Parker Instability Research Articles

Parker Instability in a Self‐gravitating Magnetized Gas Disk. I. Linear Stability Analysis

To be a formation mechanism of such large-scale structures as giant molecular clouds (GMCs) and HI superclouds, the classical Parker instability driven by external gravity has to overcome three major obstacles: The convective motion accompanying the instability generates thin sheets than large condensations. The degree of density enhancement achieved by the instability is too low to make dense interstellar clouds. The time and the length scales of the instability are significantly longer and larger than the estimated formation time and the observed mean separation of the GMCs, respectively. This paper examines whether a replacement of the driving agent from the external to the self gravity might remove these obstacles by activating the gravitational instability in the Galactic ISM disk. The self gravity can suppress the convective motions, and a cooperative action of the Jeans and the Parker instabilities can remove all the obstacles confronting the classical version of the Parker instability. The mass and mean separation of the structures resulting from the odd-parity undular mode solution are shown to agree better with the HI superclouds than with the GMCs. We briefly discuss how inclusions of the external gravity and cosmic rays would modify behaviors of the odd-parity undular mode solution.

Burial of the polar magnetic field of an accreting neutron star – II. Hydromagnetic stability of axisymmetric equilibria

The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad-Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as $\Ma = 6\times 10^{-4}\Msun$, by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to $\Ma < 10^{-4}\Msun$) into the time-dependent, ideal-magnetohydrodynamic code ZEUS-3D and loading additional mass onto the star dynamically. The rise of buoyant magnetic bubbles through the accreted layer is observed in these experiments. We also investigate the stability of the resulting hydromagnetic equilibria by perturbing them in ZEUS-3D. Surprisingly, it is observed that the equilibria are marginally stable for all $\Ma\leq 6\times 10^{-4}\Msun$; the mountain oscillates persistently when perturbed, in a combination of Alfv\'en and acoustic modes, without appreciable damping or growth, and is therefore not disrupted (apart from a transient Parker instability initially, which expels $< 1 %$ of the mass and magnetic flux).

Ellerman Bombs and Jets Associated with Resistive Flux Emergence

Using two-dimensional (2D) magnetohydrodynamic simulations we study the effects of resistive processes in the dynamics of magnetic flux emergence and its relation to Ellerman bombs and other dynamic phenomena in the Sun. The widely accepted scenario of flux emergence is the formation and expansion of Ω-shaped loops due to the Parker instability. Since the Parker instability has the largest growth rate at finite wavelength λp ~ 10H-20H, where H is the scale height (≈200 km in the solar photosphere), a number of magnetic loops may rise from the initial flux sheet if it is sufficiently long. This process is shown in our numerical simulations. The multiple emerging loops expand in the atmosphere and interact with each other, leading to magnetic reconnection. At first reconnection occurs in the lower atmosphere, which allows the sinking part of the flux sheet to emerge above the photosphere. This reconnection also causes local heating that may account for Ellerman bombs. In the later stage, reconnection between the expanding loops occurs at higher levels of the atmosphere and creates high-temperature reconnection jets, and eventually a large (λp) coronal loop is formed. Cool and dense plasma structures, which are similar to Hα surges, are also formed. This is not because of magnetic reconnection but due to the compression of the plasma in between the expanding loops.

Magnetic Burial and the Harmonic Content of Millisecond Oscillations in Thermonuclear X‐Ray Bursts

