arXiv subjects

Alexander V. Krivov

Publications and source records attributed to Alexander V. Krivov.

At least 19 recordsLinked to original sources

arXiv2026

Viscously Stirring Particle Disks into Lorentzians and Gaussians to Infer Dynamical and Collisional Masses (ARKS XIII)

Disks (Keplerian or otherwise, particulate or fluid) are often assumed to have densities that drop off vertically as Gaussians. Recent mm-wave imaging of circumstellar debris disks contradicts this assumption, revealing vertical profiles in dust that resemble Lorentzians. As part of the ARKS ALMA Large Program, we show how Lorentzians and Gaussians define an evolutionary sequence for disks of gravitationally scattering (viscously stirring) particles. When orbits are crossing and eccentricities $e \gg$ inclinations $i$, each scattering can change a particle's inclination by $\pm \,Δi \propto i$. A random walk with fixed steps in $Δi/i = Δ\ln i$ produces a thick, log normal tail at large $i$ that leads to Lorentzian tails in density. This result holds independent of the origin of the large eccentricities, which may characterize either the stirrers or the objects being stirred; what matters is that relative motions parallel to the disk midplane are faster than perpendicular motions, and that vertical displacements during encounters are smaller than horizontal displacements. After enough scatterings, $i$ comes into equipartition with $e$, $Δi$ stops exponentiating, and the vertical density relaxes to a Gaussian. We identify four regimes of dispersion-dominated viscous stirring, three of which are out-of-equipartition and where $i$ is stirred faster than $e$. The stirrers for ARKS debris disks may range from Pluto to a few times Mars in size, and be sufficiently few as to be collisionless. Or the stirrers may be even smaller, and be so numerous and collide so frequently that they source the collisional cascades that produce observable dust.

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arXiv2026

How hard is dust in debris disks?

Observational appearance of debris disks is largely controlled by collisional grinding of their dust grains. However, the mechanical strength of dust at sizes in the micrometer to millimeter range is poorly known. Recent studies suggested that dust particles in the Solar system might have a higher critical fragmentation energy $Q_{D}^*$ value than previously anticipated. Another recent study considered the Fomalhaut debris disk and found lower $Q_{D}^*$ values to provide better fits to the data. In order to constrain the mechanical strength of dust, we investigate collisional evolution of debris disks with $Q_{D}^*$ prescriptions differing by $\sim 3$ orders of magnitude. We find that, above a certain threshold $Q_{D}^*$ value, the disk's collisional evolution is dominated by rebounding -- rather than disruptive or cratering -- collisions. Rebounding (a.k.a. bouncing) collisions are those in which both impactors survive, being only slightly eroded and producing fragments that only carry a minor fraction of their mass. We show that disks dominated by rebounding collisions would have brightness profiles increasing outward outside the parent belt. Since such profiles are not observed, this places an upper limit on how hard the debris dust is allowed to be in order not to violate the observations. We derive an approximate analytic expression for this limit: $Q_{D}^* \approx (1/8) v_{K}^2(r)$ for grains close to the radiation pressure blowout size, where $v_{K}$ in the Keplerian circular speed at a distance $r$ from the star. This implies $Q_{D}^* \lesssim 10^{9...10} \,\hbox{erg}\,\hbox{g}^{-1}$ for micrometer-sized grains in typical debris disks. Even though rebounding collisions are not expected to affect debris disk evolution significantly, we emphasize that these collisions are actually much more frequent than disruptive and cratering ones in all debris disks.

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arXiv2026

The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) II. The radial structure of debris discs

The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) was recently completed to cover the lack of high-resolution observations of debris discs and to investigate the prevalence of substructures such as radial gaps and rings in a sample of 24 discs. This study characterises the radial structure of debris discs in the ARKS programme. To identify and quantify the disc substructures, we modelled all discs with a range of non-parametric and parametric approaches. We find that of the 24 discs in the sample, 5 host multiple rings, 7 are single rings that display halos or additional low-amplitude rings, and 12 are single rings with at most tentative evidence of additional substructures. The fractional ring widths that we measured are significantly narrower than previously derived values, and they follow a distribution similar to the fractional widths of individual rings resolved in protoplanetary discs. However, there exists a population of rings in debris discs that are significantly wider than those in protoplanetary discs. We also find that discs with steep inner edges consistent with planet sculpting tend to be found at smaller (<100 au) radii, while more radially extended discs tend to have shallower edges more consistent with collisional evolution. An overwhelming majority of discs have radial profiles well-described by either a double power law or double-Gaussian parametrisation. While our findings suggest that it may be possible for some debris discs to inherit their structures directly from protoplanetary discs, there exists a sizeable population of broad debris discs that cannot be explained in this way. Assuming that the distribution of millimetre dust reflects the distribution of planetesimals, mechanisms that cause rings in protoplanetary discs to migrate or debris discs to broaden soon after formation may be at play, possibly mediated by planetary migration or scattering.

