Variations on Debris Disks: Icy Planet Formation at 30-150 AU for 1-3 M☉ Main-Sequence Stars
TL;DR: In this article, the authors describe the formation of icy planets and debris disks at 30-150 AU around 1-3 M☉ stars and show that collisional cascades produce debris disks with maximum luminosity 2 × 10−3 times the stellar luminosity.
Abstract: We describe calculations for the formation of icy planets and debris disks at 30-150 AU around 1-3 M☉ stars. Debris disk formation coincides with the formation of planetary systems. As protoplanets grow, they stir leftover planetesimals to large velocities. A cascade of collisions then grinds the leftovers to dust, forming an observable debris disk. Stellar lifetimes and the collisional cascade limit the growth of protoplanets. The maximum radius of icy planets, -->rmax ≈ 1750 km, is remarkably independent of initial disk mass, stellar mass, and stellar age. These objects contain 3%-4% of the initial mass in solid material. Collisional cascades produce debris disks with maximum luminosity ~ -->2 × 10−3 times the stellar luminosity. The peak 24 μm excess varies from ~1% times the stellar photospheric flux for 1 M☉ stars to ~50 times the stellar photospheric flux for 3 M☉ stars. The peak 70-850 μm excesses are ~30-100 times the stellar photospheric flux. For all stars, the 24-160 μm excesses rise at stellar ages of 5-20 Myr, peak at 10-50 Myr, and then decline. The decline is roughly a power law, -->f t−n with -->n ≈ 0.6–1.0. This predicted evolution agrees with published observations of A-type and solar-type stars. The observed far-IR color evolution of A-type stars also matches model predictions.
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TL;DR: In this paper, it was shown that the outer regions of planetary systems, where the mass required to halt pebble accretion is large, are dominated by ice giants and that gas-giant exoplanets in wide orbits are enriched by more than 50 Earth masses of solids.
Abstract: In the solar system giant planets come in two flavours: gas giants (Jupiter and Saturn) with massive gas envelopes, and ice giants (Uranus and Neptune) with much thinner envelopes around their cores. It is poorly understood how these two classes of planets formed. High solid accretion rates, necessary to form the cores of giant planets within the life-time of protoplanetary discs, heat the envelope and prevent rapid gas contraction onto the core, unless accretion is halted. We find that, in fact, accretion of pebbles (similar to cm sized particles) is self-limiting: when a core becomes massive enough it carves a gap in the pebble disc. This halt in pebble accretion subsequently triggers the rapid collapse of the super-critical gas envelope. Unlike gas giants, ice giants do not reach this threshold mass and can only bind low-mass envelopes that are highly enriched by water vapour from sublimated icy pebbles. This offers an explanation for the compositional difference between gas giants and ice giants in the solar system. Furthermore, unlike planetesimal-driven accretion scenarios, our model allows core formation and envelope attraction within disc life-times, provided that solids in protoplanetary discs are predominantly made up of pebbles. Our results imply that the outer regions of planetary systems, where the mass required to halt pebble accretion is large, are dominated by ice giants and that gas-giant exoplanets in wide orbits are enriched by more than 50 Earth masses of solids.
404 citations
TL;DR: In this article, photometry at 3-24?m for all known members of the Upper Scorpius association (? ~ 11 Myr) is presented based on all images of these objects obtained with the Spitzer Space Telescope and the Wide-field Infrared Survey Explorer.
Abstract: We present photometry at 3-24 ?m for all known members of the Upper Scorpius association (? ~ 11 Myr) based on all images of these objects obtained with the Spitzer Space Telescope and the Wide-field Infrared Survey Explorer. We have used these data to identify the members that exhibit excess emission from circumstellar disks and estimate the evolutionary stages of these disks. Through this analysis, we have found ~50 new candidates for transitional, evolved, and debris disks. The fraction of members harboring inner primordial disks is 10% for B-G stars (M > 1.2 M ?) and increases with later types to a value of ~25% at M5 (M 0.2 M ?), in agreement with the results of previous disk surveys of smaller samples of Upper Sco members. These data indicate that the lifetimes of disks are longer at lower stellar masses and that a significant fraction of disks of low-mass stars survive for at least ~10 Myr. Finally, we demonstrate that the distribution of excess sizes in Upper Sco and the much younger Taurus star-forming region (? ~ 1 Myr) is consistent with the same, brief timescale for clearing of inner disks.
