Planetesimal formation via the streaming instability persists under turbulence driven by magnetorotational instability

Abstract

Clumping by streaming instability (SI) leading to gravitational collapse is the leading proposed mechanism for forming planetesimals, the building blocks of terrestrial planets and giant-planet cores. The critical dust-to-gas density ratio above which the SI leads to dust concentration strong enough to result in collapse depends on local dust properties and disk conditions, such as particle Stokes number, pressure gradient, and turbulence. The role of turbulence has recently drawn attention because simulations have shown that even modest levels of istropically forced turbulence can significantly increase the critical dust-to-gas ratio. However, we show that this does not hold for turbulence self-consistently generated by the magnetorotational instability (MRI). We present the first parameter study of the SI in three-dimensional, stratified, shearing-box simulations including non-ideal magnetohydrodynamics with ambipolar diffusion. Modest turbulence yields a clumping boundary similar to pure SI cases, while stronger turbulence does increase the critical dust-to-gas density ratio, though less than in the models where turbulence is isotropically forced. Particle concentration occurs inside zonal flows, large-scale structures generated by the MRI. Our results suggest that self-consistent, MRI-driven turbulence does not necessarily inhibit planetesimal formation.

Figures (5)

• Figure 1: Snapshots of the azimuthally averaged particle density for all simulations in the parameter study. For each simulation, we show the snapshot with the highest particle density among all saved outputs. The three leftmost columns correspond to simulations with $\beta_0=6\times10^4$, yielding $\alpha_{\rm SS}\sim10^{-4}$, while the three rightmost columns correspond to simulations with $\beta_0=6\times10^3$, yielding $\alpha_{\rm SS}\sim10^{-3}$. The dust-to-gas surface density ratio ($Z$) of each simulation is indicated in the top-right corner of each panel.
• Figure 2: Maximum particle density as a function of time scaled by orbital period $P$ for all simulations in the parameter study. The dotted line indicates the Hill density (Eq. \ref{['eq: Hill density']}), and the dust-to-gas surface density ratio $Z$ for each simulation is shown in the bottom-left corner of each panel.
• Figure 3: Overview of all simulations in the parameter study, showing whether they exhibit strong clumping (filled circles) or not (empty circles). Results from the 3D pure SI simulations by Lim2025_3D are shown as a solid orange line and diamond markers, where filled markers indicate strong clumping. The dashed and dotted purple lines show the comparison with Lim2024, who performed 3D SI simulations including isotropicaly forced turbulence. Our simulations with relatively weak turbulence (left panel) show $Z_{\rm crit}$ similar to the non-turbulent cases, whereas stronger turbulence (right panel) results in higher $Z_{\rm crit}$, although still significantly smaller than in the isotropically forced-turbulence models.
• Figure 4: Time evolution of the three turbulent parameters $\alpha_\mathrm{SS}$ (Eq. \ref{['eq: alpha_ss']}), $\alpha_z$ (Eq. \ref{['eq: alpha_Z']}), and $\alpha_\mathrm{D}$ (Eq. \ref{['eq: alpha_D']}), measured in simulations without particle feedback and with $\mathrm{St}=0.1$.
• Figure 5: Time evolution of the azimuthally averaged particle density (left), gas density (middle), and gas azimuthal velocity corrected for the background pressure gradient (right) at the midplane (vertically averaged $\pm1$ cell from $z=0$), for the strong-clumping runs with $\beta_0=6\times 10^4$, $\mathrm{St}=0.03$, $Z=0.01$(top) and $\beta_0=6\times 10^3$, $\mathrm{St}=0.03$, $Z=0.06$(bottom). Particles preferentially concentrate in zonal flows, identifiable as regions where the corrected $u_y'=0$ in the right column.