Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment: I. Formulation of the Problem and Method of Solution

We formulate the problem of the formation of magnetically supercritical cores in magnetically subcritical parent molecular clouds, and the subsequent collapse of the cores to high densities, past the detachment of ions from magnetic field lines and into the opaque regime. We employ the six-fluid MHD equations, accounting for the effects of grains (negative, positive and neutral) including their inelastic collisions with other species. We do not assume that the magnetic flux is frozen in any of the charged species. We derive a generalized Ohm's law that explicitly distinguishes between flux advection (and the associated process of ambipolar diffusion) and Ohmic dissipation, in order to assess the contribution of each mechanism to the increase of the mass-to-flux ratio of the central parts of a collapsing core and possibly to the resolution of the magnetic flux problem of star formation. We show how our formulation is related to and can be transformed into the traditional, directional formulation of the generalized Ohm's law, and we derive formulae for the perpendicular, parallel and Hall conductivities entering the latter, which include, for the first time, the effect of inelastic collisions between grains. In addition, we present a general (valid in any geometry) solution for the velocities of charged species as functions of the velocity of the neutrals and of the effective flux velocity (which can in turn be calculated from the dynamics of the system and Faraday's law). The last two sets of formulae can be adapted for use in any general non-ideal MHD code to study phenomena beyond star formation in magnetic clouds. The results, including a detailed parameter study, are presented in two accompanying papers.Comment: 17 pages, emulateapj; accepted for publication in the Astrophysical Journa

Mechanism of Magnetic Flux Loss in Molecular Clouds

We investigate the detailed processes working in the drift of magnetic fields in molecular clouds. To the frictional force, whereby the magnetic force is transmitted to neutral molecules, ions contribute more than half only at cloud densities $n_{\rm H} < 10^4 {\rm cm}^{-3}$, and charged grains contribute more than 90% at $n_{\rm H} > 10^6 {\rm cm}^{-3}$. Thus grains play a decisive role in the process of magnetic flux loss. Approximating the flux loss time $t_B$ by a power law $t_B \propto B^{-\gamma}$, where $B$ is the mean field strength in the cloud, we find $\gamma \approx 2$, characteristic to ambipolar diffusion, only at $n_{\rm H} < 10^7 {\rm cm}^{-3}$. At higher densities, $\gamma$ decreases steeply with $n_{\rm H}$, and finally at $n_{\rm H} \approx n_{\rm dec} \approx {\rm a few} \times 10^{11} {\rm cm}^{-3}$, where magnetic fields effectively decouple from the gas, $\gamma << 1$ is attained, reminiscent of Ohmic dissipation, though flux loss occurs about 10 times faster than by Ohmic dissipation. Ohmic dissipation is dominant only at $n_{\rm H} > 1 \times 10^{12} {\rm cm}^{-3}$. While ions and electrons drift in the direction of magnetic force at all densities, grains of opposite charges drift in opposite directions at high densities, where grains are major contributors to the frictional force. Although magnetic flux loss occurs significantly faster than by Ohmic dissipation even at very high densities as $n_{\rm H} \approx n_{\rm dec}$, the process going on at high densities is quite different from ambipolar diffusion in which particles of opposite charges are supposed to drift as one unit.Comment: 34 pages including 9 postscript figures, LaTex, accepted by Astrophysical Journal (vol.573, No.1, July 1, 2002

The Origin of Jovian Planets in Protostellar Disks: The Role of Dead Zones

The final masses of Jovian planets are attained when the tidal torques that they exert on their surrounding protostellar disks are sufficient to open gaps in the face of disk viscosity, thereby shutting off any further accretion. In sufficiently well-ionized disks, the predominant form of disk viscosity originates from the Magneto-Rotational Instability (MRI) that drives hydromagnetic disk turbulence. In the region of sufficiently low ionization rate -- the so-called dead zone -- turbulence is damped and we show that lower mass planets will be formed. We considered three ionization sources (X-rays, cosmic rays, and radioactive elements) and determined the size of a dead zone for the total ionization rate by using a radiative, hydrostatic equilibrium disk model developed by Chiang et al. (2001). We studied a range of surface mass density (Sigma_{0}=10^3 - 10^5 g cm^{-2}) and X-ray energy (kT_{x}=1 - 10 keV). We also compared the ionization rate of such a disk by X-rays with cosmic rays and find that the latter dominate X-rays in ionizing protostellar disks unless the X-ray energy is very high (5 - 10 keV). Among our major conclusions are that for typical conditions, dead zones encompass a region extending out to several AU -- the region in which terrestrial planets are found in our solar system. Our results suggest that the division between low and high mass planets in exosolar planetary systems is a consequence of the presence of a dead zone in their natal protoplanetary disks. We also find that the extent of a dead zone is mainly dependent on the disk's surface mass density. Our results provide further support for the idea that Jovian planets in exosolar systems must have migrated substantially inwards from their points of origin.Comment: 28 pages, 10 figures, accepted by Ap

Atomic Diagnostics of X-ray Irradiated Protoplanetary Disks

We study atomic line diagnostics of the inner regions of protoplanetary disks with our model of X-ray irradiated disk atmospheres which was previously used to predict observable levels of the NeII and NeIII fine-structure transitions at 12.81 and 15.55mum. We extend the X-ray ionization theory to sulfur and calculate the fraction of sulfur in S, S+, S2+ and sulfur molecules. For the D'Alessio generic T Tauri star disk, we find that the SI fine-structure line at 25.55mum is below the detection level of the Spitzer Infrared Spectrometer (IRS), in large part due to X-ray ionization of atomic S at the top of the atmosphere and to its incorporation into molecules close to the mid-plane. We predict that observable fluxes of the SII 6718/6732AA forbidden transitions are produced in the upper atmosphere at somewhat shallower depths and smaller radii than the neon fine-structure lines. This and other forbidden line transitions, such as the OI 6300/6363AA and the CI 9826/9852AA lines, serve as complementary diagnostics of X-ray irradiated disk atmospheres. We have also analyzed the potential role of the low-excitation fine-structure lines of CI, CII, and OI, which should be observable by SOFIA and Herschel.Comment: Accepted by Ap

