Core Accretion Model Research Articles

The Maximum Mass Solar Nebula and the early formation of planets

Current planet formation theories provide successful frameworks with which to interpret the array of new observational data in this field. However, each of the two main theories (core accretion, gravitational instability) is unable to explain some key aspects. In many planet formation calculations, it is usual to treat the initial properties of the planet forming disc (mass, radius, etc.) as free parameters. In this paper, we stress the importance of setting the formation of planet forming discs within the context of the formation of the central stars. By exploring the early stages of disc formation, we introduce the concept of the Maximum Mass Solar Nebula (MMSN), as opposed to the oft-used Minimum Mass Solar Nebula (here mmsn). It is evident that almost all protoplanetary discs start their evolution in a strongly self-gravitating state. In agreement with almost all previous work in this area, we conclude that on the scales relevant to planet formation these discs are not gravitationally unstable to gas fragmentation, but instead form strong, transient spiral arms. These spiral arms can act as efficient dust traps allowing the accumulation and subsequent fragmentation of the dust (but not the gas). This phase is likely to populate the disc with relatively large planetesimals on short timescales while the disc is still veiled by a dusty-gas envelope. Crucially, the early formation of large planetesimals overcomes the main barriers remaining within the core accretion model. A prediction of this picture is that essentially all observable protoplanetary discs are already planet hosting.

Steamworlds: Atmospheric Structure and Critical Mass of Planets Accreting Icy Pebbles

Abstract In the core accretion model, gas-giant planets first form a solid core, which then accretes gas from a protoplanetary disk when the core exceeds a critical mass. Here, we model the atmosphere of a core that grows by accreting ice-rich pebbles. The ice fraction of pebbles evaporates in warm regions of the atmosphere, saturating it with water vapor. Excess water precipitates to lower altitudes. Beneath an outer radiative region, the atmosphere is convective, following a moist adiabat in saturated regions due to water condensation and precipitation. Atmospheric mass, density, and temperature increase with core mass. For nominal model parameters, planets with core masses (ice + rock) between 0.08 and 0.16 Earth masses have surface temperatures between 273 and 647 K and form an ocean. In more massive planets, water exists as a supercritical convecting fluid mixed with gas from the disk. Typically, the core mass reaches a maximum (the critical mass) as a function of the total mass when the core is 2–5 Earth masses. The critical mass depends in a complicated way on pebble size, mass flux, and dust opacity due to the occasional appearance of multiple core-mass maxima. The core mass for an atmosphere of 50% hydrogen and helium may be a more robust indicator of the onset of gas accretion. This mass is typically 1–3 Earth masses for pebbles that are 50% ice by mass, increasing with opacity and pebble flux and decreasing with pebble ice/rock ratio.

Maximum mass of planetary embryos that formed in core-accretion models

We compute the maximum mass a growing planetary embryo can reach depending on the size of accreted planetesimals or pebbles, to infer the possibility of growing the cores of giant planets, and giant planets themselves. We compute the internal structure of the gas envelope of planetary embryos, to determine the core mass that is necessary to bind an envelope large enough to destroy planetesimals or pebbles while they are gravitationally captured. We also consider the effect of the advection wind originating from the protoplanetary disk, following the results of Ormel et al. (2015). We show that for low mass pebbles, once the planetary embryo is larger than ~1 Mearth, the envelope is large enough to destroy and vaporize pebbles completely before they can reach the core. The material constituting pebbles is therefore released in the planetary envelope, and later on dispersed in the protoplanetary disk, if the advection wind is strong enough. As a consequence the growth of the planetary embryo is stopped at a mass that is so small that Kelvin-Helmholtz accretion cannot lead to the accretion of significant amounts of gas. For larger planetesimals, a similar process occurs but at much larger mass, of the order of ten Earth masses, and is followed by rapid accretion of gas. If the effect of the advection is as efficient as described in Ormel al. (2015), the combined effect of the vaporization of accreted solids in the envelope of forming planetary embryos, and of this advection wind, prevents the growth of the planets at masses smaller or similar to the Earth mass in the case of formation by pebble accretion, up to a distance of the order of 10 AU. In the case of formation by accretion of large mass planetesimals, the growth of the planetary core is limited at masses ~10 Mearth but further growth of the planet can proceed by gas accretion.