286 citations
Cites background from "Variations on Debris Disks: Icy Pla..."
...For instance, Carpenter et al. (2009) found that the rapid decrease in [24] fraction from A to B stars is expected because of increased ejection of dust grains by radiation pressure (see also Kenyon & Bromley 2008)....
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TL;DR: In this article, the authors derived an analytic description of the dynamical outcome for any collision between gravity-dominated bodies and derived equations (scaling laws) to demarcate the transition between collision regimes and to describe the size and velocity distributions of the post-collision bodies.
Abstract: Collisions are the core agent of planet formation. In this work, we derive an analytic description of the dynamical outcome for any collision between gravity-dominated bodies. We conduct high-resolution simulations of collisions between planetesimals; the results are used to isolate the effects of different impact parameters on collision outcome. During growth from planetesimals to planets, collision outcomes span multiple regimes: cratering, merging, disruption, super-catastrophic disruption, and hit-and-run events. We derive equations (scaling laws) to demarcate the transition between collision regimes and to describe the size and velocity distributions of the post-collision bodies. The scaling laws are used to calculate maps of collision outcomes as a function of mass ratio, impact angle, and impact velocity, and we discuss the implications of the probability of each collision regime during planet formation. Collision outcomes are described in terms of the impact conditions and the catastrophic disruption criteria, Q*RD—the specific energy required to disperse half the total colliding mass. All planet formation and collisional evolution studies have assumed that catastrophic disruption follows pure energy scaling; however, we find that catastrophic disruption follows nearly pure momentum scaling. As a result, Q*RD is strongly dependent on the impact velocity and projectile-to-target mass ratio in addition to the total mass and impact angle. To account for the impact angle, we derive the interacting mass fraction of the projectile; the outcome of a collision is dependent on the kinetic energy of the interacting mass rather than the kinetic energy of the total mass. We also introduce a new material parameter, c*, that defines the catastrophic disruption criteria between equal-mass bodies in units of the specific gravitational binding energy. For a diverse range of planetesimal compositions and internal structures, c* has a value of 5 ± 2; whereas for strengthless planets, we find c* = 1.9 ± 0.3. We refer to the catastrophic disruption criteria for equal-mass bodies as the principal disruption curve, which is used as the reference value in the calculation of Q*RD for any collision scenario. The analytic collision model presented in this work will significantly improve the physics of collisions in numerical simulations of planet formation and collisional evolution.
284 citations
TL;DR: In this article, a catalog of excess spectra for unresolved debris disks is presented, including 64 new IRAS and Multiband Imaging Photometer for Spitzer (MIPS) debris disks candidates.
Abstract: During the Spitzer Space Telescope cryogenic mission, Guaranteed Time Observers, Legacy Teams, and General Observers obtained Infrared Spectrograph (IRS) observations of hundreds of debris disk candidates. We calibrated the spectra of 571 candidates, including 64 new IRAS and Multiband Imaging Photometer for Spitzer (MIPS) debris disks candidates, modeled their stellar photospheres, and produced a catalog of excess spectra for unresolved debris disks. For 499 targets with IRS excess but without strong spectral features (and a subset of 420 targets with additional MIPS 70 μm observations), we modeled the IRS (and MIPS data) assuming that the dust thermal emission was well-described using either a one- or two-temperature blackbody model. We calculated the probability for each model and computed the average probability to select among models. We found that the spectral energy distributions for the majority of objects (~66%) were better described using a two-temperature model with warm (T gr ~ 100-500 K) and cold (T gr ~ 50-150 K) dust populations analogous to zodiacal and Kuiper Belt dust, suggesting that planetary systems are common in debris disks and zodiacal dust is common around host stars with ages up to ~1 Gyr. We found that younger stars generally have disks with larger fractional infrared luminosities and higher grain temperatures and that higher-mass stars have disks with higher grain temperatures. We show that the increasing distance of dust around debris disks is inconsistent with self-stirred disk models, expected if these systems possess planets at 30-150 AU. Finally, we illustrate how observations of debris disks may be used to constrain the radial dependence of material in the minimum mass solar nebula.
