Planetesimal Belts Research Articles

THE DEBRIS DISK OF VEGA: A STEADY-STATE COLLISIONAL CASCADE, NATURALLY

It has been argued that the photometric data and images of the archetypical debris disk around Vega may be in contradiction with the standard, steady-state collisional scenario of the disk evolution. Here we perform physical modeling of the Vega disk "from the sources". We assume that dust is maintained by a "Kuiper belt" of parent planetesimals at ~ 100 AU and employ our collisional and radiative transfer codes to consistently model the size and radial distribution of the disk material and then thermal emission of dust. In doing so, we vary a broad set of parameters, including the stellar properties, the exact location, extension, and dynamical excitation of the planetesimal belt, chemical composition of solids, and the collisional prescription. We are able to reproduce the spectral energy distribution in the entire wavelength range from the near-infrared to millimeter, as well as the mid-IR and sub-millimeter radial brightness profiles of the Vega disk. Thus our results suggest that the Vega disk observations are compatible with a steady-state collisional dust production, and we put important constraints on the disk parameters and physical processes that sustain it. The total disk mass in < 100 km-sized bodies is estimated to be ~ 10 Earth masses. Provided that collisional cascade has been operating over much of the Vega age of ~ 350 Myr, the disk must have lost a few Earth masses of solids during that time. We also demonstrate that using an intermediate luminosity of the star between the pole and the equator, as derived from its fast rotation, is required to reproduce the debris disk observations. Finally, we show that including cratering collisions into the model is mandatory.

Collisional evolution of eccentric planetesimal swarms

Models for the steady state collisional evolution of low eccentricity planetesimal belts identify debris disks with hot dust at 1AU, like eta Corvi and HD69830, as anomalous since collisional processing should have removed most of the planetesimal mass over their >1 Gyr lifetimes. This paper looks at the effect of large planetesimal eccentricities (e>>0.3) on their collisional lifetime and the amount of mass that can remain at late times M_{late}. For an axisymmetric planetesimal disk with common pericentres and eccentricities e, we find that M_{late} \propto e^{-5/3}(1+e)^{4/3}(1-e)^{-3}. For a scattered disk-like population (i.e., common pericentres), in the absence of dynamical evolution, the mass evolution at late times would be as if only planetesimals with the largest eccentricity were present. Despite the increased remaining mass, higher eccentricities do not increase the hot emission from the collisional cascade until e>0.99, partly because most collisions occur near pericentre thus increasing the dust blow-out diameter. However, at high eccentricities (e>0.97) the blow-out population extending out from pericentre may be detectable above the collisional cascade; higher eccentricities also increase the probability of witnessing a recent collision. All of the imaging and spectroscopic constraints for eta Corvi can be explained with a single planetesimal population with pericentre at 0.75AU, apocentre at 150AU, and mass 5M_\oplus; however, the origin of such a high eccentricity population remains challenging. The mid-IR excess to HD69830 can be explained by the ongoing destruction of a debris belt produced in a recent collision in an eccentric planetesimal belt, but the lack of far-IR emission requires small bound grains to be absent from the parent planetesimal belt, possibly due to sublimation.

ORBITAL CONSTRAINTS ON THE β Pic INNER PLANET CANDIDATE WITH KECK ADAPTIVE OPTICS

A point source observed 8 AU in projection from beta Pictoris in L' (3.8 micron) imaging in 2003 has been recently presented as a planet candidate. Here we show the results of L'-band adaptive optics imaging obtained at Keck Observatory in 2008. We do not detect beta Pic b beyond a limiting radius of 0.29 arcsec, or 5.5 AU in projection, from the star. If beta Pic b is an orbiting planet, then it has moved >=0.12 arcsec (2.4 AU in projection) closer to the star in the five years separating the two epochs of observation. We examine the range of orbital parameters consistent with the observations, including likely bounds from the locations of previously inferred planetesimal belts. We find a family of low-eccentricity orbits with semimajor axes ~8-9 AU that are completely allowed, as well as a broad region of orbits with e<~0.2, a>~10 AU that are allowed if the apparent motion of the planet was towards the star in 2003. We compare this allowed space with predictions of the planetary orbital elements from the literature. Additionally, we show how similar observations in the next several years can further constrain the space of allowed orbits. Non-detections of the source through 2013 will exclude the interpretation of the candidate as a planet orbiting between the 6.4 and 16 AU planetesimal belts.

