Particulate Disks Research Articles

Planetesimals drifting through dusty and gaseous white dwarf debris discs: Types I, II and III-like migration

ABSTRACT The suite of over 60 known planetary debris discs which orbit white dwarfs, along with detections of multiple minor planets in these systems, motivate investigations about the migration properties of planetesimals embedded within the discs. Here, we determine whether any of the migration regimes which are common in (pre-)main-sequence protoplanetary discs, debris discs, and ring systems could be active and important in white dwarf discs. We investigate both dust-dominated and gas-dominated regions, and quantitatively demonstrate that Type I and Type II migration, as well as their particulate disc analogues, are too slow to be relevant in white dwarf discs. However, we find that the analogue of Type III migration for particulate discs may be rapid in the dusty regions of asteroid- or moon-generated (>1018 kg) white dwarf discs, where a planetesimal exterior to its Roche radius may migrate across the entire disc within its lifetime. This result holds over a wide range of disc boundaries, both within and exterior to 1R⊙, and such that the probability of migration occurring increases with higher disc masses.

Formation of Moons and Equatorial Ridge around Top-shaped Asteroids after Surface Landslide

Top-shaped asteroids have been observed among near-Earth asteroids. About half of them are reported to have moons (on the order of ∼1 wt.% of the top-shaped primary) and many of them have an equatorial ridge. A recent study has shown that the enigmatic top-shaped figure of asteroids (e.g., Ryugu, Bennu, and Didymos) could result from an axisymmetric landslide of the primary during a fast spin-up near the breakup rotation period. Such a landslide would inevitably form a particulate disk around an asteroid with a short timescale (∼3 hr). However, the long-term full dynamical evolution is not investigated. Here, we perform a continuous simulation (∼700 hr) that investigates the sequence of events from the surface landslide that forms a top-shaped asteroid and a particulate disk to disk evolution. We show that the disk quickly spreads and produces moons (within ∼300 hr). The mass of the formed moon is consistent with what is observed around the top-shaped asteroids. We also demonstrate that an equatorial ridge is naturally formed because a fraction of the disk particles re-accretes selectively onto the equatorial region of the primary. We envision that Ryugu and Bennu could once have an ancient moon that was later lost due to a successive moon’s orbital evolution. Alternatively, at a top-shaped asteroid that has a moon, such as Didymos, no significant orbital evolution of the moon has occurred that would result in its loss. Our study would also be qualitatively applicable to any rubble-pile asteroids near the breakup rotation period.

Scars of intense accretion episodes at metal-rich white dwarfs

A re-evaluation of time-averaged accretion rates at DBZ-type white dwarfs points to historical, time-averaged rates significantly higher than the currently observed episodes at their DAZ counterparts. The difference between the ongoing, instantaneous accretion rates witnessed at DAZ white dwarfs, which often exceed 1e8 g/s, and those inferred over the past 1e5-1e6 yr for the DBZ stars can be a few orders of magnitude, and therefore must result from high-rate episodes of tens to hundreds of years so they remain undetected to date. This paper explores the likelihood that such brief, intense accretion episodes of gas-phase material can account for existing data. For reasonable assumptions about the circumstellar gas, accretion rates approaching or exceeding 1e15 g/s are possible, similar to rates observed in quiescent cataclysmic variables, and potentially detectable with future x-ray missions or wide-field monitoring facilities. Gaseous debris that is prone to such rapid accretion may be abundant immediately following a tidal disruption event via collisions and sublimation, or if additional bodies impinge upon an extant disk. Particulate disk matter accretes at or near the Poynting-Robertson drag rate for long periods between gas-producing events, consistent with rates inferred for dusty DAZ white dwarfs. In this picture, warm DAZ stars without infrared excesses have rates consistent with accretion from particulate disks that remain undetected. This overall picture has implications for quasi-steady state models of accretion and the derived chemical composition of asteroidal debris in DBZ white dwarfs.

