Core Accretion Model Research Articles

The migrating embryo model for disk evolution

Abstract– A new view of disk evolution is emerging from self‐consistent numerical simulation modeling of the formation of circumstellar disks from the direct collapse of prestellar cloud cores. This has implications for many aspects of star and planet formation, including the growth of dust and high‐temperature processing of materials. A defining result is that the early evolution of a disk is crucially affected by the continuing mass loading from the core envelope, and is driven into recurrent phases of gravitational instability. Nonlinear spiral arms formed during these episodes fragment to form gaseous clumps in the disk. These clumps generally migrate inward due to gravitational torques arising from their interaction with a trailing spiral arm. Occasionally, a clump can open up a gap in the disk and settle into a stable orbit, revealing a direct pathway to the formation of companion stars, brown dwarfs, or giant planets. At other times, when multiple clumps are present, a low mass clump may even be ejected from the system, providing a pathway to the formation of free‐floating brown dwarfs and giant planets in addition to low mass stars. Finally, it has been suggested that the inward migration of gaseous clumps can provide the proper conditions for the transport of high‐temperature processed solids from the outer disk to the inner disk, and even possibly accelerate the formation of terrestrial planets in the inner disk. All of these features arising from clump formation and migration can be tied together conceptually in a migrating embryo model for disk evolution that can complement the well‐known core accretion model for planet formation.

Characterization of exoplanets from their formation

The research of exoplanets has entered an era in which we characterize extrasolar planets. This has become possible with measurements of radii and luminosities. Meanwhile, radial velocity surveys discover also very low-mass planets. Uniting all this observational data into one coherent picture to better understand planet formation is an important, but difficult undertaking. Our approach is to develop a model which can make testable predictions for all these observational methods. We continue to describe how we have extended our formation model into a self-consistently coupled formation and evolution model. We show how we calculate the internal structure of the solid core and radiogenic heating. We also improve the protoplanetary disk model. Finally, we conduct population synthesis calculations. We present how the planetary mass-radius relationship of planets with primordial H/He envelopes forms and evolves in time. The basic shape of the M-R relation can be understood from the core accretion model. Low-mass planets cannot bind massive envelopes, while super-critical cores necessarily trigger runway gas accretion, leading to "forbidden" zones in the M-R plane. For a given mass, there is a considerable diversity of radii. We compare the synthetic M-R relation with the observed one, finding good agreement for a>0.1 AU. The synthetic radius distribution is characterized by a strong increase towards small R, and a second, lower local maximum at ~1 Jovian radius. The increase towards small radii reflects the increase of the mass function towards low M. The second local maximum is due to the fact that radii are nearly independent of mass for giant planets. A comparison of the synthetic radius distribution with Kepler data shows agreement for R>2 Earth radii, but divergence for smaller radii. We predict that in the next few years, Kepler should find the second, local maximum at ~1 Jovian radius.

Dynamics and accretion of planetesimals

We review the basic dynamics and accretion of planetesimals by showing N-body simulations. The orbits of planetesimals evolve through two-body gravitational relaxation: viscous stirring increases the random velocity and dynamical friction realizes the equiparation of the random energy. In the early stage of planetesimal accretion the growth mode of planetesimals is runaway growth where larger planetesimals grow faster than smaller ones. When a protoplanet (runaway-growing planetesimal) exceeds a critical mass the growth mode shifts to oligarchic growth where similar-sized protoplanets grow keeping a certain orbital separation. The final stage of terrestrial planet formation is collision among protoplanets known as giant impacts. We also summarize the dynamical effects of disk gas on planets and the core accretion model for formation of gas giants and discuss the diversity of planetary systems.

