Turbulent Mixing in the Outer Solar Nebula

The effects of turbulence on the mixing of gases and dust in the outer Solar nebula are examined using 3-D MHD calculations in the shearing-box approximation with vertical stratification. The turbulence is driven by the magneto-rotational instability. The magnetic and hydrodynamic stresses in the turbulence correspond to an accretion time at the midplane about equal to the lifetimes of T Tauri disks, while accretion in the surface layers is thirty times faster. The mixing resulting from the turbulence is also fastest in the surface layers. The mixing rate is similar to the rate of radial exchange of orbital angular momentum, so that the Schmidt number is near unity. The vertical spreading of a trace species is well-matched by solutions of a damped wave equation when the flow is horizontally-averaged. The damped wave description can be used to inexpensively treat mixing in 1-D chemical models. However, even in calculations reaching a statistical steady state, the concentration at any given time varies substantially over horizontal planes, due to fluctuations in the rate and direction of the transport. In addition to mixing species that are formed under widely varying conditions, the turbulence intermittently forces the nebula away from local chemical equilibrium. The different transport rates in the surface layers and interior may affect estimates of the grain evolution and molecular abundances during the formation of the Solar system.Comment: To appear in the Astrophysical Journal; 20 pages, 9 figure

An implicit method for radiative transfer with the diffusion approximation in SPH

An implicit method for radiative transfer in SPH is described. The diffusion approximation is used, and the hydrodynamic calculations are performed by a fully three--dimensional SPH code. Instead of the energy equation of state for an ideal gas, various energy states and the dissociation of hydrogen molecules are considered in the energy calculation for a more realistic temperature and pressure determination. In order to test the implicit code, we have performed non--isothermal collapse simulations of a centrally condensed cloud, and have compared our results with those of finite difference calculations performed by MB93. The results produced by the two completely different numerical methods agree well with each other.Comment: 25 pages, 9 figure

Photon Bubbles in the Circumstellar Envelopes of Young Massive Stars

We show that the optically-thick dusty envelopes surrounding young high-mass stars are subject to the photon bubble instability. The infrared radiation passing through the envelope amplifies magnetosonic disturbances, with growth rates in our local numerical radiation MHD calculations that are consistent with a linear analysis. Modes with wavelengths comparable to the gas pressure scale height grow by more than two orders of magnitude in a thousand years, reaching non-linear amplitudes within the envelope lifetime. If the magnetic pressure in the envelope exceeds the gas pressure, the instability develops into trains of propagating shocks. Radiation escapes readily through the low-density material between the shocks, enabling accretion to continue despite the Eddington limit imposed by the dust opacity. The supersonic motions arising from the photon bubble instability can help explain the large velocity dispersions of hot molecular cores, while conditions in the shocked gas are suitable for maser emission. We conclude that the photon bubble instability may play a key role in the formation of massive stars.Comment: Accepted by the Astrophysical Journal; 18 pages, 4 figure

Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

A Keck High Resolution Spectroscopic Study of the Orion Nebula Proplyds

We present the results of spectroscopy of four bright proplyds in the Orion Nebula obtained at a velocity resolution of 6 km/s. After careful isolation of the proplyd spectra from the confusing nebular radiation, the emission line profiles are compared with those predicted by realistic dynamic/photoionization models of the objects. The spectral line widths show a clear correlation with ionization potential, which is consistent with the free expansion of a transonic, ionization-stratified, photoevaporating flow. Fitting models of such a flow simultaneously to our spectra and HST emission line imaging provides direct measurements of the proplyd size, ionized density and outflow velocity. These measurements confirm that the ionization front in the proplyds is approximately D-critical and provide the most accurate and robust estimate to date of the proplyd mass loss rate. Values of 0.7E-6 to 1.5E-6 Msun/year are found for our spectroscopic sample, although extrapolating our results to a larger sample of proplyds implies that 0.4E-6 Msun/year is more typical of the proplyds as a whole. In view of the reported limits on the masses of the circumstellar disks within the proplyds, the length of time that they can have been exposed to ionizing radiation should not greatly exceed 10,000 years - a factor of 30 less than the mean age of the proplyd stars. We review the various mechanisms that have been proposed to explain this situation, and conclude that none can plausibly work unless the disk masses are revised upwards by a substantial amount.Comment: 23 pages, 8 figures, uses emulateapj.sty, accepted for publication in The Astronomical Journal (scheduled November 1999

Resolving the Formation of Protogalaxies. III. Feedback from the First Stars

The first stars form in dark matter halos of masses ~10^6 M_sun as suggested by an increasing number of numerical simulations. Radiation feedback from these stars expels most of the gas from their shallow potential well of their surrounding dark matter halos. We use cosmological adaptive mesh refinement simulations that include self-consistent Population III star formation and feedback to examine the properties of assembling early dwarf galaxies. Accurate radiative transport is modeled with adaptive ray tracing. We include supernova explosions and follow the metal enrichment of the intergalactic medium. The calculations focus on the formation of several dwarf galaxies and their progenitors. In these halos, baryon fractions in 10^8 solar mass halos decrease by a factor of 2 with stellar feedback and by a factor of 3 with supernova explosions. We find that radiation feedback and supernova explosions increase gaseous spin parameters up to a factor of 4 and vary with time. Stellar feedback, supernova explosions, and H_2 cooling create a complex, multi-phase interstellar medium whose densities and temperatures can span up to 6 orders of magnitude at a given radius. The pair-instability supernovae of Population III stars alone enrich the halos with virial temperatures of 10^4 K to approximately 10^{-3} of solar metallicity. We find that 40% of the heavy elements resides in the intergalactic medium (IGM) at the end of our calculations. The highest metallicity gas exists in supernova remnants and very dilute regions of the IGM.Comment: 15 pages, 16 figures, accepted to ApJ. Many changes, including estimates of metal line cooling. High resolution images and movies available at http://www.slac.stanford.edu/~jwise/research/PGalaxies3

Massive stars and the energy balance of the interstellar medium. II. The 35 solar mass star and a solution to the "missing wind problem"

We continue our numerical analysis of the morphological and energetic influence of massive stars on their ambient interstellar medium for a 35 solar mass star that evolves from the main sequence through red supergiant and Wolf-Rayet phases, until it ultimately explodes as a supernova. We find that structure formation in the circumstellar gas during the early main-sequence evolution occurs as in the 60 solar mass case but is much less pronounced because of the lower mechanical wind luminosity of the star. Since on the other hand the shell-like structure of the HII region is largely preserved, effects that rely on this symmetry become more important. At the end of the stellar lifetime 1% of the energy released as Lyman continuum radiation and stellar wind has been transferred to the circumstellar gas. From this fraction 10% is kinetic energy of bulk motion, 36% is thermal energy, and the remaining 54% is ionization energy of hydrogen. The sweeping up of the slow red supergiant wind by the fast Wolf-Rayet wind produces remarkable morphological structures and emission signatures, which are compared with existing observations of the Wolf-Rayet bubble S308. Our model reproduces the correct order of magnitude of observed X-ray luminosity, the temperature of the emitting plasma as well as the limb brightening of the intensity profile. This is remarkable, because current analytical and numerical models of Wolf-Rayet bubbles fail to consistently explain these features. A key result is that almost the entire X-ray emission in this stage comes from the shell of red supergiant wind swept up by the shocked Wolf-Rayet wind rather than from the shocked Wolf-Rayet wind itself as hitherto assumed and modeled. This offers a possible solution to what is called the ``missing wind problem'' of Wolf-Rayet bubbles.Comment: 52 pages, 20 figures, 2 tables, accepted for publication in the Astrophysical Journa