The snowline in the protoplanetary disk and extrasolar planets

We investigate the behavior of the snowline in a protoplanetary disk and the relationship between the radius of the snowline and properties of molecular cloud cores. In our disk model, we consider mass influx from the gravitational collapse of a molecular cloud core, irradiation from the central star, and thermal radiation from the ambient molecular cloud gas. As the protoplanetary disk evolves, the radius of the snowline increases first to a maximum value Rmax, and then decreases in the late stage of evolution of the protoplanetary disk. The value of Rmax is dependent on the properties of molecular cloud cores (mass Mcore, angular velocity ω and temperature Tcore). Many previous works found that solid material tends to accumulate at the location of the snowline, which suggests that the snowline is the preferred location for giant planet formation. With these conclusions, we compare the values of Rmax with semimajor axes of giant planets in extrasolar systems, and find that Rmax may provide an upper limit for the locations of the formation of giant planets which are formed by the core accretion model.

The SOFIA Massive (SOMA) Star Formation Survey. I. Overview and First Results

Abstract We present an overview and first results of the Stratospheric Observatory For Infrared Astronomy Massive (SOMA) Star Formation Survey, which is using the FORCAST instrument to image massive protostars from ∼10 to 40 μm. These wavelengths trace thermal emission from warm dust, which in Core Accretion models mainly emerges from the inner regions of protostellar outflow cavities. Dust in dense core envelopes also imprints characteristic extinction patterns at these wavelengths, causing intensity peaks to shift along the outflow axis and profiles to become more symmetric at longer wavelengths. We present observational results for the first eight protostars in the survey, i.e., multiwavelength images, including some ancillary ground-based mid-infrared (MIR) observations and archival Spitzer and Herschel data. These images generally show extended MIR/FIR emission along directions consistent with those of known outflows and with shorter wavelength peak flux positions displaced from the protostar along the blueshifted, near-facing sides, thus confirming qualitative predictions of Core Accretion models. We then compile spectral energy distributions and use these to derive protostellar properties by fitting theoretical radiative transfer models. Zhang and Tan models, based on the Turbulent Core Model of McKee and Tan, imply the sources have protostellar masses m * ∼ 10–50 M ⊙ accreting at ∼10−4–10−3 M ⊙ yr−1 inside cores of initial masses M c ∼ 30–500 M ⊙ embedded in clumps with mass surface densities Σcl ∼ 0.1–3 g cm−2. Fitting the Robitaille et al. models typically leads to slightly higher protostellar masses, but with disk accretion rates ∼100× smaller. We discuss reasons for these differences and overall implications of these first survey results for massive star formation theories.

Age of Jupiter inferred from the distinct genetics and formation times of meteorites

The age of Jupiter, the largest planet in our Solar System, is still unknown. Gas-giant planet formation likely involved the growth of large solid cores, followed by the accumulation of gas onto these cores. Thus, the gas-giant cores must have formed before dissipation of the solar nebula, which likely occurred within less than 10 My after Solar System formation. Although such rapid accretion of the gas-giant cores has successfully been modeled, until now it has not been possible to date their formation. Here, using molybdenum and tungsten isotope measurements on iron meteorites, we demonstrate that meteorites derive from two genetically distinct nebular reservoirs that coexisted and remained spatially separated between ∼1 My and ∼3-4 My after Solar System formation. The most plausible mechanism for this efficient separation is the formation of Jupiter, opening a gap in the disk and preventing the exchange of material between the two reservoirs. As such, our results indicate that Jupiter's core grew to ∼20 Earth masses within <1 My, followed by a more protracted growth to ∼50 Earth masses until at least ∼3-4 My after Solar System formation. Thus, Jupiter is the oldest planet of the Solar System, and its solid core formed well before the solar nebula gas dissipated, consistent with the core accretion model for giant planet formation.

Reinforcement of the link between stellar metallicity and the zero age orbit of gas giant planet

AbstractIn 2005 we suggested a relation between the optimal locus of gas giant planet formation, prior to migration, and the metallicity of the host star, based on the core accretion model, and radial profiles of dust surface density and gas temperature. At that time, less than 200 extrasolar planets were known, limiting the scope of our analysis. Here, we take into account the expanded statistics allowed by new discoveries, in order to check the validity of some premises. We compare predictions with the present available data and results for different stellar mass ranges. We find that the zero age planetary orbit (ZAPO) hypothesis continues to hold after a two order of magnitude increase in discovered planets, as well as the prediction that planets around metal poor stars would have shorter orbits.