SUBMILLIMETER ARRAY OBSERVATIONS OF THE RX J1633.9-2442 TRANSITION DISK: EVIDENCE FOR MULTIPLE PLANETS IN THE MAKING

We present continuum high resolution Submillimeter Array (SMA) observations of the transition disk object RX J1633.9-2442, which is located in the Ophiuchus molecular cloud and has recently been identified as a likely site of ongoing giant planet formation. The observations were taken at 340 GHz (880 micron) with the SMA in its most extended configuration, resulting in an angular resolution of 0.3" (35 AU at the distance of the target). We find that the disk is highly inclined (i ~50 deg) and has an inner cavity ~25 AU in radius, which is clearly resolved by our observations. We simultaneously model the entire optical to millimeter wavelength spectral energy distribution (SED) and SMA visibilities of RX J1633.9-2442 in order to constrain the structure of its disk. We find that an empty cavity ~25 AU in radius is inconsistent with the excess emission observed at 12, 22, and 24 micron. Instead, the mid-IR excess can be modeled by either a narrow, optically thick ring at ~10 AU or an optically thin region extending from ~7 AU to ~25 AU. The inner disk (r < 5 AU) is mostly depleted of small dust grains as attested by the lack of detectable near-IR excess. We also present deep Keck aperture masking observations in the near-IR, which rule out the presence of a companion up to 500 times fainter than the primary star (in K-band) for projected separations in the 5-20 AU range. We argue that the complex structure of the RX J1633.9-2442 disk is best explained by multiple planets embedded within the disk. We also suggest that the properties and incidence of objects such as RX J1633.9-2442, T Cha, and LkCa 15 (and those of the companions recently identified to these two latter objects) are most consistent with the runaway gas accretion phase of the core accretion model, when giant planets gain their envelopes and suddenly become massive enough to open wide gaps in the disk.

THE FIRST PLANETS: THE CRITICAL METALLICITY FOR PLANET FORMATION

A rapidly growing body of observational results suggests that planet formation takes place preferentially at high metallicity. In the core accretion model of planet formation this is expected because heavy elements are needed to form the dust grains which settle into the midplane of the protoplanetary disk and coagulate to form the planetesimals from which planetary cores are assembled. As well, there is observational evidence that the lifetimes of circumstellar disks are shorter at lower metallicities, likely due to greater susceptibility to photoevaporation. Here we estimate the minimum metallicity for planet formation, by comparing the timescale for dust grain growth and settling to that for disk photoevaporation. For a wide range of circumstellar disk models and dust grain properties, we find that the critical metallicity above which planets can form is a function of the distance r at which the planet orbits its host star. With the iron abundance relative to that of the Sun [Fe/H] as a proxy for the metallicity, we estimate a lower limit for the critical abundance for planet formation of [Fe/H]_crit ~ -1.5 + log(r/1 AU), where an astronomical unit (AU) is the distance between the Earth and the Sun. This prediction is in agreement with the available observational data, and carries implications for the properties of the first planets and for the emergence of life in the early Universe. In particular, it implies that the first Earth-like planets likely formed from circumstellar disks with metallicities Z > 0.1 Z_Sun. If planets are found to orbit stars with metallicities below the critical metallicity, this may be a strong challenge to the core accretion model.

Metallicity of solar-type stars with debris discs and planets

Around 16% of the solar-like stars in our neighbourhood show IR-excesses due to debris discs and a fraction of them are known to host planets. We aim to determine in a homogeneous way the metallicity of a sample of stars with known debris discs and planets. Our analysis includes the calculation of the fundamental stellar parameters by applying the iron ionisation equilibrium conditions to several isolated Fe I and Fe II lines. The metallicity distributions of the different stellar samples suggest that there is a transition toward higher metallicities from stars with neither debris discs nor planets to stars hosting giant planets. Stars with debris discs and stars with neither debris nor planets follow a similar metallicity distribution, although the distribution of the first ones might be shifted towards higher metallicities. Stars with debris discs and planets have the same metallicity behaviour as stars hosting planets, irrespective of whether the planets are low-mass or gas giants. In the case of debris discs and giant planets, the planets are usually cool, -semimajor axis larger than 0.1 AU. The data also suggest that stars with debris discs and cool giant planets tend to have a low dust luminosity, and are among the less luminous debris discs known. We also find evidence of an anticorrelation between the luminosity of the dust and the planet eccentricity. Our data show that the presence of planets, not the debris disc, correlates with the stellar metallicity. The results confirm that core-accretion models represent suitable scenarios for debris disc and planet formation. Dynamical instabilities produced by eccentric giant planets could explain the suggested dust luminosity trends observed for stars with debris discs and planets.

