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

Nonlinear Criterion for the Stability of Molecular Clouds

Dynamically significant magnetic fields are routinely observed in molecular clouds, with mass-to-flux ratio lambda = (2 pi sqrt{G}) (Sigma/B) ~ 1 (here Sigma is the total column density and B is the field strength). It is widely believed that ``subcritical'' clouds with lambda < 1 cannot collapse, based on virial arguments by Mestel and Spitzer and a linear stability analysis by Nakano and Nakamura. Here we confirm, using high resolution numerical models that begin with a strongly supersonic velocity dispersion, that this criterion is a fully nonlinear stability condition. All the high-resolution models with lambda <= 0.95 form ``Spitzer sheets'' but collapse no further. All models with lambda >= 1.02 collapse to the maximum numerically resolvable density. We also investigate other factors determining the collapse time for supercritical models. We show that there is a strong stochastic element in the collapse time: models that differ only in details of their initial conditions can have collapse times that vary by as much as a factor of 3. The collapse time cannot be determined from just the velocity dispersion; it depends also on its distribution. Finally, we discuss the astrophysical implications of our results.Comment: 11 pages, 5 figure

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

Planet formation around stars of various masses: The snow line and the frequency of giant planets

We use a semi-analytic circumstellar disk model that considers movement of the snow line through evolution of accretion and the central star to investigate how gas giant frequency changes with stellar mass. The snow line distance changes weakly with stellar mass; thus giant planets form over a wide range of spectral types. The probability that a given star has at least one gas giant increases linearly with stellar mass from 0.4 M_sun to 3 M_sun. Stars more massive than 3 M_sun evolve quickly to the main-sequence, which pushes the snow line to 10-15 AU before protoplanets form and limits the range of disk masses that form giant planet cores. If the frequency of gas giants around solar-mass stars is 6%, we predict occurrence rates of 1% for 0.4 M_sun stars and 10% for 1.5 M_sun stars. This result is largely insensitive to our assumed model parameters. Finally, the movement of the snow line as stars >2.5 M_sun move to the main-sequence may allow the ocean planets suggested by Leger et. al. to form without migration.Comment: Accepted to ApJ. 12 pages of emulateap

How is chiral symmetry restored at finite density?

Taking into account pseudoscalar as well as scalar condensates, we reexamine the chiral restoration path on the chiral manifold. We shall see both condensates coherently produce a density wave at a certain density, which delays chiral restoration as density or temperature is increased.Comment: 4 pages, 2 figures; proc. of QM0

Small Structures via Thermal Instability of Partially Ionized Plasma. I. Condensation Mode

(Shortened) Thermal instability of partially ionized plasma is investigated by linear perturbation analysis. According to the previous studies under the one fluid approach, the thermal instability is suppressed due to the magnetic pressure. However, the previous studies did not precisely consider the effect of the ion-neutral friction, since they did not treat the flow as two fluid which is composed of ions and neutrals. Then, we revisit the effect of the ion-neutral friction of the two fluid to the growth of the thermal instability. According to our study, (1) The instability which is characterized by the mean molecular weight of neutrals is suppressed via the ion-neutral friction only when the magnetic field and the friction are sufficiently strong. The suppression owing to the friction occurs even along the field line. If the magnetic field and the friction are not so strong, the instability is not stabilized. (2) The effect of the friction and the magnetic field is mainly reduction of the growth rate of the thermal instability of weakly ionized plasma. (3) The effect of friction does not affect the critical wavelength lambdaF for the thermal instability. This yields that lambdaF of the weakly ionized plasma is not enlarged even when the magnetic field exists. We insist that the thermal instability of the weakly ionized plasma in the magnetic field can grow up even at the small length scale where the instability under the assumption of the one fluid plasma can not grow owing to the stabilization by the magnetic field. (4) The wavelength of the maximum growth rate of the instability shifts shortward according to the decrement of the growth rate, because the friction is effective at rather larger scale. Therefore, smaller structures are expected to appear than those without the ion-neutral friction.Comment: To appear in Ap