Local interstellar gasdynamical stability in spiral arm flow

The stability of two-dimensional interstellar gas flow passing through a spiral potential has been investigated. The background flow is assumed to move in a tightly wound potential, which may be regarded as external or self-generated. The unperturbed flow, which may be time dependent, is self-gravitating and satisfies the Roberts equations of motion. A polytropic, single-fluid assumption has been used. Magnetic effects are not considered. The motivation behind this work is to try to understand how much of the diversity of spiral arm morphology can be understood by large scale gas dynamical processes alone. To this end, it is suggested that spurring and feathering, and forming molecular cloud complexes may be closely related in the sense of having dynamically similar origins

Local Axisymmetric Diffusive Stability of Weakly-Magnetized, Differentially-Rotating, Stratified Fluids

We study the local stability of stratified, differentially-rotating fluids to axisymmetric perturbations in the presence of a weak magnetic field and of finite resistivity, viscosity and heat conductivity. This is a generalization of the Goldreich-Schubert-Fricke (GSF) double-diffusive analysis to the magnetized and resistive, triple-diffusive case. Our fifth-order dispersion relation admits a novel branch which describes a magnetized version of multi-diffusive modes. We derive necessary conditions for axisymmetric stability in the inviscid and perfect-conductor (double-diffusive) limits. In each case, rotation must be constant on cylinders and angular velocity must not decrease with distance from the rotation axis for stability, irrespective of the relative strength of viscous, resistive and heat diffusion. Therefore, in both double-diffusive limits, solid body rotation marginally satisfies our stability criteria. The role of weak magnetic fields is essential to reach these conclusions. The triple-diffusive situation is more complex, and its stability criteria are not easily stated. Numerical analysis of our general dispersion relation confirms our analytic double-diffusive criteria, but also shows that an unstable double-diffusive situation can be significantly stabilized by the addition of a third, ostensibly weaker, diffusion process. We describe a numerical application to the Sun's upper radiative zone and establish that it would be subject to unstable multi-diffusive modes if moderate or strong radial gradients of angular velocity were present.Comment: 29 pages, 1 table, accepted for publication in Ap

The Non-Linear Dependence of Flux on Black Hole Mass and Accretion Rate in Core Dominated Jets

We derive the non-linear relation between the core flux F_{nu} of accretion powered jets at a given frequency and the mass M of the central compact object. For scale invariant jet models, the mathematical structure of the equations describing the synchrotron emission from jets enables us to cancel out the model dependent complications of jet dynamics, retaining only a simple, model independent algebraic relation between F_{nu} and M. This approach allows us to derive the F_{nu}-M relation for any accretion disk scenario that provides a set of input boundary conditions for the magnetic field and the relativistic particle pressure in the jet, such as standard and advection dominated accretion flow (ADAF) disk solutions. Surprisingly, the mass dependence of F_{nu} is very similar in different accretion scenarios. For typical flat-spectrum core dominated radio jets and standard accretion scenarios we find F_{nu}~M^{17/12}. The 7-9 orders of magnitude difference in black hole mass between microquasars and AGN jets imply that AGN jets must be about 3-4 orders of magnitude more radio loud than microquasars, i.e., the ratio of radio to bolometric luminosity is much smaller in microquasars than in AGN jets. Because of the generality of these results, measurements of this F_{nu}-M dependence are a powerful probe of jet and accretion physics. We show how our analysis can be extended to derive a similar scaling relation between the accretion rate mdot and F_{nu} for different accretion disk models. For radiatively inefficient accretion modes we find that the flat spectrum emission follows F_{nu}~(mdot*M)^{17/12}.Comment: Added key words and acknowledgements, minor editorial corrections. 6 pages, to appear in MNRAS 343, L59-L6

Differential Rotation and Turbulence in Extended HI Disks

When present, extended disks of neutral hydrogen around spiral galaxies show a remarkably uniform velocity dispersion of approx 6 km/s. Since stellar winds and supernovae are largely absent in such regions, neither the magnitude nor the constancy of this number can be accounted for in the classical picture in which interstellar turbulence is driven by stellar energy sources. Here we suggest that magnetic fields with strengths of a few microgauss in these extended disks allow energy to be extracted from galactic differential rotation through MHD driven turbulence. The magnitude and constancy of the observed velocity dispersion may be understood if its value is Alfvenic. Moreover, by providing a simple explanation for a lower bound to the gaseous velocity fluctuations, MHD processes may account for the sharp outer edge to star formation in galaxy disks.Comment: 9 pages, no figures, to appear in ApJ, LaTeX uses aas2pp4.sty, eliminated duplicate paragrap

MAGMA: a 3D, Lagrangian magnetohydrodynamics code for merger applications

We present a new, completely Lagrangian magnetohydrodynamics code that is based on the SPH method. The equations of self-gravitating hydrodynamics are derived self-consistently from a Lagrangian and account for variable smoothing length (``grad-h''-) terms in both the hydrodynamic and the gravitational acceleration equations. The evolution of the magnetic field is formulated in terms of so-called Euler potentials which are advected with the fluid and thus guarantee the MHD flux-freezing condition. This formulation is equivalent to a vector potential approach and therefore fulfills the $\vec{\nabla}\cdot\vec{B}=0$-constraint by construction. Extensive tests in one, two and three dimensions are presented. The tests demonstrate the excellent conservation properties of the code and show the clear superiority of the Euler potentials over earlier magnetic SPH formulations.Comment: 18 pages, 17 Figures, a high resolution copy of the paper can be found at http://www.faculty.iu-bremen.de/srosswog/MAGMA.pd