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arXiv2026

The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) III: The vertical structure of debris disks

Debris disks -- collisionally sustained belts of dust and sometimes gas around main sequence stars -- are remnants of planet formation processes and are found in systems ${\gtrsim}10$ Myr old. Millimeter-wavelength observations are particularly important, as the grains probed by these observations are not strongly affected by radiation pressure and stellar winds, allowing them to probe the dynamics of large bodies producing dust. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) is analyzing high-resolution observations of 24 debris disks to enable the characterization of debris disk substructures across a large sample for the first time. For the most highly inclined disks, it is possible to recover the vertical structure of the disk. We aim to model and analyze the most highly inclined systems in the ARKS sample in order to uniformly extract the vertical dust distributions for a sample of well-resolved debris disks. We employed both parametric and nonparametric methods to constrain the vertical dust distributions for the most highly inclined ARKS targets. We find a broad range of aspect ratios, revealing a wide diversity in vertical structure, with a range of best-fit parametric values of $0.0026 \leq h_{\rm HWHM} \leq 0.193$ and a median best-fit value of $h_{\rm HWHM}=0.021$. The results obtained by nonparametric modeling are generally consistent with the parametric modeling results. We find that five of the 13 disks are consistent with having total disk masses less than that of Neptune (17 $M_{\oplus}$), assuming stirring by internal processes (self-stirring and collisional and frictional damping). Furthermore, most systems show a significant preference for a Lorentzian vertical profile rather than a Gaussian.

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arXiv2025

Fomalhaut's debris disc is not dominated by primordial Plutos

A key challenge in debris-disc science is that we do not know the masses of debris discs, nor the sizes of the largest debris bodies. This is because modern observations can only detect objects up to centimetre sizes, whilst larger planetesimals, which dominate disc mass, remain hidden. We must therefore use other arguments, such as dynamics, to indirectly infer disc masses and body sizes. This paper presents a new method, applicable to narrow debris discs like Fomalhaut. We argue that such discs cannot be too massive, nor the largest bodies too large, otherwise they would self-scatter and the disc would be much broader than observed. Using n-body dynamics and collisional theory, we demonstrate that the mass of Fomalhaut's disc cannot be dominated by primordial Plutos. Instead, if the mass is dominated by primordial bodies, then they should have radii below $300^{+80}_{-70}$ km ($0.3 \pm 0.1$ RPluto) and above $5^{+20}_{-4}$ km. Such bodies would each have less than 1 per cent the mass of Pluto. Our conclusions are robust to additional physics, including shepherding planets and collisional damping. Our results provide independent, dynamical support for the idea that the masses of bright debris discs are dominated by objects smaller than Pluto.

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arXiv2025

Hot exozodiacal dust around Fomalhaut: The MATISSE perspective

Excess over the stellar photospheric emission of main-sequence stars has been found in interferometric near-infrared observations, and is attributed to the presence of hot exozodiacal dust (HEZD). As part of our effort to detect and characterize HEZD around the nearby A3 V star Fomalhaut, we carried out the first interferometric observations with the MATISSE instrument at the VLTI in the photometric bands L and M for the Fomalhaut system. Assuming a dust distribution either as a narrow ring or spherical shell for modeling the HEZD, we aim to constrain the HEZD parameters by generating visibilities and fitting them to the MATISSE data using different approaches. The L band data provide a marginal detection of circumstellar radiation, potentially caused by the presence of HEZD, which is only the second detection of HEZD emission in the L band. An analysis of the data with different fitting approaches showed that the best-fit values for the HEZD parameters are consistent with those of previous Fomalhaut observations, which underlines the functionality of MATISSE. Assuming a dust ring, it would have an inner ring radius of $0.11\ \mathrm{au}$, an outer ring radius of $0.12\ \mathrm{au}$, a narrow dust grain size distribution around a dust grain radius constrained by $0.53\ μ\mathrm{m}$, and a total dust mass of $3.25\times 10^{-10}\ \rm{M}_{\oplus}$. Finally, the results indicate that the choice of the geometric model has a more significant impact on the derived dust-to-star flux ratio than the specific fitting approach applied. Since different dust-to-star flux ratios can result from the applied fitting approaches, this also has an impact on the parameter values of the HEZD around Fomalhaut and most likely for other HEZD systems. Moreover, further NIR and MIR data are required for a more comprehensive description of the emission originating in the vicinity of Fomalhaut.

