Toward a Deterministic Model of Planetary Formation. I. A Desert in the Mass and Semimajor Axis Distributions of Extrasolar Planets

By Shigeru Ida, D. Lin. 2003

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In an attempt to develop a deterministic theory for planet formation, we examine the accretion of cores of giant planets from planetesimals, gas accretion onto the cores, and their orbital migration. We adopt a working model for nascent protostellar disks with a wide variety of surface density distributions in order to explore the range of diversity among extrasolar planetary systems. We evaluate the cores' mass growth rate c through runaway planetesimal accretion and oligarchic growth. The accretion rate of cores is estimated with a two-body approximation. In the inner regions of disks, the cores' eccentricity is effectively damped by their tidal interaction with the ambient disk gas and their early growth is stalled by "isolation." In the outer regions, the cores' growth rate is much smaller. If some cores can acquire more mass than a critical value of several Earth masses during the persistence of the disk gas, they would be able to rapidly accrete gas and evolve into gas giant planets. The gas accretion process is initially regulated by the Kelvin-Helmholtz contraction of the planets' gas envelope. Based on the assumption that the exponential decay of the disk gas mass occurs on the timescales ~106-107 yr and that the disk mass distribution is comparable to those inferred from the observations of circumstellar disks of T Tauri stars, we carry out simulations to predict the distributions of masses and semimajor axes of extrasolar planets. In disks as massive as the minimum-mass disk for the solar system, gas giants can form only slightly outside the "ice boundary" at a few AU. However, cores can rapidly grow above the critical mass inside the ice boundary in protostellar disks with 5 times more heavy elements than those of the minimum-mass disk. Thereafter, these massive cores accrete gas prior to its depletion and evolve into gas giants. The limited persistence of the disk gas and the decline in the stellar gravity prevent the formation of cores capable of efficient gas accretion outside 20-30 AU. Unimpeded dynamical accretion of gas is a runaway process that is terminated when the residual gas is depleted either globally or locally in the form of a gap in the vicinity of their orbits. Since planets' masses grow rapidly from 10 to 100 M⊕, the gas giant planets rarely form with asymptotic masses in this intermediate range. Our model predicts a paucity of extrasolar planets with mass in the range 10-100 M⊕ and semimajor axis less than 3 AU. We refer to this deficit as a "planet desert." We also examine the dynamical evolution of protoplanets by considering the effect of orbital migration of giant planets due to their tidal interactions with the gas disks, after they have opened up gaps in the disks. The effect of migration is to sharpen the boundaries and to enhance the contrast of the planet desert. It also clarifies the separation between the three populations of rocky, gas giant, and ice giant planets. Based on our results, we suggest that the planets' mass versus semimajor axes diagram can provide strong constraints on the dominant formation processes of planets analogous to the implications of the color-magnitude diagram on the paths of stellar evolution. We show that the mass and semimajor axis distributions generated in our simulations for the gas giants are consistent with those of the known extrasolar planets. Our results also indicate that a large fraction (90%-95%) of the planets that have migrated to within 0.05 AU must have perished. Future observations can determine the existence and the boundaries of the planet desert in this diagram, which can be used to extrapolate the ubiquity of rocky planets around nearby stars. Finally, the long-term dynamical interaction between planets of various masses can lead to both eccentricity excitation and scattering of planets to large semimajor axes. These effects are to be included in future models.

Subfields: Astronomy and Astrophysics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/c34d4c10d9895abed1b3845a57e4e81f3fbff08b

