Bar Instability Research Articles

Absorbable Stabilisation of the Bar in Minimally Invasive Repair of Pectus Excavatum

The minimally invasive repair of pectus excavatum has become the preferred technique in most centres. One of the most important technical points for the final result is stabilisation of the bar, usually obtained by one or two metal stabilisers. Recently, long-term absorbable stabilisers have become available (LactoSorb, Biomet, Jacksonville, FL, USA). Made of poly-L-lactic and polyglycolic acid, they have been introduced with the aim of reducing local discomfort and making removal of the bar easier. Their efficacy for the stabilisation of the bar has not been proved yet. In this paper we compare the surgical outcome in two groups of patients, one treated with metallic and the other with absorbable stabilisers. A total of 280 patients underwent pectus excavatum repair using a Nuss technique in two centres. In 194 patients (group 1), operated on since 2001, the metallic stabiliser was used. In 86 patients (group 2), operated on since February 2007, the LactoSorb stabiliser was preferred. We compared both groups in terms of surgical details, local symptoms or complications, and bar instability rate. The surgical technique for the stabilisation of the bar was identical in both groups, but in group 1 the stabiliser was fastened to the bar with a steel wire, while in group 2 polyglycolic sutures were used. No differences in local discomfort or postoperative pain were observed between the groups. The LactoSorb stabiliser was palpable for at least 6-9 months, and progressively disappeared at 9-12 months. In group 1 we observed 6 local complications. In particular, two patients presented with infection, one of them associated with a skin lesion and opening over the metallic stabiliser (revision of the wound was performed). Another patient developed a thoracic wall haematoma after suffering a trauma over the metallic stabiliser, 13 months after operation. Three patients developed a seroma. In group 2 we observed 3 subcutaneous swellings at the site of the LactoSorb stabiliser at 6, 8 and 9 months after the operation. We did not observe either skin lesions or infections. In the group with metallic stabiliser, 3 patients (1.5 %) had bar dislocation, while we did not observe bar instability in the group with LactoSorb stabiliser. LactoSorb stabiliser is safe and effective for stabilising the bar in pectus surgery. We suggest its routine use as it appears to be less traumatic and could make bar removal easier.

Resolving the Formation of Protogalaxies. II. Central Gravitational Collapse

Numerous cosmological hydrodynamic studies have addressed the formation of galaxies. Here we choose to study the first stages of galaxy formation, including nonequilibrium atomic primordial gas cooling, gravity, and hydrodynamics. Using initial conditions appropriate for the concordance cosmological model of structure formation, we perform two adaptive mesh refinement simulations of ~108 M☉ galaxies at high redshift. The calculations resolve the Jeans length at all times with more than 16 cells and capture over 14 orders of magnitude in length scales. In both cases, the dense, 105 solar mass, one parsec central regions are found to contract rapidly and have turbulent Mach numbers up to 4. Despite the ever decreasing Jeans length of the isothermal gas, we only find one site of fragmentation during the collapse. However, rotational secular bar instabilities transport angular momentum outward in the central parsec as the gas continues to collapse and lead to multiple nested unstable fragments with decreasing masses down to sub-Jupiter mass scales. Although these numerical experiments neglect star formation and feedback, they clearly highlight the physics of turbulence in gravitationally collapsing gas. The angular momentum segregation seen in our calculations plays an important role in theories that form supermassive black holes from gaseous collapse.

Bars in Cuspy Dark Halos

AbstractWe examine the bar instability in models with an exponential disk and a cuspy NFW-like dark matter (DM) halo inspired by cosmological simulations. Bar evolution is studied as a function of numerical resolution in a sequence of models spanning 104 – 108 DM particles - including a multi-mass model with an effective resolution of 1010. The goal is to find convergence in dynamical behaviour. We characterize the bar growth, the buckling instability, pattern speed decay through resonant transfer of angular momentum, and possible destruction of the DM halo cusp. Overall, most characteristics converge in behaviour for halos containing more than 107 particles in detail. Notably, the formation of the bar does not destroy the density cusp in this case. These higher resolution simulations clearly illustrate the importance of discrete resonances in transporting angular momentum from the bar to the halo.

