Rapid growth of gas-giant cores by pebble accretion (1205.3030v2)

Abstract: The observed lifetimes of gaseous protoplanetary discs place strong constraints on gas and ice giant formation in the core accretion scenario. The approximately 10-Earth-mass solid core responsible for the attraction of the gaseous envelope has to form before gas dissipation in the protoplanetary disc is completed within 1-10 million years. Building up the core by collisions between km-sized planetesimals fails to meet this time-scale constraint, especially at wide stellar separations. Nonetheless, gas-giant planets are detected by direct imaging at wide orbital distances. In this paper, we numerically study the growth of cores by the accretion of cm-sized pebbles loosely coupled to the gas. We measure the accretion rate onto seed masses ranging from a large planetesimal to a fully grown 10-Earth-mass core and test different particle sizes. The numerical results are in good agreement with our analytic expressions, indicating the existence of two accretion regimes, one set by the azimuthal and radial particle drift for the lower seed masses and the other, for higher masses, by the velocity at the edge of the Hill sphere. In the former, the optimally accreted particle size increases with core mass, while in the latter the optimal size is centimeters, independent of core mass. We discuss the implications for rapid core growth of gas-giant and ice-giant cores. We conclude that pebble accretion can resolve the long-standing core accretion time-scale conflict. This requires a near-unity dust-to-gas ratio in the midplane, particle growth to mm and cm and the formation of massive planetesimals or low radial pressure support. The core growth time-scale is shortened by a factor 30-1,000 at 5 AU and by a factor 100-10,000 at 50 AU, compared to the gravitationally focused accretion of, respectively, low-scale-height planetesimal fragments or standard km-sized planetesimals.

• The paper introduces a pebble accretion model that offers a viable mechanism for rapidly forming gas-giant cores, addressing the time-scale challenges of planetesimal collisions.
• It distinguishes two accretion regimes—drift for low seed masses and Hill accretion for larger cores—with strong agreement between numerical simulations and analytical results.
• The findings suggest that favorable protoplanetary conditions, such as enhanced dust-to-gas ratios, can accelerate core growth by factors between 30 and 10,000 compared to classical models.

An Analytical and Numerical Study of Rapid Gas-Giant Core Growth via Pebble Accretion

This paper presents a comprehensive investigation into the formation of gas-giant cores through pebble accretion, challenging the traditional model of planetesimal collision accretion. The authors, Lambrechts and Johansen, deliver both numerical simulations and analytical calculations to address the time-scale constraints posed by the observed lifetimes of protoplanetary gaseous disks. Central to their argument is the inefficiency of kilometer-sized planetesimal collisions to account for the rapid core growth of observed gas giants, particularly at wide stellar separations. Instead, they propose that pebble accretion—a mechanism involving the capture of centimeter-sized particles loosely coupled to gas—can effectively form cores within the necessary time scales.

Numerical and Analytical Agreement

The authors utilize numerical models to evaluate the accretion rate of seed masses, ranging from large planetesimals to fully grown 10-Earth-mass cores, under varying particle sizes. Impressively, they report strong alignment between their simulations and analytical expressions, suggesting two distinct accretion regimes. For lower seed masses, accretion is characterized by azimuthal and radial particle drift. In contrast, higher seed masses exhibit accretion governed by velocities at the Hill sphere's edge.

Key Insights into Accretion Regimes

• Drift Accretion Regime: In this regime, pebble accretion becomes limited by particle drift relative to the core, with an optimal pebble size increasing in proportion to core growth. This mechanism, while potentially effective over shorter orbital distances, faces efficiency challenges at wider stellar separations if dust-to-gas ratios are not favorable.
• Hill Accretion Regime: The Hill regime dominates as cores grow larger. Here, accretion becomes less sensitive to core mass and more influenced by orbital mechanics, allowing for rapid core growth by capturing pebbles from within the entire Hill sphere. A consistent optimal pebble size of centimeters is identified, regardless of core mass.

Implications and Formation Efficiency

The authors argue that pebble accretion can solve the core accretion time-scale problem, especially at wide orbital distances, provided that protoplanetary conditions support elevated dust-to-gas ratios and suitable pressure gradients for particle growth. Their findings suggest that core growth timescale shortens significantly—by factors of 30 to 1,000 at 5 AU and 100 to 10,000 at 50 AU—when compared to classical planetesimal accretion models.

This paper reveals a potential pathway for the efficient formation of not only gas giants like Jupiter and Saturn but also ice giants such as Uranus and Neptune. Given the presence of observed exoplanets at wide separations, the findings indicate that pebble accretion could be a prevalent mechanism in planetary system evolution, accommodating both rapid and spatially wide core formation processes.

Future Directions

Further research is encouraged to build on this foundational work by exploring the effects of turbulence, diverse particle size distributions, and the planet's migration on accretion efficiency. Additionally, addressing the backreaction of particles on the gas flow and extending the simulations to include more comprehensive global models could provide deeper insights. The implications of these findings may not only influence theoretical models of planet formation but also guide observational strategies targeting young planetary systems and the conditions leading to their rapid assembly.

By introducing a pebble-based accretion scenario, this paper challenges conventional views, offering a viable and compelling model for understanding the rapid formation of gas-giant cores in diverse stellar environments. The authors’ combination of robust numerical and analytical approaches makes significant strides in reconciling theoretical models with observational constraints on planet formation time scales.