The lifetime of a planetary disc which orbits a white dwarf represents a crucial input parameter into evolutionary models of that system. Here we apply a purely analytical formalism to estimate lifetimes of the debris phase of these discs, before they are ground down into dust or are subject to sublimation from the white dwarf. We compute maximum lifetimes for three different types of white dwarf discs, formed from (i) radiative YORP breakup of exo-asteroids along the giant branch phases at 2-100 au, (ii) radiation-less spin-up disruption of these minor planets at $\sim 1.5-4.5R_{\odot}$, and (iii) tidal disruption of minor or major planets within about $1.3R_{\odot}$. We display these maximum lifetimes as a function of disc mass and extent, constituent planetesimal properties, and representative orbital excitations of eccentricity and inclination. We find that YORP discs with masses up to $10^{24}$ kg live long enough to provide a reservoir of surviving cm-sized pebbles and m- to km-sized boulders that can be perturbed intact to white dwarfs with cooling ages of up to 10 Gyr. Debris discs formed from the spin or tidal disruption of these minor planets or major planets can survive in a steady state for up to respectively 1 Myr or 0.01 Myr, although most tidal discs would leave a steady state within about 1 yr. Our results illustrate that dust-less planetesimal transit detections are plausible, and would provide particularly robust evolutionary constraints. Our formalism can easily be adapted to individual systems and future discoveries.
The photospheres of some white dwarfs are "polluted" by accretion of material from their surrounding planetary debris. White dwarfs with dust disks are often heavily polluted and high-resolution spectroscopic observations of these systems can be used to infer the chemical compositions of extrasolar planetary material. Here, we report spectroscopic observation and analysis of 19 white dwarfs with dust disks or candidate disks. The overall abundance pattern very much resembles that of bulk Earth and we are starting to build a large enough sample to probe a wide range of planetary compositions. W…
Several hundred stars older than 10 million years have been observed to have infrared excesses. These observations are explained by dust grains formed by the collisional fragmentation of hidden planetesimals. Such dusty planetesimal discs are known as debris discs. In a dynamically cold planetesimal disc, collisional coagulation of planetesimals produces planetary embryos which then stir the surrounding leftover planetesimals. Thus, the collisional fragmentation of planetesimals that results from planet formation forms a debris disc. We aim to determine the properties of the underlying planete…
We report nine years of optical spectroscopy of the metal-polluted white dwarf SDSS J104341.53+085558.2, which presents morphological variations of the line profiles of the 8600 Å Ca II triplet emission from the gaseous component of its debris disc. Similar changes in the shape of the Ca II triplet have also been observed in two other systems that host a gaseous disc, and are likely related to the same mechanism. We report the Mg, Si, and Ca abundances of the debris detected in the photosphere of SDSS J1043+0855, place upper limits on O and Fe, and derive an accretion rate of (2.5 - 12)x$10^8$…
Being the first of its kind, the white dwarf WD 1145+017 exhibits a complex system of disintegrating debris which offers a unique opportunity to study its disruption process in real time. Even with plenty of transit observations there are no clear constraints on the masses or eccentricities of such debris. Using $N$-body simulations we show that masses greater than approximately $10^{20}$ kg (a tenth of the mass of Ceres) or orbits that are not nearly circular ($\mathrm{eccentricity}>10^{-3}$) dramatically increase the chances of the system becoming unstable within two years, which would contr…
WD 0145+234 is a white dwarf that is accreting metals from a circumstellar disc of planetary material. It has exhibited a substantial and sustained increase in 3-5 micron flux since 2018. Follow-up Spitzer photometry reveals that emission from the disc had begun to decrease by late 2019. Stochastic brightening events superimposed on the decline in brightness suggest the liberation of dust during collisional evolution of the circumstellar solids. A simple model is used to show that the observations are indeed consistent with ongoing collisions. Rare emission lines from circumstellar gas have be…