THE MASS–METALLICITY RELATION FOR GIANT PLANETS

ABSTRACT Exoplanet discoveries of recent years have provided a great deal of new data for studying the bulk compositions of giant planets. Here we identify 47 transiting giant planets (20 M ⊕ &lt; M &lt; 20 M J) whose stellar insolations are low enough (F * &lt; 2 × 108 erg s−1 cm−2, or roughly T eff &lt; 1000) that they are not affected by the hot-Jupiter radius inflation mechanism(s). We compute a set of new thermal and structural evolution models and use these models in comparison with properties of the 47 transiting planets (mass, radius, age) to determine their heavy element masses. A clear correlation emerges between the planetary heavy element mass M z and the total planet mass, approximately of the form . This finding is consistent with the core-accretion model of planet formation. We also study how stellar metallicity [Fe/H] affects planetary metal-enrichment and find a weaker correlation than has previously been reported from studies with smaller sample sizes. We confirm a strong relationship between the planetary metal-enrichment relative to the parent star Z planet/Z star and the planetary mass, but see no relation in Z planet/Z star with planet orbital properties or stellar mass. The large heavy element masses of many planets (&gt;50 M ⊕) suggest significant amounts of heavy elements in H/He envelopes, rather than cores, such that metal-enriched giant planet atmospheres should be the rule. We also discuss a model of core-accretion planet formation in a one-dimensional disk and show that it agrees well with our derived relation between mass and Z planet/Z star.

Zero age planetary orbit of gas giant planets revisited: reinforcement of the link with stellar metallicity

In 2005 we suggested a relation between the optimal locus of gas giant planet formation, prior to migration, and the metallicity of the host star, based on the core accretion model and radial profiles of dust surface density and gas temperature. At that time, less than two hundred extrasolar planets were known, limiting the scope of our analysis. Here we take into account the expanded statistics allowed by new discoveries, in order to check the validity of some premises. We compare predictions with the present available data and results for different stellar mass ranges. We find that the Zero Age Planetary Orbit (ZAPO) hypothesis continues to hold after a one order of magnitude increase in discovered planets. In particular, the prediction that metal poor stars harbor planets with an average radius distinctively lower than metal rich ones is still evident in the statistics, and cannot be explained away by chaotic planetary formation mechanisms involving migration and gravitational interaction between planets. The ZAPO hypothesis predicts that in metal poor stars the planets are formed nearer their host stars; as a consequence, they are more frequently engulfed by the stars during the migration process or stripped of their gaseous envelops. The depleted number of gas giant planets around metal poor stars would then be the result of the synergy between low formation probability, as predicted by the core accretion model, and high destruction probability, for the ones that are formed.

THE PROPERTIES OF HEAVY ELEMENTS IN GIANT PLANET ENVELOPES

ABSTRACT The core-accretion model for giant planet formation suggests a two-layer picture for the initial structure of Jovian planets, with heavy elements in a dense core and a thick H–He envelope. Late planetesimal accretion and core erosion could potentially enrich the H–He envelope in heavy elements, which is supported by the threefold solar metallicity that was measured in Jupiter’s atmosphere by the Galileo entry probe. In order to reproduce the observed gravitational moments of Jupiter and Saturn, models for their interiors include heavy elements, Z, in various proportions. However, their effect on the equation of state of the hydrogen–helium mixtures has not been investigated beyond the ideal mixing approximation. In this article, we report results from ab initio simulations of fully interacting H–He–Z mixtures in order to characterize their equation of state and to analyze possible consequences for the interior structure and evolution of giant planets. Considering C, N, O, Si, Fe, MgO, and SiO2, we show that the behavior of heavy elements in H–He mixtures may still be represented by an ideal mixture if the effective volumes and internal energies are chosen appropriately. In the case of oxygen, we also compute the effect on the entropy. We find the resulting changes in the temperature–pressure profile to be small. A homogeneous distribution of 2% oxygen by mass changes the temperature in Jupiter’s interior by only 80 K.

Composition of early planetary atmospheres – I. Connecting disc astrochemistry to the formation of planetary atmospheres

