Formation of super-Earths around low-mass stars: evolution of an icy dead zone

TL;DR

This paper investigates how icy regions and dead zones in protoplanetary discs influence in-situ formation of close-in super-Earths, focusing on stars of $0.1$, $0.5$, and $1\,M_\odot$. It develops a 1D time-dependent disc model with a layered MRI structure, combining MRI-active surface layers and a self-gravity–driven dead zone, and explores steady-state and evolving snow lines under varying $\Sigma_{\rm crit}$. The main finding is that an inner icy region within the dead zone can be extended and persist longer around M-dwarfs (especially for low $\Sigma_{\rm crit}$), potentially increasing the solid reservoir available for near-star planet formation, while solar-mass stars tend to have smaller, shorter-lived inner icy zones. The work highlights a plausible mechanism linking disc MHD/gravito-turbulence physics to the observed high occurrence of close-in super-Earths around low-mass stars, and provides a framework for connecting disc thermodynamics, accretion variability, and planet formation outcomes.

Abstract

Exoplanet observations show that close-in super-Earths are more common around M-dwarfs than around solar mass stars. Since the snow line in a protoplanetary disc plays a crucial role in determining the amount of solid material available for planet formation, we explore the icy regions of protoplanetary discs around stars with masses 0.1, 0.5 and 1 $\rm M_\odot$. In a protoplanetary disc, a dead zone, where the magneto-rotational instability (MRI) is suppressed, provides a quiescent region for solids to settle to the mid-plane and planets to form. Viscosity may be driven in the dead zone by gravitational instability if enough material builds up. Heating from the gravitational instability can trigger the MRI and an accretion outburst onto the star. There may be two icy regions in a disc: (1) far from the star and (2) in the dead zone close to the star. We solve the 1D disc equations to find steady state solutions and time-dependent evolution with different values for the critical surface density in the MRI-active surface layers. Larger surface density in the MRI-active surface layers reduces the extent and lifetime of the inner icy region. The inner icy region in the dead zone around a solar mass star is small and short-lived. Around M-dwarfs, the size of the inner icy region is more persistent and oscillates between the accretion outbursts in the region 0.1-1 au. An extended icy region within the dead zone of a disc around M-dwarfs may promote the formation of more numerous and massive close-in super-Earths.

Figures (8)

• Figure 1: Sketch of the protoplanetary disc structure. In the inner region of the disc, where the gas is sufficiently hot ($T_{\rm c} > T_{\rm crit}$), the gas is ionized and well-coupled to the magnetic field, allowing the MRI to operate effectively. At larger radii, where the temperature is lower, the MRI is suppressed due to insufficient ionization, leading to the formation of a layered disc structure. MRI turbulence occurs in the thin surface layers ionized by cosmic rays or X-rays (with $\Sigma=\Sigma_{ \rm crit}$), while the cold mid-plane forms a "dead zone" where the MRI is inactive. In the outer parts of the disc, where the surface density is low enough ($\Sigma < \Sigma_{\rm crit}$) for cosmic rays to penetrate to the mid-plane, the disc becomes fully MRI-active again. The outer parts of the dead zone may be heated by self-gravity if sufficient material builds up. The shaded regions in the figure indicate two possible icy zones within the disc: (1) an outer icy region far from the star and (2) an inner icy region located within the dead zone, closer to the star.
• Figure 2: The structure of the disc as a function of the steady-state accretion rate through the disc for stellar mass $M=1\,\rm M_\odot$. The shaded regions show where the disc can be icy. The critical surface density is $\Sigma_{\rm crit}=2\,\rm g\, cm^{-2}$ (upper left), $\Sigma_{\rm crit}=20\,\rm g\, cm^{-2}$ (upper right) and $\Sigma_{\rm crit}=200\,\rm g\, cm^{-2}$ (lower). Solid lines indicate boundaries of the disc structure. The vertical black line shows where the disc transitions from a fully turbulent disc without a dead zone (low accretion rates) to a layered disc (high accretion rates). For the lowest $\Sigma_{\rm crit}$, the disc is always layered. The solid green lines show the radius at which $T_{\rm c}=T_{\rm crit}=800\,\rm K$ for a fully MRI-active disc (see Section \ref{['sec:FMRI']}). The solid light blue lines show the critical radius for the transition to the MRI branch in the outer part of the disc (where $\Sigma=\Sigma_{\rm crit}$, see Section \ref{['sec:FMRI']}). The magenta lines show where $T_{\rm c}=T_{\rm crit}=800\, \rm K$ in the self-gravitating disc (see Section \ref{['sec:SGSS']}.). The dashed lines indicate snow line radii. The dashed red lines show where the $T_{\rm irr}=T_{\rm snow}=145\,\rm K$ (see Section \ref{['subsec:irr dics']}). The dashed yellow lines show the radius at which $T_{\rm c}=T_{\rm snow}=145$K for a fully MRI-active disc. The dashed blue lines show the snow line radius in a self-gravitating disc. The outer dark-shaded icy region is bounded by steady disc solutions and does not evolve in time. The light-shaded region can be icy, but since the disc is not in a steady state in a dead zone region, the icy region may evolve in time (see Section \ref{['sec:icy']}).
• Figure 3: Same as Fig. \ref{['fig:vallet1']} except $M=0.5\,\rm M_\odot$.
• Figure 4: Same as Fig. \ref{['fig:vallet1']} except $M=0.1\,\rm M_\odot$.
• Figure 5: Time-dependent simulations for a disc around a star with mass $M=1\,\rm M_\odot$ with initial infall rate $\dot M_{\rm i}=2\times 10^{-5}\,\rm M_\odot \, yr^{-1}$, and $\Sigma_{\rm crit}=2$ (top left panel), 20 (top right panel), and $200\,\rm g\,cm^{-2}$ (bottom panel). Top row of each panel: The accretion rate onto the star over time. The red dashed lines show the infall accretion rate given by equation (\ref{['eq:mdot']}). The light blue lines show the accretion rate onto the star. Bottom row of each panel: The evolution of the icy regions within the disc over time. The gray areas indicate the regions of the disc where the temperature at the mid-plane disc is low enough for ice to exist ($T_{\rm c}<T_{\rm snow}$).The region enclosed by the purple line illustrates how the extent of the dead zone evolves over time.At times where there are no purple lines, there is no dead zone, and the disc is fully turbulent.