Runaway accretion of metals from compact discs of debris on to white dwarfs

Abstract It was recently proposed that metal-rich white dwarfs (WDs) accrete their metals from compact discs of debris found to exist around more than a dozen of them. At the same time, elemental abundances measured in atmospheres of some WDs imply vigorous metal accretion at rates up to 1011 g s−1, far in excess of what can be supplied solely by Poynting–Robertson drag acting on such discs of debris. To explain this observation we propose a model, in which rapid transport of metals from the disc on to the WD naturally results from interaction between this particulate disc and a spatially coexisting disc of metallic gas. The latter is fed by evaporation of debris particles at the sublimation radius located at several tens of WD radii. Because of pressure support the gaseous disc orbits the WD slower than the particulate disc. Resultant azimuthal drift between them at speed ≲1 m s−1 causes aerodynamic drag on the disc of solids and drives inward migration of its constituent particles. Upon reaching the sublimation radius, particles evaporate, enhancing the density of the metallic gaseous disc and leading to positive feedback. Under favourable circumstances (low viscosity in the disc of metallic gas and efficient aerodynamic coupling between the discs) a system evolves in a runaway fashion, destroying the discs of debris on time-scale of ∼105 yr, and giving rise to high metal accretion rates up to g s−1, in agreement with observations.

METAL ACCRETION ONTO WHITE DWARFS CAUSED BY POYNTING-ROBERTSON DRAG ON THEIR DEBRIS DISKS

Recent discoveries of compact (sizes $<R_\odot$) debris disks around more than a dozen of metal-rich white dwarfs (WDs) suggest that pollution of these stars with metals may be caused by accretion of high-Z material from the disk. But the mechanism responsible for efficient transfer of mass from a particulate disk to the WD atmosphere has not yet been identified. Here we demonstrate that radiation of the WD can effectively drive accretion of matter through the disk towards the sublimation radius (located at several tens of WD radii), where particles evaporate, feeding a disk of metal gas accreting onto the WD. We show that, contrary to some previous claims, Poynting-Robertson (PR) drag on the debris disk is effective at providing metal accretion rate $\dot M_{PR}\sim 10^8$ g/s and higher, scaling quadratically with WD effective temperature. We compare our results with observations and show that, as expected, no WD hosting a particulate debris disk shows evidence of metal accretion rate below that produced by the PR drag. Existence of WDs accreting metals at rates significantly higher than $\dot M_{PR}$ suggests that another mechanism in addition to PR drag drives accretion of high-Z elements in these systems.

N-body Simulation of the Evolution of a Protolunar Disk

We performed N-body simulations of dense particulate disks and quantitatively analyzed angular momentum transfer processes therein. Angular momentum transfer is dominated by both gravitational torque and particles' collective motion associated with the structure. These processes depend on surface density, and do not depend on particle size or number if the structure is resolved enough.

Angular Momentum Transfer in a Protolunar Disk

We numerically calculated angular momentum transfer processes in a dense particulate disk within the Roche limit by global N-body simulations, up to N = 105, for parameters corresponding to a protolunar disk generated by a giant impact on a proto-Earth. In the simulations, both self-gravity and inelastic physical collisions are included. We first formalized expressions for angular momentum transfer rate including self-gravity and calculated the transfer rate with the results of our N-body simulations. Spiral structure is formed within the Roche limit by self-gravity and energy dissipation of inelastic collisions, and angular momentum is effectively transferred outward. Angular momentum transfer is dominated by both gravitational torque due to the spiral structure and particles' collective motion associated with the structure. Since formation and evolution of the spiral structure is regulated by the disk surface density, the angular momentum transfer rate depends on surface density, but not on particle size or number, so that the timescale of evolution of a particulate disk is independent of the number of particles (N) that is used to represent the disk, if N is large enough to represent the spiral structure. With N = 105, the detailed spiral structure is resolved, while it is only poorly resolved with N = 103; however, we found that calculated angular momentum transfer does not change as long as N ≳ 103.

