Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence

Using the WKB approximation we perform a linear stability analysis for a rotational flow of a viscous and electrically conducting fluid in an external azimuthal magnetic field that has an arbitrary radial profile B_{phi}(R). In the inductionless approximation, we find the growth rate of the three-dimensional perturbation in a closed form and demonstrate in particular that it can be positive when the velocity profile is Keplerian and the magnetic field profile is slightly shallower than R^{-1}.Comment: 15 pages, 2 figures, slightly extended, the case of finite Rm treated, results were partially presented at the IUTAM Symposium on Vortex Dynamics, Fukuoka, Japan, March 10 201

Magnetic Susceptibility for CaV4O9CaV_4O_9

We examine experimental magnetic susceptibility $\chi^{tot}(T)$ for CaV$_4$O$_9$ by fitting with fitting function $\alpha \chi^{mag}(T) + c$. The function $\chi^{mag}(T)$ is a power series of 1/T and the lowest order term is fixed as $C/T$, where $C$ is the Curie constant as determined by the experimental $g$-value (g=1.96). Fitting parameters are $\alpha$, $c$ and expansion coefficients except for the first one in $\chi^{mag}(T)$. We determine $\alpha$ and $c$ as $\alpha \simeq$ 0.73 and $c\simeq$ 0 for an experimental sample. We interpret $\alpha$ as the volume fraction of CaV$_4$O$_9$ in the sample and $\chi^{mag}(T)$ as the susceptibility for the pure CaV$_4$O$_9$. The result of $\alpha \ne 1$ means that the sample includes nonmagnetic components. This interpretation consists with the result of a perturbation theory and a neutron scattering experiment.Comment: 4pages, 4figure

Evolution of Multiphase Hot Interstellar Medium in Elliptical Galaxies

We present the results of a variety of simulations concerning the evolution of multiphase (inhomogeneous) hot interstellar medium (ISM) in elliptical galaxies. We assume the gases ejected from stars do not mix globally with the circumferential gas. The ejected gas components evolve separately according to their birth time, position, and origin. We consider cases where supernova remnants (SNRs) mix with local ISM. The components with high metal abundance and/or high density cool and drop out of the hot ISM gas faster than the other components because of their high metal abundance and/or density. This makes the average metal abundance of the hot ISM low. Furthermore, since the metal abundance of mass-loss gas decreases with radius, gas inflow from outer region makes the average metal abundance of the hot ISM smaller than that of mass-loss gas in the inner region. As gas ejection rate of stellar system decreases, mass fraction of mass-loss gas ejected at outer region increases in a galaxy. If the mixing of SNRs is ineffective, our model predicts that observed [Si/Fe] and [Mg/Fe] should decrease towards the galactic center because of strong iron emission by SNRs. In the outer region, where the cooling of time of the ISM is long, the selective cooling is ineffective and most of gas components remain hot. Thus, the metal abundance of the ISM in this region directly reflects that of the gas ejected from stars. Our model shows that supernovae are not effective heating sources in the inner region of elliptical galaxies, because most of the energy released by them radiates. Therefore, cooling flow is established even if the supernova rate is high. Mixing of SNRs with ambient ISM makes the energy transfer between supernova explosion and ambient ISM more effective.Comment: 21 pages (AASTeX), 14 figures, accepted for publication in The Astrophysical Journa

Competing Spin-Gap Phases in a Frustrated Quantum Spin System in Two Dimensions

We investigate quantum phase transitions among the spin-gap phases and the magnetically ordered phases in a two-dimensional frustrated antiferromagnetic spin system, which interpolates several important models such as the orthogonal-dimer model as well as the model on the 1/5-depleted square lattice. By computing the ground state energy, the staggered susceptibility and the spin gap by means of the series expansion method, we determine the ground-state phase diagram and discuss the role of geometrical frustration. In particular, it is found that a RVB-type spin-gap phase proposed recently for the orthogonal-dimer system is adiabatically connected to the plaquette phase known for the 1/5-depleted square-lattice model.Comment: 6 pages, to appear in JPSJ 70 (2001