Our knowledge of white dwarf planetary systems predominately arises from the region within a few Solar radii of the white dwarfs, where minor planets break up, form rings and discs, and accrete onto the star. The entry location, angle and speed into this Roche sphere has rarely been explored but crucially determines the initial geometry of the debris, accretion rates onto the photosphere, and ultimately the composition of the minor planet. Here we evolve a total of over 10^5 asteroids with single-planet N-body simulations across the giant branch and white dwarf stellar evolution phases to quan…
White dwarfs containing orbiting planetesimals or their debris represent crucial benchmarks by which theoretical investigations of post-main-sequence planetary systems may be calibrated. The photometric transit signatures of likely planetary debris in the ZTF J0139+5245 white dwarf system has an orbital period of about 110 days. An asteroid which breaks up to produce this debris may spin itself to destruction through repeated close encounters with the star without entering its Roche radius and without influence from the white dwarf's luminosity. Here, we place coupled constraints on the orbita…
Circumstellar disks of planetary debris are now known or suspected to closely orbit hundreds of white dwarf stars. To date, both data and theory support disks that are entirely contained within the preceding giant stellar radii, and hence must have been produced during the white dwarf phase. This picture is strengthened by the signature of material falling onto the pristine stellar surfaces; disks are always detected together with atmospheric heavy elements. The physical link between this debris and the white dwarf host abundances enables unique insight into the bulk chemistry of extrasolar pl…
Debris disks around single white dwarfs are thought to be the remains of planetary bodies disrupted by tidal forces. Ongoing accretion of the hereby produced dust allows to detect the planetary material in the white dwarf photosphere and to conclude on its chemical composition. As an alternative, the composition can in principle be determined directly from the emission lines of the sometimes additionally observed gaseous component of the disks. To this aim, we perform spectral modeling with our non-LTE code for accretion disks. We have obtained new observations of Ton 345 in order to look for …
Debris discs which orbit white dwarfs are signatures of remnant planetary systems. We present twelve years of optical spectroscopy of the metal-polluted white dwarf SDSS J1228+1040, which shows a steady variation in the morphology of the 8600 Å Ca II triplet line profiles from the gaseous component of its debris disc. We identify additional emission lines of O I, Mg I, Mg II, Fe II and Ca II in the deep co-added spectra. These emission features (including Ca H & K) exhibit a wide range in strength and morphology with respect to each other and to the Ca II triplet, indicating different intensit…
Metal pollution in white dwarf photospheres originates from the accretion of some combination of planets, moons, asteroids, comets, boulders, pebbles and dust. When large bodies reside in dynamically stagnant locations -- unable themselves to pollute nor even closely approach the white dwarf -- then smaller reservoirs of impact debris may become a complementary or the primary source of metal pollutants. Here, we take a first step towards exploring this possibility by computing limits on the recoil mass that escapes the gravitational pull of the target object following a single impact onto an a…
The formation channel of the tens of compact debris discs which orbit white dwarfs (WDs) at a distance of one Solar radius remains unknown. Asteroids that survive the giant branch stellar phases beyond a few au are assumed to be dynamically thrust towards the WD and tidally disrupted within its Roche radius, generating extremely eccentric (e>0.98) rings. Here, we establish that WD radiation compresses and circularizes the orbits of super-micron to cm-sized ring constituents to entirely within the WD's Roche radius. We derive a closed algebraic formula which well-approximates the shrinking time…
More than a decade after astronomers realized that disrupted planetary material likely pollutes the surfaces of many white dwarf stars, the discovery of transiting debris orbiting the white dwarf WD 1145+017 has opened the door to new explorations of this process. We describe the observational evidence for transiting planetary material and the current theoretical understanding (and in some cases lack thereof) of the phenomenon.
