A dearth of small particles in debris disks: An energy-constrained smallest fragment size

A prescription for the fragment size distribution resulting from dust grain collisions is essential when modelling a range of astrophysical systems, such as debris disks and planetary rings. While the slope of the fragment size distribution and the size of the largest fragment are well known, the behaviour of the distribution at the small size end is theoretically and experimentally poorly understood. This leads debris disk codes to generally assume a limit equal to, or below, the radiation blow-out size. We use energy conservation to analytically derive a lower boundary of the fragment size distribution for a range of collider mass ratios. Focussing on collisions between equal-sized bodies, we apply the method to debris disks. For a given collider mass, the size of the smallest fragments is found to depend on collision velocity, material parameters, and the size of the largest fragment. We provide a physically motivated recipe for the calculation of the smallest fragment, which can be easily implemented in codes for modelling collisional systems. For plausible parameters, our results are consistent with the observed predominance of grains much larger than the blow-out size in Fomalhaut's main belt and in the Herschel cold debris disks.Comment: 5 pages, 3 figures, Accepted for publication as a Letter in Astronomy & Astrophysic

Erosion of dust aggregates

Aims: The aim of this work is to gain a deeper insight into how much different aggregate types are affected by erosion. Especially, it is important to study the influence of the velocity of the impacting projectiles. We also want to provide models for dust growth in protoplanetary disks with simple recipes to account for erosion effects. Methods: To study the erosion of dust aggregates we employed a molecular dynamics approach that features a detailed micro-physical model of the interaction of spherical grains. For the first time, the model has been extended by introducing a new visco-elastic damping force which requires a proper calibration. Afterwards, different sample generation methods were used to cover a wide range of aggregate types. Results: The visco-elastic damping force introduced in this work turns out to be crucial to reproduce results obtained from laboratory experiments. After proper calibration, we find that erosion occurs for impact velocities of 5 m/s and above. Though fractal aggregates as formed during the first growth phase are most susceptible to erosion, we observe erosion of aggregates with rather compact surfaces as well. Conclusions: We find that bombarding a larger target aggregate with small projectiles results in erosion for impact velocities as low as a few m/s. More compact aggregates suffer less from erosion. With increasing projectile size the transition from accretion to erosion is shifted to higher velocities. This allows larger bodies to grow through high velocity collisions with smaller aggregates.Comment: accepted for publication in Astronomy & Astrophysic

A Lagrangian Model for Dust Evolution in Protoplanetary Disks: Formation of Wet and Dry Planetesimals at Different Stellar Masses

We introduce a new Lagrangian smooth-particle method to model the growth and drift of pebbles in protoplanetary disks. The Lagrangian nature of the model makes it especially suited to follow characteristics of individual (groups of) particles, such as their composition. In this work we focus on the water content of solid particles. Planetesimal formation via streaming instability is taken into account, partly based on previous results on streaming instability outside the water snowline that were presented in Schoonenberg & Ormel (2017). We validate our model by reproducing earlier results from the literature and apply our model to steady-state viscous gas disks (with constant gas accretion rate) around stars with different masses. We also present various other models where we explore the effects of pebble accretion, the fragmentation velocity threshold, the global metallicity of the disk, and a time-dependent gas accretion rate. We find that planetesimals preferentially form in a local annulus outside the water snowline, at early times in the lifetime of the disk ($\lesssim$$10^{5} \: \rm{yr}$), when the pebble mass fluxes are high enough to trigger the streaming instability. During this first phase in the planet formation process, the snowline location hardly changes due to slow viscous evolution, and we conclude that assuming a constant gas accretion rate is justified in this first stage. The efficiency of converting the solids reservoir of the disk to planetesimals depends on the location of the water snowline. Cooler disks with a closer-in water snowline are more efficient at producing planetesimals than hotter disks where the water snowline is located further away from the star. Therefore, low-mass stars tend to form planetesimals more efficiently, but any correlation may be overshadowed by the spread in disk properties.Comment: 18 pages, 15 figures, accepted for publication in A&

System-level fractionation of carbon from disk and planetesimal processing

Finding and characterizing extrasolar Earth analogs will rely on interpretation of the planetary system's environmental context. The total budget and fractionation between C-H-O species sensitively affect the climatic and geodynamic state of terrestrial worlds, but their main delivery channels are poorly constrained. We connect numerical models of volatile chemistry and pebble coagulation in the circumstellar disk with the internal compositional evolution of planetesimals during the primary accretion phase. Our simulations demonstrate that disk chemistry and degassing from planetesimals operate on comparable timescales and can fractionate the relative abundances of major water and carbon carriers by orders of magnitude. As a result, individual planetary systems with significant planetesimal processing display increased correlation in the volatile budget of planetary building blocks relative to no internal heating. Planetesimal processing in a subset of systems increases the variance of volatile contents across planetary systems. Our simulations thus suggest that exoplanetary atmospheric compositions may provide constraints on $when$ a specific planet formed.Comment: Accepted for publication in ApJL; 10 pages, 4 figures; summaries available at https://bit.ly/LichtenbergKrijt21blog (blog) and https://bit.ly/LichtenbergKrijt21video (video

Systematic Variations of CO Gas Abundance with Radius in Gas-rich Protoplanetary Disks

CO is the most widely used gas tracer of protoplanetary disks. Its abundance is usually assumed to be an interstellar ratio throughout the warm molecular layer of the disk. But recent observations of low CO gas abundance in many protoplanetary disks challenge our understanding of physical and chemical evolutions in disks. Here we investigate the CO abundance structures in four well-studied disks and compare their structures with predictions of chemical processing of CO and transport of CO ice-coated dust grains in disks. We use spatially resolved CO isotopologue line observations and detailed thermo-chemical models to derive CO abundance structures. We find that the CO abundance varies with radius by an order of magnitude in these disks. We show that although chemical processes can efficiently reduce the total column of CO gas within 1 Myr under an ISM level of cosmic-ray ionization rate, the depletion mostly occurs at the deep region of a disk. Without sufficient vertical mixing, the surface layer is not depleted enough to reproduce weak CO emissions observed. The radial profiles of CO depletion in three disks are qualitatively consistent with predictions of pebble formation, settling, and drifting in disks. But the dust evolution alone cannot fully explain the high depletion observed in some disks. These results suggest that dust evolution may play a significant role in transporting volatile materials and a coupled chemical-dynamical study is necessary to understand what raw materials are available for planet formation at different distances from the central star.Comment: 17 pages, 8 figures, accepted for publication in the Ap