The Effects of Metallicity, and Grain Growth and Settling on the Early Evolution of Gaseous Protoplanets

Giant protoplanets formed by gravitational instability in the outer regions of circumstellar disks go through an early phase of quasi-static contraction during which radii are large and internal temperatures are low. The main source of opacity in these objects is dust grains. We investigate two problems involving the effect of opacity on the evolution of planets of 3, 5, and 7 M_J. First, we pick three different overall metallicities for the planet and simply scale the opacity accordingly. We show that higher metallicity results in slower contraction as a result of higher opacity. It is found that the pre-collapse time scale is proportional to the metallicity. In this scenario, survival of giant planets formed by gravitational instability is predicted to be more likely around low-metallicity stars, since they evolve to the point of collapse to small size on shorter time scales. But metal-rich planets, as a result of longer contraction times, have the best opportunity to capture planetesimals and form heavy-element cores. Second, we investigate the effects of opacity reduction as a result of grain growth and settling, for the same three planetary masses and for three different values of overall metallicity. When these processes are included, the pre-collapse time scale is found to be of order 1000 years for the three masses, significantly shorter than the time scale calculated without these effects. In this case the time scale is found to be relatively insensitive to planetary mass and composition. However, the effects of planetary rotation and accretion of gas and dust, which could increase the timescale, are not included in the calculation. The short time scale we find would preclude metal enrichment by planetesimal capture, as well as heavy-element core formation, over a large range of planetary masses and metallicities.Comment: 22 pages, accepted to Icaru

Optimal Linear Parameter-Varying Control Design for a Pressurized Water Reactors

The applicability of employing parameter-dependent control to a nuclear pressurized water reactor is investigated. The synthesis techque produces a controller which achieves specified performance against the worst-case time variation of a measurable parameter which enters the plant in a linear fractional manner. The plant can thus have widely varying dynamics over the operating range. The results indicate this control technique is comparable to linear control when small operating ranges are considered

Numerical two-dimensional calculations of the formation of the solar nebula

Numerical two dimensional calculations of the formation of the solar nebula are presented. The following subject areas are covered: (1) observational constraints of the properties of the initial solar nebula; (2) the physical problem; (3) review if two dimensional calculations of the formation phase; (4) recent models with hydrodynamics and radiative transport; and (5) further evolution of the system

Care Management of Patients With Complex Health Care Needs

Explores how patients' complexity of healthcare needs, vulnerability, and age affect the cost and quality of their health care. Examines the potential for care management to improve quality of care and reduce costs, elements of success, and challenges

Determination of the Interior Structure of Transiting Planets in Multiple-Planet Systems

Tidal dissipation within a short-period transiting extrasolar planet perturbed by a companion object can drive orbital evolution of the system to a so-called tidal fixed point, in which the apsidal lines of the transiting planet and its perturber are aligned, and for which variations in the orbital eccentricities of both planet and perturber are damped out. Significant contributions to the apsidal precession rate are made by the secular planet-planet interaction, by general relativity, and by the gravitational quadropole fields created by the transiting planet's tidal and rotational distortions. The fixed-point orbital eccentricity of the inner planet is therefore a strong function of the planet's interior structure. We illustrate these ideas in the specific context of the recently discovered HAT-P-13 exo-planetary system, and show that one can already glean important insights into the physical properties of the inner transiting planet. We present structural models of the planet, which indicate that its observed radius can be maintained for a one-parameter sequence of models that properly vary core mass and tidal energy dissipation in the interior. We use an octopole-order secular theory of the orbital dynamics to derive the dependence of the inner planet's eccentricity, on its tidal Love number. We find that the currently measured eccentricity, implies 0.116 < k2_{b} < 0.425, 0 M_{Earth}<M_{core}<120 M_{Earth}$, and Q_{b} < 300,000. Improved measurement of the eccentricity will soon allow for far tighter limits to be placed on all three of these quantities, and will provide an unprecedented probe into the interior structure of an extrasolar planet.Comment: 13 pages, 2 figures, submitted to ApJ Letter