Matter accreting onto the magnetic poles of a neutron star spreads under gravity towards the magnetic equator, burying the polar magnetic field and compressing it into a narrow equatorial belt. Steady-state, Grad-Shafranov calculations with a self-consistent mass-flux distribution (and a semi-quantitative treatment of Ohmic diffusion) show that, for $\Ma \gtrsim 10^{-5}\Msun$, the maximum field strength and latitudinal half-width of the equatorial magnetic belt are $B_{\rm max} = 5.6\times 10^{15} (\Ma/10^{-4}\Msun)^{0.32}$ G and $\Delta\theta = \max[3^{\circ} (\Ma/10^{-4}\Msun)^{-1.5},3^{\circ} (\Ma/10^{-4}\Msun)^{0.5}(\dot{M}_{\rm a}/10^{-8}\Msun {\rm yr}^{-1})^{-0.5}]$ respectively, where $\Ma$ is the total accreted mass and $\dot{M}_{\rm a}$ is the accretion rate. It is shown that the belt prevents north-south heat transport by conduction, convection, radiation, and ageostrophic shear. This may explain why millisecond oscillations observed in the tails of thermonuclear (type I) X-ray bursts in low-mass X-ray binaries are highly sinusoidal: the thermonuclear flame is sequestered in the magnetic hemisphere which ignites first. The model is also consistent with the occasional occurrence of closely spaced pairs of bursts. Time-dependent, ideal-magnetohydrodynamic simulations confirm that the equatorial belt is not disrupted by Parker and interchange instabilities.

Flow instabilities of magnetic flux tubes

Context. The stability properties of filamentary magnetic structures are relevant for the storage and dynamics of magnetic fields in stellar convection zones and possibly also in other astrophysical contexts. Aims. In a series of papers we study the effect of external and internal flows on the stability of magnetic flux tubes. In this paper we consider the effect of a flow perpendicular to a straight, horizontal flux tube embedded in a gravitationally stratified fluid. The flow acts on the flux tube by exerting an aerodynamic drag force and by modifying the pressure stratification in the background medium. Methods. We carry out a Lagrangian linear stability analysis in the framework of the approximation of thin magnetic flux tubes. Results. The external flow can drive monotonic and oscillatory instability (overstability). The stability condition depends on direction and magnitude of the external velocity as well as on its first and second derivatives with respect to depth. The range of the flow-driven instabilities typically extends to modes with much shorter wavelengths than for the buoyancy-driven undulatory Parker instability. Conclusions. Perpendicular flows with Alfvenic Mach number of order unity can drive monotonic as well as oscillatory instability of thin magnetic flux tubes. Such instability can affect the storage of magnetic flux in stellar interiors.

Molecular Loops in the Galactic Center: Evidence for Magnetic Flotation

The central few hundred parsecs of the Milky Way host a massive black hole and exhibit very violent gas motion and high temperatures in molecular gas. The origin of these properties has been a mystery for the past four decades. Wide-field imaging of the (12)CO (rotational quantum number J = 1 to 0) 2.6-millimeter spectrum has revealed huge loops of dense molecular gas with strong velocity dispersions in the galactic center. We present a magnetic flotation model to explain that the formation of the loops is due to magnetic buoyancy caused by the Parker instability. The model has the potential to offer a coherent explanation for the origin of the violent motion and extensive heating of the molecular gas in the galactic center.

Cloud formation from large-scale instabilities

AbstractWe discuss recent advances in cloud formation via gravitational instability under the action of self-gravity, magnetic fields, rotational shear, active stars, and/or stellar spiral arms. When shear is strong and the spiral arms are weak, applicable to flocculent galaxies at large, swing amplification exhibits nonlinear threshold behavior such that disks with a Toomre parameter Q &lt; Qc experience gravitational runaway. For most realistic conditions, local models yield Qc ~ 1.4, similar to the observed star formation thresholds. When shear is weak, on the other hand, as in galactic central parts or inside spiral arms, magneto-Jeans instability is very powerful to form spiral-arm substructures including gaseous spurs and giant clouds. The wiggle and Parker instabilities proposed for cloud formation appear to be suppressed by strong non-steady motions inherent in vertically-extended spiral shocks, suggesting that gravitational instability is a primary candidate for cloud formation.