254 citations
TL;DR: In this paper, a full suite of Spitzer observations were used to characterize the debris disk around HR 8799 and explore how its properties are related to the recently discovered set of three massive planets orbiting the star.
Abstract: We have obtained a full suite of Spitzer observations to characterize the debris disk around HR 8799 and to explore how its properties are related to the recently discovered set of three massive planets orbiting the star. We distinguish three components to the debris system: (1) warm dust (T ~ 150 K) orbiting within the innermost planet; (2) a broad zone of cold dust (T ~ 45 K) with a sharp inner edge orbiting just outside the outermost planet and presumably sculpted by it; and (3) a dramatic halo of small grains originating in the cold dust component. The high level of dynamical activity implied by this halo may arise due to enhanced gravitational stirring by the massive planets. The relatively young age of HR 8799 places it in an important early stage of development and may provide some help in understanding the interaction of planets and planetary debris, an important process in the evolution of our own solar system.
250 citations
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5,246 citations
"Variations on Debris Disks: Icy Pla..." refers methods in this paper
...…a simple relation for the median size rmax of the largest object as a function of initial disk mass and semimajor axis, we adopt a simple function rmax(a) = r0 e −(ai/a0)αr (29) and use an amoeba algorithm (Press et al. 1992) to derive the fitting parameters a0, r0, and αr as a function of time....
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TL;DR: Protostars and Planets VI brings together more than 250 contributing authors at the forefront of their field, conveying the latest results in this research area and establishing a new foundation for advancing our understanding of stellar and planetary formation as mentioned in this paper.
4,461 citations
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"Variations on Debris Disks: Icy Pla..." refers background or methods in this paper
...For velocity damping from gas drag, we follow Wetherill & Stewart (1993) and write dhgd,ik dt = −βik πCD 2mik ρgasV 2 gasr 2 ik, (10) and dvgd,ik dt = −(1 − βik) πCD 2mik ρgasV 2 gasr 2 ik, (11) where CD = 0.5 is the drag coefficient, βik = hik/(h 2 ik + v 2 ik) 1/2, ρgas is the gas density, η is the relative gas velocity, and Vgas = (Vik(Vik + η)) 1/2 is the mean relative velocity of the gas (see Adachi et al. 1976; Weidenschilling 1977b; Wetherill & Stewart 1993)....
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...For dust grains with sizes & 10 µm, the collision time is much shorter than the time to remove particles by gas drag (Adachi et al. 1976) or by Poynting-Robertson drag (Burns, Lamy, & Soter 1979)....
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...For a 1 M⊙ central star, models with Σ0 ≈ 0.1–0.2 g cm−2 at a0 = 30 AU have a mass in icy solids comparable to the minimum mass solar nebula (MMSN hereafter; Weidenschilling 1977a; Hayashi 1981)....
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...…ρgasV 2 gasr 2 ik, (11) where CD = 0.5 is the drag coefficient, βik = hik/(h 2 ik + v 2 ik) 1/2, ρgas is the gas density, η is the relative gas velocity, and Vgas = (Vik(Vik + η)) 1/2 is the mean relative velocity of the gas (see Adachi et al. 1976; Weidenschilling 1977b; Wetherill & Stewart 1993)....
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