We present a model of the early chemical composition and elemental abundances of planetary atmospheres based on the cumulative gaseous chemical species that are accreted onto planets forming by core accretion from evolving protoplanetary disks. The astrochemistry of the host disk is computed using an ionization driven, non-equilibrium chemistry network within viscously evolving disk models. We accrete gas giant planets whose orbital evolution is controlled by planet traps using the standard core accretion model and track the chemical composition of the material that is accreted onto the protoplanet. We choose a fiducial disk model and evolve planets in 3 traps - water ice line, dead zone and heat transition. For a disk with a lifetime of 4.1 Myr we produce two Hot Jupiters (M = 1.43, 2.67 M$_{\rm Jupiter}$, r = 0.15, 0.11 AU) in the heat transition and ice line trap and one failed core (M = 0.003 M$_{\rm Jupiter}$, r =3.7 AU) in the dead zone. These planets are found with mixing ratios for CO and H$_2$O of $1.99\times 10^{-4}$, $5.0\times 10^{-4}$ respectively for both Hot Jupiters. Additionally for these planets we find CO$_2$ and CH$_4$, with mixing ratios of $1.8\times 10^{-6}\rightarrow 9.8\times 10^{-10}$ and $1.1\times 10^{-8}\rightarrow 2.3\times 10^{-10}$ respectively. These ranges correspond well with the mixing ratio ranges that have been inferred through the detection of emission spectra from Hot Jupiters by multiple authors. We compute a carbon-to-oxygen ratio of 0.227 for the ice line planet and 0.279 for the heat transition planet. These planets accreted their gas inside the ice line, hence the sub-solar C/O.

OGLE-2012-BLG-0724LB: A SATURN-MASS PLANET AROUND AN M DWARF

ABSTRACT We report the discovery of a planet by the microlensing method, OGLE-2012-BLG-0724Lb. Although the duration of the planetary signal for this event was one of the shortest seen for a planetary event, the anomaly was well covered thanks to high-cadence observations taken by the survey groups OGLE and MOA. By analyzing the light curve, this planetary system is found to have a mass ratio q = ( 1.58 ± 0.15 ) × 10 − 3 . By conducting a Bayesian analysis, we estimate that the host star is an M dwarf with a mass of M L = 0.29 − 0.16 + 0.33 M ☉ located at D L = 6.7 − 1.2 + 1.1 kpc away from the Earth and the companion’s mass is m P = 0.47 − 0.26 + 0.54 M Jup . The projected planet–host separation is a ⊥ = 1.6 − 0.3 + 0.4 AU . Because the lens–source relative proper motion is relatively high, future high-resolution images would detect the lens host star and determine the lens properties uniquely. This system is likely a Saturn-mass exoplanet around an M dwarf, and such systems are commonly detected by gravitational microlensing. This adds another example of a possible pileup of sub-Jupiters ( 0.2 &lt; m P / M Jup &lt; 1 ) in contrast to a lack of Jupiters ( ∼ 1 – 2 M Jup ) around M dwarfs, supporting the prediction by core accretion models that Jupiter-mass or more massive planets are unlikely to form around M dwarfs.

Planets, debris and their host metallicity correlations

Recent observations of debris discs, believed to be made up of remnant planetesimals, brought a number of surprises. Debris disc presence does not correlate with the host star's metallicity, and may anti-correlate with the presence of gas giant planets. These observations contradict both assumptions and predictions of the highly successful Core Accretion model of planet formation. Here we explore predictions of the alternative Tidal Downsizing (TD) scenario of planet formation. In TD, small planets and planetesimal debris is made only when gas fragments, predecessors of giant planets, are tidally disrupted. We show that these disruptions are rare in discs around high metallicity stars but release more debris per disruption than their low [M/H] analogs. This predicts no simple relation between debris disc presence and host star's [M/H], as observed. A detected gas giant planet implies in TD that its predecessor fragment was not disputed, potentially explaining why DDs are less likely to be found around stars with gas giants. Less massive planets should correlate with DD presence, and sub-Saturn planets ($M_{p} \sim 50 \M_{\oplus}$) should correlate with DD presence stronger than sub-Neptunes ($M_{p} \leq 15 \M_{\oplus}$). These predicted planet-DD correlations will be diluted and weakened in observations by planetary systems' long term evolution and multi-fragment effects neglected here. Finally, although presently difficult to observe, DDs around M dwarf stars should be more prevalent than around Solar type stars.