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arXiv2023

Increasing planet-stirring efficiency of debris disks by "projectile stirring" and "resonant stirring"

Extrasolar debris disks are detected by observing dust, which is thought to be released during planetesimal collisions. This implies that planetesimals are dynamically excited ("stirred"), such that collisions are sufficiently common and violent. The most frequently considered stirring mechanisms are self-stirring by disk self-gravity, and planet-stirring via secular interactions. However, these models face problems when considering disk mass, self-gravity, and planet eccentricity, leading to the possibility that other, unexplored mechanisms instead stir debris. We hypothesize that planet-stirring could be more efficient than the traditional secular model implies, due to two additional mechanisms. First, a planet at the inner edge of a debris disk can scatter massive bodies onto eccentric, disk-crossing orbits, which then excite debris ("projectile stirring"). Second, a planet can stir debris over a wide region via broad mean-motion resonances, both at and between nominal resonance locations ("resonant stirring"). Both mechanisms can be effective even for low-eccentricity planets, unlike secular-planet-stirring. We run N-body simulations across a broad parameter space, to determine the viability of these new stirring mechanisms. We quantify stirring levels using a bespoke program for assessing Rebound debris simulations, which we make publicly available. We find that even low-mass projectiles can stir disks, and verify this with a simple analytic criterion. We also show that resonant stirring is effective for planets above ~0.5 MJup. By proving that these mechanisms can increase planet-stirring efficiency, we demonstrate that planets could still be stirring debris disks even in cases where conventional (secular) planet-stirring is insufficient.

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arXiv2023

The effect of sculpting planets on the steepness of debris-disc inner edges

Debris discs are our best means to probe the outer regions of planetary systems. Many studies assume that planets lie at the inner edges of debris discs, akin to Neptune and the Kuiper Belt, and use the disc morphologies to constrain those otherwise-undetectable planets. However, this produces a degeneracy in planet mass and semimajor axis. We investigate the effect of a sculpting planet on the radial surface-density profile at the disc inner edge, and show that this degeneracy can be broken by considering the steepness of the edge profile. Like previous studies, we show that a planet on a circular orbit ejects unstable debris and excites surviving material through mean-motion resonances. For a non-migrating, circular-orbit planet, in the case where collisions are negligible, the steepness of the disc inner edge depends on the planet-to-star mass ratio and the initial-disc excitation level. We provide a simple analytic model to infer planet properties from the steepness of ALMA-resolved disc edges. We also perform a collisional analysis, showing that a purely planet-sculpted disc would be distinguishable from a purely collisional disc and that, whilst collisions flatten planet-sculpted edges, they are unlikely to fully erase a planet's signature. Finally, we apply our results to ALMA-resolved debris discs and show that, whilst many inner edges are too steep to be explained by collisions alone, they are too flat to arise through completed sculpting by non-migrating, circular-orbit planets. We discuss implications of this for the architectures, histories and dynamics in the outer regions of planetary systems.