WILL THE LARGE SYNOPTIC SURVEY TELESCOPE DETECT EXTRA-SOLAR PLANETESIMALS ENTERING THE SOLAR SYSTEM?

Planetesimal formation is a common by-product of the star formation process. Taking the dynamical history of the Solar system as a guideline -- in which the planetesimal belts were heavily depleted due to graviational perburbation with the giant planets -- and assuming similar processes have take place in other planetary systems, one would expect the interestellar space to be filled with extra-solar planetesimals. However, not a single one of these objects has been detected so far entering the Solar system, even though it would clearly be distinguishable from a Solar system comet due to its highly hyperbolic orbit. The Large Synoptic Survey Telescope (LSST) will provide wide coverage maps of the sky to a very high sensitivity, ideal to detect moving objects like comets, both active and inactive. In anticipation of these observations, we estimate how many inactive "interstellar comets" might be detected during the duration of the survey. The calculation takes into account estimates (from observations and models) of the number density of stars, the amount of solids available to form planetesimals, the frequency of planet and planetesimal formation, the efficiency of planetesimal ejection, and the possible size distribution of these small bodies.

Can gas in young debris disks be constrained by their radial brightness profiles?

Disks around young stars are known to evolve from optically thick, gas-dominated protoplanetary disks to optically thin, almost gas-free debris disks. It is thought that the primordial gas is largely removed at ages of ~10 Myr, but it is difficult to discern the true gas densities from gas observations. This suggests using observations of dust: it has been argued that gas, if present with higher densities, would lead to flatter radial profiles of the dust density and surface brightness than those actually observed. However, here we show that these profiles are surprisingly insensitive to variation of the parameters of a central star, location of the dust-producing planetesimal belt, dustiness of the disk and - most importantly - the parameters of the ambient gas. This result holds for a wide range of gas densities (three orders of magnitude), for different radial distributions of the gas temperature, and different gas compositions. The brightness profile slopes of -3...-4 we find are the same that were theoretically found for gas-free debris disks, and they are the same as actually retrieved from observations of many debris disks. Our specific results for three young (10-30 Myr old), spatially resolved, edge-on debris disks (beta Pic, HD 32297, and AU Mic) show that the observed radial profiles of the surface brightness do not pose any stringent constraints on the gas component of the disk. We cannot exclude that outer parts of the systems may have retained substantial amounts of primordial gas which is not evident in the gas observations (e.g. as much as 50 Earth masses for beta Pic). However, the possibility that gas, most likely secondary, is only present in little to moderate amounts, as deduced from gas detections (e.g. ~0.05 Earth masses in the beta Pic disk), remains open, too.

Limits on the location of planetesimal formation in self-gravitating protostellar discs

Abstract In this Letter, we show that if planetesimals form in spiral features in self-gravitating discs, as previously suggested by the idealized simulations of Rice et al., then in realistic protostellar discs, this process will be restricted to the outer regions of the disc (i.e. at radii in excess of several tens of au). This restriction relates to the requirement that dust has to be concentrated in spiral features on a time-scale that is less than the (roughly dynamical) lifetime of such features, and that such rapid accumulation requires spiral features whose fractional amplitude is not much less than unity. This in turn requires that the cooling time-scale of the gas is relatively short, which restricts the process to the outer disc. We point out that the efficient conversion of a large fraction of the primordial dust in the disc into planetesimals could rescue this material from the well-known problem of rapid inward migration at an approximate metre-size scale and that in principle the collisional evolution of these objects could help to resupply small dust to the protostellar disc. We also point out the possible implications of this scenario for the location of planetesimal belts inferred in debris discs around main sequence stars, but stress that further dynamical studies are required in order to establish whether the disc retains a memory of the initial site of planetesimal creation.