FEEDBACK EFFECTS ON LOW-MASS STAR FORMATION

Protostellar feedback, both radiation and bipolar outflows, dramatically affects the fragmentation and mass accretion from star-forming cores. We use ORION, an adaptive mesh refinement gravito-radiation-hydrodynamics code, to simulate the formation of a cluster of low-mass stars, including both radiative transfer and protostellar outflows. We ran four simulations to isolate the individual effects of radiation feedback and outflow feedback as well as the combination of the two. Outflows reduce protostellar masses and accretion rates each by a factor of three and therefore reduce protostellar luminosities by an order of magnitude. Thus, while radiation feedback suppresses fragmentation, outflows render protostellar radiation largely irrelevant for low-mass star formation above a mass scale of 0.05 M_sun. We find initial fragmentation of our cloud at half the global Jeans length, ~ 0.1 pc. With insufficient protostellar radiation to stop it, these 0.1 pc cores fragment repeatedly, forming typically 10 stars each. The accretion rate in these stars scales with mass as predicted from core accretion models that include both thermal and turbulent motions. We find that protostellar outflows do not significantly affect the overall cloud dynamics, in the absence of magnetic fields, due to their small opening angles and poor coupling to the dense gas. The outflows reduce the mass from the cores by 2/3, giving a core to star efficiency ~ 1/3. The simulation with radiation and outflows reproduces the observed protostellar luminosity function. All of the simulations can reproduce observed core mass functions, though they are sensitive to telescope resolution. The simulation with both radiation and outflows reproduces the galactic IMF and the two-point correlation function of the cores observed in rho Oph.

THE EFFECTS OF SNOWLINES ON C/O IN PLANETARY ATMOSPHERES

The C/O ratio is predicted to regulate the atmospheric chemistry in hot Jupiters. Recent observations suggest that some exo-planets, e.g. Wasp 12- b, have atmospheric C/O ratios substantially different from the solar value of 0.54. In this paper we present a mechanism that can produce such atmospheric deviations from the stellar C/O ratio. In protoplanetary disks, different snowlines of oxygen- and carbon-rich ices, especially water and carbon monoxide, will result in systematic variations in the C/O ratio both in the gas and in the condensed phase. In particular, between the H2O and CO snowlines most oxygen is present in icy grains - the building blocks of planetary cores in the core accretion model - while most carbon remains in the gas-phase. This region is coincidental with the giant-planet forming zone for a range of observed protoplanetary disks. Based on standard core accretion models of planet formation, gas giants that sweep up most of their atmospheres from disk gas outside of the water snowline will have C/O?1, while atmospheres significantly contaminated by evaporating planetesimals will have stellar or sub-stellar C/O when formed at the same disk radius. The overall metallicity will also depend on the atmosphere formation mechanism, and exoplanetary atmospheric compositions may therefore provide constraints on where and how a specific planet formed.

Exoplanets

Exoplanets

KEPLEREXOPLANET CANDIDATE HOST STARS ARE PREFERENTIALLY METAL RICH

We find that Kepler exoplanet candidate (EC) host stars are preferentially metal-rich, including the low-mass stellar hosts of small-radius ECs. The last observation confirms a tentative hint that there is a correlation between the metallicity of low-mass stars and the presence of low-mass and small-radius exoplanets. In particular, we compare the J-H--g-r color-color distribution of Kepler EC host stars with a control sample of dwarf stars selected from the ~150,000 stars observed during Q1 and Q2 of the Kepler mission but with no detected planets. We find that at J-H = 0.30 characteristic of solar-type stars, the average g-r color of stars that host giant ECs is 4-sigma redder than the average color of the stars in the control sample. At the same time, the average g-r color of solar-type stars that host small-radius ECs is indistinguishable from the average color of the stars in the control sample. In addition, we find that at J-H = 0.62 indicative of late K dwarfs, the average g-r color of stars that host small-radius ECs is 4-sigma redder than the average color of the stars in the control sample. These offsets are unlikely to be caused by differential reddening, age differences between the two populations, or the presence of giant stars in the control sample. Stellar models suggest that the first color offset is due to a 0.2 dex enhancement in [Fe/H] of the giant EC host population at M_star = 1 M_Sun, while Sloan photometry of M 67 and NGC 6791 suggests that the second color offset is due to a similar [Fe/H] enhancement of the small-radius EC host population at M_star = 0.7 M_Sun. These correlations are a natural consequence of the core-accretion model of planet formation.