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arXiv2023

The clumpy structure of $ε$ Eridani's debris disc revisited by ALMA

$ε$ Eridani is the closest star to our Sun known to host a debris disc. Prior observations in the (sub-)millimetre regime have potentially detected clumpy structure in the disc and attributed this to interactions with an (as yet) undetected planet. However, the prior observations were unable to distinguish between structure in the disc and background confusion. Here we present the first ALMA image of the entire disc, which has a resolution of 1.6"$\times$1.2". We clearly detect the star, the main belt and two point sources. The resolution and sensitivity of this data allow us to clearly distinguish background galaxies (that show up as point sources) from the disc emission. We show that the two point sources are consistent with background galaxies. After taking account of these, we find that resolved residuals are still present in the main belt, including two clumps with a $>3σ$ significance -- one to the east of the star and the other to the northwest. We perform $n$-body simulations to demonstrate that a migrating planet can form structures similar to those observed by trapping planetesimals in resonances. We find that the observed features can be reproduced by a migrating planet trapping planetesimals in the 2:1 mean motion resonance and the symmetry of the most prominent clumps means that the planet should have a position angle of either ${\sim10^\circ}$ or ${\sim190^\circ}$. Observations over multiple epochs are necessary to test whether the observed features rotate around the star.

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arXiv2022

Hot exozodis: cometary supply without trapping is unlikely to be the mechanism

Excess near-infrared emission is detected around one fifth of main-sequence stars, but its nature is a mystery. These excesses are interpreted as thermal emission from populations of small, hot dust very close to their stars (`hot exozodis'), but such grains should rapidly sublimate or be blown out of the system. To date, no model has fully explained this phenomenon. One mechanism commonly suggested in the literature is cometary supply, where star-grazing comets deposit dust close to the star, replenishing losses from grain sublimation and blowout. However, we show that this mechanism alone is very unlikely to be responsible for hot exozodis. We model the trajectory and size evolution of dust grains released by star-grazing comets, to establish the dust and comet properties required to reproduce hot-exozodi observations. We find that cometary supply alone can only reproduce observations if dust ejecta has an extremely steep size distribution upon release, and the dust-deposition rate is extraordinarily high. These requirements strongly contradict our current understanding of cometary dust and planetary systems. Cometary supply is therefore unlikely to be solely responsible for hot exozodis, so may need to be combined with some dust-trapping mechanism (such as gas or magnetic trapping) if it is to reproduce observations.

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arXiv2022

Planet populations inferred from debris discs: insights from 178 debris systems in the ISPY, LEECH and LIStEN planet-hunting surveys

We know little about the outermost exoplanets in planetary systems, because our detection methods are insensitive to moderate-mass planets on wide orbits. However, debris discs can probe the outer-planet population, because dynamical modelling of observed discs can reveal properties of perturbing planets. We use four sculpting and stirring arguments to infer planet properties in 178 debris-disc systems from the ISPY, LEECH and LIStEN planet-hunting surveys. Similar analyses are often conducted for individual discs, but we consider a large sample in a consistent manner. We aim to predict the population of wide-separation planets, gain insight into the formation and evolution histories of planetary systems, and determine the feasibility of detecting these planets in the near future. We show that a `typical' cold debris disc likely requires a Neptune- to Saturn-mass planet at 10-100 au, with some needing Jupiter-mass perturbers. Our predicted planets are currently undetectable, but modest detection-limit improvements (e.g. from JWST) should reveal many such perturbers. We find that planets thought to be perturbing debris discs at late times are similar to those inferred to be forming in protoplanetary discs, so these could be the same population if newly formed planets do not migrate as far as currently thought. Alternatively, young planets could rapidly sculpt debris before migrating inwards, meaning that the responsible planets are more massive (and located further inwards) than debris-disc studies assume. We combine self-stirring and size-distribution modelling to show that many debris discs cannot be self-stirred without having unreasonably high masses; planet- or companion-stirring may therefore be the dominant mechanism in many (perhaps all) debris discs. Finally, we provide catalogues of planet predictions, and identify promising targets for future planet searches.

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arXiv2021

Fomalhaut b could be massive and sculpting the narrow, eccentric debris disc, if in mean-motion resonance with it