Convective magneto-rotational instabilities in accretion disks

We present a study of instabilities occuring in thick magnetized accretion disks. We calculate the growth rates of these instabilities and characterise precisely the contribution of the magneto-rotational and the convective mechanism. All our calculations are performed in radially stratified disks in the cylindrical limit. The numerical calculations are performed using the appropriate local dispersion equation solver discussed in Blokland et al. (2005). A comparison with recent results by Narayan et al. (2002) shows excellent agreement with their approximate growth rates only if the disks are weakly magnetized. However, for disks close to equipartition, the dispersion equation from Narayan et al. (2002) loses its validity. Our calculations allow for a quantitative determination of the increase of the growth rate due to the magneto-rotational mechanism. We find that the increase of the growth rate for long wavelength convective modes caused by this mechanism is almost neglible. On the other hand, the growth rate of short wavelength instabilities can be significantly increased by this mechanism, reaching values up to 60%.Comment: 10 pages, 9 figures, Accepted for publication in Astronomy & Astrophysic

On the Minimum Energy Configuration of a Rotating Barotropic Fluid: A Response to Narayan & Pringle astro-ph\/0208161

The authors respond to the commentary listed in the title

Simulations of MHD Instabilities in Intracluster Medium Including Anisotropic Thermal Conduction

We perform a suite of simulations of cooling cores in clusters of galaxies in order to investigate the effect of the recently discovered heat flux buoyancy instability (HBI) on the evolution of cores. Our models follow the 3-dimensional magnetohydrodynamics (MHD) of cooling cluster cores and capture the effects of anisotropic heat conduction along the lines of magnetic field, but do not account for the cosmological setting of clusters or the presence of AGN. Our model clusters can be divided into three groups according to their final thermodynamical state: catastrophically collapsing cores, isothermal cores, and an intermediate group whose final state is determined by the initial configuration of magnetic field. Modeled cores that are reminiscent of real cluster cores show evolution towards thermal collapse on a time scale which is prolonged by a factor of ~2-10 compared with the zero-conduction cases. The principal effect of the HBI is to re-orient field lines to be perpendicular to the temperature gradient. Once the field has been wrapped up onto spherical surfaces surrounding the core, the core is insulated from further conductive heating (with the effective thermal conduction suppressed to less than 1/100th of the Spitzer value) and proceeds to collapse. We speculate that, in real clusters, the central AGN and possibly mergers play the role of "stirrers," periodically disrupting the azimuthal field structure and allowing thermal conduction to sporadically heat the core.Comment: 16 pages, 3 tables, 17 figures, accepted to ApJ with minor revisions, to appear in Volume 704, Oct 20, 2009 issu

Magnetothermal instabilities in magnetized anisotropic plasmas

Using the transport equations for an ideal anisotropic collisionless plasma derived from the Vlasov equation by the 16-moment method, we analyse the influence of pressure anisotropy exhibited by collisionless magnetized plasmas on the magnetothermal (MTI) and heat-flux-driven buoyancy (HBI) instabilities. We calculate the dispersion relation and the growth rates for these instabilities in the presence of a background heat flux and for configurations with static pressure anisotropy, finding that when the frequency at which heat conduction acts is much larger than any other frequency in the system (i.e. weak magnetic field) the pressure anisotropy has no effect on the MTI/HBI, provided the degree of anisotropy is small. In contrast, when this ordering of timescales does not apply the instability criteria depend on pressure anisotropy. Specifically, the growth time of the instabilities in the anisotropic case can be almost one order of magnitude smaller than its isotropic counterpart. We conclude that in plasmas where pressure anisotropy is present the MTI/HBI are modified. However, in environments with low magnetic fields and small anisotropy such as the ICM the results obtained from the 16-moment equations under the approximations considered are similar to those obtained from ideal MHD.Comment: v3: 16 pages, 2 figures, fixed typos, added references and a final note on related wor

On Nonshearing Magnetic Configurations in Differentially Rotating Disks

A new class of disk MHD equilibrium solutions is described, which is valid within the standard local (``shearing sheet'') approximation scheme. These solutions have the following remarkable property: velocity streamlines and magnetic lines of force rotate rigidly, even in the presence of differential rotation. This situation comes about because the Lorentz forces acting upon modified epicycles compel fluid elements to follow magnetic lines of force. Field line (and streamline) configurations may be elliptical or hyperbolic, prograde or retrograde. These structures have previously known hydrodynamical analogs: the ``planet'' solutions described by Goodman, Narayan, & Goldreich. The primary focus of this investigation is configurations in the disk plane. A related family of solutions lying in a vertical plane is briefly discussed; other families of solutions may exist. Whether these MHD structures are stable is not yet known, but could readily be determined by three-dimensional simulations. If stable or quasi-stable, these simple structures may find important applications in both accretion and galactic disks