Formation of Spiral‐Arm Spurs and Bound Clouds in Vertically Stratified Galactic Gas Disks

(Abridged) We investigate the growth of spiral-arm substructure in vertically stratified, self-gravitating, galactic gas disks, using local numerical MHD simulations. Our new models extend our previous 2D studies (Kim & Ostriker 2002), which showed that a magnetized spiral shock in a thin disk can undergo magneto-Jeans instability (MJI), resulting in interarm spur structures and massive fragments. Similar spur features have recently been seen in high-resolution observations of several galaxies. Here, we consider two sets of numerical models: 2D models that use a thick-disk gravitational kernel, and 3D runs with explicit vertical stratification. When disks are sufficiently magnetized and self-gravitating, the result in both sorts of models is the growth of spiral-arm substructure similar to that in our previous razor-thin models. Reduced self-gravity in thick disks increases the spur spacing to ~10 times the Jeans length at the arm peak. Bound clouds that form from spur fragmentation have masses ~(1-3)x10^7 Msun each, a factor ~3-8 times larger than in razor-thin models with the same gas surface density and stellar spiral arm strength. We find that unmagnetized or weakly magnetized 2D models are unstable to the wiggle instability (WI) previously identified by Wada & Koda (2004), and proposed as a potential spur- and clump-forming mechanism. However,our fully 3D models do not show this effect. Non-steady motions and strong vertical shear prevent coherent vortical structures from forming, evidently suppressing the WI that appears in 2D (isothermal) runs. We also find no clear traces of Parker instability in the nonlinear spiral arm substructures that emerge (in self-gravitating models), although conceivably Parker modes may help seed the MJI at early stages since azimuthal wavelengths are similar.

From Parker and thermal instabilities to the formation of giant molecular clouds

AbstractWe study the Parker instability (PI) under the influence of heating and cooling processes. We distinguish two models with different heating functions. On the base of linear stability analysis, we find that the properties of PI in such a system are significantly different with respect to the adiabatic and isothermal cases. We find that in case of thermally stable equilibrium, PI operating in presence of additional heating sources, postulated by Reynolds et al. (1999), and cooling described by Dalgarno &amp; McCray (1972), leads to a decrease of temperature in magnetic valleys. Numerical simulations show that this behavior promotes a transition of gas to thermally unstable regime. In consequence the gas density grows up by an order of magnitude and the condensed gas clumps acquire compact shapes. Our results lead to the conclusion that PI can trigger the formation of giant molecular clouds complexes. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Dynamo coefficients in Parker unstable disks with cosmic rays

AbstractWe investigate a three‐dimensional (3D) numerical model of the Parker instability with cosmic rays and shear in a galactic disk and compute the components of the dynamo coefficients $ \hat \alpha $ and $ \hat \beta $ from the electromotive force (EMF) obtained directly from our simulations. In our model we apply well‐known statistical procedures in order to fit the modeled EMF in terms of the dynamo tensors. Nevertheless, we do not solve all problems with the physical interpretation of the dynamo tensors prescribed in the way of Rädler (1980). We find that the presented methods give us the possibility to compute the coefficients with a desired statistical quality. The obtained values of αxx (along the radial direction in a galaxy) are of order of a few km/s, while the values of αyy (along the azimuthal direction) are one order of magnitude smaller. (© 2006 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Erratum: Intermediate Nonlinear Evolution of the Parker Instability: Formation of Convection-Induced Discontinuities and Absence of Finite-Time Singularities [Phys. Rev. Lett.96, 065001 (2006)

Erratum: Intermediate Nonlinear Evolution of the Parker Instability: Formation of Convection-Induced Discontinuities and Absence of Finite-Time Singularities [Phys. Rev. Lett.<b>96</b>, 065001 (2006)

On the influence of cooling and heating processes on Parker instability

We study Parker instability (PI) operating in a non-adiabatic, gravitationally stratified, interstellar medium. We discuss models with two kinds of heating mechanisms. The first one results from photoionization models. The other, relying on supplemental sources, has been postulated by Reynolds, Haffner & Tufte. The cooling rate, corresponding to radiative losses, is an approximation to the one given by Dalgarno & McCray. An unperturbed state of the system represents a magnetohydrostatic and thermal equilibrium. We perform linear stability analysis by solving the boundary value problem. We find that the maximum growth rate of PI rises for increasing magnitudes of non-adiabatic effects. In the pure photoionization model, the maximum growth rate of the general non-adiabatic case coincides with the isothermal limit. Adding other sources of heat leads to a maximum growth rate that is larger than the one corresponding to the isothermal limit. We find that the influence of the supplemental heating on PI also leads to a decrease in temperature in magnetic valleys. Finally, we conclude that the initial gas cooling due to the action of PI may promote a subsequent onset of thermal instability in magnetic valleys and formation of giant molecular clouds.

