Resonant Trapping of Planetesimals by Planet Migration: Debris Disk Clumps and Vega's Similarity to the Solar System

This paper describes a model which can explain the observed clumpy structures of debris disks. Clumps arise because after a planetary system forms its planets migrate due to angular momentum exchange with the remaining planetesimals. Outward migration of the outermost planet traps planetesimals outside its orbit into its resonances and resonant forces cause azimuthal structure in their distribution. The model is based on numerical simulations of planets of different masses, Mpl, migrating at different rates, dapl/dt, through a dynamically cold (e<0.01) planetesimal disk initially at a semimajor axis a. Trapping probabilities and the resulting azimuthal structures are presented for a planet's 2:1, 5:3, 3:2, and 4:3 resonances. Seven possible dynamical structures are identified from migrations defined by mu=Mpl/Mstar and theta=dapl/dt*sqrt(a/Mstar). Application of this model to the 850um image of Vega's disk shows its two clumps of unequal brightness can be explained by the migration of a Neptune-mass planet from 40 to 65AU over 56Myr; tight constraints are set on possible ranges of these parameters. The clumps are caused by planetesimals in the 3:2 and 2:1 resonances; the asymmetry arises because of the overabundance of planetesimals in the 2:1(u) over the 2:1(l) resonance. The similarity of this migration to that proposed for our own Neptune hints that Vega's planetary system may be much more akin to the solar system than previously thought. Predictions are made which would substantiate this model, such as the orbital motion of the clumpy pattern, the location of the planet, and the presence of lower level clumps.Comment: 30 pages, accepted by Ap

Do Two Temperature Debris Disks Have Multiple Belts?

We present a study of debris disks whose spectra are well modelled by dust emission at two different temperatures. These disks are typically assumed to be a sign of multiple belts, which in only a few cases have been confirmed via high resolution observations. We first compile a sample of two-temperature disks to derive their properties, summarised by the ratios of the warm and cool component temperatures and fractional luminosities. The ratio of warm to cool temperatures is constant in the range 2-4, and the temperatures of both warm and cool components increases with stellar mass. We then explore whether this emission can arise from dust in a single narrow belt, with the range of temperatures arising from the size variation of grain temperatures. This model can produce two-temperature spectra for Sun-like stars, but is not supported where it can be tested by observed disk sizes and far-IR/mm spectral slopes. Therefore, while some two-temperature disks arise from single belts, it is probable that most have multiple spatial components. These disks are plausibly similar to the outer Solar System's configuration of Asteroid and Edgeworth-Kuiper belts separated by giant planets. Alternatively, the inner component could arise from inward scattering of material from the outer belt, again due to intervening planets. In either case, we suggest that the ratio of warm/cool component temperatures is indicative of the scale of outer planetary systems, which typically span a factor of about ten in radius.Comment: accepted to MNRA

Collisional Processes in Extrasolar Planetsimal Disks - Dust Clumps in Fomalhaut's Debris Disk

This paper presents a model for the outcome of collisions between planetesimals in a debris disk and assesses the impact of collisional processes on the structure and size distribution of the disk. The model is presented by its application to Fomalhaut's collisionally replenished dust disk; a recent 450 micron image of this disk shows a clump embedded within it with a flux ~5 per cent of the total. The following conclusions are drawn: (i) SED modelling is consistent with Fomalhaut's disk having a collisional cascade size distribution extending from bodies 0.2 m in diameter down to 7 micron-sized dust. (ii) Collisional lifetime arguments imply that the cascade starts with planetesimals 1.5-4 km in diameter. Any larger bodies must be predominantly primordial. (iii) Constraints on the timescale for the ignition of the cascade are consistent with these primordial planetesimals having a distribution that extends up to 1000km, resulting in a disk mass of 5-10 times the minimum mass solar nebula. (iv) The debris disk is expected to be intrinsically clumpy, since planetesimal collisions result in dust clumps. The intrinsic clumpiness of Fomalhaut's disk is below current detection limits, but could be detectable by future observatories such as the ALMA, and could provide the only way of determining the primordial planetesimal population. (v) The observed clump could have originated in a collision between two runaway planetesimals, both larger than 1400 km diameter. It is unlikely that we should witness such an event unless both the formation of these runaways and the ignition of the collisional cascade occurred within the last ~10 Myr. (vi) Another explanation for Fomalhaut's clump is that ~5 per cent of the planetesimals in the ring are trapped in 1:2 resonance with a planet orbiting at 80 AU.Comment: 21 pages, 13 figures, accepted by MNRA

The Insignificance of P-R Drag in Detectable Extrasolar Planetesimal Belts

This paper considers a simple model in which dust produced in a planetesimal belt migrates in toward the star due to P-R drag suffering destructive collisions with other dust grains on the way. Assuming the dust is all of the same size, the resulting surface density distribution can be derived analytically and depends only on the parameter eta0=5000tau*sqrt(Mstar/r)/beta; this parameter can be determined observationally with the hypothesis that beta=0.5. For massive belts in which eta0>>1 dust is confined to the planetesimal belt, while the surface density of more tenuous belts, in which eta0<<1, is constant with distance from the star. The emission spectrum of dust from planetesimal belts at different distances from different mass stars shows that the dust belts which have been detected to date should have eta0>>1; dust belts with eta0<<1 are hard to detect as they are much fainter than the stellar photosphere. This is confirmed for a sample of 37 debris disk candidates for which eta0 was determined to be >10. This means that these disks are so massive that mutual collisions prevent dust from reaching the inner regions of these systems and P-R drag can be ignored when studying their dynamics. Models for the formation of structure in debris disks by the trapping of particles into planetary resonances by P-R drag should be reconsidered. However, since collisions do not halt 100% of the dust, this means that in the absence of planetary companions debris disk systems should be populated by small quantities of hot dust which may be detectable in the mid-IR. Even in disks with eta0<<1 the temperature of dust emission is shown to be a reliable tracer of the planetesimal distribution meaning that inner holes in the dust distribution imply a lack of colliding planetesimals in the inner regions.Comment: 6 pages. Accepted by A&

Resolving the terrestrial planet forming regions of HD113766 and HD172555 with MIDI

We present new MIDI interferometric and VISIR spectroscopic observations of HD113766 and HD172555. Additionally we present VISIR 11um and 18um imaging observations of HD113766. These sources represent the youngest (16Myr and 12Myr old respectively) debris disc hosts with emission on <<10AU scales. We find that the disc of HD113766 is partially resolved on baselines of 42-102m, with variations in resolution with baseline length consistent with a Gaussian model for the disc with FWHM of 1.2-1.6AU (9-12mas). This is consistent with the VISIR observations which place an upper limit of 0."14 (17AU) on the emission, with no evidence for extended emission at larger distances. For HD172555 the MIDI observations are consistent with complete resolution of the disc emission on all baselines of lengths 56-93m, putting the dust at a distance of >1AU (>35mas). When combined with limits from TReCS imaging the dust at ~10um is constrained to lie somewhere in the region 1-8AU. Observations at ~18um reveal extended disc emission which could originate from the outer edge of a broad disc, the inner parts of which are also detected but not resolved at 10um, or from a spatially distinct component. These observations provide the most accurate direct measurements of the location of dust at 1-8AU that might originate from the collisions expected during terrestrial planet formation. These observations provide valuable constraints for models of the composition of discs at this epoch and provide a foundation for future studies to examine in more detail the morphology of debris discs.Comment: 22 pages, 19 figures, accepted for publication in MNRA