An experimental test of whether bar instability contributes to the formation, periodicity and maintenance of pool–riffle sequences

AbstractPool–riffle sequences (PRSs) are periodic river‐bed morphologies with wavelengths several times the channel width. Causes of PRS formation and maintenance are not clearly understood, which may limit the effectiveness of protection and rehabilitation measures. Some confusion has existed about whether the PRS morphology is the same as or distinct from alternate bars. In this paper we investigate whether the bar instability forming alternate bars also contributes to PRS formation, periodicity and maintenance. This was unclear because bar instability occurs only when the ratio of channel width/depth exceeds a critical value, generally understood to be approximately 10, which is larger than the width‐to‐depth ratio of many PRSs. A mobile‐bed physical model is used to test whether bar instability occurs in channels characteristic of PRS morphology, with low width‐to‐depth ratio, and high relative roughness. The physical model was scaled from a prototype PRS in a gravel and cobble bed river. Alternate bars formed in the model at channel width‐to‐depth ratios as low as 3·8. The wavelength of the alternate bars formed was generally 2·2–5 times channel width, which was similar to the prototype PRS. Therefore, bar instability can occur in virtually all PRSs, and it contributes to the widespread formation of periodic PRS morphology. The model showed that maintenance of the bar height in the prototype PRS also depends on variations in channel width. It is concluded that periodic PRSs are formed and maintained by the interaction between bar instability, and flow deflections associated with variations in channel geometry such as width variation. Resonance between bar instability and three‐dimensional bed forms such as alternate bars and variations in channel geometry. Variations in channel geometry are also important in determining the location and dimensions of individual pools and bars. Copyright © 2008 John Wiley & Sons, Ltd.

Faraday resonance in dynamical bar instability of differentially rotating stars

We investigate the nonlinear behavior of the dynamically unstable rotating star for the bar mode by three-dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the unstable bar mode, and that its characteristic frequency is twice that of the bar mode, which oscillates mainly along the equatorial plane. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.

Star formation and bar instability in cosmological halos

Context. This is the third in a series of papers presenting the first attempt to analyse the growth of the bar instability in a consistent cosmological scenario. In the previous two articles, we explored the role of the cosmology on stellar disks and the impact of the gaseous component on a disk embedded in a cosmological dark matter halo. Aims. The aim of this paper is to point out the impact of the star formation on the bar instability inside disks having different gas fractions. Methods. We performed cosmological simulations of the same disk-to-halo mass systems as in the previous works where the star formation was not triggered. We compared the results of the new simulations with the previous ones to investigate the effect of the star formation by analysing the morphology of the stellar components, the bar strength, the behaviour of the pattern speed. We followed the gas and the central mass concentration during the evolution and their impact on the bar strength. Results. A stellar bar, lasting 10 Gyr, is still living at z = 0 in all our cosmological simulations. The central mass concentration of gas and of the new stars has a mild effect on the ellipticity of the bar but is not able to destroy it, and at z = 0 the stellar bar strength is enhanced by the star formation. The bar pattern speed decreases with the disk evolution.

Symmetry breaking in nonlinear growth of bar instability

We investigate the nonlinear behaviour of the dynamically unstable rotating star for the bar mode by three dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the unstable bar mode, and that its characteristic frequency is twice as that of the bar mode, which oscillates mainly along the equatorial plane. The numerical results also indicate that the vertical oscillation amplifies another waves with odd azimuthal wave-numbers in the horizontal plane like Faraday resonance. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.

