Clumping Instability Research Articles

Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays

An array of spheres descending slowly through a viscous fluid always clumps [J.M. Crowley, J. Fluid Mech. {\bf 45}, 151 (1971)]. We show that anisotropic particle shape qualitatively transforms this iconic instability of collective sedimentation. In experiment and theory on disks, aligned facing their neighbours in a horizontal one-dimensional lattice and settling at Reynolds number $\sim 10^{-4}$ in a quasi-two-dimensional slab geometry, we find that for large enough lattice spacing the coupling of disk orientation and translation rescues the array from the clumping instability. Despite the absence of inertia the resulting dynamics displays the wavelike excitations of a mass-and-spring array, with a conserved "momentum" in the form of the collective tilt of the disks and an emergent spring stiffness from the viscous hydrodynamic interaction. However, the non-normal character of the dynamical matrix leads to algebraic growth of perturbations even in the linearly stable regime. Stability analysis demarcates a phase boundary in the plane of wavenumber and lattice spacing, separating the regimes of algebraically growing waves and clumping, in quantitative agreement with our experiments. Anisotropic shape thus suppresses the classic linear instability of sedimenting sphere arrays, introduces a new conserved variable, and opens a window to the physics of transient growth of linearly stable modes.

Surround and Squash: the impact of superbubbles on the interstellar medium in Scorpius–Centaurus OB2

Context. Feedback by massive stars shapes the interstellar medium and is thought to influence subsequent star formation. The details of this process are under debate. Aims. We exploited observational constraints on stars, gas, and nucleosynthesis ashes for the closest region with recent massive-star formation, Scorpius–Centaurus OB2, and combined them with three-dimensional (3D) hydrodynamical simulations in order to address the physics and history of the Scorpius–Centaurus superbubble. Methods. We used published cold gas observations of continuum and molecular lines from Planck, Herschel, and APEX. We analysed the Galactic All Sky Survey (GASS) to investigate shell structures in atomic hydrogen, and used Hipparcos and Gaia data in combination with interstellar absorption against stars to obtain new constraints for the distance to the Hi features. Hot gas is traced in soft X-rays via the ROSAT all sky survey. Nucleosynthesis ejecta from massive stars were traced with new INTEGRAL spectrometer observations via 26Al radioactivity. We also performed 3D hydrodynamical simulations for the Sco–Cen superbubble. Results. Soft X-rays and a now more significant detection of 26Al confirm recent (≈1 Myr ago) input of mass, energy, and nucleosynthesis ejecta, likely from a supernova in the Upper Scorpius (USco) subgroup. We confirm a large supershell around the entire OB association and perform a 3D hydrodynamics simulation with a conservative massive star population that reproduces the morphology of the superbubble. High-resolution GASS observations reveal a nested, filamentary supershell. The filaments are possibly related to the Vishniac clumping instability, but molecular gas (Lupus I) is only present where the shell coincides with the connecting line between the subgroups of the OB association, suggesting a connection to the cloud, probably an elongated sheet, out of which the OB association formed. Stars have formed sequentially in the subgroups of the OB association and currently form in Lupus I. To investigate the impact of massive star feedback on extended clouds, we simulate the interaction of a turbulent cloud with the hot, pressurised gas in a superbubble. The hot gas fills the tenuous regions of the cloud and compresses the denser parts. Stars formed in these dense clumps would have distinct spatial and kinematic distributions. Conclusions. The combined results from observations and simulations are consistent with a scenario where dense gas was initially distributed in a band elongated in the direction now occupied by the OB association. Superbubbles powered by massive stars would then repeatedly break out of the elongated parent cloud, and surround and squash the denser parts of the gas sheet and thus induce more star formation. The expected spatial and kinematic distribution of stars is consistent with observations of Sco–Cen. The scenario might apply to many similar regions in the Galaxy and also to active galactic nucleus (AGN)-related superbubbles.

