Self-Similar Magnetocentrifugal Disk Winds with Cylindrical Asymptotics

We construct a two-parameter family of models for self-collimated, radially self-similar magnetized outflows from accretion disks. A flow at zero initial poloidal speed leaves the surface of a rotating disk and is accelerated and redirected toward the pole by helical magnetic fields threading the disk. At large distances from the disk, the flow streamlines asymptote to wrap around the surfaces of nested cylinders. In constrast to previous disk wind modeling, we have explicitly implemented the cylindrical asymptotic boundary condition to examine the consequences for flow dynamics. The solutions are characterized by the logarithmic gradient of the magnetic field strength and the ratios between the footpoint radius R_0 and asymptotic radius R_1 of streamlines; the Alfven radius must be found as an eigenvalue. Cylindrical solutions require the magnetic field to drop less steeply than 1/R. We find that the asymptotic poloidal speed on any streamline is typically just a few tenths of the Kepler speed at the corresponding disk footpoint. The asymptotic toroidal Alfven speed is, however, a few times the footpoint Kepler speed. We discuss the implications of the models for interpretations of observed optical jets and molecular outflows from young stellar systems. We suggest that the difficulty of achieving strong collimation in vector velocity simultaneously with a final speed comparable to the disk rotation rate argues against isolated jets and in favor of models with broader winds.Comment: 39 pages, Latex (uses AAS Latex macros), 6 eps figures, postscript preprint with embedded figures available from http://www.astro.umd.edu/~ostriker/professional/publications.html , to appear in ApJ 9/1/9

Critical phenomena in Newtonian gravity

We investigate the stability of self-similar solutions for a gravitationally collapsing isothermal sphere in Newtonian gravity by means of a normal mode analysis. It is found that the Hunter series of solutions are highly unstable, while neither the Larson-Penston solution nor the homogeneous collapse one have an analytic unstable mode. Since the homogeneous collapse solution is known to suffer the kink instability, the present result and recent numerical simulations strongly support a proposition that the Larson-Penston solution will be realized in astrophysical situations. It is also found that the Hunter (A) solution has a single unstable mode, which implies that it is a critical solution associated with some critical phenomena which are analogous to those in general relativity. The critical exponent $\gamma$ is calculated as $\gamma\simeq 0.10567$. In contrast to the general relativistic case, the order parameter will be the collapsed mass. In order to obtain a complete picture of the Newtonian critical phenomena, full numerical simulations will be needed.Comment: 25 pages, 7 figures, accepted for publication in Physical Review

The role of Hall diffusion in the magnetically threaded thin accretion discs

We study role of the Hall diffusion in the magnetic star-disc interaction. In a simplified steady state configuration, the total torque is calculated in terms of the fastness parameter and a new term because of the Hall diffusion. We show the total torque reduces as the Hall term becomes more significant. Also, the critical fastness parameter (at which the total torque is zero) reduces because of the Hall diffusion.Comment: Accepted for publication in Astrophysics and Space Scienc

Dynamic Evolution of a Quasi-Spherical General Polytropic Magnetofluid with Self-Gravity

In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In particular, this MHD model analysis frees the scaling parameter $n$ in the conventional polytropic self-similar transformation from the constraint of $n+\gamma=2$ with $\gamma$ being the polytropic index and therefore substantially generalizes earlier analysis results on polytropic gas dynamics that has a constant specific entropy everywhere in space at all time. On the basis of the self-similar nonlinear MHD ordinary differential equations, we examine behaviours of the magnetosonic critical curves, the MHD shock conditions, and various asymptotic solutions. We then construct global semi-complete self-similar MHD solutions using a combination of analytical and numerical means and indicate plausible astrophysical applications of these magnetized flow solutions with or without MHD shocks.Comment: 21 pages, 7 figures, accepted for publication in APS

No Go Theorem for Kinematic Self-Similarity with A Polytropic Equation of State

We have investigated spherically symmetric spacetimes which contain a perfect fluid obeying the polytropic equation of state and admit a kinematic self-similar vector of the second kind which is neither parallel nor orthogonal to the fluid flow. We have assumed two kinds of polytropic equations of state and shown in general relativity that such spacetimes must be vacuum.Comment: 5 pages, no figures. Revtex. One word added to the title. Final version to appear in Physical Review D as a Brief Repor

