Axisymmetric Magnetorotational Instability in Viscous Accretion Disks

Axisymmetric magnetorotational instability (MRI) in viscous accretion disks is investigated by linear analysis and two-dimensional nonlinear simulations. The linear growth of the viscous MRI is characterized by the Reynolds number defined as $R_{\rm MRI} \equiv v_A^2/\nu\Omega$, where $v_A$ is the Alfv{\'e}n velocity, $\nu$ is the kinematic viscosity, and $\Omega$ is the angular velocity of the disk. Although the linear growth rate is suppressed considerably as the Reynolds number decreases, the nonlinear behavior is found to be almost independent of $R_{\rm MRI}$. At the nonlinear evolutionary stage, a two-channel flow continues growing and the Maxwell stress increases until the end of calculations even though the Reynolds number is much smaller than unity. A large portion of the injected energy to the system is converted to the magnetic energy. The gain rate of the thermal energy, on the other hand, is found to be much larger than the viscous heating rate. Nonlinear behavior of the MRI in the viscous regime and its difference from that in the highly resistive regime can be explained schematically by using the characteristics of the linear dispersion relation. Applying our results to the case with both the viscosity and resistivity, it is anticipated that the critical value of the Lundquist number $S_{\rm MRI} \equiv v_A^2/\eta\Omega$ for active turbulence depends on the magnetic Prandtl number $S_{{\rm MRI},c} \propto Pm^{1/2}$ in the regime of $Pm \gg 1$ and remains constant when $Pm \ll 1$, where $Pm \equiv S_{\rm MRI}/R_{\rm MRI} = \nu/\eta$ and $\eta$ is the magnetic diffusivity.Comment: Accepted for publication in ApJ -- 18 pages, 9 figures, 1 tabl

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

Ferromagnetism and Superconductivity in the multi-orbital Hubbard Model: Hund's Rule Coupling versus Crystal-Field Splitting

The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting $\Delta$, the fully polarized ferromagnetism which is observed in the strong coupling regime becomes unstable against the partially polarized ferromagnetism when the Hund's rule coupling $J$ is smaller than a certain critical value of order of $\Delta$. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between the Hund's rule coupling and the crystal-field splitting. The superconducting phase with the Luttinger liquid parameter $K_{\rho}>1$ is observed for the singlet ground state in this region.Comment: 4 pages,5 figures,submitted to J.Phys.Soc.Jp

Angular Momentum Transport by MHD Turbulence in Accretion Disks: Gas Pressure Dependence of the Saturation Level of the Magnetorotational Instability

The saturation level of the magnetorotational instability (MRI) is investigated using three-dimensional MHD simulations. The shearing box approximation is adopted and the vertical component of gravity is ignored, so that the evolution of the MRI is followed in a small local part of the disk. We focus on the dependence of the saturation level of the stress on the gas pressure, which is a key assumption in the standard alpha disk model. From our numerical experiments it is found that there is a weak power-law relation between the saturation level of the Maxwell stress and the gas pressure in the nonlinear regime; the higher the gas pressure, the larger the stress. Although the power-law index depends slightly on the initial field geometry, the relationship between stress and gas pressure is independent of the initial field strength, and is unaffected by Ohmic dissipation if the magnetic Reynolds number is at least 10. The relationship is the same in adiabatic calculations, where pressure increases over time, and nearly-isothermal calculations, where pressure varies little with time. Our numerical results are qualitatively consistent with an idea that the saturation level of the MRI is determined by a balance between the growth of the MRI and the dissipation of the field through reconnection. The quantitative interpretation of the pressure-stress relation, however, may require advances in the theoretical understanding of non-steady magnetic reconnection.Comment: 45 pages, 5 tables, 17 figures, accepted for publication in Ap

Electronic States and Superconducting Transition Temperature based on the Tomonaga-Luttinger liquid in Pr2_{2}Ba4_{4}Cu7_{7}O15−δ_{15-\delta}

An NQR experiment revealed superconductivity of Pr$_2$Ba$_4$Cu$_7$O$_{15-\delta}$ (Pr247) to be realized on CuO double chain layers and suggests possibility of novel one-dimensional(1D) superconductivity. To clarify the nature of the 1D superconductivity, we calculate the band dispersions of Pr247 by using the generalized gradient approximation(GGA). It indicates that Fermi surface of CuO double chains is well described to the electronic structure of a quasi-1D system. Assuming the zigzag Hubbard chain model to be an effective model of the system, we derive tight binding parameters of the model from a fit to the result of GGA. Based on the Tomonaga-Luttinger liquid theory, we estimate transition temperature ($T_c$) of the quasi-1D zigzag Hubbard model from the calculated value of the Luttinger liquid parameter $K_{\rho}$. The result of $T_c$ is consistent with that of experiments in Pr247 and it suggests that the mechanism of the superconductivity is well understood within the concept of the Tomonaga-Luttinger liquid.Comment: 4 pages, 5 figure

Local Axisymmetric Simulations of Magneto-Rotational Instability in Radiation-Dominated Accretion Disks

We perform numerical simulations of magneto-rotational instability in a local patch of accretion disk in which radiation pressure exceeds gas pressure. Such conditions may occur in the central regions of disks surrounding compact objects in active galactic nuclei and Galactic X-ray sources. We assume axisymmetry, and neglect vertical stratification. The growth rates of the instability on initially uniform magnetic fields are consistent with the linear analysis of Blaes & Socrates 2001. As is the case when radiation effects are neglected, the non-linear development of the instability leads to transitory turbulence when the initial magnetic field has no net vertical flux. During the turbulent phase, angular momentum is transported outwards. The Maxwell stress is a few times the Reynolds stress, and their sum is about four times the mean pressure in the vertical component of the magnetic field. For magnetic pressure exceeding gas pressure, turbulent fluctuations in the field produce density contrasts about equal to the ratio of magnetic to gas pressure. These are many times larger than in the corresponding gas pressure dominated situation, and may have profound implications for the steady-state vertical structure of radiation-dominated disks. Diffusion of radiation from compressed regions damps turbulent motions, converting kinetic energy into photon energy.Comment: 36 pages, 9 figures; accepted by the Astrophysical Journa