Morphodynamic modeling of erodible laminar channels

A two-dimensional model for the erosion generated by viscous free-surface flows, based on the shallow-water equations and the lubrication approximation, is presented. It has a family of self-similar solutions for straight erodible channels, with an aspect ratio that increases in time. It is also shown, through a simplified stability analysis, that a laminar river can generate various bar instabilities very similar to those observed in natural rivers. This theoretical similarity reflects the meandering and braiding tendencies of laminar rivers indicated by F. Métivier and P. Meunier [J. Hydrol. 27, 22 (2003)]. Finally, we propose a simple scenario for the transition between patterns observed in experimental erodible channels.

Initial conditions for disc galaxies

We present a general recipe for constructing N-body realizations of galaxies comprising near spherical and disc components. First, an exact spherical distribution function for the spheroids (halo and bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N-body realization of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.

Evolution of stellar-gaseous disks in cosmological halos

INAF-Osservatorio Astronomico di Padova. Vicolo Osservatorio 5 - 35122 Padova. Italy. e-mail: paola.mazzei@oapd.inaf.itReceived/AcceptedABSTRACTAims.We explore the growth and the evolution of the bar instability in stellar-gaseous disks embedded in a suitable dark matter halo evolvingin a fully consistent cosmological framework. The aim of this paper is to point out the impact of different gas fractions on the bar formation,inside disks of different disk-to-halo mass ratio, and the role of the cosmological framework.Methods.We perform cosmological simulations with the same disk-to-halo mass ratios as in a previous work where the gas was not taken intoaccount. We compare results of the new simulations with the previous ones to investigate the effect of the gas by analysing the morphology ofthe stellar and gaseous components, the stellar bar strength and the behaviour of its pattern speed.Results.In our cosmological simulations, inside dark-matter dominated disks, a stellar bar, lasting 10 Gyr, is still living at z = 0 even if thegaseous fraction exceeds half of the disk mass. However, in the most massive disks we find a threshold value (0.2) of the gas fraction able todestroy the bar.The stellar bar strength is enhanced by the gas and in the more massive disks higher gas fractions increase the bar pattern speed.Key words. galaxies: spirals, structure, evolution, halos, kinematics and dynamics

Radial-orbit instability of a family of anisotropic Hernquist models with and without a supermassive black hole

We present a method to investigate the non-radial stability of a spherical anisotropic system that hosts a central supermassive black hole (SBH). Such systems have never been tested before for stability, although high anisotropies have been considered in the dynamical models that were used to estimate the masses of the central putative SBHs. A family of analytical anisotropic spherical Hernquist models with and without a black hole were investigated by means of N-body simulations. A clear trend emerges that the SBH has a significant effect on the overall stability of the system, that is, an SBH with a mass of a few per cent of the total mass of the galaxy can prevent or reduce the bar instabilities in anisotropic systems. Its mass determines not only the strength of the instability reduction, but also the time in which this occurs. These effects are most significant for models with strong radial anisotropies. Furthermore, our analysis shows that unstable systems with similar SBHs but with different anisotropy radii evolve differently: highly radial systems become oblate, while more isotropic models tend to form into prolate structures. In addition to this study, we also present a Monte Carlo algorithm to generate particles in spherical anisotropic systems.

Angular momentum transport and disc morphology in smoothed particle hydrodynamics simulations of galaxy formation

