to resolve the region of initial disk formation and at the same time to include the outer regions in the calculation. The central part of the protostar is modeled approximately. Initial conditions are systematically varied to investigate their influence on the evolution and final configuration of central star plus circumstellar disk. The initial state for the standard case is a centrally condensed molecular cloud core of one solar mass with a mean density of 8 x 10 exp -18 g/cu cm and a specific angular momentum at the outer edge of 7 x 10 exp 20 sq cm/s. The collapse is followed for 8 x 10 exp 4 yr, at which point 0.45 solar mass is contained in a rapidly rotating central object and most of the remainder in a surrounding equilibrium disk. The stability of this final structure is qualitatively analyzed.

Yorke, Harold W.↗

NASA NTRS1993

Luminosity functions for very low mass stars and brown dwarfs

A theoretical investigation of the luminosity function for low-mass objects to constrain the stellar initial mass function at the low-mass end is reported. The ways in which luminosity functions for low-mass stars are affected by star formation histories, brown dwarf and premain-sequence cooling rates and main-sequence mass luminosity relations, and the IMF are examined. Cooling rates and the mass-luminosity relation are determined through a new series of evolutionary calculations for very low mass stars and brown dwarfs in the range 0.05-0.50 solar mass. Model luminosity functions are constructed for specific comparison with the results of four recent observational surveys. The likelihood that the stellar mass function in the solar neighborhood is increasing at masses near the bottom of the main sequence and perhaps at lower masses is confirmed. In the most optimistic case, brown dwarfs contribute half of the local missing disk mass. The actual contribution is likely to be considerably less.

Laughlin, Gregory↗