Magnetic interactions and media noise in rigid disks

This paper discusses the relationship between media-noise and magnetic properties. Two topics in longitudinal barium ferrite (Ba-ferrite) particulate rigid disks are mainly investigated; the relationship between media-noise characteristics and interparticle magnetic interactions, and the particle-size effect in read/write properties. For the first topic, a series of longitudinal Ba-ferrite disks with a variation in volumetric particle-packing densities are investigated. The magnetomotive force dependences or reverse DC-erase noise are measured and compared with interaction field factor. For the second topic, the particle-size effect in read/write properties of Ba-ferrite particulate disks are described compared with the those of Co–γFe 2O 3 particulate disks. The magnetic interactions in Ba-ferrite disks consist of two mechanisms: the interparticle positive interactions in stacks of Ba-ferrite particles, and the negative interactions between the stacks in which the magnetic moments of the Ba-ferrite platelet particles are aligned in the stack direction. H c and switching field distribution values depend on interparticle interactions and extra stack-like particle interactions. Media noise depends on particle size. These ideas are effective for thin film media without exchange of magnetic interactions.

Evolution of a Circumterrestrial Disk and Formation of a Single Moon

We investigate the evolution of a circumterrestrial disk of debris generated by a giant impact on Earth and the dynamical characteristics of the moon accreted from the disk by using high-resolution N-body simulation. We find that in most cases the disk evolution results in the formation of a single large moon on a nearly circular orbit close to the equatorial plane of the initial disk just outside the Roche limit, which is consistent with the previous work by S. Ida et al. (1997, Nature 389, 353–357). The efficiency of incorporation of disk material into a moon is 10–55%, which increases with the initial specific angular momentum of the disk. These results hardly depend on the initial condition of the disk as long as the mass of the disk is 2 to 4 times the present lunar mass and most mass of the disk exists inside the Roche limit. The timescale of the disk evolution is determined mainly by the surface density of the disk because mass transfer to the outside of the Roche limit and formation of lunar seeds are regulated by collective behavior of disk particles. The evolution of the disk is summarized as follows: The disk contracts through collisional damping. As the velocity dispersion of disk particles decreases, particle clumps grow inside the Roche limit. The clumps become elongated due to Keplerian shear, which forms spiral arm-like structure. Particles are transfered to the outside of the Roche limit through the gravitational torque exerted by the spiral arms. When a tip of a spiral arm goes beyond the Roche limit, it collapses into a small moonlet. The rapid accretion of these small moonlets forms a lunar seed. The seed exclusively grows by sweeping up particles transfered over the Roche limit. When the moon becomes large enough to gravitationally dominate the disk, it pushes the rest of the inner disk to Earth. The formation timescale of the moon is of the order of 1 month if a particulate disk is assumed and the effect of melting/vaporization is not included.

A gas-kinetic stability analysis of self-gravitating and collisional particulate disks with application to Saturn’s rings

Linear theory is used to determine the stability of the self-gravitating, rapidly (and nonuniformly) rotating, two-dimensional, and collisional particulate disk against small-amplitude gravity perturbations. A gas-kinetic theory approach is used by exploring the combined system of the Boltzmann and the Poisson equations. The effects of physical collisions between particles are taken into account by using in the Boltzmann kinetic equation a Krook model integral of collisions modified to allow collisions to be inelastic. It is shown that as a direct result of the classical Jeans instability and a secular dissipative-type instability of small-amplitude gravity disturbances (e.g. those produced by a spontaneous perturbation and/or a companion system) the disk is subdivided into numerous irregular ringlets, with size and spacing of the order of 4 πρ≈2 πh, where ρ≈ c r/ κ is the mean epicyclic radius, c r is the radial dispersion of random velocities of particles, κ is the local epicyclic frequency, and h≈2 ρ is the typical thickness of the system. The present research is aimed above all at explaining the origin of various structures in highly flattened, rapidly rotating systems of mutually gravitating particles. In particular, it is suggested that forthcoming Cassini spacecraft high-resolution images may reveal this kind of hyperfine ∼2 πh≲100 m structure in the main rings A, B, and C of the Saturnian ring system.

