Closed-form expressions for particle relative velocities induced by turbulence

Ormel, Chris W.; Cuzzi, Jeffrey N.

doi:10.1051/0004-6361:20066899

Cited by 427 publications

(525 citation statements)

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“…We therefore focus on the intermediate velocity regime. In particular, the relative velocity between two equal solid spheres of 1 < τ 0 /t s < Re 1/2 is (Ormel & Cuzzi 2007) , where n d is the dust number density and R gd = 100 is the standard gas-to-dust density ratio by mass.…”

Section: Discussionmentioning

confidence: 99%

“…Then, the surface area-to-mass ratio of the dust particles is of critical importance since this quantity determines the amount of coupling between the dust particles and the gas. We use the analytic approximations of Ormel & Cuzzi (2007) for the relative velocity between two particles. These expressions only include contributions that arise as a result of the particle's inertia in a turbulent velocity field and do not contain contributions that arise from gyroresonance acceleration (see, e.g., Yan et al 2004).…”

Section: Working Modelmentioning

confidence: 99%

“…Völk et al (1980) have pioneered a study to statistically account for the collective effects of all eddies by dividing the eddies into two classes -"strong" and "weak" -depending on the turn-over time of the eddy with respect to the particle friction time. Ormel & Cuzzi (2007) approximated the framework of Völk et al (1980) and Markiewicz et al (1991) to provide closed-form expressions for the relative motion between two solid particles. In general three regimes can be distinguished:…”

Section: Appendix A: Analytical Backgroundmentioning

confidence: 99%

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Dust coagulation and fragmentation in molecular clouds

Ormel¹,

Paszun²,

Dominik³

et al. 2009

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248

337

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The cores in molecular clouds are the densest and coldest regions of the interstellar medium (ISM). In these regions ISM-dust grains have the potential to coagulate. This study investigates the collisional evolution of the dust population by combining two models: a binary model that simulates the collision between two aggregates and a coagulation model that computes the dust size distribution with time. In the first, results from a parameter study quantify the outcome of the collision -sticking, fragmentation (shattering, breakage, and erosion) -and the effects on the internal structure of the particles in tabular format. These tables are then used as input for the dust evolution model, which is applied to an homogeneous and static cloud of temperature 10 K and gas densities between 10 3 and 10 7 cm −3 . The coagulation is followed locally on timescales of ∼10 7 yr. We find that the growth can be divided into two stages: a growth dominated phase and a fragmentation dominated phase. Initially, the mass distribution is relatively narrow and shifts to larger sizes with time. At a certain point, dependent on the material properties of the grains as well as on the gas density, collision velocities will become sufficiently energetic to fragment particles, halting the growth and replenishing particles of lower mass. Eventually, a steady state is reached, where the mass distribution is characterized by a mass spectrum of approximately equal amount of mass per logarithmic size bin. The amount of growth that is achieved depends on the cloud's lifetime. If clouds exist on free-fall timescales the effects of coagulation on the dust size distribution are very minor. On the other hand, if clouds have long-term support mechanisms, the impact of coagulation is important, resulting in a significant decrease of the opacity on timescales longer than the initial collision timescale between big grains.

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Section: Discussionmentioning

confidence: 99%

Section: Working Modelmentioning

confidence: 99%

Section: Appendix A: Analytical Backgroundmentioning

confidence: 99%

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Dust coagulation and fragmentation in molecular clouds

Ormel¹,

Paszun²,

Dominik³

et al. 2009

A&A

Self Cite

248

337

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“…For protoplanetary disks, u col is not determined as simply as that for debris disks. Collisions between small particles have u col u col,crit , while u col is close to u col,crit for collisions with large particles (e.g., Ormel & Cuzzi 2007).…”

Section: Total Ejecta Massmentioning

confidence: 97%

Growth efficiency of dust aggregates through collisions with high mass ratios

Wada

Tanaka

Okuzumi

et al. 2013

A&A

165

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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“…We have used a simple analytical model derived by Blum (2004), and checked by Ormel et al (2009), who compared it with their Monte Carlo simulation and demonstrated it is valid for average molecular cloud conditions, with densities of 10 5 cm −3 , temperature of 10 K, and at intermediate velocity regimes 2 (Ossenkopf 1993;Ormel et al 2009;Ormel & Cuzzi 2007). The analytical model is based on the assumption of a monodisperse distribution of spherical particles.…”

Section: A Simple Analytical Modelmentioning

confidence: 99%

Search for grain growth toward the center of L1544

Chacón-Tanarro

Caselli

Bizzocchi

et al. 2017

A&A

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In dense and cold molecular clouds dust grains are surrounded by thick icy mantles. It is however not clear if dust growth and coagulation take place before the switch-on of a protostar. This is an important issue, as the presence of large grains may affect the chemical structure of dense cloud cores, including the dynamically important ionization fraction, and the future evolution of solids in protoplanetary disks. To study this further, we focus on L1544, one of the most centrally concentrated pre-stellar cores on the verge of star formation, and with a well-known physical structure. We observed L1544 at 1.2 and 2 mm using NIKA, a new receiver at the IRAM 30 m telescope, and we used data from the Herschel Space Observatory archive. We find no evidence of grain growth towards the center of L1544 at the available angular resolution. Therefore, we conclude that single dish observations do not allow us to investigate grain growth toward the pre-stellar core L1544 and high sensitivity interferometer observations are needed. We predict that dust grains can grow to 200 µm in size toward the central ∼300 au of L1544. This will imply a dust opacity change by a factor of ∼2.5 at 1.2 mm, which can be detected using the Atacama Large Millimeter and submillimeter Array (ALMA) at different wavelengths and with an angular resolution of 2 .

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Closed-form expressions for particle relative velocities induced by turbulence

Cited by 427 publications

References 10 publications

Dust coagulation and fragmentation in molecular clouds

Dust coagulation and fragmentation in molecular clouds

Growth efficiency of dust aggregates through collisions with high mass ratios

Search for grain growth toward the center of L1544

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