Debris disc stirring by secular perturbations from giant planets

Detectable debris discs are thought to require dynamical excitation (`stirring'), so that planetesimal collisions release large quantities of dust. We investigate the effects of the secular perturbations of a planet, which may lie at a significant distance from the planetesimal disc, to see if these perturbations can stir the disc, and if so over what time-scale. The secular perturbations cause orbits at different semi-major axes to precess at different rates, and after some time t_cross initially non-intersecting orbits begin to cross. We show that t_cross is proportional to a_disc^(9/2)/(m_pl e_pl a_pl^3), where m_pl, e_pl and a_pl are the mass, eccentricity, and semi-major axis of the planet, and a_disc is the semi-major axis of the disc. This time-scale can be faster than that for the growth of planetesimals to Pluto's size within the outer disc. We also calculate the magnitude of the relative velocities induced amongst planetesimals and infer that a planet's perturbations can typically cause destructive collisions out to 100's of AU. Recently formed planets can thus have a significant impact on planet formation in the outer disc which may be curtailed by the formation of giant planets much closer to the star. The presence of an observed debris disc does not require the presence of Pluto-sized objects within it, since it can also have been stirred by a planet not in the disc. For the star epsilon Eridani, we find that the known RV planet can excite the planetesimal belt at 60 AU sufficiently to cause destructive collisions of bodies up to 100 km in size, on a time-scale of 40 Myr.

A possible architecture of the planetary system HR 8799

HR8799 is a nearby A-type star with a debris disk and three planetary candidates recently imaged directly. We undertake a coherent analysis of various portions of observational data on all known components of the system. The goal is to elucidate the architecture and evolutionary status of the system. We try to further constrain the age and orientation of the system, orbits and masses of the companions, as well as the location of dust. From the high luminosity of debris dust and dynamical constraints, we argue for a rather young system's age of <50Myr. The system must be seen nearly, but not exactly, pole-on. Our analysis of the stellar rotational velocity yields an inclination of 13-30deg, whereas i>20deg is needed for the system to be dynamically stable, which suggests a probable inclination range of 20-30deg. The spectral energy distribution is naturally reproduced with two dust rings associated with two planetesimal belts. The inner "asteroid belt" is located at ~10AU inside the orbit of the innermost companion and a "Kuiper belt" at >100AU is just exterior to the orbit of the outermost companion. The dust masses in the inner and outer ring are estimated to be ~1E-05 and 4E-02 M_earth, respectively. We show that all three planetary candidates may be stable in the mass range suggested in the discovery paper by Marois et al. 2008 (between 5 and 13 Jupiter masses), but only for some of all possible orientations. Stable orbits imply a double (4:2:1) mean-motion resonance between all three companions. We finally show that in the cases where the companions themselves are orbitally stable, the dust-producing planetesimal belts are also stable against planetary perturbations.

PLANET-PLANET SCATTERING IN PLANETESIMAL DISKS

We study the final architecture of planetary systems that evolve under the combined effects of planet-planet and planetesimal scattering. Using N-body simulations we investigate the dynamics of marginally unstable systems of gas and ice giants both in isolation and when the planets form interior to a planetesimal belt. The unstable isolated systems evolve under planet-planet scattering to yield an eccentricity distribution that matches that observed for extrasolar planets. When planetesimals are included the outcome depends upon the total mass of the planets. For M tot 1 MJ the final eccentricity distribution remains broad, whereas for M tot 1 MJ a combination of divergent orbital evolution and recircularization of scattered planets results in a preponderance of nearly circular final orbits. We also study the fate of marginally stable multiple planet systems in the presence of planetesimal disks, and find that for high planet masses the majority of such systems evolve into resonance. A significant fraction leads to resonant chains that are planetary analogs of Jupiter's Galilean satellites. We predict that a transition from eccentric to near-circular orbits will be observed once extrasolar planet surveys detect sub-Jovian mass planets at orbital radii of a 5-10 AU.