The Interplay between Radiation Pressure and the Photoelectric Instability in Optically Thin Disks of Gas and Dust

Abstract In optically thin disks, dust grains are photoelectrically stripped of electrons by starlight, heating nearby gas and possibly creating a dust clumping instability—the photoelectric instability (PeI)—that significantly alters global disk structure. In the current work, we use the Pencil Code to perform the first numerical models of the PeI that include stellar radiation pressure on dust grains in order to explore the parameter regime in which the instability operates. In some models with low gas and dust surface densities, we see a variety of dust structures, including sharp concentric rings. In the most gas- and dust-rich models, nonaxisymmetric clumps, arcs, and spiral arms emerge that represent dust surface density enhancements of factors of ∼5–20. In one high gas surface density model, we include a large, low-order gas viscosity and find that it observably smooths the structures that form in the gas and dust, suggesting that resolved images of a given disk may be useful for deriving constraints on the effective viscosity of its gas. Our models show that radiation pressure does not preclude the formation of complex structure from the PeI, but the qualitative manifestation of the PeI depends strongly on the parameters of the system. The PeI may provide an explanation for unusual disk morphologies, such as the moving blobs of the AU Mic disk, the asymmetric dust distribution of the 49 Ceti disk, and the rings and arcs found in the HD 141569A disk.

Sudden end of X-ray outbursts around periastron of Circinus X-1 observed with MAXI

Abstract MAXI/GSC (Monitor of All-sky X-ray Image/Gas Slit Camera) observed 21 outbursts from Circinus X-1 between 2009 August and 2013 December. Although 14 outbursts showed ordinary gradual decays, in seven others we found a sudden drop in luminosity on a time scale of a few hours around the periastron, and then the outbursts terminated. These sudden drops started at the estimated luminosity of a few times 1037 erg s−1 and their luminosities dropped to ≲3 × 1036 erg s−1. We offer three interpretations of the sharp luminosity decrease: (1) the end of the outburst during its dip, (2) the propeller effect, and (3) the stripping effect by the stellar wind of the companion star. It is difficult to explain the phenomenon by any of these interpretations alone. The interpretation of (1) is possible for only two outbursts on the assumption of rapid decay. The propeller effect (2) is expected to occur at a constant luminosity, which is incompatible with the observed facts. In the stripping effect (3), the ram pressure of a typical stellar wind is not sufficient to blow most of the accretion disk off. In this paper, we discuss the possibility of a modified stripping effect by assuming other additional conditions such as wind clumping and disk instability.

Clumping and quantum order: quantum gravitational dynamics of NUT charge

Gravitational instantons with NUT charge are magnetic monopoles upon dimensional reduction. We determine whether NUT charge can proliferate via the Polyakov mechanism and partially screen gravitational interactions. In semiclassical Einstein gravity, Taub-NUT instantons experience a universal attractive force in the path integral that prevents proliferation. This attraction further leads to semiclassical clumping instabilities, similar to the known instabilities of hot flat space and the Kaluza-Klein vacuum. Beyond pure Einstein gravity, NUT proliferation depends on the following question: is the mass of a gravitational instanton in the theory always greater than its NUT charge? Using spinorial methods we show that the answer to this question is `yes' if all matter fields obey a natural Euclidean energy condition. Therefore, the attractive force between instantons in the path integral wins out and gravity is dynamically protected against screening. Semiclassical gravity with a compactified circle can be self-consistently quantum ordered, at the cost of suffering from clumping instabilities.

Formation of sharp eccentric rings in debris disks with gas but without planets

'Debris disks' around young stars (analogues of the Kuiper Belt in our Solar System) show a variety of non-trivial structures attributed to planetary perturbations and used to constrain the properties of those planets. However, these analyses have largely ignored the fact that some debris disks are found to contain small quantities of gas, a component that all such disks should contain at some level. Several debris disks have been measured with a dust-to-gas ratio of about unity, at which the effect of hydrodynamics on the structure of the disk cannot be ignored. Here we report linear and nonlinear modelling that shows that dust-gas interactions can produce some of the key patterns attributed to planets. We find a robust clumping instability that organizes the dust into narrow, eccentric rings, similar to the Fomalhaut debris disk. The conclusion that such disks might contain planets is not necessarily required to explain these systems.

Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity

This paper investigates the hydrodynamic performances of an SPH code incorporating an artificial heat conductivity term in which the adopted signal velocity is applicable when gravity is present. In accordance with previous findings it is shown that the performances of SPH to describe the development of Kelvin-Helmholtz instabilities depend strongly on the consistency of the initial condition set-up and on the leading error in the momentum equation due to incomplete kernel sampling. An error and stability analysis shows that the quartic B-spline kernel (M_5) possesses very good stability properties and we propose its use with a large neighbor number, between ~50 (2D) to ~ 100 (3D), to improve convergence in simulation results without being affected by the so-called clumping instability. SPH simulations of the blob test show that in the regime of strong supersonic flows an appropriate limiting condition, which depends on the Prandtl number, must be imposed on the artificial conductivity SPH coefficients in order to avoid an unphysical amount of heat diffusion. Results from hydrodynamic simulations that include self-gravity show profiles of hydrodynamic variables that are in much better agreement with those produced using mesh-based codes. In particular, the final levels of core entropies in cosmological simulations of galaxy clusters are consistent with those found using AMR codes. Finally, results of the Rayleigh-Taylor instability test demonstrate that in the regime of very subsonic flows the code has still several difficulties in the treatment of hydrodynamic instabilities. These problems being intrinsically due to the way in which in standard SPH gradients are calculated and not to the implementation of the artificial conductivity term.

Improving convergence in smoothed particle hydrodynamics simulations without pairing instability

The numerical convergence of smoothed particle hydrodynamics (SPH) can be severely restricted by random force errors induced by particle disorder, especially in shear flows, which are ubiquitous in astrophysics. The increase in the number NH of neighbours when switching to more extended smoothing kernels at fixed resolution (using an appropriate definition for the SPH resolution scale) is insufficient to combat these errors. Consequently, trading resolution for better convergence is necessary, but for traditional smoothing kernels this option is limited by the pairing (or clumping) instability. Therefore, we investigate the suitability of the Wendland functions as smoothing kernels and compare them with the traditional B-splines. Linear stability analysis in three dimensions and test simulations demonstrate that the Wendland kernels avoid the pairing instability for all NH, despite having vanishing derivative at the origin (disproving traditional ideas about the origin of this instability; instead, we uncover a relation with the kernel Fourier transform and give an explanation in terms of the SPH density estimator). The Wendland kernels are computationally more convenient than the higher-order B-splines, allowing large NH and hence better numerical convergence (note that computational costs rise sub-linear with NH). Our analysis also shows that at low NH the quartic spline kernel with NH ~= 60 obtains much better convergence then the standard cubic spline.

RpSPH: a novel smoothed particle hydrodynamics algorithm

We suggest a novel discretisation of the momentum equation for Smoothed Particle Hydrodynamics (SPH) and show that it significantly improves the accuracy of the obtained solutions. Our new formulation which we refer to as relative pressure SPH, rpSPH, evaluates the pressure force in respect to the local pressure. It respects Newtons first law of motion and applies forces to particles only when there is a net force acting upon them. This is in contrast to standard SPH which explicitly uses Newtons third law of motion continuously applying equal but opposite forces between particles. rpSPH does not show the unphysical particle noise, the clumping or banding instability, unphysical surface tension, and unphysical scattering of different mass particles found for standard SPH. At the same time it uses fewer computational operations. and only changes a single line in existing SPH codes. We demonstrate its performance on isobaric uniform density distributions, uniform density shearing flows, the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, the Sod shock tube, the Sedov-Taylor blast wave and a cosmological integration of the Santa Barbara galaxy cluster formation test. rpSPH is an improvement these cases. The improvements come at the cost of giving up exact momentum conservation of the scheme. Consequently one can also obtain unphysical solutions particularly at low resolutions.

Resolving mixing in smoothed particle hydrodynamics

Standard formulations of smoothed particle hydrodynamics (SPH) are unable to resolve mixing at fluid boundaries. We use an error and stability analysis of the generalised SPH equations of motion to prove that this is due to two distinct problems. The first is a leading order error in the momentum equation. This should decrease with increasing neighbour number, but does not because numerical instabilities cause the kernel to be irregularly sampled. We identify two important instabilities: the clumping instability and the banding instability, and we show that both are cured by a suitable choice of kernel. The second problem is the local mixing instability (LMI). This occurs as particles attempt to mix on the kernel scale, but are unable to due to entropy conservation. The result is a pressure discontinuity at boundaries that pushes fluids of different entropy apart. We cure the LMI by using a weighted density estimate that ensures that pressures are single valued throughout the flow. This also gives a better volume estimate for the particles, reducing errors in the continuity and momentum equations. We demonstrate mixing in our new Optimised Smoothed Particle Hydrodynamics (OSPH) scheme using a Kelvin Helmholtz instability (KHI) test with density contrast 1:2, and the 'blob test' - a 1:10 density ratio gas sphere in a wind tunnel - finding excellent agreement between OSPH and Eulerian codes.

