Steady-State Size Distribution for the Self-Similar Collision Cascade

Tanaka, Hidekazu; Inaba, Satoshi; Nakazawa, Kiyoshi

doi:10.1006/icar.1996.0170

Cited by 204 publications

(202 citation statements)

References 1 publication

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“…Since Q * D is independent of M proj , the differential number density is proportional to M −11/6 with M being grain mass . This mass dependence is the same as the classical theory of collisional cascade (Dohnanyi 1969;Tanaka et al 1996). For protoplanetary disks, u col is not determined as simply as that for debris disks.…”

Section: Total Ejecta Massmentioning

confidence: 90%

Growth efficiency of dust aggregates through collisions with high mass ratios

Wada

Tanaka

Okuzumi

et al. 2013

A&A

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170

198

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Context. Collisional growth of dust aggregates is an essential process in forming planetesimals in protoplanetary disks, but disruption through high-velocity collisions (disruption barrier) could prohibit the dust growth. Mass transfer through very different-sized collisions has been suggested as a way to circumvent the disruption barrier. Aims. We examine how the collisional growth efficiency of dust aggregates with different impact parameters depends on the size and the mass ratio of colliding aggregates. Methods. We used an N-body code to numerically simulate the collisions of different-sized aggregates. Results. Our results show that high values for the impact parameter are important and that the growth efficiency averaged over the impact parameter does not depend on the aggregate size, although the growth efficiency for nearly head-on collisions increases with size. We also find that the averaged growth efficiency tends to increase with increasing mass ratio of colliding aggregates. However, the critical collision velocity, above which the growth efficiency becomes negative, does not strongly depend on the mass ratio. These results indicate that icy dust can grow through high-velocity offset collisions at several tens of m s −1 , the maximum collision velocity experienced in protoplanetary disks, whereas it is still difficult for silicate dust to grow in protoplanetary disks.

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Section: Total Ejecta Massmentioning

confidence: 90%

Growth efficiency of dust aggregates through collisions with high mass ratios

Wada

Tanaka

Okuzumi

et al. 2013

A&A

Self Cite

170

198

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“…(43). A collisional cascade yields a size distribution characterized by q ∼ 7/2 (Tanaka et al 1996). (This corresponds to a mass distribution dN/dM p ∝ M −11/6 p .)…”

Section: Planetesimal Size Distribution and Filtering Massmentioning

confidence: 99%

On the filtering and processing of dust by planetesimals

Guillot

Ida

Ormel

2014

A&A

141

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Context. Circumstellar disks are known to contain a significant mass in dust ranging from micron to centimeter size. Meteorites are evidence that individual grains of those sizes were collected and assembled into planetesimals in the young solar system. Aims. We assess the efficiency of dust collection of a swarm of non-drifting planetesimals with radii ranging from 1 to 10 3 km and beyond. Methods. We calculate the collision probability of dust drifting in the disk due to gas drag by planetesimal accounting for several regimes depending on the size of the planetesimal, dust, and orbital distance: the geometric, Safronov, settling, and three-body regimes. We also include a hydrodynamical regime to account for the fact that small grains tend to be carried by the gas flow around planetesimals. Results. We provide expressions for the collision probability of dust by planetesimals and for the filtering efficiency by a swarm of planetesimals. For standard turbulence conditions (i.e., a turbulence parameter α = 10 −2 ), filtering is found to be inefficient, meaning that when crossing a minimum-mass solar nebula (MMSN) belt of planetesimals extending between 0.1 AU and 35 AU most dust particles are eventually accreted by the central star rather than colliding with planetesimals. However, if the disk is weakly turbulent (α = 10 −4 ) filtering becomes efficient in two regimes: (i) when planetesimals are all smaller than about 10 km in size, in which case collisions mostly take place in the geometric regime; and (ii) when planetary embryos larger than about 1000 km in size dominate the distribution, have a scale height smaller than one tenth of the gas scale height, and dust is of millimeter size or larger in which case most collisions take place in the settling regime. These two regimes have very different properties: we find that the local filtering efficiency x filter,MMSN scales with r −7/4 (where r is the orbital distance) in the geometric regime, but with r −1/4 to r 1/4 in the settling regime. This implies that the filtering of dust by small planetesimals should occur close to the central star and with a short spread in orbital distances. On the other hand, the filtering by embryos in the settling regime is expected to be more gradual and determined by the extent of the disk of embryos. Dust particles much smaller than millimeter size tend only to be captured by the smallest planetesimals because they otherwise move on gas streamlines and their collisions take place in the hydrodynamical regime. Conclusions. Our results hint at an inside-out formation of planetesimals in the infant solar system because small planetesimals in the geometrical limit can filter dust much more efficiently close to the central star. However, even a fully-formed belt of planetesimals such as the MMSN only marginally captures inward-drifting dust and this seems to imply that dust in the protosolar disk has been filtered by planetesimals even smaller than 1 km (not included in this study) or that it has been assembled into planetesi...

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“…Written in this form, it was assumed that the disc contains a Dohnanyi size distribution of bodies (Dohnanyi 1969), with a power index of 7 2 (Tanaka et al 1996) between the smallest size body that is not blown out of the system by radiation pressure and the significantly larger maximum size for bodies in the disc, D max . The mass is dominated by the largest bodies.…”

Section: The Survival Timescale Of Massive Outer Beltsmentioning

confidence: 99%

“…Although model dependant, detailed numerical modelling (e.g. Thébault et al 2003;Thébault & Augereau 2007;Krivov et al 2006;Löhne et al 2008) finds that the ratio of the total mass of the disc to the observed dust mass calculated using realistic size distributions does not differ significantly from simplistic estimates made using the size distribution from a steady state collisional cascade (n(D)dD ∝ D 7/2 dD, Dohnanyi 1969, with a power index of 7 2 , Tanaka et al 1996). Thus, the calculated values for the mass should not vary too dramatically.…”

Section: Uncertaintiesmentioning

confidence: 99%

Scattering of small bodies by planets: a potential origin for exozodiacal dust?

Bonsor

Augereau

Thébault

2012

A&A

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High levels of exozodiacal dust are observed around a growing number of main sequence stars. The origin of such dust is not clear, given that it has a short lifetime against both collisions and radiative forces. Even a collisional cascade with km-sized parent bodies, as suggested to explain outer debris discs, cannot survive sufficiently long. In this work we investigate whether the observed exozodiacal dust could originate from an outer planetesimal belt. We investigate the scattering processes in stable planetary systems to determine whether sufficient material could be scattered inwards in order to retain the exozodiacal dust at its currently observed levels. We use N-body simulations to investigate the efficiency of this scattering and its dependence on the architecture of the planetary system. The results of these simulations can be used to assess the ability of hypothetical chains of planets to produce exozodi in observed systems. We find that for older (>100 Myr) stars with exozodiacal dust, a massive, large radii (>20 AU) outer belt and a chain of tightly packed, low-mass planets would be required to retain the dust at its currently observed levels. This brings into question how many, if any, real systems possess such a contrived architecture and are therefore capable of scattering at sufficiently high rates to retain exozodi dust on long timescales.

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Steady-State Size Distribution for the Self-Similar Collision Cascade

Cited by 204 publications

References 1 publication

Growth efficiency of dust aggregates through collisions with high mass ratios

Growth efficiency of dust aggregates through collisions with high mass ratios

On the filtering and processing of dust by planetesimals

Scattering of small bodies by planets: a potential origin for exozodiacal dust?

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