Intermediate Nonlinear Evolution of the Parker Instability: Formation of Convection-Induced Discontinuities and Absence of Finite-Time Singularities

Direct numerical simulations of the line-tied Parker (or magnetic Rayleigh-Taylor) instability, based on the fully compressible ideal magnetohydrodynamic equations, are presented. In the intermediate nonlinear phase, the instability continues to grow exponentially in time and the plasma tends to develop convection-induced discontinuities in the form of shocklike coherent structures. No evidence of finite-time singularities is seen.

Parker‐Jeans Instability of Gaseous Disks Including the Effect of Cosmic Rays

We use linear analysis to examine the effect of cosmic rays (CRs) on the Parker-Jeans instability of magnetized self-gravitating gaseous disks. We adopt a slab equilibrium model in which the gravity (including self-gravity) is perpendicular to the mid-plane, the magnetic field lies along the slab. CR is described as a fluid and only along magnetic field lines diffusion is considered. The linearised equations are solved numerically. The system is susceptible to Parker-Jeans instability. In general the system is less unstable when the CR diffusion coefficient is smaller (i.e., the coupling between the CRs and plasma is stronger). The system is also less unstable if CR pressure is larger. This is a reminiscence of the fact that Jeans instability and Parker instability are less unstable when the gas pressure is larger (or temperature is higher). Moreover, for large CR diffusion coefficient (or small CR pressure), perturbations parallel to the magnetic field are more unstable than those perpendicular to it. The other governing factor on the growth rate of the perturbations in different directions is the thickness of the disk or the strength of the external pressure on the disk. In fact, this is the determining factor in some parameter regimes.

Dynamo coefficients in Parker unstable disks with cosmic rays and shear

We report a three-dimensional (3D) numerical model of the Parker instability with cosmic rays and shear in a galactic disk and compute the components of the dynamo coefficients a and,8 from the electromotive forces obtained from simulations. For the first time we apply well-known statistical procedures to fit the modeled electromotive forces in terms of the dynamo tensors. We compare our results with kinematic and other methods of dynamo coefficient estimation. Although we do not solve all problems with the physical interpretation of the dynamo tensors we find that the presented methods give us the ability to compute them with the desired statistical quality. The obtained values of α xx (along the radial direction in galaxy) and α zz are of the order of a few km s -1 while the value of α yy (along the azimuthal direction) is one or two orders of magnitude smaller.

Three-Dimensional Magnetohydrodynamic Simulation of Nonlinear Magnetic Buoyancy Instability of Flux Sheets with Magnetic Shear

Abstract A series of three-dimensional magnetohydrodynamic simulations is used to study the nonlinear evolution of the magnetic buoyancy instability of a magnetic flux sheet with magnetic shear. A horizontal flux sheet that is initially placed below the solar photosphere is susceptible to both the interchange instability and the Parker instability (the undular mode of the magnetic buoyancy instability). The growth rate in the linear stage of the instability in the numerical simulation is consistent with that predicted by linear theory. In the nonlinear stage, the development depends on the initial perturbation as well as the initial magnetic field configuration (i.e., the presence of magnetic shear). When an initial perturbation is assumed to be periodic, the emerging flux rises to the corona and the magnetic field expands like a potential field, as observed in 2D simulations. When an initial non-periodic perturbation or random perturbations are assumed, the magnetic flux expands horizontally when the magnetic field emerges a little into the photosphere. The distribution of the magnetic field and gas tends to be in a new state of magnetohydrostatic equilibrium. When magnetic shear is present in the initial magnetic flux sheets, the interchange mode is stabilized so that the emerging loop is higher than in the no magnetic shear case. We discuss how the presented results are related to the emerging flux observed on the Sun.