Recent results suggest that the two planets in the HD 82943 system are inclined to the sky plane by 20 +/- 4deg. Here, we show that the debris disk in this system is inclined by 27 +/- 4deg, thus adding strength to the derived planet inclinations and suggesting that the planets and debris disk are consistent with being aligned at a level similar to the Solar System. Further, the stellar equator is inferred to be inclined by 28 +/- 4deg, suggesting that the entire star - planet - disk system is aligned, the first time such alignment has been tested for radial velocity discovered planets on ~AU …
White dwarfs which exhibit transit signatures of planetary debris and accreted planetary material provide exceptional opportunities to probe the material composition and dynamical structure of planetary systems. Although previous theoretical work investigating the role of minor body disruption around white dwarfs has focussed on spherical bodies, Solar System asteroids can be more accurately modelled as triaxial ellipsoids. Here we present an analytical framework to identify the type of disruption (tidal fragmentation, total sublimation or direct impact) experienced by triaxial asteroids appro…
Observations of debris disks, the products of the collisional evolution of rocky planetesimals, can be used to trace planetary activity across a wide range of stellar types. The most common end points of stellar evolution are no exception as debris disks have been observed around several dozen white dwarf stars. But instead of planetary formation, post-main-sequence debris disks are a signpost of planetary destruction, resulting in compact debris disks from the tidal disruption of remnant planetesimals. In this work, we present the discovery of five new debris disks around white dwarf stars wi…
HR 8799 is a four planet system that also hosts a debris disk. By numerically integrating both planets and a planetesimal disk, we find interactions between an exterior planetesimal disk and the planets can influence the lifetime of the system. We first consider resonant planetary configurations that remained stable for at least 7 Myrs sans debris disk. An exterior debris disk with only 1 per cent the mass of the outermost planet (approximately a Neptune mass) was sufficiently large enough to pull the system out of resonance after 2 to 6 Myrs. Secondly, we consider configurations which are uns…
Observations of debris disks allow for the study of planetary systems, even where planets have not been detected. However, debris disks are often only characterized by unresolved infrared excesses that resemble featureless blackbodies, and the location of the emitting dust is uncertain due to a degeneracy with the dust grain properties. Here we characterize the Spitzer IRS spectra of 22 debris disks exhibiting 10 micron silicate emission features. Such features arise from small warm dust grains, and their presence can significantly constrain the orbital location of the emitting debris. We find…
Observational estimates of the lifetimes and inferred accretion rates from debris discs around polluted white dwarfs are often inconsistent with the predictions of models of shielded Poynting-Robertson drag on the dust particles in the discs. Moreover, many cool polluted white dwarfs do not show any observational evidence of accompanying discs. This may be explained, in part, if the debris discs had shorter lifetimes and higher accretion rates than predicted by Poynting-Robertson drag alone. We consider the role of a magnetic field on tidally disrupted diamagnetic debris and its subsequent eff…
We make use of a new hybrid method to simulate the long-term, multiple-orbit disc formation through tidal disruptions of rocky bodies by white dwarfs, at high-resolution and realistic semi-major axis. We perform the largest-yet suite of simulations for dwarf and terrestrial planets, spanning four orders of magnitude in mass, various pericentre distances and semi-major axes between 3 AU and 150 AU. This large phase space of tidal disruption conditions has not been accessible through the use of previous codes. We analyse the statistical and structural properties of the emerging debris discs, as …
25%-50% of all white dwarfs (WDs) host observable and dynamically active remnant planetary systems based on the presence of close-in circumstellar dust and gas and photospheric metal pollution. Currently-accepted theoretical explanations for the origin of this matter include asteroids that survive the star's giant branch evolution at au-scale distances and are subsequently perturbed onto WD-grazing orbits following stellar mass loss. In this work we investigate the tidal disruption of these highly-eccentric (e > 0.98) asteroids as they approach and tidally disrupt around the WD. We analyticall…