The star Fomalhaut hosts a narrow, eccentric debris disc, plus a highly eccentric companion Fomalhaut b. It is often argued that Fomalhaut b cannot have significant mass, otherwise it would quickly perturb the disc. We show that material in internal mean-motion resonances with a massive, coplanar Fomalhaut b would actually be long-term stable, and occupy orbits similar to the observed debris. Furthermore, millimetre dust released in collisions between resonant bodies could reproduce the width, shape and orientation of the observed disc. We first re-examine the possible orbits of Fomalhaut b, assuming that it moves under gravity alone. If Fomalhaut b orbits close to the disc midplane then its orbit crosses the disc, and the two are apsidally aligned. This alignment may hint at an ongoing dynamical interaction. Using the observationally allowed orbits, we then model the interaction between a massive Fomalhaut b and debris. Whilst most debris is unstable in such an extreme configuration, we identify several resonant populations that remain stable for the stellar lifetime, despite crossing the orbit of Fomalhaut b. This debris occupies low-eccentricity orbits similar to the observed debris ring. These resonant bodies would have a clumpy distribution, but dust released in collisions between them would form a narrow, relatively smooth ring similar to observations. We show that if Fomalhaut b has a mass between those of Earth and Jupiter then, far from removing the observed debris, it could actually be sculpting it through resonant interactions.

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arXiv2020

Resolving the outer ring of HD 38206 using ALMA and constraining limits on planets in the system

HD 38206 is an A0V star in the Columba association, hosting a debris disc first discovered by IRAS. Further observations by Spitzer and Herschel showed that the disc has two components, likely analogous to the asteroid and Kuiper belts of the Solar System. The young age of this star makes it a prime target for direct imaging planet searches. Possible planets in the system can be constrained using the debris disc. Here we present the first ALMA observations of the system's Kuiper belt and fit them using a forward modelling MCMC approach. We detect an extended disc of dust peaking at around 180 au with a width of 140 au. The disc is close to edge on and shows tentative signs of an asymmetry best fit by an eccentricity of $0.25^{+0.10}_{-0.09}$. We use the fitted parameters to determine limits on the masses of planets interior to the cold belt. We determine that a minimum of four planets are required, each with a minimum mass of 0.64 M$_J$, in order to clear the gap between the asteroid and Kuiper belts of the system. If we make the assumption that the outermost planet is responsible for the stirring of the disc, the location of its inner edge and the eccentricity of the disc, then we can more tightly predict its eccentricity, mass and semimajor axis to be $e_{\rm{p}}=0.34^{+0.20}_{-0.13}$, $m_{\rm{p}}=0.7^{+0.5}_{-0.3}\,\rm{M}_{\rm{J}}$ and $a_{\rm{p}}=76^{+12}_{-13}\,\rm{au}$.

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arXiv2020

First L band detection of hot exozodiacal dust with VLTI/MATISSE

For the first time we observed the emission of hot exozodiacal dust in L band. We used the new instrument MATISSE at the Very Large Telescope Interferometer to detect the hot dust around $κ$ Tuc with a significance of 3$σ$ to 6$σ$ at wavelengths between 3.37 and 3.85 $μ$m and a dust-to-star flux ratio of 5 to 7 %. We modelled the spectral energy distribution based on the new L band data alone and in combination with H band data published previously. In all cases we find 0.58 $μ$m grains of amorphous carbon to fit the $κ$ Tuc observations the best, however, also nanometre or micrometre grains and other carbons or silicates reproduce the observations well. Since the H band data revealed a temporal variability, while our L band data were taken at a different epoch, we combine them in different ways. Depending on the approach, the best fits are obtained for a narrow dust ring at a stellar distance in the 0.1 to 0.29 au range and thus with a temperature between 940 and 1430 K. Within the 1$σ$ uncertainty dust location and temperature are confined to 0.032 - 1.18 au and 600 - 2000 K.

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arXiv2020

Observability of Debris Discs around M-stars

Debris discs are second generation dusty discs formed by collisions of planetesimals. Many debris discs have been found and resolved around hot and solar-type stars. However, only a handful have been discovered around M-stars, and the reasons for their paucity remain unclear. Here we check whether the sensitivity and wavelength coverage of present-day telescopes are simply unfavourable for detection of these discs or if they are truly rare. We approach this question by looking at the Herschel/DEBRIS survey that has searched for debris discs including M-type stars. Assuming that these cool-star discs are "similar" to those of the hotter stars in some sense (i.e., in terms of dust location, temperature, fractional luminosity, or mass), we check whether this survey should have found them. With our procedure we can reproduce the $2.1^{+4.5}_{-1.7}$% detection rate of M-star debris discs of the DEBRIS survey, which implies that these discs can indeed be similar to discs around hotter stars and just avoid detection. We then apply this procedure to IRAM NIKA-2 and ALMA bands 3, 6 and 7 to predict possible detection rates and give recommendations for future observations. We do not favour observing with IRAM, since it leads to detection rates lower than for the DEBRIS survey, with 0.6%-4.5% for a 15 min observation. ALMA observations, with detection rates 0.9%-7.2%, do not offer a significant improvement either, and so we conclude that more sensitive far-infrared and single dish sub-millimetre telescopes are necessary to discover the missing population of M-star debris discs.