COMPANIONS TO APOGEE STARS. I. A MILKY WAY-SPANNING CATALOG OF STELLAR AND SUBSTELLAR COMPANION CANDIDATES AND THEIR DIVERSE HOSTS

ABSTRACT In its three years of operation, the Sloan Digital Sky Survey Apache Point Observatory Galactic Evolution Experiment (APOGEE-1) observed &gt;14,000 stars with enough epochs over a sufficient temporal baseline for the fitting of Keplerian orbits. We present the custom orbit-fitting pipeline used to create this catalog, which includes novel quality metrics that account for the phase and velocity coverage of a fitted Keplerian orbit. With a typical radial velocity precision of ∼100–200 m s−1, APOGEE can probe systems with small separation companions down to a few Jupiter masses. Here we present initial results from a catalog of 382 of the most compelling stellar and substellar companion candidates detected by APOGEE, which orbit a variety of host stars in diverse Galactic environments. Of these, 376 have no previously known small separation companion. The distribution of companion candidates in this catalog shows evidence for an extremely truncated brown dwarf (BD) desert with a paucity of BD companions only for systems with a &lt; ?> 0.1–0.2 AU, with no indication of a desert at larger orbital separation. We propose a few potential explanations of this result, some which invoke this catalog’s many small separation companion candidates found orbiting evolved stars. Furthermore, 16 BD and planet candidates have been identified around metal-poor ([Fe/H] &lt; −0.5) stars in this catalog, which may challenge the core accretion model for companions &gt; 10 M Jup ?> . Finally, we find all types of companions are ubiquitous throughout the Galactic disk with candidate planetary-mass and BD companions to distances of ∼6 and ∼16 kpc, respectively.

OUTFLOW-CONFINED H ii REGIONS. I. FIRST SIGNPOSTS OF MASSIVE STAR FORMATION

ABSTRACT We present an evolutionary sequence of models of the photoionized disk-wind outflow around forming massive stars based on the Core Accretion model. The outflow is expected to be the first structure to be ionized by the protostar and can confine the expansion of the H ii region, especially in lateral directions in the plane of the accretion disk. The ionizing luminosity increases as Kelvin–Helmholz contraction proceeds, and the H ii region is formed when the stellar mass reaches ∼10– 20 M &CircleDot; ?> depending on the initial cloud core properties. Although some part of the outer disk surface remains neutral due to shielding by the inner disk and the disk wind, almost the whole of the outflow is ionized in 103– 10 4 y r ?> after initial H ii region formation. Having calculated the extent and temperature structure of the H ii region within the immediate protostellar environment, we then make predictions for the strength of its free–free continuum and recombination line emission. The free–free radio emission from the ionized outflow has a flux density of ∼(20–200) &times; ( &ngr; / 10 GHz ) p mJy ?> for a source at a distance of 1 kpc with a spectral index p ≃ 0.4–0.7, and the apparent size is typically ∼500 AU at 10 GHz. The H 40 &agr; ?> line profile has a width of about 100 km s - 1 ?> . These properties of our model are consistent with observed radio winds and jets around forming massive protostars.

Delay of planet formation at large radius and the outward decrease in mass and gas content of Jovian planets

A prominent observation of the solar system is that the mass and gas content of Jovian planets decrease outward with orbital radius, except that, in terms of these properties, Neptune is almost the same as Uranus. In previous studies, the solar nebula was assumed to preexist and the formation process of the solar nebula was not considered. It was therefore assumed that planet formation at different radii started at the same time in the solar nebula. We show that planet formation at different radii does not start at the same time and is delayed at large radii. We suggest that this delay might be one of the factors that causes the outward decrease in the masses of Jovian planets. The nebula starts to form from its inner part because of the inside-out collapse of its progenitorial molecular cloud core. The nebula then expands outward due to viscosity. Material first reaches a small radius and then reaches a larger radius, so planet formation is delayed at the large radius. The later the material reaches a planet's location, the less time it has to gain mass and gas content. Hence, the delay tends to cause the outward decrease in mass and gas content of Jovian planets. Our nebula model shows that the material reaches Jupiter, Saturn, Uranus and Neptune at t = 0.40, 0.57, 1.50 and 6.29 × 106 yr, respectively. We discuss the effects of time delay on the masses of Jovian planets in the framework of the core accretion model of planet formation. Saturn's formation is not delayed by much time relative to Jupiter so that they both reach the rapid gas accretion phase and become gas giants. However, the delay in formation of Uranus and Neptune is long and might be one of the factors that cause them not to reach the rapid gas accretion phase before the gas nebula is dispersed. Saturn has less time to go through the rapid gas accretion, so Saturn's mass and gas content are significantly less than those of Jupiter.

Comparison of Low-Mass and High-Mass Star Formation

AbstractI review theoretical models of star formation and how they apply across the stellar mass spectrum. Several distinct theories are under active study for massive star formation, especiallyTurbulent Core Accretion,Competitive AccretionandProtostellar Mergers, leading to distinct observational predictions. These include the types of initial conditions, the structure of infall envelopes, disks and outflows, and the relation of massive star formation to star cluster formation. Even for Core Accretion models, there are several major uncertainties related to the timescale of collapse, the relative importance of different processes for preventing fragmentation in massive cores, and the nature of disks and outflows. I end by discussing some recent observational results that are helping to improve our understanding of these processes.