Gas giant formation with small cores triggered by envelope pollution by icy planetesimals

We have investigated how envelope pollution by icy planetesimals affects the critical core mass for gas giant formation and the gas accretion time-scales. In the core-accretion model, runaway gas accretion is triggered after a core reaches a critical core mass. All the previous studies on the core-accretion model assumed that the envelope has the solar composition uniformly. In fact, the envelope is likely polluted by evaporated materials of icy planetesimals because icy planetesimals going through the envelope experience mass loss via strong ablation and most of their masses are deposited in the deep envelope. In this paper, we have demonstrated that envelope pollution in general lowers the critical core masses and hastens gas accretion on to the protoplanet because of the increase in the molecular weight and reduction of adiabatic temperature gradient. Widely- and highly-polluted envelopes allow smaller cores to form massive envelopes before disc dissipation. Our results suggest that envelope pollution in the course of planetary accretion has the potential to trigger gas giant formation with small cores. We propose that it is necessary to take into account envelope pollution by icy planetesimals when we discuss gas giant formation based on the core-accretion model.

THE PROTOSTELLAR LUMINOSITY FUNCTION

The protostellar luminosity function (PLF) is the present-day luminosity function of the protostars in a region of star formation. It is determined using the protostellar mass function (PMF) in combination with a stellar evolutionary model that provides the luminosity as a function of instantaneous and final stellar mass. As in McKee & Offner (2010), we consider three main accretion models: the Isothermal Sphere model, the Turbulent Core model, and an approximation of the Competitive Accretion model. We also consider the effect of an accretion rate that tapers off linearly in time and an accelerating star formation rate. For each model, we characterize the luminosity distribution using the mean, median, maximum, ratio of the median to the mean, standard deviation of the logarithm of the luminosity, and the fraction of very low luminosity objects. We compare the models with bolometric luminosities observed in local star forming regions and find that models with an approximately constant accretion time, such as the Turbulent Core and Competitive Accretion models, appear to agree better with observation than those with a constant accretion rate, such as the Isothermal Sphere model. We show that observations of the mean protostellar luminosity in these nearby regions of low-mass star formation suggest a mean star formation time of 0.3$\pm$0.1 Myr. Such a timescale, together with some accretion that occurs non-radiatively and some that occurs in high-accretion, episodic bursts, resolves the classical "luminosity problem" in low-mass star formation, in which observed protostellar luminosities are significantly less than predicted. An accelerating star formation rate is one possible way of reconciling the observed star formation time and mean luminosity.

The Red MSX Source survey: critical tests of accretion models for the formation of massive stars

There is currently no accepted theoretical framework for the formation of the most massive stars, and the manner in which protostars continue to accrete and grow in mass beyond \sim10Msun is still a controversial topic. In this study we use several prescriptions of stellar accretion and a description of the Galactic gas distribution to simulate the luminosities and spatial distribution of massive protostellar population of the Galaxy. We then compare the observables of each simulation to the results of the Red MSX Source (RMS) survey, a recently compiled database of massive young stellar objects. We find that the observations are best matched by accretion rates which increase as the protostar grows in mass, such as those predicted by the turbulent core and competitive accretion (i.e. Bondi-Hoyle) models. These 'accelerating accretion' models provide very good qualitative and quantitative fits to the data, though we are unable to distinguish between these two models on our simulations alone. We rule out models with accretion rates which are constant with time, and those which are initially very high and which fall away with time, as these produce results which are quantitatively and/or qualitatively incompatible with the observations. To simultaneously match the low- and high-luminosity YSO distribution we require the inclusion of a 'swollen-star' pre-main-sequence phase, the length of which is well-described by the Kelvin-Helmholz timescale. Our results suggest that the lifetime of the YSO phase is \sim 10^5yrs, whereas the compact Hii-region phase lasts between \sim 2 - 4 \times 10^5yrs depending on the final mass of the star. Finally, the absolute numbers of YSOs are best matched by a globally averaged star-formation rate for the Galaxy of 1.5-2Msun/yr.