Gravoturbulent planetesimal formation

We present a new scenario for the rapid formation of planetesimals based on the combined effects of turbulence and gravity. While it was generally accepted that these two effects cancel each other out, we found their interaction to be extremely beneficial for the accumulation of larger objects bound by gravity. Meter-sized objects get concentrated by turbulence; these over-densities start to get enhanced even further due to a clumping instability and finally densities are large enough that heaps of boulders fit into their combined Roche Lobe. At the same time, the residual velocity is low enough to allow for further collapse. Typical object masses that result in our numerical simulations are in the order of the minor planet Ceres.

Linear and nonlinear evolution of azimuthal clumping instabilities in a Z-pinch wire array

This paper presents an analytic theory on the linear and nonlinear evolution of the most unstable azimuthal clumping mode, known as the pi-mode, in a discrete wire array. In the pi-mode, neighboring wires of the array pair-up as a result of the mutual attraction of the wires which carry current in the same direction. The analytic solution displays two regimes, where the collective interactions of all wires dominate, versus where the interaction of the neighboring, single wire dominates. This solution was corroborated by two vastly different numerical codes which were used to simulate arrays with both high wire numbers (up to 600) and low wire number (8). All solutions show that azimuthal clumping of discrete wires occurs before appreciable radial motion of the wires. Thus, absence of azimuthal clumping of wires in comparison with the wires’ radial motion may imply substantial lack of wire currents. While the present theory and simulations have ignored the plasma corona and axial variations, it is argued that their effects, and the complete account of the three-dimensional feature of the pi-mode, together with a scaling study of the wire number, may be expediently simulated by using only one single wire in an annular wedge with a reflection condition imposed on the wedge’s boundary.

Models for the X‐ray spectra and variability of luminous accreting black holes

AbstractThe X‐ray spectra of luminous Seyfert 1 galaxies often appear to be reflection dominated. In a number of Narrow Line Seyfert 1 (NLS1) galaxies and galactic black holes in the very high state, the variability of the continuum and of the iron line are decoupled, the reflected component being often much less variable than the continuum. These properties have been interpreted as effects of gravitational light bending. In this framework, we present detailed Monte‐Carlo simulations of the reflection continuum in the Kerr metric. These calculations confirm that the spectra and variability behaviour of these sources can be reproduced by the light bending model. As an alternative to the light bending model, we show that similar observational properties are expected from radiation pressure dominated discs subject to violent clumping instabilities and, as a result, have a highly inhomogeneous two‐phase structure. In this model, most of the observed spectral and variability features originate from the complex geometrical structure of the inner regions of near‐Eddington accretion flows and are therefore a signature of accretion physics rather than general relativity. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On the X-ray spectra of luminous, inhomogeneous accretion flows

We discuss the expected X-ray spectral and variability properties of black hole accretion discs at high luminosity, under the hypothesis that radiation pressure dominated discs are subject to violent clumping instabilities and, as a result, have a highly inhomogeneous two-phase structure. After deriving the full accretion disc solutions explicitly in terms of the parameters of the model, we study their radiative properties both with a simple two-zones model, treatable analytically, and with radiative transfer simulations which account simultaneously for energy balance and Comptonisation in the hot phase, together with reflection, reprocessing, ionization and thermal balance in the cold phase. We show that, if not only the density, but also the heating rate within these flows is inhomogeneous, then complex reflection-dominated spectra can be obtained for a high enough covering fraction of the cold phase. In general, large reflection components in the observed X-ray spectra should be associated with strong soft excesses, resulting from the combined emission of ionized atomic emission lines. The variability properties of such systems are such that, even when contributing to a large fraction of the hard X-ray spectrum, the reflection component is less variable than the power-law like emission originating from the hot Comptonising phase, in agreement with what is observed in many Narrow Line Seyfert 1 galaxies and bright Seyfert 1. Our model falls within the family of those trying to explain the complex X-ray spectra of bright AGN with ionized reflection, but presents an alternative, specific, physically motivated, geometrical setup for the complex multi-phase structure of the inner regions of near-Eddington accretion flows.