Local stability criterion for the Saturnian ring system

The self-gravitating particulate disk of the Saturnian ring system is studied using linear theory to determine its evolution and stability against gravitational Jeans-type perturbations. The analysis is carried out in approximation of the basically homogeneous and two-dimensional system. In addition, the case is considered with rare collisions between particles when the squared epicyclic frequency κ 2 as well as the squared orbital angular frequency Ω 2 greatly exceeds the squared frequency of interparticle physical collisions ν c 2; that is, the analysis presented here is valid only in the regime of low optical depth in Saturn's rings, τ⋍ ν c Ω <1 . According to observations, such low optical depth regions can be found in the C ring, the inner portions of the B ring at distances r<100 000 km and the A ring at distances r>123 000 km from the planetary center. The analogy with magnetized plasma problems is utilized by applying the so-called single particle dynamics method (the Lagrangian description): The motion of an “average” particle is considered. In the framework of this analytical method the local dispersion relation for small-amplitude oscillations is derived. Using the dispersion relation, an analysis is given of the dispersion law both for axisymmetric (radial) and nonaxisymmetric (spiral) Jeans perturbations. The main result, which follows from the dispersion relation, is the local stability criterion. The criterion generalizes the well-known Toomre's one ( Astrophys. J. 139, 1217–1238, 1964) for spiral gravity perturbations. The dynamical behavior of the different models of Saturn's ring disk is studied by N-body computer simulations in order to confirm the validity of the generalized stability criterion. The numerical method of local simulations (or N-body simulations in a Hill's approximation) is applied. It is shown that the stability criterion obtained from the computer models is in general agreement with the theoretical prediction. It is proposed that as a direct result of the Jeans instability of nonaxisymmetric perturbations the Saturnian ring disk is subdivided into numerous irregular ringlets. with size and spacing of the order 50–100 m. Forth-coming Cassini spacecraft high-resolution images of Saturn's rings may reveal this kind of structure.

Resonant excitation of density waves in Saturn's rings

The dynamics of regions in the Saturnian ring system with rare collisions between particles, that is, Ω 2⪢ν c 2 , where Ω is the orbital angular frequency and ν c the collision frequency, is considered. According to observations, such low optical depth regions can be found in the C ring, the inner portions of the B ring and the A ring. Kinetic theory with the Vlasov and Poisson equations is used to obtain the eigen-frequencies of oscillations propagating in the plane of the system. In the considered case of rare collisions the resulting kinetic equation for the perturbed distribution function can be solved by successive approximations, neglecting the effect of binary particle collisions in the zeroth-order approximation. An oscillating instability of the kinetic type is discussed. This instability of a particulate disk is similar to the magneto-drift instability first discovered by Krall and Rosenbluth ( Physics Fluids 6, 254–265, 1963) in a nonuniform magnetic plasma, and belongs to the class of microinstabilities of an inhomogeneous plasma. The cause of the oscillating instability in Saturn's rings is a resonant interaction of drifting particles with nonaxisymmetric Jeans-stable waves at the corotation. The waves that may be produced by the corotation-resonance interaction represent non-radial normal modes of the gravitationally stable disk modified by a particle drift. It is shown that density waves are effectively excited at this resonance: the growth rate of the mode of maximum instability is large, Im ω∗∼Ω. The resonant excitation of density waves investigated in the present paper may be proposed as the cause of the irregular, small-scale ∼ 100 m structure in regions of low optical depth in Saturn's rings. It is suggested that Cassini spacecraft high-resolution images of low optical depth regions will show this kind of structure.