The discovery of numerous debris disks around white dwarfs (WDs), gave rise to extensive study of such disks and their role in polluting WDs, but the formation and evolution of these disks is not yet well understood. Here we study the role of aeolian (wind) erosion in the evolution of solids in WD debris disks. Aeolian erosion is a destructive process that plays a key role in shaping the properties and size-distribution of planetesimals, boulders and pebbles in gaseous protoplanetary disks. Our analysis of aeolian erosion in WD debris disks shows it can also play an important role in these env…
Giant impacts refer to collisions between two objects each of which is massive enough to be considered at least a planetary embryo. The putative collision suffered by the proto-Earth that created the Moon is a prime example, though most Solar System bodies bear signatures of such collisions. Current planet formation models predict that an epoch of giant impacts may be inevitable, and observations of debris around other stars are providing mounting evidence that giant impacts feature in the evolution of many planetary systems. This chapter reviews giant impacts, focussing on what we can learn a…
We present follow-up photometry and spectroscopy of ZTF J0328$-$1219 strengthening its status as a white dwarf exhibiting transiting planetary debris. Using TESS and Zwicky Transient Facility photometry, along with follow-up high speed photometry from various observatories, we find evidence for two significant periods of variability at 9.937 and 11.2 hr. We interpret these as most likely the orbital periods of different debris clumps. Changes in the detailed dip structures within the light curves are observed on nightly, weekly, and monthly timescales, reminiscent of the dynamic behavior obser…
The gap between two component debris disks is often taken to be carved by intervening planets scattering away the remnant planetesimals. We employ N-body simulations to determine how the time needed to clear the gap depends on the location of the gap and the mass of the planets. We invert this relation, and provide an equation for the minimum planet mass, and another for the expected number of such planets, that must be present to produce an observed gap for a star of a given age. We show how this can be combined with upper limits on the planetary system from direct imaging non-detections (suc…
Dynamical interactions between planets and debris disks may sculpt the disk structure and impact planetary orbits, but only a few systems with both imaged planets and spatially resolved debris disks are known. With the Caltech Submm Observatory (CSO), we have observed the HR 8799 debris disk at 350μm. The 350μm map is the first spatially resolved measurement of the debris disk encircling the HR 8799 planetary system at this wavelength. Both the flux and size of the emission are consistent with a Kuiper belt of dust extending from ~100-300 AU. Although the resolution of the current map is limit…
We present detailed characterization of the extremely dusty main sequence star TYC 8830 410 1. This system hosts inner planetary system dust (Tdust~300 K) with a fractional infrared luminosity of ~1%. Mid-infrared spectroscopy reveals a strong, mildy-crystalline solid-state emission feature. TYC 8830 410 1 (spectral type G9V) has a 49.5" separation M4-type companion co-moving and co-distant with it, and we estimate a system age of ~600 Myr. TYC 8830 410 1 also experiences "dipper"-like dimming events as detected by ASAS-SN, TESS, and characterized in more detail with the LCOGT. These recurring…
We consider the observational signatures of giant impacts between planetary embryos. While the debris released in the impact remains in a clump for only a single orbit, there is a much longer lasting asymmetry caused by the fact that all debris must pass through the collision-point. The resulting asymmetry is stationary, it does not orbit the star. The debris is concentrated in a clump at the collision-point, with a more diffuse structure on the opposite side. The asymmetry lasts for typically around 1000 orbital periods of the progenitor, which can be several Myr at distances of ~50 AU. We de…
We identify two ultra-cool ($T_\mathrm{eff} < 4000$ K) metal-polluted (DZ) white dwarfs WDJ2147$-$4035 and WDJ1922$+$0233 as the coolest and second coolest DZ stars known to date with $T_\mathrm{eff} \approx 3050$ K and $T_\mathrm{eff} \approx 3340$ K, respectively. Strong atmospheric collision-induced absorption (CIA) causes the suppression of red optical and infra-red flux in WDJ1922$+$0233, resulting in an unusually blue colour given its low temperature. WDJ2147$-$4035 has moderate infra-red CIA yet has the reddest optical colours known for a DZ white dwarf. Microphysics improvements to the…
We present HST ultraviolet spectroscopy of the white dwarfs PG0843+516, PG1015+161, SDSS1228+1040, and GALEX1931+0117, which accrete circumstellar planetary debris formed from the destruction of asteroids. Combined with optical data, a minimum of five and a maximum of eleven different metals are detected in their photospheres. With metal sinking time scales of only a few days, these stars are in accretion/diffusion equilibrium, and the photospheric abundances closely reflect those of the circumstellar material. We find C/Si ratios that are consistent with that of the bulk Earth, corroborating …