Evolution of Debris Disks

Circumstellar dust exists around several hundred main sequence stars. For the youngest stars, that dust could be a remnant of the protoplanetary disk. Mostly it is inferred to be continuously replenished through collisions between planetesimals in belts analogous to the Solar System's asteroid and Kuiper belts, or in collisions between growing protoplanets. The evolution of a star's debris disk is indicative of the evolution of its planetesimal belts and may be influenced by planet formation processes, which can continue throughout the first gigayear as the planetary system settles to a stable configuration and planets form at large radii. Evidence for that evolution comes from infrared photometry of large numbers of debris disks, providing snapshots of the dust present at different evolutionary phases, as well as from images of debris disk structure. This review describes the theoretical framework within which debris disk evolution takes place and shows how that framework has been constrained by observations.

The Complete Census of 70 μm–Bright Debris Disks within “The Formation and Evolution of Planetary Systems”SpitzerLegacy Survey of Sun‐like Stars

We report detection of cool dust surrounding solar-type stars from observations performed as part of the Spitzer Legacy Science Program FEPS. From a sample of 328 stars having ages ~0.003-3 Gyr we have selected sources with 70 μm flux densities indicating excess in their SEDs above expected photospheric emission. Six strong excess sources are likely primordial circumstellar disks, remnants of the star formation process. Another 25 sources having ≥3 σ excesses are associated with dusty debris disks, generated by collisions within planetesimal belts that are possibly stirred by existing planets. Six additional sources with ≥2 σ excesses require confirmation as debris disks. In our analysis, most (>80%) 70 μm excess sources have ≥3 σ excesses at 33 μm as well, while only a minority ( 1/3 of the debris sources we find that multiple temperature components are suggested, implying a dust distribution extending over many tens of AU. Because the disks are dominated by collisional processes, the parent body (planetesimal) belts may be extended as well. Preliminary assessment of the statistics of cold debris around Sun-like stars shows that ~10% of FEPS targets with masses between 0.6 and 1.8 M☉ and ages between 30 Myr and 3 Gyr exhibit excess 70 μm emission. We find that fractional excess amplitudes appear higher for younger stars and that there may be a trend in 70 μm excess frequency with stellar mass.

The total number of giant planets in debris discs with central clearings

Infrared spectra from the Spitzer Space Telescope (SSC) of many debris discs are well fit with a single blackbody temperature which suggest clearings within the disc. We assume that clearings are caused by orbital instability in multiple planet systems with similar configurations to our own. These planets remove dust-generating planetesimal belts as well as dust generated by the outer disc that is scattered or drifts into the clearing. From numerical integrations, we estimate a minimum planet spacing required for orbital instability (and so planetesimal and dust removal) as a function of system age and planet mass. We estimate that a 10 8 yr old debris disc with a dust disc edge at a radius of 50 au hosted by an A star must contain approximately five Neptune mass planets between the clearing radius and the iceline in order to remove all primordial objects within it. We infer that known debris disc systems contain at least a fifth of a Jupiter mass in massive planets. The number of planets and spacing required is insensitive to the assumed planet mass. However, an order of magnitude higher total mass in planets could reside in these systems if the planets are more massive.

Collisional velocities and rates in resonant planetesimal belts

We consider a belt of small bodies around a star, captured in one of the external or 1:1 mean-motion resonances with a massive perturber. The objects in the belt collide with each other. Combining methods of celestial mechanics and statistical physics, we calculate mean collisional velocities and collisional rates, averaged over the belt. The results are compared to collisional velocities and rates in a similar, but non-resonant belt, as predicted by the particle-in-a-box method. It is found that the effect of the resonant lock on the velocities is rather small, while on the rates more substantial. The collisional rates between objects in an external resonance are by about a factor of two higher than those in a similar belt of objects not locked in a resonance. For Trojans under the same conditions, the collisional rates may be enhanced by up to an order of magnitude. Our results imply, in particular, shorter collisional lifetimes of resonant Kuiper belt objects in the solar system and higher efficiency of dust production by resonant planetesimals in debris disks around other stars.