Superconductivity in a Two-Orbital Hubbard Model with Electron and Hole Fermi Pockets: Application in Iron Oxypnictide Superconductors

We investigate the electronic states of a one-dimensional two-orbital Hubbard model with band splitting by the exact diagonalization method. The Luttinger liquid parameter $K_{\rho}$ is calculated to obtain superconducting (SC) phase diagram as a function of on-site interactions: the intra- and inter-orbital Coulomb $U$ and $U'$, the Hund coupling $J$, and the pair transfer $J'$. In this model, electron and hole Fermi pockets are produced when the Fermi level crosses both the upper and lower orbital bands. We find that the system shows two types of SC phases, the SC \Roman{u'-large} for $U>U'$ and the SC \Roman{u-large} for $U<U'$, in the wide parameter region including both weak and strong correlation regimes. Pairing correlation functions indicate that the most dominant pairing for the SC \Roman{u'-large} (SC \Roman{u-large}) is the intersite (on-site) intraorbital spin-singlet with (without) sign reversal of the order parameters between two Fermi pockets. The result of the SC \Roman{u'-large} is consistent with the sign-reversing s-wave pairing that has recently been proposed for iron oxypnictide superconductors.Comment: 5 pages, 8 figures, to appear in J. Phys. Soc. Jpn., Vol.78, No.12, p.12470

Turbulent Mixing and the Dead Zone in Protostellar Disks

We investigate the conditions for the presence of a magnetically inactive dead zone in protostellar disks, using 3-D shearing-box MHD calculations including vertical stratification, Ohmic resistivity and time-dependent ionization chemistry. Activity driven by the magnetorotational instability fills the whole thickness of the disk at 5 AU, provided cosmic ray ionization is present, small grains are absent and the gas-phase metal abundance is sufficiently high. At 1 AU the larger column density of 1700 g/cm^2 means the midplane is shielded from ionizing particles and remains magnetorotationally stable even under the most favorable conditions considered. Nevertheless the dead zone is effectively eliminated. Turbulence mixes free charges into the interior as they recombine, leading to a slight coupling of the midplane gas to the magnetic fields. Weak, large-scale radial fields diffuse to the midplane where they are sheared out to produce stronger azimuthal fields. The resulting midplane accretion stresses are just a few times less than in the surface layers on average.Comment: to appear in the Astrophysical Journal; 25 pages, 10 figure

Modeling the gamma-ray emission produced by runaway cosmic rays in the environment of RX J1713.7-3946

Diffusive shock acceleration in supernova remnants is the most widely invoked paradigm to explain the Galactic cosmic ray spectrum. Cosmic rays escaping supernova remnants diffuse in the interstellar medium and collide with the ambient atomic and molecular gas. From such collisions gamma-rays are created, which can possibly provide the first evidence of a parent population of runaway cosmic rays. We present model predictions for the GeV to TeV gamma-ray emission produced by the collisions of runaway cosmic rays with the gas in the environment surrounding the shell-type supernova remnant RX J1713.7-3946. The spectral and spatial distributions of the emission, which depend upon the source age, the source injection history, the diffusion regime and the distribution of the ambient gas, as mapped by the LAB and NANTEN surveys, are studied in detail. In particular, we find for the region surrounding RX J1713-3946, that depending on the energy one is observing at, one may observe startlingly different spectra or may not detect any enhanced emission with respect to the diffuse emission contributed by background cosmic rays. This result has important implications for current and future gamma-ray experiments.Comment: version published on PAS

Interstellar Gas and X-rays toward the Young Supernova Remnant RCW 86; Pursuit of the Origin of the Thermal and Non-Thermal X-ray

We have analyzed the atomic and molecular gas using the 21 cm HI and 2.6/1.3 mm CO emissions toward the young supernova remnant (SNR) RCW 86 in order to identify the interstellar medium with which the shock waves of the SNR interact. We have found an HI intensity depression in the velocity range between $-46$ and $-28$ km s$^{-1}$ toward the SNR, suggesting a cavity in the interstellar medium. The HI cavity coincides with the thermal and non-thermal emitting X-ray shell. The thermal X-rays are coincident with the edge of the HI distribution, which indicates a strong density gradient, while the non-thermal X-rays are found toward the less dense, inner part of the HI cavity. The most significant non-thermal X-rays are seen toward the southwestern part of the shell where the HI gas traces the dense and cold component. We also identified CO clouds which are likely interacting with the SNR shock waves in the same velocity range as the HI, although the CO clouds are distributed only in a limited part of the SNR shell. The most massive cloud is located in the southeastern part of the shell, showing detailed correspondence with the thermal X-rays. These CO clouds show an enhanced CO $J$ = 2-1/1-0 intensity ratio, suggesting heating/compression by the shock front. We interpret that the shock-cloud interaction enhances non-thermal X-rays in the southwest and the thermal X-rays are emitted by the shock-heated gas of density 10-100 cm$^{-3}$. Moreover, we can clearly see an HI envelope around the CO cloud, suggesting that the progenitor had a weaker wind than the massive progenitor of the core-collapse SNR RX J1713.7$-$3949. It seems likely that the progenitor of RCW 86 was a system consisting of a white dwarf and a low-mass star with low-velocity accretion winds.Comment: 19 pages, 15 figures, 4 tables, accepted for publication in Journal of High Energy Astrophysics (JHEAp