DIVERSITY OF EXTRASOLAR PLANETS AND DIVERSITY OF MOLECULAR CLOUD CORES. II. MASSES OF GAS GIANT PLANETS

In Paper I, we suggested that the diversity of extrasolar planets might originate from the diversity of molecular cloud cores and specifically illustrated the relationship between semi-major axes of planets in a planetary system and the properties of its progenitor cloud core. In this paper, we investigate the dependence of the mass of a giant planet on the progenitor core properties. We give numerical results of planet masses as a function of the core properties by using the core accretion model of planet formation. Comparing with observations, our model could explain the range and the most frequent values of observed masses of gas giant planets. Our calculations could interpret the observed pileup of gas giants at and the distinct deficit of gas giants from ∼0.05 to . Our calculations indicate that it is difficult to form gas giant planets outside and the intermediate mass planets might be found at ∼15–30 AU as the observing technique advances. We suggest a formation mechanism of super-Jupiters in the framework of the core accretion model of planet formation. A super-Jupiter can form under the condition that a disk is gravitationally unstable (high viscosity) when a protoplanet opens the deep gap. Our calculations infer that the upper limit of super-Jupiter masses, the range of semi-major axes, and the occurrence rate of super-Jupiters increase with the central star mass. We find that gas giant planets should commonly exist around various stellar masses.

Dust in protoplanetary disks: observations

Solid particles, usually referred to as dust, are a crucial component of interstellar matter and of planet forming disks surrounding young stars. Despite the relatively small mass fraction of ≈1% (in the solar neighborhood of our galaxy; this number may differ substantially in other galaxies) that interstellar grains represent of the total mass budget of interstellar matter, dust grains play an important role in the physics and chemistry of interstellar matter. This is because of the opacity dust grains at short (optical, UV) wavelengths, and the surface they provide for chemical reactions. In addition, dust grains play a pivotal role in the planet formation process: in the core accretion model of planet formation, the growth of dust grains from the microscopic size range to large, cm-sized or larger grains is the first step in planet formation. Not only the grain size distribution is affected by planet formation. Chemical and physical processes alter the structure and chemical composition of dust grains as they enter the protoplanetary disk and move closer to the forming star. Therefore, a lot can be learned about the way stars and planets are formed by observations of dust in protoplanetary disks. Ideally, one would like to measure the dust mass, the grain size distribution, grain structure (porosity, fluffiness), the chemical composition, and all of these as a function of position in the disk. Fortunately, several observational diagnostics are available to derive constrains on these quantities. In combination with rapidly increasing quality of the data (spatial and spectral resolution), a lot of progress has been made in our understanding of dust evolution in protoplanetary disks. An excellent review of dust evolution in protoplanetary disks can be found in Testi et al. (2014).

ORBITAL CIRCULARIZATION OF A PLANET ACCRETING DISK GAS: THE FORMATION OF DISTANT JUPITERS IN CIRCULAR ORBITS BASED ON A CORE ACCRETION MODEL

Recently, gas giant planets in nearly circular orbits with large semimajor axes ($a \sim$ 30--1000AU) have been detected by direct imaging. We have investigated orbital evolution in a formation scenario for such planets, based on core accretion model: i) Icy cores accrete from planetesimals at $\lesssim$ 30AU, ii) they are scattered outward by an emerging nearby gas giant to acquire highly eccentric orbits, and iii) their orbits are circularized through accretion of disk gas in outer regions, where they spend most of time. We analytically derived equations to describe the orbital circularization through the gas accretion. Numerical integrations of these equations show that the eccentricity decreases by a factor of more than 5 during the planetary mass increases by a factor of 10. Because runaway gas accretion increases planetary mass by $\sim$ 10--300, the orbits are sufficiently circularized. On the other hand, $a$ is reduced at most only by a factor of 2, leaving the planets in outer regions. If the relative velocity damping by shock is considered, the circularization is slowed down, but still efficient enough. Therefore, this scenario potentially accounts for the formation of observed distant jupiters in nearly circular orbits. If the apocenter distances of the scattered cores are larger than the disk sizes, their $a$ shrink to a quarter of the disk sizes; the $a$-distribution of distant giants could reflect outer edges of the disks in a similar way that those of hot jupiters may reflect inner edges.