Luminous debris disks of warm dust in the terrestrial planet zones around solar-like stars are recently found to vary, indicative of ongoing large-scale collisions of rocky objects. We use Spitzer 3.6 and 4.5 μm time-series observations in 2012 and 2013 (extended to 2014 in one case) to monitor 5 more debris disks with unusually high fractional luminosities ("extreme debris disk"), including P1121 in the open cluster M47 (80 Myr), HD 15407A in the AB Dor moving group (80 Myr), HD 23514 in the Pleiades (120 Myr), HD 145263 in the Upper Sco Association (10 Myr), and the field star BD+20 307 (>1 …
Producing planetary debris exterior to white dwarf Roche radii through sublimative rotational fission
Centre for Exoplanets and Habitability, University of Warwick（系外行星与宜居性中心，华威大学）；Centre for Space Domain Awareness, University of Warwick（太空态势感知中心，华威大学）；Department of Physics, University of Warwick（物理系，华威大学）；The Planetary Science Institute（行星科学研究所）；Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin（航空航天工程与工程力学系，德克萨斯大学奥斯汀分校）
Thousands of confirmed and candidate exoplanets have been identified in recent years. Consequently, theoretical research on the formation and dynamical evolution of planetary systems has seen a boost, and the processes of planet-planet scattering, secular evolution, and interaction between planets and gas/debris disks have been well-studied. Almost all of this work has focused on the formation and evolution of isolated planetary systems, and neglect the effect of external influences, such as the gravitational interaction with neighbouring stars. Most stars, however, form in clustered environme…
Debris disks are evidence that stars harbor reservoirs of dust-producing plantesimals on spatial scales similar the solar system. Debris disks present a wide range of sizes and structural features and there is growing evidence that, in some cases, they might be the result of the dynamical perturbations of a massive planet. Our solar system also harbors a debris disk and some of its properties resemble those of extra-solar debris disks. This contribution discusses how the study of debris disks with SPICA can shed light on the diversity of planetary systems, the link between debris disks and pla…
White dwarfs that accrete the debris of tidally disrupted asteroids provide the opportunity to measure the bulk composition of the building blocks, or fragments, of exoplanets. This technique has established a diversity in compositions comparable to what is observed in the solar system, suggesting that the formation of rocky planets is a generic process. Whereas the relative abundances of lithophile and siderophile elements within the planetary debris can be used to investigate whether exoplanets undergo differentiation, the composition studies carried out so far lack unambiguous tracers of pl…
Debris disk is a catch-all term that can be used to refer to any component of a planetary system which is not an actual planet. In the Solar System this refers to the asteroids and comets in the Asteroid and Kuiper belts as well as the dust and gas derived from them, such as the zodiacal cloud. Studying the structure of extrasolar debris disks provides unique constraints on the underlying planetary system and on the processes of planet formation and protoplanetary disk evolution. Debris disks also have important implications for processes affecting the planets, such as impact events that may s…
The atmospheres of a large proportion of white dwarf stars are polluted by heavy elements that are expected to sink out of visible layers on short timescales. This has been interpreted as a signature of ongoing accretion of debris from asteroids, comets, and giant planets. This scenario is supported by the detection of debris discs and transits of planetary fragments around some white dwarfs. However, photospheric metals are only indirect evidence for ongoing accretion, and the inferred accretion rates and parent body compositions heavily depend on models of diffusion and mixing processes with…
Multi-epoch infrared photometry from Spitzer is used to monitor circumstellar discs at white dwarfs, which are consistent with disrupted minor planets whose debris is accreted and chemically reflected by their host stars. Widespread infrared variability is found across the population of 37 stars with two or more epochs. Larger flux changes occur on longer time-scales, reaching several tens of per cent over baselines of a few years. The canonical model of a geometrically thin, optically thick disc is thus insufficient, as it cannot give rise to the observed behaviour. Optically thin dust best a…
A significant fraction of main-sequence stars are encircled by dusty debris discs, where the short-lived dust particles are replenished through collisions between planetesimals. Most destructive collisions occur when the orbits of smaller bodies are dynamically stirred up, either by the gravitational effect of locally formed Pluto-sized planetesimals (self-stirring scenario), or via secular perturbation caused by an inner giant planet (planetary stirring). The relative importance of these scenarios in debris systems is unknown. Here we present new Herschel Space Observatory imagery of 11 discs…