Negative Energy and Angular Momentum Modes of Thin Accretion Disks

This work derives the linearized equations of motion, the Lagrangian density, the Hamiltonian density, and the canonical angular momentum density for general perturbations [$\propto \exp(im\phi)$ with $m=0,\pm 1,..$] of a geometrically thin self-gravitating, homentropic fluid disk including the pressure. The theory is applied to ``eccentric,'' $m=\pm 1$ perturbations of a geometrically thin Keplerian disk. We find $m=1$ modes at low frequencies relative to the Keplerian frequency. Further, it shown that these modes can have negative energy and negative angular momentum. The radial propagation of these low frequency $m=1$ modes can transport angular momentum away from the inner region of a disk and thus increase the rate of mass accretion. Depending on the radial boundary conditions there can be discrete low-frequency, negative-energy, $m=1$ modes.Comment: 24 pages, 8 figure

Studies of Dense Cores with ALMA

Dense cores are the simplest star-forming sites that we know, but despite their simplicity, they still hold a number of mysteries that limit our understanding of how solar-type stars form. ALMA promises to revolutionize our knowledge of every stage in the life of a core, from the pre-stellar phase to the final disruption by the newly born star. This contribution presents a brief review of the evolution of dense cores and illustrates particular questions that will greatly benefit from the increase in resolution and sensitivity expected from ALMAComment: 6 pages, 2 figures, to appear in Astrophysics and Space Science, special issue of "Science with ALMA: a new era for Astrophysics" conference, ed. Dr. Bachille

Dynamic Evolution Model of Isothermal Voids and Shocks

We explore self-similar hydrodynamic evolution of central voids embedded in an isothermal gas of spherical symmetry under the self-gravity. More specifically, we study voids expanding at constant radial speeds in an isothermal gas and construct all types of possible void solutions without or with shocks in surrounding envelopes. We examine properties of void boundaries and outer envelopes. Voids without shocks are all bounded by overdense shells and either inflows or outflows in the outer envelope may occur. These solutions, referred to as type $\mathcal{X}$ void solutions, are further divided into subtypes $\mathcal{X}_{\rm I}$ and $\mathcal{X}_{\rm II}$ according to their characteristic behaviours across the sonic critical line (SCL). Void solutions with shocks in envelopes are referred to as type $\mathcal{Z}$ voids and can have both dense and quasi-smooth edges. Asymptotically, outflows, breezes, inflows, accretions and static outer envelopes may all surround such type $\mathcal{Z}$ voids. Both cases of constant and varying temperatures across isothermal shock fronts are analyzed; they are referred to as types $\mathcal{Z}_{\rm I}$ and $\mathcal{Z}_{\rm II}$ void shock solutions. We apply the `phase net matching procedure' to construct various self-similar void solutions. We also present analysis on void generation mechanisms and describe several astrophysical applications. By including self-gravity, gas pressure and shocks, our isothermal self-similar void (ISSV) model is adaptable to various astrophysical systems such as planetary nebulae, hot bubbles and superbubbles in the interstellar medium as well as supernova remnants.Comment: 24 pages, 13 figuers, accepted by ApS

Gamma rays from molecular clouds

It is believed that the observed diffuse gamma ray emission from the galactic plane is the result of interactions between cosmic rays and the interstellar gas. Such emission can be amplified if cosmic rays penetrate into dense molecular clouds. The propagation of cosmic rays inside a molecular cloud has been studied assuming an arbitrary energy and space dependent diffusion coefficient. If the diffusion coefficient inside the cloud is significantly smaller compared to the average one derived for the galactic disk, the observed gamma ray spectrum appears harder than the cosmic ray spectrum, mainly due to the slower penetration of the low energy particles towards the core of the cloud. This may produce a great variety of gamma ray spectra.Comment: Proceeding of "The multi messenger approach to high energy gamma ray sources", Barcelona, June 200

Interstellar MHD Turbulence and Star Formation

This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic motions in the roughly isothermal cold atomic and molecular components. Within this context, we discuss: i) the production and statistical distribution of turbulent density fluctuations in both isothermal and polytropic media; ii) the nature of the clumps produced by thermal instability, noting that, contrary to classical ideas, they in general accrete mass from their environment; iii) the density-magnetic field correlation (or lack thereof) in turbulent density fluctuations, as a consequence of the superposition of the different wave modes in the turbulent flow; iv) the evolution of the mass-to-magnetic flux ratio (MFR) in density fluctuations as they are built up by dynamic compressions; v) the formation of cold, dense clouds aided by thermal instability; vi) the expectation that star-forming molecular clouds are likely to be undergoing global gravitational contraction, rather than being near equilibrium, and vii) the regulation of the star formation rate (SFR) in such gravitationally contracting clouds by stellar feedback which, rather than keeping the clouds from collapsing, evaporates and diperses them while they collapse.Comment: 43 pages. Invited chapter for the book "Magnetic Fields in Diffuse Media", edited by Elisabete de Gouveia dal Pino and Alex Lazarian. Revised as per referee's recommendation