A Spherical Model for "Starless" Cores of Magnetic Molecular Clouds and Dynamical Effects of Dust Grains

In the standard picture of isolated star formation, dense ``starless'' cores are formed out of magnetic molecular clouds due to ambipolar diffusion. Under the simplest spherical geometry, I demonstrate that ``starless'' cores formed this way naturally exhibit a large scale inward motion, whose size and speed are comparable to those detected recently by Taffala et al. and Williams et al. in ``starless'' core L1544. My model clouds have a relatively low mass (of order 10 $M_\odot$) and low field strength (of order 10 $\mu$G) to begin with. They evolve into a density profile with a central plateau surrounded by a power-law envelope, as found previously. The density in the envelope decreases with radius more steeply than those found by Mouschovias and collaborators for the more strongly magnetized, disk-like clouds. At high enough densities, dust grains become dynamically important by greatly enhancing the coupling between magnetic field and the neutral cloud matter. The trapping of magnetic flux associated with the enhanced coupling leads, in the spherical geometry, to a rapid assemblage of mass by the central protostar, which exacerbates the so-called ``luminosity problem'' in star formation.Comment: 27 pages, 4 figures, accepted by Ap

The role of damped Alfven waves on magnetospheric accretion models of young stars

We examine the role of Alfven wave damping in heating the plasma in the magnetic funnels of magnetospheric accretion models of young stars. We study four different damping mechanisms of the Alfven waves: nonlinear, turbulent, viscous-resistive and collisional. Two different possible origins for the Alfven waves are discussed: 1) Alfven waves generated at the surface of the star by the shock produced by the infalling matter; and 2) Alfven waves generated locally in the funnel by the Kelvin-Helmholtz instability. We find that, in general, the damping lengths are smaller than the tube length. Since thermal conduction in the tube is not efficient, Alfven waves generated only at the star's surface cannot heat the tube to the temperatures necessary to fit the observations. Only for very low frequency Alfven waves ~10^{-5} the ion cyclotron frequency, is the viscous-resistive damping length greater than the tube length. In this case, the Alfven waves produced at the surface of the star are able to heat the whole tube. Otherwise, local production of Alfven waves is required to explain the observations. The turbulence level is calculated for different frequencies for optically thin and thick media. We find that turbulent velocities varies greatly for different damping mechanisms, reaching \~100 km s^{-1} for the collisional damping of small frequency waves.Comment: 29 pages, 12 figures, to appear in The Astrophysical Journa

2-D models of layered protoplanetary discs: I. The ring instability

In this work we use the radiation hydrodynamic code TRAMP to perform a two-dimensional axially symmetric model of the layered disc. Using this model we follow the accumulation of mass in the dead zone due to the radially varying accretion rate. We found a new type of instability which causes the dead zone to split into rings. This "ring instability" works due to the positive feedback between the thickness of the dead zone and the mass accumulation rate. We give an analytical description of this instability, taking into account non-zero thickness of the dead zone and deviations from the Keplerian rotational velocity. The analytical model agrees reasonably well with results of numerical simulations. Finally, we speculate about the possible role of the ring instability in protoplanetary discs and in the formation of planets.Comment: 9 pages, 5 figures, accepted for publication in MNRA

Molecular Evolution in Collapsing Prestellar Cores

We have investigated the evolution and distribution of molecules in collapsing prestellar cores via numerical chemical models, adopting the Larson-Penston solution and its delayed analogues to study collapse. Molecular abundances and distributions in a collapsing core are determined by the balance among the dynamical, chemical and adsorption time scales. When the central density n_H of a prestellar core with the Larson-Penston flow rises to 3 10^6 cm^{-3}, the CCS and CO column densities are calculated to show central holes of radius 7000 AU and 4000 AU, respectively, while the column density of N2H+ is centrally peaked. These predictions are consistent with observations of L1544. If the dynamical time scale of the core is larger than that of the Larson-Penston solution owing to magnetic fields, rotation, or turbulence, the column densities of CO and CCS are smaller, and their holes are larger than in the Larson-Penston core with the same central gas density. On the other hand, N2H+ and NH3 are more abundant in the more slowly collapsing core. Therefore, molecular distributions can probe the collapse time scale of prestellar cores. Deuterium fractionation has also been studied via numerical calculations. The deuterium fraction in molecules increases as a core evolves and molecular depletion onto grains proceeds. When the central density of the core is n_H=3 10^6 cm^{-3}, the ratio DCO+/HCO+ at the center is in the range 0.06-0.27, depending on the collapse time scale and adsorption energy; this range is in reasonable agreement with the observed value in L1544.Comment: 21 pages, 17 figure

Double In Situ Approach for the Preparation of Polymer Nanocomposite with Multi-functionality

A novel one-step synthetic route, the double in situ approach, is used to produce both TiO2nanoparticles and polymer (PET), and simultaneously forming a nanocomposite with multi-functionality. The method uses the release of water during esterification to hydrolyze titanium (IV) butoxide (Ti(OBu)4) forming nano-TiO2in the polymerization vessel. This new approach is of general significance in the preparation of polymer nanocomposites, and will lead to a new route in the synthesis of multi-functional polymer nanocomposites