Toward a Deterministic Model of Planetary Formation VII: Eccentricity Distribution of Gas Giants

The ubiquity of planets and diversity of planetary systems reveal planet formation encompass many complex and competing processes. In this series of papers, we develop and upgrade a population synthesis model as a tool to identify the dominant physical effects and to calibrate the range of physical conditions. Recent planet searches leads to the discovery of many multiple-planet systems. Any theoretical models of their origins must take into account dynamical interaction between emerging protoplanets. Here, we introduce a prescription to approximate the close encounters between multiple planets. We apply this method to simulate the growth, migration, and dynamical interaction of planetary systems. Our models show that in relatively massive disks, several gas giants and rocky/icy planets emerge, migrate, and undergo dynamical instability. Secular perturbation between planets leads to orbital crossings, eccentricity excitation, and planetary ejection. In disks with modest masses, two or less gas giants form with multiple super-Earths. Orbital stability in these systems is generally maintained and they retain the kinematic structure after gas in their natal disks is depleted. These results reproduce the observed planetary mass-eccentricity and semimajor axis-eccentricity correlations. They also suggest that emerging gas giants can scatter residual cores to the outer disk regions. Subsequent in situ gas accretion onto these cores can lead to the formation of distant (> 30AU) gas giants with nearly circular orbits.Comment: 54 pages, 14 Figures; accepted for publication in Astrophysical Journa

Self-pressurization of a flightweight liquid hydrogen storage tank subjected to low heat flux

Results are presented for an experimental investigation of self-pressurization and thermal stratification of a 4.89 cu m liquid hydrogen (LH2) storage tank subjected to low heat flux (0.35, 2.0, and 3.5 W/sq m) under normal gravity conditions. Tests were performed at fill levels of 83 to 84 percent (by volume). The LH2 tank was representative of future spacecraft tankage, having a low mass-to-volume ratio and high performance multilayer thermal insulation. Results show that the pressure rise rate and thermal stratification increase with increasing heat flux. At the lowest heat flux, the pressure rise rate is comparable to the homogenous rate, while at the highest heat flux, the rate is more than three times the homogeneous rate. It was found that initial conditions have a significant impact on the initial pressure rise rate. The quasi-steady pressure rise rates are nearly independent of the initial condition after an initial transient period has passed

A pressure control analysis of cryogenic storage systems

Self-pressurization of cryogenic storage tanks due to heat leak through the thermal protection system is examined along with the performance of various pressure control technologies for application in microgravity environments. Methods of pressure control such as fluid mixing, passive thermodynamic venting, and active thermodynamic venting are analyzed using the homogeneous thermodynamic model. Simplified equations suggested may be used to characterize the performance of various pressure control systems and to design space experiments

Self-pressurization of a flightweight liquid hydrogen tank: Effects of fill level at low wall heat flux

Experimental results are presented for the self pressurization and thermal stratification of a 4.89 cu m liquid hydrogen storage tank subjected to low heat flux (2.0 and 3.5 W/sq m) in normal gravity. The test tank was representative of future spacecraft tankage, having a low mass to volume ratio and high performance multilayer thermal insulation. Tests were performed at fill levels of 29 and 49 pcts. (by volume) and complement previous tests at 83 pct. fill. As the heat flux increases, the pressure rise rate at each fill level exceeds the homogeneous rate by an increasing ratio. Herein, this ratio did not exceed a value of 2. The slowest pressure rise rate was observed for the 49 pct. fill level at both heat fluxes. This result is attributed to the oblate spheroidal tank geometry which introduces the variables of wetted wall area, liquid-vapor interfacial area, and ratio of side wall to bottom heating as a function of fill level or liquid depth. Initial tank thermal conditions were found to affect the initial pressure rise rate. Quasi steady pressure rise rates are independent of starting conditions

Eccentricity Evolution of Extrasolar Multiple Planetary Systems due to the Depletion of Nascent Protostellar Disks

Most extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets' mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semi-major axis ratios. But, prior to the disk depletion, self gravity of the planets' nascent disks dominates the precession eigenfrequencies. We examine here the initial evolution of young planets' eccentricity due to the apsidal libration or circulation induced by both the secular interaction between them and the self gravity of their nascent disks. We show that as the latter effect declines adiabatically with disk depletion, the modulation amplitude of the planets' relative phase of periapse is approximately invariant despite the time-asymmetrical exchange of angular momentum between planets. However, as the young planets' orbits pass through a state of secular resonance, their mean eccentricities undergo systematic quantitative changes. For applications, we analyze the eccentricity evolution of planets around Upsilon Andromedae and HD168443 during the epoch of protostellar disk depletion. We find that the disk depletion can change the planets' eccentricity ratio. However, the relatively large amplitude of the planets' eccentricity cannot be excited if all the planets had small initial eccentricities.Comment: 50 pages including 11 figures, submitted to Ap

Finite Density Algorithm in Lattice QCD -- a Canonical Ensemble Approach

I will review the finite density algorithm for lattice QCD based on finite chemical potential and summarize the associated difficulties. I will propose a canonical ensemble approach which projects out the finite baryon number sector from the fermion determinant. For this algorithm to work, it requires an efficient method for calculating the fermion determinant and a Monte Carlo algorithm which accommodates unbiased estimate of the probability. I shall report on the progress made along this direction with the Pad\'{e} - Z$_2$ estimator of the determinant and its implementation in the newly developed Noisy Monte Carlo algorithm.Comment: Invited talk at Nankai Symposium on Mathematical Physics, Tianjin, Oct. 2001, 18 pages, 3 figures; expanded and references adde

Storage and recall of weak coherent optical pulses with an efficiency of 25%

We demonstrate experimentally a quantum memory scheme for the storage of weak coherent light pulses in an inhomogeneously broadened optical transition in a Pr^{3+}: YSO crystal at 2.1 K. Precise optical pumping using a frequency stable (about 1kHz linewidth) laser is employed to create a highly controllable Atomic Frequency Comb (AFC) structure. We report single photon storage and retrieval efficiencies of 25%, based on coherent photon echo type re-emission in the forward direction. The coherence property of the quantum memory is proved through interference between a super Gaussian pulse and the emitted echo. Backward retrieval of the photon echo emission has potential for increasing storage and recall efficiency.Comment: 5,

Twisted and Nontwisted Bifurcations Induced by Diffusion

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling. Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex files. Hard copy of figures available on request from [email protected]