Debris discs consist of belts of bodies ranging in size from dust grains to planetesimals; these belts are visible markers of planetary systems around other stars that can reveal the influence of extrasolar planets through their shape and structure. Two key stirring mechanisms -- self-stirring by planetesimals and secular perturbation by an external giant planet -- have been identified to explain the dynamics of planetesimal belts; their relative importance has been studied independently, but are yet to be considered in combination. In this work we perform a suite of 286 N-body simulations exp…
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 po…
The dynamical evolution of planetary systems leaves observable signatures in debris disks. Optical images trace micron-sized grains, which are strongly affected by stellar radiation and need not coincide with their parent body population. Observations of mm-size grains accurately trace parent bodies, but previous images lack the resolution and sensitivity needed to characterize the ring's morphology. Here we present ALMA 350 GHz observations of the Fomalhaut debris ring. These observations demonstrate that the parent body population is 13-19 AU wide with a sharp inner and outer boundary. We di…
The cool white dwarf SDSS J124231.07+522626.6 exhibits photospheric absorption lines of 8 distinct heavy elements in medium resolution optical spectra, notably including oxygen. The Teff = 13000 K atmosphere is helium-dominated, but the convection zone contains significant amounts of hydrogen and oxygen. The four most common rock-forming elements (O, Mg, Si, and Fe) account for almost all the accreted mass, totalling at least 1.2e+24 g, similar to the mass of Ceres. The time-averaged accretion rate is 2e+10 g/s, one of the highest rates inferred among all known metal-polluted white dwarfs. We …
We explore whether assumptions about dust grain shape affect resulting estimates of the composition and grain size distribution of the AU Microscopii (AU Mic) debris disk from scattered light data collected by Lomax et al. (2018). The near edge-on orientation of the AU Mic debris disk makes it ideal for studying the effect of the scattering phase function (SPF) on the measured flux ratios as a function of wavelength and projected distance. Previous efforts to model the AU Mic debris disk have invoked a variety of dust grain compositions and explored the effect of porosity, but did not undertak…
We report a Spitzer/IRAC search for infrared excesses around white dwarfs, including 14 newly-observed targets and 16 unpublished archived stars. We find a substantial infrared excess around two warm white dwarfs --- J220934.84+122336.5 and WD 0843+516, the latter apparently being the hottest white dwarf known to display a close-in dust disk. Extending previous studies, we find that the fraction of white dwarfs with dust disks increases as the star's temperature increases; for stars cooler than 10,000 K, even the most heavily polluted ones do not have ~1000 K dust. There is tentative evidence …
V488 Persei is the most extreme debris disk known in terms of the fraction of the stellar luminosity it intercepts and reradiates. The infrared output of its disk is extremely variable, similar in this respect to the most variable disk known previously, that around ID8 in NGC 2547. We show that the variations are likely to be due to collisions of large planetesimals (> 100 km in diameter) in a belt being stirred gravitationally by a planetary or low-mass-brown-dwarf member of a planetary system around the star. The dust being produced by the resulting collisions is falling into the star due to…
Circumstantial evidence suggests that most known extra-solar planetary systems are survivors of violent dynamical instabilities. Here we explore how giant planet instabilities affect the formation and survival of terrestrial planets. We simulate planetary system evolution around Sun-like stars from initial conditions that comprise: an inner disk of planetesimals and planetary embryos, three giant planets at Jupiter-Saturn distances, and a massive outer planetesimal disk. We then calculate dust production rates and debris disk SEDs assuming that each planetesimal particle represents an ensemble…
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 pr…
This paper describes Herschel observations of the nearby (8.5pc) G5V multi-exoplanet host star 61 Vir at 70-500micron carried out by the DEBRIS survey. These reveal emission that is extended out to >15arcsec with a morphology that can be fitted by a nearly edge-on (77deg inclination) radially broad (from 30AU to >100AU) debris disk of fractional luminosity 2.7x10^-5, with two unrelated sources nearby that are more prominent at longer wavelengths. Chance alignment with a background object seen at 1.4GHz provides potential for confusion, but the star's 1.4"/yr proper motion allows Spitzer 70micr…