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arXiv2020

Solution to the debris disc mass problem: planetesimals are born small?

Debris belts on the periphery of planetary systems, encompassing the region occupied by planetary orbits, are massive analogues of the Solar system's Kuiper belt. They are detected by thermal emission of dust released in collisions amongst directly unobservable larger bodies that carry most of the debris disc mass. We estimate the total mass of the discs by extrapolating up the mass of emitting dust with the help of collisional cascade models. The resulting mass of bright debris discs appears to be unrealistically large, exceeding the mass of solids available in the systems at the preceding protoplanetary stage. We discuss this "mass problem" in detail and investigate possible solutions to it. These include uncertainties in the dust opacity and planetesimal strength, variation of the bulk density with size, steepening of the size distribution by damping processes, the role of the unknown "collisional age" of the discs, and dust production in recent giant impacts. While we cannot rule out the possibility that a combination of these might help, we argue that the easiest solution would be to assume that planetesimals in systems with bright debris discs were "born small", with sizes in the kilometre range, especially at large distances from the stars. This conclusion would necessitate revisions to the existing planetesimal formation models, and may have a range of implications for planet formation. We also discuss potential tests to constrain the largest planetesimal sizes and debris disc masses.

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arXiv2020

Gas trapping of hot dust around main-sequence stars

In 2006 Vega was discovered to display excess near-infrared emission. Surveys now detect this phenomenon for one fifth of main-sequence stars, across various spectral types and ages. The excesses are interpreted as populations of small, hot dust grains very close to their stars, which must originate from comets or asteroids. However, the presence of such grains in copious amounts is mysterious, since they should rapidly sublimate or be blown out of the system. Here we investigate a potential mechanism to generate excesses: dust migrating inwards under radiation forces sublimates near the star, releasing modest quantities of gas which then traps subsequent grains. This mechanism requires neither specialised system architectures nor high dust supply rates, and could operate across diverse stellar types and ages. The model naturally reproduces many features of inferred dust populations, in particular their location, preference for small grains, steep size distribution, and dust location scaling with stellar luminosity. For Sun-like stars the mechanism can produce 2.2 micron excesses that are an order of magnitude larger than those at 8.5 micron, as required by observations. However, for A-type stars the simulated near-infrared excesses were only twice those in the mid infrared; grains would have to be 5-10 times smaller than those trapped in our model to be able to explain observed near-infrared excesses around A stars. Further progress with any hot dust explanation for A stars requires a means for grains to become very hot without either rapidly sublimating or being blown out of the system.

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arXiv2019

Dust Spreading in Debris Discs: Do Small Grains Cling on to Their Birth Environment?

Debris discs are dusty belts of planetesimals around main-sequence stars, similar to the asteroid and Kuiper belts in our solar system. The planetesimals cannot be observed directly, yet they produce detectable dust in mutual collisions. Observing the dust, we can try to infer properties of invisible planetesimals. Here we address the question of what is the best way to measure the location of outer planetesimal belts that encompass extrasolar planetary systems. A standard method is using resolved images at mm-wavelengths, which reveal dust grains with sizes comparable to the observational wavelength. Smaller grains seen in the infrared (IR) are subject to several non-gravitational forces that drag them away from their birth rings, and so may not closely trace the parent bodies. In this study, we examine whether imaging of debris discs at shorter wavelengths might enable determining the spatial location of the exo-Kuiper belts with sufficient accuracy. We find that around M-type stars the dust best visible in the mid-IR is efficiently displaced inward from their birth location by stellar winds, causing the discs to look more compact in mid-IR images than they actually are. However, around earlier-type stars where the majority of debris discs is found, discs are still the brightest at the birth ring location in the mid-IR regime. Thus, sensitive IR facilities with good angular resolution, such as MIRI on JWST, will enable tracing exo-Kuiper belts in nearby debris disc systems.

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