Steady State Evolution of Debris Disks around A Stars

In this paper a simple analytical model for the steady-state evolution of debris disks due to collisions is confronted with Spitzer observations of main sequence A stars. All stars are assumed to have planetesimal belts with a distribution of initial masses and radii. In the model disk mass is constant until the largest planetesimals reach collisional equilibrium whereupon the mass falls off oc 1/t. We find that the detection statistics and trends seen at both 24 and 70um can be fitted well by the model. While there is no need to invoke stochastic evolution or delayed stirring to explain the statistics, a moderate rate of stochastic events is not ruled out. Potentially anomalous systems are identified by a high dust luminosity compared with the maximum permissible in the model (HD3003, HD38678, HD115892, HD172555). Their planetesimals may have unusual properties (high strength or low eccentricity) or this dust could be transient. While transient phenomena are also favored for a few systems in the literature, the overall success of our model, which assumes planetesimals in all belts have the same strength, eccentricity and maximum size, suggests a large degree of uniformity in the outcome of planet formation. The distribution of planetesimal belt radii, once corrected for detection bias, follows N(r) oc r^{-0.8+-0.3} for 3-120AU. Since the inner edge is often attributed to an unseen planet, this provides a unique constraint on the planetary systems of A stars. It is also shown that P-R drag may sculpt the inner edges of A star disks close to the Spitzer detection threshold (HD2262, HD19356, HD106591, HD115892). This model can be readily applied to the interpretation of future surveys, and predictions are made for the upcoming SCUBA-2 survey, including that >17% of A stars should be detectable at 850um.

Debris Disks in Main‐Sequence Binary Systems

We observed 69 A3-F8 main sequence binary star systems using the Multiband Imaging Photometer for Spitzer onboard the Spitzer Space Telescope. We find emission significantly in excess of predicted photospheric flux levels for 9(+4/-3)% and 40(+7/-6)% of these systems at 24 and 70 microns, respectively. Twenty two systems total have excess emission, including four systems that show excess emission at both wavelengths. A very large fraction (nearly 60%) of observed binary systems with small (<3 AU) separations have excess thermal mission. We interpret the observed infrared excesses as thermal emission from dust produced by collisions in planetesimal belts. The incidence of debris disks around main sequence A3-F8 binaries is marginally higher than that for single old AFGK stars. Whatever combination of nature (birth conditions of binary systems) and nurture (interactions between the two stars) drives the evolution of debris disks in binary systems, it is clear that planetesimal formation is not inhibited to any great degree. We model these dust disks through fitting the spectral energy distributions and derive typical dust temperatures in the range 100--200 K and typical fractional luminosities around 10^-5, with both parameters similar to other Spitzer-discovered debris disks. Our calculated dust temperatures suggest that about half the excesses we observe are derived from circumbinary planetesimal belts and around one third of the excesses clearly suggest circumstellar material. Three systems with excesses have dust in dynamically unstable regions, and we discuss possible scenarios for the origin of this short-lived dust.

Transience of Hot Dust around Sun‐like Stars

In this paper a simple model for the steady state evolution of debris disks due to collisions is developed and confronted with the properties of the emerging population of seven Sun-like stars that have hot dust at 10 AU (η Corvi and HD 72905); one has three Neptune mass planets at <1 AU (HD 69830); all exhibit strong mid-IR silicate features. We consider the most likely origin for this transient dust to be a dynamical instability that scattered planetesimals inward from a more distant planetesimal belt in an event akin to the late heavy bombardment in our own system, the dust being released from such planetesimals in collisions and sublimation.

