Earth-Mass Planets in Tandem Disks

TL;DR

Earth-mass terrestrial planets form naturally in tandem protosolar disks through accumulation at MRI-suppressed boundaries. Rocky planets originate at the inner MRI front and subsequently migrate outward under gas torques, with the accretion environment and particle flux guiding planet masses; for representative disk accretion rate $\dot{M}=10^{-7.08}\,M_⊙\,\text{yr}^{-1}$, the model yields a total rocky mass of about $1.99\,M_⊕$, with Earth- and Venus-like planets emerging, consistent with the solar system. The work offers a unified framework linking MRI physics, pebble accretion, and migration to terrestrial-planet architectures and explores implications for Mars, Mercury, Moon formation, and the emergence of super-Earths and hot Jupiters. It highlights necessary future extensions to integrate giant-planet formation, outer Solar System structure, and chemical evolution into a comprehensive solar-system formation theory.

Abstract

This paper presents a new terrestrial planet formation theory demonstrating that Earth-mass planets form naturally in tandem protosolar disks. Our model builds upon tandem planet formation theory (Ebisuzaki and Imaeda 2017; Imaeda and Ebisuzaki 2017a,b, 2018), incorporating magneto-rotational instability (MRI) suppression (Balbus and Hawley 1991; Hawley and Balbus 1991), porous particle aggregation (Okuzumi et al. 2012; Kataoka et al. 2013), and standard planet formation mechanisms (e.g., Safronov 1969; Hayashi et al. 1985). In a tandem proto-solar disk, planets form at two distinct locations: the inner and outer edges of the MRI-suppressed region, where solid particles accumulate. The inner edge produces rocky planets, while the outer edge forms gas giants. When planetesimals reach Earth-sized mass at the inner MRI edge, they migrate outward due to gas disk torque. For a protosolar disk accretion rate of M_dot = 10^-7.08 solar masses per year (Case D), the total solid mass at the inner MRI edge reaches 1.99 Earth masses, producing two Earth-mass planets. This result closely matches the solar system's terrestrial planet distribution (Earth and Venus), which comprises 92% of total terrestrial planet mass, providing strong support for our formation mechanism.

Figures (10)

• Figure 1: The structure of Tandem protoplanetary disk. The disk consists of three regions, the inner turbulent region (ITR), the magneto-rotational instability (MRI) suppressed region (MSR), and the outer turbulent region (OTR) (Ebisuzaki2017; Imaeda2017aImaeda2017bImaeda2018)
• Figure 2: Radial profile of midplane temperature ($T_m$), Elsasser number ($\Lambda$), $\alpha$-value ($\bar{\alpha}$), column density ($\Sigma$), $\eta$-value ($\eta$), and normalized torque ($\Gamma/\Gamma_0$) Paardekooper2009Lyra2010Paardekooper2010Paardekooper2014 in the disk for accretion rate of $\dot{M} = 10^{-7.0} M_\odot\,\mathrm{yr}^{-1}$.
• Figure 3: Time scale of migration and mass of planet. Each solid line means different of accretion rate.
• Figure 4: The accretion rate ($\dot{M}$) is assumed to decrease exponentially with a decay timescale, with the central star mass set to $1\,M_\odot$.
• Figure 5: Mass of the terrestrial planet formation region. We assume that the mass is decided by accretion rate ($\dot{M}$) and particle fraction ($f_{\mathrm{p}}$) of protosolar disk. A dash line is the total mass of the rocky planets of the solar system ($M_{\mathrm{Rocky}} \sim 1.98\,M_{\oplus}$) (the sum of Mercury, Venus, Earth, and Mars).