We perform controlled N-body/smoothed particle hydrodynamics simulations of disc galaxy formation by cooling a rotating gaseous mass distribution inside equilibrium cuspy spherical and triaxial dark matter haloes. We systematically study the angular momentum transport and the disc morphology as we increase the number of dark matter and gas particles from 10 4 to 10 6 , and decrease the gravitational softening from 2 kpc to 50 pc. The angular momentum transport, disc morphology and radial profiles depend sensitively on force and mass resolution. At low resolution, similar to that used in most current cosmological simulations, the cold gas component has lost half of its initial angular momentum via different mechanisms. The angular momentum is transferred primarily to the hot halo component, by resolution-dependent hydrodynamical and gravitational torques; the latter arising from asymmetries in the mass distribution. In addition, disc particles can lose angular momentum while they are still in the hot phase by artificial viscosity. In the central disc, particles can transfer away over 99 per cent of their initial angular momentum due to spiral structure and/or the presence of a central bar. The strength of this transport also depends on force and mass resolution - large softening will suppress the bar instability, and low mass resolution enhances the spiral structure. This complex interplay between resolution and angular momentum transfer highlights the complexity of simulations of galaxy formation even in isolated haloes. With 10 6 gas and dark matter particles, disc particles lose only 10-20 per cent of their original angular momentum, yet we are unable to produce pure exponential profiles due to the steep density peak of baryons within the central kpc. We speculate that the central luminosity excess observed in many Sc-Sd galaxies may be due to star formation in gas that has been transported to the central regions by spiral patterns.

Evolution of spiral galaxies in modified gravity

We compare N -body simulations of isolated galaxies performed in both frameworks of modified Newtonian dynamics (MOND) and Newtonian gravity with dark matter (DM). We have developed a multigrid code able to efficiently solve the modified Poisson equation derived from the Lagrangian formalism AQUAL. We take particular care of the boundary conditions that are a crucial point in MOND. The 3-dimensional dynamics of initially identical stellar discs is studied in both models. In Newtonian gravity the live DM halo is chosen to fit the rotation curve of the MOND galaxy. For the same value of the Toomre parameter (Q T ), galactic discs in MOND develop a bar instability sooner than in the DM model. In a second phase the MOND bars weaken while the DM bars continue to grow by exchanging angular momentum with the halo. The bar pattern speed evolves quite differently in the two models: there is no dynamical friction on the MOND bars so they keep a constant pattern speed while the DM bars slow down significantly. This affects the position of resonance like the corotation and the peanut. The peanut lobes in the DM model move radially outward while they keep the same position in MOND. Simulations of (only stellar) galaxies of different types on the Hubble sequence lead to a statistical bar frequency that is closer to observations for the MOND than the DM model.

A note on bar instabilities in very wide rivers

The instability of sediment-carrying rivers to bar instabilities is investigated in very wide rivers. Previous investigations of such problems in rivers of finite width are in fact inconsistent. We show how the equations used previously can be sensibly rescaled to take account of the approximations used to derive them. The eigenrelation which describes disturbances in wide rivers is therefore independent of the width parameter and we show how the solution of the initial value problem leads to a propagating wave system with the length of the bars typically about three times the spanwise length.

The role of the gas in the bar instability. A cosmological approach

AbstractThe growth and the evolution of the bar instability in stellar-gaseous disks embedded in a dark matter halo evolving in a cosmological framework is explored. We point out the impact of different gas fractions on the bar formation, inside disks of different disk-to-halo mass ratio.

Evolution of Spiral Galaxies in Modified Gravity

We present N-body simulations performed in the framework of MOND. This work is based on a numerical resolution of the modified Poisson equation derived from a Lagrangian theory of MOND. This equation is a nonlinear partial differential equation, so we first developed a code that solves this kind of equations using multigrid techniques. We compared the dynamical behaviour of a typical isolated galaxy in Newton CDM model and MOND model. In this approach, pure stellar disc are considered. For the same value of the Toomre parameter (QT), galactic discs in MOND develop a bar instability sooner than in the DM model. In a second phase the MOND bars weaken while the DM bars continue to grow by exchanging angular momentum with the halo. The bar pattern speed evolves quite differently in the two models, this affects the position of resonance like the corotation and the peanut. Then we studied the evolution of several galactic discs representing the Hubble sequence, in both models. These simulations lead to a statistical bar frequency which is closer to observations for the MOND than the DM model.

