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

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

Ring Formation in Magnetically Subcritical Clouds and Multiple Star Formation

We study numerically the ambipolar diffusion-driven evolution of non-rotating, magnetically subcritical, disk-like molecular clouds, assuming axisymmetry. Previous similar studies have concentrated on the formation of single magnetically supercritical cores at the cloud center, which collapse to form isolated stars. We show that, for a cloud with many Jeans masses and a relatively flat mass distribution near the center, a magnetically supercritical ring is produced instead. The supercritical ring contains a mass well above the Jeans limit. It is expected to break up, through both gravitational and possibly magnetic interchange instabilities, into a number of supercritical dense cores, whose dynamic collapse may give rise to a burst of star formation. Non-axisymmetric calculations are needed to follow in detail the expected ring fragmentation into multiple cores and the subsequent core evolution. Implications of our results on multiple star formation in general and the northwestern cluster of protostars in the Serpens molecular cloud core in particular are discussed.Comment: 25 pages, 4 figures, to appear in 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

On Proper Polynomial Maps of C2.\mathbb{C}^2.

Two proper polynomial maps $f_1, f_2 \colon \mathbb{C}^2 \longrightarrow \mathbb{C}^2$ are said to be \emph{equivalent} if there exist $\Phi_1, \Phi_2 \in \textrm{Aut}(\mathbb{C}^2)$ such that $f_2=\Phi_2 \circ f_1 \circ \Phi_1$. We investigate proper polynomial maps of arbitrary topological degree $d \geq 2$ up to equivalence. Under the further assumption that the maps are Galois coverings we also provide the complete description of equivalence classes. This widely extends previous results obtained by Lamy in the case $d=2$.Comment: 15 pages. Final version, to appear in Journal of Geometric Analysi

Formation and Collapse of Nonaxisymmetric Protostellar Cores in Planar Magnetic Interstellar Clouds: Formulation of the Problem and Linear Analysis

We formulate the problem of the formation and collapse of nonaxisymmetric protostellar cores in weakly ionized, self-gravitating, magnetic molecular clouds. In our formulation, molecular clouds are approximated as isothermal, thin (but with finite thickness) sheets. We present the governing dynamical equations for the multifluid system of neutral gas and ions, including ambipolar diffusion, and also a self-consistent treatment of thermal pressure, gravitational, and magnetic (pressure and tension) forces. The dimensionless free parameters characterizing model clouds are discussed. The response of cloud models to linear perturbations is also examined, with particular emphasis on length and time scales for the growth of gravitational instability in magnetically subcritical and supercritical clouds. We investigate their dependence on a cloud's initial mass-to-magnetic-flux ratio (normalized to the critical value for collapse), the dimensionless initial neutral-ion collision time, and also the relative external pressure exerted on a model cloud. Among our results, we find that nearly-critical model clouds have significantly larger characteristic instability lengthscales than do more distinctly sub- or supercritical models. Another result is that the effect of a greater external pressure is to reduce the critical lengthscale for instability. Numerical simulations showing the evolution of model clouds during the linear regime of evolution are also presented, and compared to the results of the dispersion analysis. They are found to be in agreement with the dispersion results, and confirm the dependence of the characteristic length and time scales on parameters such as the initial mass-to-flux ratio and relative external pressure.Comment: 30 pages, 7 figures Accepted by Ap

Cross sections for pentaquark baryon production from protons in reactions induced by hadrons and photons

Using hadronic Lagrangians that include the interaction of pentaquark $\Theta^+$ baryon with $K$ and $N$, we evaluate the cross sections for its production from meson-proton, proton-proton, and photon-proton reactions near threshold. With empirical coupling constants and form factors, the predicted cross sections are about 1.5 mb in kaon-proton reactions, 0.1 mb in rho-nucleon reactions, 0.05 mb in pion-nucleon reactions, 20 $\mu$b in proton-proton reactions, and 40 nb in photon-proton reactions.Comment: 14 pages, 7 figure

Nonlinear Hydromagnetic Wave Support of a Stratified Molecular Cloud

We perform numerical simulations of nonlinear MHD waves in a gravitationally stratified molecular cloud that is bounded by a hot and tenuous external medium. We study the relation between the strength of the turbulence and various global properties of a molecular cloud, within a 1.5-dimensional approximation. Under the influence of a driving source of Alfvenic disturbances, the cloud is lifted up by the pressure of MHD waves and reaches a steady-state characterized by oscillations about a new time-averaged equilibrium state. The nonlinear effect results in the generation of longitudinal motions and many shock waves; however, the wave kinetic energy remains predominantly in transverse, rather than longitudinal, motions. There is an approximate equipartition of energy between the transverse velocity and fluctuating magnetic field (aspredicted by small-amplitude theory) in the region of the stratified cloud which contains most of the mass; however, this relation breaks down in the outer regions, particularly near the cloud surface, where the motions have a standing-wave character. This means that the Chandrasekhar-Fermi formula applied to molecular clouds must be significantly modified in such regions. Models of an ensemble of clouds show that, for various strengths of the input energy, the velocity dispersion in the cloud $\sigma \propto Z^{0.5}$, where $Z$ is a characteristic size of the cloud.Furthermore, $\sigma$ is always comparable to the mean Alfven velocity of the cloud, consistent with observational results.Comment: 16 pages, 15 figures, emulateapj, to appear in ApJ, 2003 Oct 1, higher resolution figures at http://www.astro.uwo.ca/~basu/pub.html or http://www.astro.uwo.ca/~kudoh/pub.htm