Evidence for Universality in the Initial Planetesimal Mass Function

Abstract

Planetesimals may form from the gravitational collapse of dense particle clumps initiated by the streaming instability. We use simulations of aerodynamically coupled gas-particle mixtures to investigate whether the properties of planetesimals formed in this way depend upon the sizes of the particles that participate in the instability. Based on three high-resolution simulations that span a range of dimensionless stopping times 6 10 2 3   t -, no statistically significant differences in the initial planetesimal mass function are found. The mass functions are fit by a power law, dN dM M p p p µ -, with p=1.5-1.7 and errors of p 0.1 D » . Comparing the particle density fields prior to collapse, we find that the high-wavenumber power spectra are similarly indistinguishable, though the large-scale geometry of structures induced via the streaming instability is significantly different between all three cases. We interpret the results as evidence for a near-universal slope to the mass function, arising from the small-scale structure of streaming-induced turbulence.

Demographics of Planetesimals Formed by the Streaming Instability

“…To simulate the formation of planetesimals, we use the ATHENA code with a similar setup to Simon et al (2017). In Section 2.1, we briefly introduce the numerical methods employed in ATHENA for modeling the coupled dynamics of gas and particles, including the self-gravity of solids, in a protoplanetary disk (see Bai & Stone 2010c;Simon et al 2016, for more details).…”

“…Run II has (τ s , Z) = (0.3, 0.02) and a lower resolution in a larger domain. The data of Run II are directly taken from Simon et al (2017), and our Run I is a higher resolution version of another simulation in Simon et al (2017). The relation between particle size and τ s depends on uncertain properties of particles and gas disk.…”

“…The effects of both the clump finding algorithm -PLAN (blue) vs. a previous method (cyan) -and simulation resolution -higher (orange) vs. lower (blue) -are shown. Both the cyan and blue curves analyze a simulation snapshot from Simon et al (2017) which has half the resolution and twice the box size as our run I. The orange curve analyzes a Run I snapshot, with planetesimal numbers augmented by a factor of 4 to compensate for the smaller surface area.…”

“…Appendix A gives a model fitting example in detail. Our maximum likelihood estimator is similar to what used in Simon et al (2016Simon et al ( , 2017; Abod et al (2018) but we use bootstrapping to estimate parameter uncertainties. A different method of parameter estimation is used by Johansen et al (2015); Schäfer et al (2017), etc., who applied curve fitting routines to the CDF.…”

“…The SI is an aerodynamic instability arising from the relative drift and the mutual drag forces between gas and et al 2017; Drążkowska et al 2016;Drążkowska & Alibert 2017;Schoonenberg & Ormel 2017). Previous studies have also shown that high-resolution SI simulations with self-gravity can produce a broad initial top-heavy mass distribution of planetesimals Simon et al 2016Simon et al , 2017.…”