Near-infrared polarimetric imaging of the bipolar nebula OH 231.8+4.2: The death of a beta Pic-like system

The source OH 231.8+4.2 consists of a Mira variable star embedded in a highly collimated bipolar nebula, and thus appears to be representative of a transitional stage between red giant and planetary nebula. We obtained polarimetric near-infrared images of this source to ascertain its density structure. The patterns of polarization revealed in J and K images are characteristic of scattering of light from the central star by dust distributed in bipolar lobes. The signature of a dense circumstellar disk, previously hypothesized to explain the obscuration of the central star at optical and near-infrared wavelengths, is evident in the polarization maps and in a map of J-K color. Combined with the polarization information, the measured color gradients across the bipolar lobes suggest that the lobes are evacuated bubbles. We use the images to derive absorbing and scattering column densities of dust grains as functions of position within the nebula. The results for the total absorbing and scattering dust masses are similar, at 10 <SUP>-2</SUP> Solar mass. This similarity lends further weight to a model in which the bulk of the dust mass of the nebula lies along the lobe walls. Various lines of evidence suggest that only a small fraction of the total nebula mass resides in the circumstellar disk. This finding would appear to set OH 231.8+4.2 apart from other classical evolved bipolar nebulae, in which disks may dominate the circumstellar masses. We consider the possibility that the disk in OH 231.8+4.2 originated as a result of the influence of a binary companion to the Mira variable. Alternatively, we propose that the OH 231.8+4.2 nebula may be the end point of stellar evolution for an early A star that was surrounded throughout its main-sequence lifetime by a particulate disk. Such a disk might have resembled the dusty disk around beta Pic and, like that structure, would have had to be continually replenished in order to survive until the central star's ascent of the red giant branch. This model naturally explains this confinement of bipolar planetary nebulae to low galactic latitudes.

Agglomerates and media-noise of ultra-thin coated rigid disks

This paper discusses the media-noise properties of ultra-thin coated rigid disks and their origin. The ultra-thin coated rigid disks using Co-γFe 2O 3 fine particles were obtained after spin-coating Al-substrates with magnetic paints. Thickness values between 0.12 and 0.33 μm were obtained after controlled spin-coating. After removing high protrusions on disk-surfaces, the read/write properties of ultra-thin coated rigid disks were investigated using a MIG head. The media-noise properties of the ultra-thin coated disks were compared with those of a conventional particulate disk and a thin film disk. The signal-recorded noises, the dc-erase noise, and the reverse dc-erase (RDC) noises were measured. A peculiar recording density dependence for the signal-recorded noise was found. The signal-recorded noise of the ultra-thin coated disks has a maximum value at a density of 17.5 kFCI. In the region below 17.5 kFCI, the signal-recorded noise increases like a thin film disk as the recording density increases. In the region larger than 17.5 kFCI, the signal-recorded noise decreases like a conventional particulate disk as the recording density increases from 17.5 kFCI. This peculiar dependence is caused by cohered agglomerates which consist of randomly oriented magnetic particles in the magnetic layer of the ultra-thin coated disks.

Velocity streaming of IRAS main-sequence disk stars and the episodic enhancement of particulate disks by interstellar clouds

We have discovered evidence of velocity streaming in a set of nearby main-sequence A-type IRAS disk stars. This conservatively chosen set of the five most significant particulate-disk stars consists of β Pic, α Lyr, α Psa, β Leo, and ζ Lep. Monte Carlo simulations were used to compare the velocity dispersion of this set to the dispersions of sets chosen at random from the remaining 17 main-sequence A stars listed in the Gliese catalog (<22 pc). It was found that dispersion velocities less than those of the particulate-disk star set occurred by chance in only 2% of the cases. Small dispersion velocities are normally indicative of streaming clusters or young field stars. However, the velocity dispersion of the set of particulate-disk stars is inconsistent with either interpretation

