The Effect of the Hall Term on the Nonlinear Evolution of the Magnetorotational Instability: I. Local Axisymmetric Simulations

The effect of the Hall term on the evolution of the magnetorotational instability (MRI) in weakly ionized accretion disks is investigated using local axisymmetric simulations. First, we show that the Hall term has important effects on the MRI when the temperature and density in the disk is below a few thousand K and between 10^13 and 10^18 cm^{-3} respectively. Such conditions can occur in the quiescent phase of dwarf nova disks, or in the inner part (inside 10 - 100 AU) of protoplanetary disks. When the Hall term is important, the properties of the MRI are dependent on the direction of the magnetic field with respect to the angular velocity vector \Omega. If the disk is threaded by a uniform vertical field oriented in the same sense as \Omega, the axisymmetric evolution of the MRI is an exponentially growing two-channel flow without saturation. When the field is oppositely directed to \Omega, however, small scale fluctuations prevent the nonlinear growth of the channel flow and the MRI evolves into MHD turbulence. These results are anticipated from the characteristics of the linear dispersion relation. In axisymmetry on a field with zero-net flux, the evolution of the MRI is independent of the size of the Hall term relative to the inductive term. The evolution in this case is determined mostly by the effect of ohmic dissipation.Comment: 31 pages, 3 tables, 12 figures, accepted for publication in ApJ, postscript version also available from http://www.astro.umd.edu/~sano/publications

Gas pressure sintering of Beta-Sialon with Z=3

An experiment conducted on beta-sialon in atmospheric pressure, using a temperature of 2000 C and 4 MPa nitrogen atmosphere, is described. Thermal decomposition was inhibited by the increase of the nitrogen gas pressure

TMC-1C: an accreting starless core

We have mapped the starless core TMC-1C in a variety of molecular lines with the IRAM 30m telescope. High density tracers show clear signs of self-absorption and sub-sonic infall asymmetries are present in N2H+ (1-0) and DCO+ (2-1) lines. The inward velocity profile in N2H+ (1-0) is extended over a region of about 7,000 AU in radius around the dust continuum peak, which is the most extended ``infalling'' region observed in a starless core with this tracer. The kinetic temperature (~12 K) measured from C17O and C18O suggests that their emission comes from a shell outside the colder interior traced by the mm continuum dust. The C18O (2-1) excitation temperature drops from 12 K to ~10 K away from the center. This is consistent with a volume density drop of the gas traced by the C18O lines, from ~4x10^4 cm^-3 towards the dust peak to ~6x10^3 cm^-3 at a projected distance from the dust peak of 80" (or 11,000 AU). The column density implied by the gas and dust show similar N2H+ and CO depletion factors (f_D < 6). This can be explained with a simple scenario in which: (i) the TMC-1C core is embedded in a relatively dense environment (H2 ~10^4 cm^-3), where CO is mostly in the gas phase and the N2H+ abundance had time to reach equilibrium values; (ii) the surrounding material (rich in CO and N2H+) is accreting onto the dense core nucleus; (iii) TMC-1C is older than 3x10^5 yr, to account for the observed abundance of N2H+ across the core (~10^-10 w.r.t. H2); and (iv) the core nucleus is either much younger (~10^4 yr) or ``undepleted'' material from the surrounding envelope has fallen towards it in the past 10,000 yr.Comment: 29 pages, including 5 tables and 15 figure

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

Gas-grain models for interstellar anion chemistry

Long-chain hydrocarbon anions CnH- (n=4, 6, 8) have recently been found to be abundant in a variety of interstellar clouds. In order to explain their large abundances in the denser (prestellar/protostellar) environments, new chemical models are constructed that include gas-grain interactions. Models including accretion of gas-phase species onto dust grains and cosmic-ray-induced desorption of atoms are able to reproduce the observed anion-to-neutral ratios, as well as the absolute abundances of anionic and neutral carbon chains, with a reasonable degree of accuracy. Due to their destructive effects, the depletion of oxygen atoms onto dust results in substantially greater polyyne and anion abundances in high-density gas (with n_{H_2} >~ 10^5 cm^{-3}). The large abundances of carbon-chain-bearing species observed in the envelopes of protostars such as L1527 can thus be explained without the need for warm carbon-chain chemistry. The C6H- anion-to-neutral ratio is found to be most sensitive to the atomic O and H abundances and the electron density. Therefore, as a core evolves, falling atomic abundances and rising electron densities are found to result in increasing anion-to-neutral ratios. Inclusion of cosmic-ray desorption of atoms in high-density models delays freeze-out, which results in a more temporally-stable anion-to-neutral ratio, in better agreement with observations. Our models include reactions between oxygen atoms and carbon-chain anions to produce carbon-chain-oxide species C6O, C7O, HC6O and HC7O, the abundances of which depend on the assumed branching ratios for associative electron detachment

The chemistry of multiply deuterated molecules in protoplanetary disks. I. The outer disk

We present new models of the deuterium chemistry in protoplanetary disks, including, for the first time, multiply deuterated species. We use these models to explore whether observations in combination with models can give us clues as to which desorption processes occur in disks. We find, in common with other authors, that photodesorption can allow strongly bound molecules such as HDO to exist in the gas phase in a layer above the midplane. Models including this process give the best agreement with the observations. In the midplane, cosmic ray heating can desorb weakly bound molecules such as CO and N$_2$. We find the observations suggest that N$_2$ is gaseous in this region, but that CO must be retained on the grains to account for the observed DCO$^+$/HCO$^+$. This could be achieved by CO having a higher binding energy than N$_2$ (as may be the case when these molecules are accreted onto water ice) or by a smaller cosmic ray desorption rate for CO than assumed here, as suggested by recent theoretical work. For gaseous molecules the calculated deuteration can be greatly changed by chemical processing in the disk from the input molecular cloud values. On the grains singly deuterated species tend to retain the D/H ratio set in the molecular cloud, whereas multiply deuterated species are more affected by the disk chemistry. Consequently the D/H ratios observed in comets may be partly set in the parent cloud and partly in the disk, depending on the molecule.Comment: Accepted for publication in ApJ. 48 pages, 8 figure

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

Magnetic fields in protoplanetary disks

Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary discs. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface, and magnetically-driven mixing has implications for disk chemistry and evolution of the grain population. However, the weak ionisation of protoplanetary discs means that magnetic fields may not be able to effectively couple to the matter. I present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas. For a standard population of 0.1 micron grains the active surface layers have a combined column of about 2 g/cm^2 at 1 AU; by the time grains have aggregated to 3 microns the active surface density is 80 g/cm^2. In the absence of grains, x-rays maintain magnetic coupling to 10% of the disk material at 1 AU (150 g/cm^2). At 5 AU the entire disk thickness becomes active once grains have aggregated to 1 micron in size.Comment: 11 pages, 11 figs, aastex.cls. Accepted for publication in Astrophysics & Space Science. v3 corrects bibliograph