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

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

Second and higher-order quasi-normal modes in binary black hole mergers

Black hole (BH) oscillations known as quasi-normal modes (QNMs) are one of the most important gravitational wave (GW) sources. We propose that higher perturbative order of QNMs, generated by nonlinear gravitational interaction near the BHs, are detectable and worth searching for in observations and simulations of binary BH mergers. We calculate the metric perturbations to second-order and explicitly regularize the master equation at the horizon and spatial infinity. We find that the second-order QNMs have frequencies twice the first-order ones and the GW amplitude is up to ~10% that of the first-order one. The QNM frequency would also shift blueward up to ~1%. This provides a new test of general relativity as well as a possible distance indicator.Comment: 5 pages, 1 figure, accepted for publication in PRD Rapid Communication

Analysis of high resolution satellite data for cosmic gamma ray bursts

Cosmic gamma ray bursts detected a germanium spectrometer on the low altitude satellite 1972-076B were surveyed. Several bursts with durations ranging from approximately 0.032 to 15 seconds were found and are tabulated. The frequency of occurrence/intensity distribution of these events was compared with the S to the -3/2 power curve of confirmed events. The longer duration events fall above the S to the -3/2 power curve of confirmed events, suggesting they are perhaps not all true cosmic gamma-ray bursts. The narrow duration events fall closely on the S to the -3/2 power curve. The survey also revealed several counting rate spikes, with durations comparable to confirmed gamma-ray bursts, which were shown to be of magnetospheric origin. Confirmation that energetic electrons were responsible for these bursts was achieved from analysis of all data from the complete payload of gamma-ray and energetic particle detectors on board the satellite. The analyses also revealed that the narrowness of the spikes was primarily spatial rather than temporal in character

Quark condensate in nuclear matter based on Nuclear Schwinger-Dyson formalism

The effects of higher order corrections of ring diagrams for the quark condensate are studied by using the bare vertex Nuclear Schwinger Dyson formalism based on $\sigma$-$\omega$ model. At the high density the quark condensate is reduced by the higher order contribution of ring diagrams more than the mean field theory or the Hartree-Fock

Parametric instability in dark molecular clouds

The present work investigates the parametric instability of parallel propagating circularly polarized Alfven(pump) waves in a weakly ionized molecular cloud. It is shown that the relative drift between the plasma particles gives rise to the Hall effect resulting in the modified pump wave characteristics. Although the linearized fluid equations with periodic coefficients are difficult to solve analytically, it is shown that a linear transformation can remove the periodic dependence. The resulting linearized equations with constant coefficients are used to derive an algebraic dispersion relation. The growth rate of the parametric instability is a sensitive function of the amplitude of the pump wave as well as to the ratio of the pump and the modified dust-cyclotron frequencies. The instability is insensitive to the plasma-beta The results are applied to the molecular clouds.Comment: 27 page, 5 figures, accepted in Ap

Second Order Quasi-Normal Mode of the Schwarzschild Black Hole

We formulate and calculate the second order quasi-normal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational wave (GW) from a distorted BH, so called ringdown, is well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numerically solve the second order Zerilli equation by implementing the modified Leaver's continued fraction method. The second order QNM frequencies are found to be twice the first order ones, and the GW amplitude is up to $\sim 10$ that of the first order for the binary BH mergers. Since the second order QNMs always exist, we can use their detections (i) to test the nonlinearity of general relativity, in particular the no-hair theorem, (ii) to remove fake events in the data analysis of QNM GWs and (iii) to measure the distance to the BH.Comment: 23 pages, no figur