The IC 2391 supercluster

Sixty-three field stars and the sparse cluster IC 2391 have been identified as members of the IC 2391 supercluster. The members have at least 95% of their space motion, directed toward (A,D)=(5 h .82, −12°.44). Like members of the very similar Pleiades supercluster, the IC 2391 supercluster contains objects of two ages : t=8×19 7 and 2.5×10 8 yr. A prototype very active chromosphere (VAC) star and the enigmatic giant variable TZ For are supercluster members together with two A-type stars suspected of possessing particulate disks. An especially interesting member is the system of Xi Cep (HR 8417) in which the two brightest components are greatly undermassive

Thin-film recording media: Challenges for physics and magnetism in the 1990s (invited)

Thin-film recording media introduced commercially to rigid disk drives in the early 1980s revolutionized the rigid disk industry. By the end of the decade, particulate disk technology accounted for less than half of the worldwide shipped disks and is expected to disappear from rigid disk drives altogether in the 1990s. The implementation of thin-film technology required entirely new disk fabrication processes and new insights into magnetic materials and microstructures. A review of the fundamental magnetic reasons for implementing thin-film technology will be given, followed by a discussion of the physics and magnetics of thin films. The technology is not completely understood and needs to be examined because of the continued increase of recording densities in rigid disk drives. Discussion will concentrate on thin films suitable for horizontal recording. Topics to be considered are those deemed important from a disk product development view and include thin-film media noise, anisotropy, and magnetic alloys and microstructures.

The Influence of Aluminum Oxide Particles in Magnetic Coating on Head/Disk Wear

The particulate magnetic disks commonly used in magnetic disk storage systems contain aluminum-oxide (Al2O3) particles to reinforce the strength of their magnetic coating. In this paper, the influence of these particles on the tribological characteristics of particulate disks is investigated using two types of ferrite materials for flying heads and particulate disks with four different levels of Al2O3 content. As the Al2O3 content increases, the wear mode changes from the adhesive wear to the abrasive wear. Owing to this transition, the head wear becomes increasingly severe while the durability of the particulate disk improves. Regarding the differences between ferrite materials, relatively soft Mn-Zn ferrite shows worse wear results than hard Ni-Zn ferrite. In particular, it is found that Mn-Zn fertile is worn even by the γ-Fe2O3 particles of the particulate disks. In the combination of ferrite materials and particulate disks used here, an Al2O3 content of around 8 percent is optimum to avoid headcrash, which is one of the most serious problems in magnetic disk storage systems.

Viscosity and mass transport in nonuniform Keplerian disks

A new quantitative formalism describing the dynamics of a Keplerian particulate disk, based on a heuristic description of viscous transport, permits study of rings with a wide range of ensemble and individual particle properties. Here the formalism is developed and applied to the case of a ring with a radial gradient in optical thickness. A steady-state solution for the velocity distribution directly gives the radial mass transport, as well as the viscosity. The formula for viscosity is identical to that derived a decade earlier by Goldreich and Tremaine for a uniform disk, thus validating the assumption by various workers that it could be applied to nonuniform disks, for example in consideration of ringlet instabilities. Our analytical method involves solving a novel form of the Krook equation by separating the distribution of collisional products in phase space into a symmetrical component and a remainder that can be approximated by delta functions. Unlike most past approaches, a Gaussian form for the solution is not assumed. In the case described here, the model is simplified in common with past work (e.g., small, uniform particles and Krook-type treatment of collisions), but the general approach is extendable to less artificially restricted cases.

Determination of lubricant film thickness on a particulate disk surface by atomic force microscopy

The ability of the atomic force microscope (AFM) to measure the lubricant film thickness on the surface of particulate disks is demonstrated, and experimental results are presented. AFM measure the thickness of the lubricant film at a particular location on the disk surface with a lateral resolution of the order of the AFM tip radius, approximately 1000 AA. For an unused disk, 50-70 AA of lubricant thickness is found. After the disk has been in use for several years, the lubricant thickness decreases to 35-55 AA. In both cases, the lubricant is uniformly distributed on the disk surface, although somewhat more uniformly on the used disk. For all types of disks studied, most of the lubricant resides below the disk surface, presumably in the medium's porosity, with only a molecular thin film of lubricant on the surface. >