Linear Parameter-Varying Control of a Ducted Fan Engine

Parameter-dependent control techniques are applied to a vectored thrust, ducted fan engine. The synthesis technique is based on the solution of Linear Matrix Inequalities and produces a controller which achieves specified performance against the worst-case time variation of measurable parameters entering the plant in a linear fractional manner. Thus the plant can have widely varying dynamics over the operating range. The controller designed performs extremely well, and is compared to an ℋ∞ controller

Models of the formation of the planets in the 47 UMa system

Formation of planets in the 47 UMa system is followed in an evolving protoplanetary disk composed of gas and solids. The evolution of the disk is calculated from an early stage, when all solids, assumed to be high-temperature silicates, are in the dust form, to the stage when most solids are locked in planetesimals. The simulation of planetary evolution starts with a solid embryo of ~1 Earth mass, and proceeds according to the core accretion -- gas capture model. Orbital parameters are kept constant, and it is assumed that the environment of each planet is not perturbed by the second planet. It is found that conditions suitable for both planets to form within several Myr are easily created, and maintained throughout the formation time, in disks with $\alpha \approx 0.01$. In such disks, a planet of 2.6 Jupiter masses (the minimum for the inner planet of the 47 UMa system) may be formed at 2.1 AU from the star in \~3 Myr, while a planet of 0.89 Jupiter masses (the minimum for the outer planet) may be formed at 3.95 AU from the star in about the same time. The formation of planets is possible as a result of a significant enhancement of the surface density of solids between 1.0 and 4.0 AU, which results from the evolution of a disk with an initially uniform gas-to-dust ratio of 167 and an initial radius of 40 AU.Comment: Accepted for publication in A&A. 10 pages, 10 figure

Tidal and Magnetic Interactions between a Hot Jupiter and its Host Star in the Magnetospheric Cavity of a Protoplanetary Disk

We present a simplified model to study the orbital evolution of a young hot Jupiter inside the magnetospheric cavity of a proto-planetary disk. The model takes into account the disk locking of stellar spin as well as the tidal and magnetic interactions between the star and the planet. We focus on the orbital evolution starting from the orbit in the 2:1 resonance with the inner edge of the disk, followed by the inward and then outward orbital migration driven by the tidal and magnetic torques as well as the Roche-lobe overflow of the tidally inflated planet. The goal in this paper is to study how the orbital evolution inside the magnetospheric cavity depends on the cavity size, planet mass, and orbital eccentricity. In the present work, we only target the mass range from 0.7 to 2 Jupiter masses. In the case of the large cavity corresponding to the rotational period ~ 7 days, the planet of mass >1 Jupiter mass with moderate initial eccentricities (>~ 0.3) can move to the region < 0.03 AU from its central star in 10^7 years, while the planet of mass <1 Jupiter mass cannot. We estimate the critical eccentricity beyond which the planet of a given mass will overflow its Roche radius and finally lose all of its gas onto the star due to runaway mass loss. In the case of the small cavity corresponding to the rotational period ~ 3 days, all of the simulated planets lose all of their gas even in circular orbits. Our results for the orbital evolution of young hot Jupiters may have the potential to explain the absence of low-mass giant planets inside ~ 0.03 AU from their dwarf stars revealed by transit surveys.Comment: 29 pages, 6 figures, 1 table. accepted for publication by Ap

Evolution of Ohmically Heated Hot Jupiters

We present calculations of thermal evolution of Hot Jupiters with various masses and effective temperatures under Ohmic dissipation. The resulting evolutionary sequences show a clear tendency towards inflated radii for effective temperatures that give rise to significant ionization of alkali metals in the atmosphere, compatible with the trend of the data. The degree of inflation shows that Ohmic dissipation, along with the likely variability in heavy element content can account for all of the currently detected radius anomalies. Furthermore, we find that in absence of a massive core, low-mass hot Jupiters can over-flow their Roche-lobes and evaporate on Gyr time-scales, possibly leaving behind small rocky cores.Comment: Accepted to The Astrophysical Journal (2011) 735-2, 9 pages, 8 figures, updated figures 2-