Dust Distribution in Gas Disks. II. Self‐induced Ring Formation through a Clumping Instability

Debris rings of dust are found around young luminous stars such as HR 4796A and HD 141569. Some of these entities have sharp edges and gaps, which have been interpreted as evidence for the presence of shepherding and embedded planets. Here we show that gaps and sharp edges in the debris disks of dust can also be spontaneously self-generated if they are embedded in optically thin regions of gaseous disks. This clumping instability arises in regions where an enhancement in the dust density leads to local gas temperature and pressure increases. Consequently, the relative motion between the gas and the dust is modified. The subsequent hydrodynamic drag on the dust particles leads to further enhancement of their concentration. We show that this process is linearly unstable and leads to the formation of ringlike structures within the estimated lifetime of such young objects. Once the gas is removed (e.g., by photoevaporation), the structures are frozen and will persist, even when the gas might not be observable anymore.

Azimuthal clumping instabilities in a Z-pinch wire array

A simple model is constructed to evaluate the temporal evolution of azimuthal clumping instabilities in a cylindrical array of current-carrying wires. An analytic scaling law is derived, which shows that randomly seeded perturbations evolve at the rate of the fastest unstable mode, almost from the start. This instability is entirely analogous to the Jeans instability in a self-gravitating disk, where the mutual attraction of gravity is replaced by the mutual attraction among the current-carrying wires.

Modeling spatial patterns in Dictyostelium

The life cycle of Dictyostelium discoideum provides a striking example of the transition from single cell behavior to multicellular cooperativity. In this paper the status of the attempts at making semiquantitative models of the aggregation phase of this cycle is reviewed. Specifically, it is discussed how the propagation of cAMP waves is a typical example of excitable signaling, which is then rendered unstable by coupling to cell chemotaxis. To investigate the streaming pattern that emerges from this clumping instability, we next turn to a new simulation strategy, which couples dynamical cell-like entities ("bions") to continuum chemical concentration fields. Finally, we discuss two directions for further research: One is the study of the robustness with respect to the variation of system parameters (such as the cell density) exhibited by the biological system, but not by any simple model. The other concerns going beyond the aggregation phase to tackle the three-dimensional problem of slug formation and motion.

Fine Structures Appeared in the Spectrum of SN1993J

It was pointed out that Type Ⅱ supernovae would develop instabilities and asymmetric structure during its explosion. SN1987A, for the first time, provided direct and convincing observational evidence of such behavior. SN1993J confirmed this, too. On July 12, 1993, we obtained a low resolution (5.3 /pixel) spectrum of SN1993J using the 2.16 m telescope in Beijing Astronomical Observatory. We found that many fine structures appeared in the [OI] and H_x lines. This showed that clumping, chemical mixing and strong instabilities had occurred in the ejecta of

Turbulent relaxation in magnetohydrodynamic plasma

Magnetohydrodynamic (MHD) clump instability is considered as a turbulent relaxation mechanism for current carrying plasma. Predictions of the instability are compared with results from laboratory fusion experiments as well as computer simulations. For the tokamak, the predictions include safety factor [q(a)≤3] and Lundquist number [S≥104] thresholds, a magnetic helicity conserving radial electric field profile, and a voltage spike time of 0.1τRS−1/3, where τR is the resistive time. It is argued that the voltage spike that signals a tokamak disruption is due to the global conservation of magnetic helicity during the instability. In the reversed field pinch (RFP), clump steady states corresponding to B0z field reversed Taylor states at pinch parameters θ≥1.2, for S≥102, and magnetic fluctuation levels δB scaling as S−3/8 and θ3 are predicted. Reasonable agreement is obtained. The MHD clump instability appears to provide a unified picture of tokamak disruptions, where it occurs intermittently in its growth phase, and RFP ‘‘quiescent’’ states, where it is continuously present in its steady state turbulence phase.

Steady-state magnetohydrodynamic clump turbulence

The turbulent steady state of the magnetohydrodynamic (MHD) clump instability [Phys. Fluids 31, 2122 (1988)] is investigated. The steady state is determined by the balance between clump growth by turbulent mixing and clump decay by field line stochasticity. The turbulent fields driving the mixing are generated self-consistently from Ampère’s law and conserve the magnetic helicity. In the steady state, the mean current and magnetic field satisfy J0=μB0, where μ depends on the mean-square fluctuation level. Above this critical point (J0>μB0), the plasma is MHD clump unstable. MHD clump instability is a dynamical route to the force-free, Taylor state. For the steady state to exist, μ must exceed a threshold on the order of that required for B0z field reversal. Steady-state MHD clump turbulence corresponds to field reversed Taylor states. From the μ threshold condition, the steady-state fluctuation spectrum (δBrms/B) is calculated and shown to increase with mean driving current as θ3, where θ is the pinch parameter.