Turbulence Regulates the Rate of Planetesimal Formation via Gravitational Collapse. (arXiv:2001.10000v2 [astro-ph.EP] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Gole_D/0/1/0/all/0/1">Daniel A. Gole</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Simon_J/0/1/0/all/0/1">Jacob B. Simon</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Li_R/0/1/0/all/0/1">Rixin Li</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Youdin_A/0/1/0/all/0/1">Andrew N. Youdin</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Armitage_P/0/1/0/all/0/1">Philip J. Armitage</a>

We study how the interaction between the streaming instability and intrinsic

gas-phase turbulence affects planetesimal formation via gravitational collapse

in protoplanetary disks. Turbulence impedes the formation of particle clumps by

acting as an effective turbulent diffusivity, but it can also promote

planetesimal formation by concentrating solids, for example in zonal flows. We

quantify the effect of turbulent diffusivity using numerical simulations of the

streaming instability in small local domains, forced with velocity

perturbations that establish approximately Kolmogorov-like turbulence. We find

that planetesimal formation is suppressed by turbulence once velocity

fluctuations exceed $langle delta v^2 rangle simeq 10^{-3.5} – 10^{-3}

c_s^2$. Turbulence whose strength is just below the threshold reduces the rate

at which solids are bound into clumps. Our results suggest that the

well-established turbulent thickening of the mid-plane solid layer is the

primary mechanism by which turbulence influences planetesimal formation and

that planetesimal formation requires a mid-plane solid-to-gas ratio $epsilon

gtrsim 0.5$. We also quantify the initial planetesimal mass function using a

new clump-tracking method to determine each planetesimal mass shortly after

collapse. For models in which planetesimals form, we show that the mass

function is well-described by a broken power law, whose parameters are robust

to the inclusion and strength of imposed turbulence. Turbulence in

protoplanetary disks is likely to substantially exceed the threshold for

planetesimal formation at radii where temperatures $T gtrsim 10^3 {rm K}$

lead to thermal ionization. Planetesimal formation may therefore be unviable in

the inner disk out to 2-3 times the dust sublimation radius.

We study how the interaction between the streaming instability and intrinsic

gas-phase turbulence affects planetesimal formation via gravitational collapse

in protoplanetary disks. Turbulence impedes the formation of particle clumps by

acting as an effective turbulent diffusivity, but it can also promote

planetesimal formation by concentrating solids, for example in zonal flows. We

quantify the effect of turbulent diffusivity using numerical simulations of the

streaming instability in small local domains, forced with velocity

perturbations that establish approximately Kolmogorov-like turbulence. We find

that planetesimal formation is suppressed by turbulence once velocity

fluctuations exceed $langle delta v^2 rangle simeq 10^{-3.5} – 10^{-3}

c_s^2$. Turbulence whose strength is just below the threshold reduces the rate

at which solids are bound into clumps. Our results suggest that the

well-established turbulent thickening of the mid-plane solid layer is the

primary mechanism by which turbulence influences planetesimal formation and

that planetesimal formation requires a mid-plane solid-to-gas ratio $epsilon

gtrsim 0.5$. We also quantify the initial planetesimal mass function using a

new clump-tracking method to determine each planetesimal mass shortly after

collapse. For models in which planetesimals form, we show that the mass

function is well-described by a broken power law, whose parameters are robust

to the inclusion and strength of imposed turbulence. Turbulence in

protoplanetary disks is likely to substantially exceed the threshold for

planetesimal formation at radii where temperatures $T gtrsim 10^3 {rm K}$

lead to thermal ionization. Planetesimal formation may therefore be unviable in

the inner disk out to 2-3 times the dust sublimation radius.

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