FORMATION OF INTERMEDIATE-SCALE STRUCTURES IN SPIRAL GALAXIES

Disk galaxies abound with intermediate-scale structures such as OB star complexes, giant clouds, and dust spurs in a close geometrical association with spiral arms. Various mechanisms have been proposed as candidates for their origin, but a comprehensive theory should encompass fundamental physical agents such as self-gravity, magnetic fields, galactic differential rotation, and spiral arms, all of which are known to exist in disk galaxies. Recent numerical simulations incorporating all these physical processes show that magneto-Jeans instability (MJI), in which magnetic tension resists the stabilizing Coriolis force of galaxy rotation, is much more powerful than swing-amplification or the Parker instability in forming self-gravitating intermediate-scale structures. The MJI occurring in shearing and expanding flows off spiral arms rapidly forms structures elongated along the direction perpendicular to the arms, remarkably similar to dust spurs seen in HST images of spiral galaxies. In highly nonlinear stages, these spurs fragment to form bound clumps, possibly evolving into bright arm and interarm H II regions, suggesting that all these intermediate-scale structures in spiral galaxies probably share a common dynamical origin.

Resistive Emergence of Undulatory Flux Tubes

During its 2000 January flight, the Flare Genesis Experiment observed the gradual emergence of a bipolar active region, by recording a series of high-resolution photospheric vector magnetograms and images in the blue wing of the Hα line. Previous analyses of these data revealed the occurrence of many small-scale, transient Hα brightenings identified as Ellerman bombs (EBs). They occur during the flux emergence, and many of them are located near moving magnetic dipoles in which the vector magnetic field is nearly tangential to the photosphere. A linear force-free field extrapolation of one of the magnetograms was performed to study the magnetic topology of small-scale EBs and their possible role in the flux emergence process. We found that 23 out of 47 EBs are cospatial with bald patches (BPs), while 15 are located at the footpoints of very flat separatrix field lines passing through distant BPs. We conclude that EBs can be due to magnetic reconnection, not only at BP locations, but also along their separatrices, occurring in the low chromosphere. The topological analysis reveals, for the first time, that many EBs and BPs are linked by a hierarchy of elongated flux tubes showing aperiodic spatial undulations, whose wavelengths are typically above the threshold of the Parker instability. These findings suggest that arch filament systems and coronal loops do not result from the smooth emergence of large-scale Ω-loops from below the photosphere, but rather from the rise of undulatory flux tubes whose upper parts emerge because of the Parker instability and whose dipped lower parts emerge because of magnetic reconnection. EBs are then the signature of this resistive emergence of undulatory flux tubes.

The origin of giant molecular clouds

The parameters of molecular clouds formed via the Parker instability with dominant radiative losses are estimated. In this scenario, the cloud parameters (such as their mean densities and masses) should depend on galactocentric radius. This dependence is determined mainly by radial variations of the gas metallicity and the flux of heating radiation in the Galaxy. Due to the development of the interchange mode of the Parker instability, the angular momentum of the clouds will not necessarily be parallel to the galactic rotation axis.

EFFICIENT COMPUTATION OF MAGNETO-HYDRODYNAMIC PHENOMENA IN ASTROPHYSICS BY CCUP-MOCCT METHOD

We proved that the CIP (Constrained Interpolation Profile/Cubic Interpolated Pseudoparticle)-MOCCT (Method of Characteristics/Constrained Transport) is capable of treating MHD phenomena using a mesh several times coarser than the conventional schemes. Comparing the present method with the modified Lax-Wendroff methods in the Parker instability in two and three dimensions, the superiority of the CIP scheme has been demonstrated from its low numerical phase error and damping rate. In addition, we employ the CIP-CUP (CIP-combined unified procedure/CCUP) method that solves the Poisson equation for pressure in order to make the present scheme more stable. This method is able to treat the pressure scale height having just one grid, which is five times coarser than the conventional scheme, as well as the magnetic reconnection, which has been described with a coarse grid.