Dust distributions in debris disks: effects of gravity, radiation pressure and collisions

We model a typical debris disk, treated as an idealized ensemble of dust particles, exposed to stellar gravity and direct radiation pressure and experiencing fragmenting collisions. Applying the kinetic method of statistical physics, written in orbital elements, we calculate size and spatial distibutions expected in a steady-state disk, investigate timescales needed to reach the steady state, and calculate mass loss rates. Particular numerical examples are given for the debris disk around Vega. The disk should comprise a population of larger grains in bound orbits and a population of smaller particles in hyperbolic orbits. The cross section area is dominated by the smallest grains that still can stay in bound orbits, for Vega about 10 μm in radius. The size distribution is wavy, implying secondary peaks in the size distribution at larger sizes. The radial profile of the pole-on surface density or the optical depth in the steady-state disk has a power-law index between about - 1 and -2. It cannot be much steeper even if dust production is confined to a narrow planetesimal belt, because collisional grinding produces smaller and smaller grains, and radiation pressure pumps up their orbital eccentricities and spreads them outward, which flattens the radial profile. The timescales to reach a steady state depend on grain sizes and distance from the star. For Vega, they are about 1 Myr for grains up to some hundred μm at 100 AU. The total mass of the Vega disk needed to produce the observed amount of micron and submillimeter-sized dust does not exceed several earth masses for an upper size limit of parent bodies of about 1 km. The collisional depletion of the disk occurs on Gyr timescales.

First Two‐Micron Imaging Polarimetry of β Pictoris

High-resolution K-band imaging polarimetry of the β Pic dust disk has been conducted with adaptive optics and a coronagraph using the Subaru 8.2 m telescope. Polarization of ~10% is detected out to r ~ 120 AU with a centrosymmetric vector pattern around the central star, confirming that the disk is seen as an infrared reflection nebula. We have modeled our near-infrared and previous optical polarization results in terms of dust scattering in the disk and have found that both the degrees of polarization and the radial intensity profiles are well reproduced. We argue that the observed characteristics of the disk dust are consistent with the presence of ice-filled fluffy aggregates consisting of submicron grains in the β Pic system. There is a gap around 100 AU in both the intensity and polarization profiles, which suggests a paucity of planetesimals in this region. The radial intensity profile also shows ripple-like structures, which are indicative of the presence of multiple planetesimal belts, as in the case of the M-type Vega-like star AU Mic.

Formation and Evolution of Planetary Systems: Cold Outer Disks Associated with Sun‐like Stars

We present the discovery of debris systems around three solar mass stars based upon observations performed with the Spitzer Space Telescope as part of a Legacy Science Program, ``the Formation and Evolution of Planetary Systems'' (FEPS). We also confirm the presence of debris around two other stars. All the stars exhibit infrared emission in excess of the expected photospheres in the 70 micron band, but are consistent with photospheric emission at <= 33 micron. This restricts the maximum temperature of debris in equilibrium with the stellar radiation to T < 70 K. We find that these sources are relatively old in the FEPS sample, in the age range 0.7 - 3 Gyr. Based on models of the spectral energy distributions, we suggest that these debris systems represent materials generated by collisions of planetesimal belts. We speculate on the nature of these systems through comparisons to our own Kuiper Belt, and on the likely planet(s) responsible for stirring the system and ultimately releasing dust through collisions. We further report observations of a nearby star HD 13974 (d =11 pc) that is indistinguishable from a bare photosphere at both 24 micron and 70 micron. The observations place strong upper limits on the presence of any cold dust in this nearby system (L_IR/L_* < 10^{-5.2}).

THE LATEST RESULTS FROM SUBARU TELESCOPE

The latest scientific highlights obtained with the Subaru telescope are given together with its current status and on-going instrumentation. We have been successfully operating the telescope and 8 observatory instruments (including an adaptive optics system) since January 1999, when the first light was accomplished. Open-use of Subaru began in December 2000. Subaru has a unique capability of its prime focus among other 8-10 meter class telescopes and has an excellent imaging performance as a result of its sophisticated active optics combined with the high stability of the sky at Mauna Kea. Scientific highlights are given on the discoveries of the most distant galaxies, spiral structure on a protoplanetary disk around AB Aur, and planetesimal belts in the debris disk around <TEX>$\beta$</TEX> Pic. Brief summaries are given for three new instruments: the Multi-Object Infrared Camera and Spectrograph (MOIRCS), 188 element adaptive optics system, and Fiber Multi-Object Spectrograph (FMOS)