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Citations in the corpus

Characterization of exoplanets from their formation - I. Models of combined planet formation and evolution (2012, background): “Such a higher accretion rate is important for the depth of the so-called “planetary desert” (Ida & Lin 2004): the higher the possible accretion rates, the lower the number of planets of intermediate masses (ca. 10−100 M⊕, see the discussions in Mordasini et al. 2009a, 2011b).”
Models of giant planet formation with migration and disc evolution (2004, methodology): “(21) Finally, we also take into account the ejection of planetesimals due to the planet, using the ejection rate given by Ida & Lin (2004): accretion rate ejection rate = ( Vesc,disk Vsurf,planet )4 , (22) where Vesc,disk = √ 2GM⊙/aplanet is the escape velocity form the central star, at the…”
The HARPS survey for southern extra-solar planets. II. A 14 Earth-masses exoplanet around μ Arae (2004, background): “Once this core reaches a critical mass (mcrit), accretion of gas in a runaway fashion becomes possible and the mass of the planet increases rapidly (e.g. Ida & Lin 2004b).”
TOWARD CHEMICAL CONSTRAINTS ON HOT JUPITER MIGRATION (2014, methodology): “We adopt the Type II migration rate used by Ida & Lin (2004), though other migration prescriptions are possible(e.g. Mordasini et al. 2009).”
THE MASS DEPENDENCE BETWEEN PROTOPLANETARY DISKS AND THEIR STELLAR HOSTS (2013, background): “…distribution of disk masses, f(Md), has been invoked as a key factor in accounting for the diverse demographic properties of the exoplanets (e.g., Ida & Lin 2004, 2008; Alibert et al. 2005; Mordasini et al. 2009), and scaling trends between Md and other star/disk properties are speculated to…”
KEPLER MISSION STELLAR AND INSTRUMENT NOISE PROPERTIES (2011, background): “Do the statistical trends primarily follow from the physics of planet formation (Gould & Eastman 2011; Ida & Lin 2004), or is there a strong contribution from observational incompleteness given the larger than anticipated noise levels (Jenkins et al. 2010b; Christiansen et al. 2010)?”
THE LICK-CARNEGIE EXOPLANET SURVEY: A URANUS-MASS FOURTH PLANET FOR GJ 876 IN AN EXTRASOLAR LAPLACE CONFIGURATION (2010, background): “A zeroth-order prediction of the core-accretion paradigm for giant planet formation is that the frequency of readily detectable giant planets should increase with both increasing stellar metallicity and with increasing stellar mass (Laughlin et al. 2004; Ida & Lin 2004, 2005).”
Formation of Hot Planets by a Combination of Planet Scattering, Tidal Circularization, and the Kozai Mechanism (2008, background): “In relativelymassive and/ormetal-rich disks,multiple gas giants are likely to form (e.g., Kokubo & Ida 2002; Ida & Lin 2004a, 2004b, 2008).”
RETIRED A STARS AND THEIR COMPANIONS. III. COMPARING THE MASS–PERIOD DISTRIBUTIONS OF PLANETS AROUND A-TYPE STARS AND SUN-LIKE STARS (2009, methodology): “…Carlo simulations of Jovian planet formation and migration around IM stars and, using simple stellar mass-dependent gas disk lifetime relations (Kennedy & Kenyon 2009) and Type II migration models (Ida & Lin 2004), was able to successfully reproduce the observed dearth of short-period planets.”
Detection of a Neptune-Mass Planet in the ρ1 Cancri System Using the Hobby-Eberly Telescope (2004, background): “An alternative hypothesis is that ρ1 Cancri e formed as a much more massive gas giant planet before it began its inward type II migration to its present orbital radius (Ida & Lin 2004).”
The Gemini Deep Planet Survey (2007, background): “…solid material (hence [Fe/H]) in the protoplanetary disk , precluding formation of Jupiter mass plan- 2 Lafrenière et al. ets at distances greater than 15–20 AU (e.g. Pollack et al. 1996; Ida & Lin 2004), where the low density of planetesimals would lead to prohibitively long formation timescales.”
Inevitability of Plate Tectonics on Super-Earths (2007, background): “Planets with masses larger than 10M⊕ can start to retain gas during formation (Ida and Lin 2004).”
Toward a Deterministic Model of Planetary Formation. IV. Effects of Type I Migration (2008, methodology): “But these cores can coalesce through giant impacts during and after the severe depletion of the disk gas (Kominami & Ida 2002; Ida & Lin 2004a).”
Structure and Evolution of Nearby Stars with Planets. II. Physical Properties of ~1000 Cool Stars from the SPOCS Catalog (2006, background): “One explanation posits that planets are more efficiently formed around stars with higher metallicity because of the higher fraction of solids available in the circumstellar disk (Ida & Lin 2004b).”
PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS. II. EXTENSION TO FAINTER SOURCES (2010, background): “…to elucidate the physical processes involved in making planets by incorporating the observed properties of circumstellar disks and successfully reproducing the demographic characteristics of the planets in our Solar System and those around other stars (e.g., Ida & Lin 2004; Mordasini et al. 2009).”
Extrasolar planet population synthesis - II. Statistical comparison with observations (2009, methodology): “…recently shown that they find a minimum in the planetary mass spectrum at 100-1000 M⊕ if they use a formation model similar to Ida & Lin (2004a) but couple it to solid and gas accretion rates which fit the results of Fortier et al. (2007), rather than a minimum at 10-100 M⊕ as in Ida & Lin (2004a).”
Internal structure of massive terrestrial planets (2005, background): “Su h expe tations are based in part on theoreti al work that shows no eviden e pre luding planet formation in the 1− 10 M⊕ mass range (e.g. Ida and Lin 2004), even in planetary systems with Hot Jupiters (Lunine et al. 2004).”
Wide-Field InfrarRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report (2015, background): “Furthermore, this parameter space is largely disjoint from both the planets in our solar system, and from the three largest reservoirs of planets that are predicted by many planet formation theories (e.g. Ida & Lin 2004, Mordasini et al. 2009).”