Effect of suspended load on sandbar instability

We analyze bars in sandy rivers when a significant portion of the sediment load is carried in suspension. First, we investigate the ability of a depth‐averaged formulation of both the hydrodynamics and sediment transport recently developed for slowly varying flows to capture the main mechanisms of sandbar formation. The exercise turns out to be successful and opens the way to the development of analytical and numerical models of the nonlinear development of sandbars requiring a feasible computational effort. Second, we make use of the depth‐averaged approach to analyze the nature of bar instability in sandy rivers applying Briggs criterion to distinguish between the convectively and absolutely unstable asymptotic response to an initial boundary value perturbation of bed topography. This analysis allows us to conclude that in the presence of suspended load, instability remains convective. The practical implications of such findings are discussed.

Nonlinear Evolution Equations and the Braiding of Weakly Transporting Flows Over Gravel Beds

The flow of a river that transports sediment in the form of gravel as bedload is investigated for the case when the transport is small. The linear stability of such flows is discussed and used to formulate some strongly nonlinear investigations describing the interaction of bar instabilities that are known to occur. The key spatial scales in the asymptotic limit of small transport are identified, and highly nonlinear evolution equations derived for each case. A generalized KDV equation is found to govern the nonlinear evolution at small wavenumbers, while at O(1) wavenumbers an infinite set of “triad-like” amplitude equations describes the flow. The interactions demonstrate the natural tendency of rivers of width significantly higher than the critical width at which instability first occurs to form complex patterns that may be associated with braided rivers. The weak transport limit used in our anaysis makes our work directly relevant to rivers experiencing flood conditions where the onset of a flood causes transport to begin. The results shown suggest that in the highly nonlinear stages, bars take the form of slabs tilted in the flow direction with steep edges. In addition, it is found that there is no equilibrium state. These findings are consistent with observations.

Low T/|W| dynamical instability in differentially rotating stars: diagnosis with canonical angular momentum

We study the nature of non-axisymmetric dynamical instabilities in differentially rotating stars with both linear eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We especially investigate the following three types of instability; the one-armed spiral instability, the low T/|W| bar instability, and the high T/|W| bar instability, where T is the rotational kinetic energy and W is the gravitational potential energy. The nature of the dynamical instabilities is clarified by using a canonical angular momentum as a diagnostic. We find that the one-armed spiral and the low T/|W| bar instabilities occur around the corotation radius, and they grow through the inflow of canonical angular momentum around the corotation radius. The result is a clear contrast to that of a classical dynamical bar instability in high T/|W|. We also discuss the feature of gravitational waves generated from these three types of instability.

Growing Live Disks within Cosmologically Assembling Asymmetric Halos: Washing Out the Halo Prolateness

We study the growth of galactic disks in live triaxial DM halos. The halos have been assembled through constrained realizations method and evolved from the linear regime using cosmological simulations. The `seed' disks have been inserted at redshift z=3 and increased in mass tenfold over various time periods, ~1-3 Gyr, with the halo responding quasi-adiabatically to this process. We follow the dynamical and secular evolution of the disk-halo system and analyze changes in the most important parameters, like 3-D DM shapes, stellar and DM radial density profiles, stellar bar development, etc. We find that a growing disk is responsible for washing out the halo prolateness and for diluting its flatness over a period of time comparable to the disk growth. Moreover, we find that a disk which contributes more to the overall rotation curve in the system is also more efficient in axisymmetrizing the halo, without accelerating the halo figure rotation. The observational corollary is that the maximal disks probably reside in nearly axisymmetric halos, while disks whose rotation is dominated by the halo at all radii are expected to reside in more prolate halos. The halo shape is sensitive to the final disk mass, but is independent of how the seed disk is introduced into the system. We also expect that the massive disks are subject to a bar instability, while light disks have this instability damped by the halo triaxiality. Implications to the cosmological evolution of disks embedded in asymmetric halos are discussed and so are the corollaries for the observed fraction of stellar bars. Finally, the halo responds to the stellar bar by developing a gravitational wake -- a `ghost' bar of its own which is almost in-phase with that in the disk.