Experimental Design for the Gemini Planet Imager

ABSTRACTThe Gemini Planet Imager (GPI) is a high-performance adaptive optics system being designed and built for the Gemini Observatory. GPI is optimized for high-contrast imaging, combining precise and accurate wavefront control, diffraction suppression, and a speckle-suppressing science camera with integral field and polarimetry capabilities. The primary science goal for GPI is the direct detection and characterization of young, Jovian-mass exoplanets. For plausible assumptions about the distribution of gas giant properties at large semimajor axes, GPI will be capable of detecting more than 10% of gas giants more massive than 0.5 MJ around stars younger than 100 Myr and nearer than 75 pc. For systems younger than 1 Gyr, gas giants more massive than 8 MJ and with semimajor axes greater than 15 AU are detected with completeness greater than 50%. A survey targeting young stars in the solar neighborhood will help determine the formation mechanism of gas giant planets by studying them at ages where planet brightness depends upon formation mechanism. Such a survey will also be sensitive to planets at semimajor axes, comparable with the gas giants in our own solar system. In the simple, and idealized, situation in which planets formed by either the “hot-start” model of Burrows et al. or the core accretion model of Marley et al., a few tens of detected planets are sufficient to distinguish how planets form.

The first stages of planet formation in binary systems: how far can dust coagulation proceed?

We examine the first phase of the core accretion model, namely the dust growth/fragmentation in binary systems. In our model, a gas and dust disk is present around the primary star and is perturbed by the secondary. We study the effects of a secondary with/without eccentricity on the dust population to determine what sizes the aggregates can reach and how that compares to the dust population in disks around single stars. We find that the secondary star has two effects on the dust population. 1.) The disk is truncated due to the presence of the secondary star and the maximum mass of the particles is decreased in the lowered gas densities. This effect is dominant in the outer disk. 2.) The perturbation of the secondary pumps up the eccentricity of the gas disk, which in turn increases the relative velocity between the dust and the gas. Therefore the maximum particle sizes are further decreased. The second effect of the secondary influences the entire disk. Coagulation is efficiently reduced even at the very inner parts of the disk. The average mass of the particles is reduced by four orders of magnitude (as a consequence, the stopping time is reduced by one order of magnitude) in disks around binary systems compared to dust in disks around single stars.

ON THE VOLATILE ENRICHMENTS AND HEAVY ELEMENT CONTENT IN HD189733b

Favored theories of giant planet formation center around two main paradigms, namely the core accretion model and the gravitational instability model. These two formation scenarios support the hypothesis that the giant planet metallicities should be higher or equal to that of the parent star. Meanwhile, spectra of the transiting hot Jupiter HD189733b suggest that carbon and oxygen abundances range from depleted to enriched with respect to the star. Here, using a model describing the formation sequence and composition of planetesimals in the protoplanetary disk, we determine the range of volatile abundances in the envelope of HD189733b that is consistent with the 20–80 M⊕ of heavy elements estimated to be present in the planet's envelope. We then compare the inferred carbon and oxygen abundances to those retrieved from spectroscopy, and we find a range of supersolar values that directly fit both spectra and internal structure models. In some cases, we find that the apparent contradiction between the subsolar elemental abundances and the mass of heavy elements predicted in HD189733b by internal structure models can be explained by the presence of large amounts of carbon molecules in the form of polycyclic aromatic hydrocarbons and soots in the upper layers of the envelope, as suggested by recent photochemical models. A diagnostic test that would confirm the presence of these compounds in the envelope is the detection of acetylene. Several alternative hypotheses that could also explain the subsolar metallicity of HD189733b are formulated: the possibility of differential settling in its envelope, the presence of a larger core that did not erode with time, a mass of heavy elements lower than the one predicted by interior models, a heavy element budget resulting from the accretion of volatile-poor planetesimals in specific circumstances, or the combination of all these mechanisms.

Theory of planet formation and comparison with observation

The planetary mass-radius diagram is an observational result of central importance to understand planet formation. We present an updated version of our planet formation model based on the core accretion paradigm which allows to calculate planetary radii and luminosities during the entire formation and evolution of the planets. We first study with it the formation of Jupiter, and compare with previous works. Then we conduct planetary population synthesis calculations to obtain a synthetic mass-radius diagram which we compare with the observed one. Except for bloated Hot Jupiters which can be explained only with additional mechanisms related to their proximity to the star, we find a good agreement of the general shape of the observed and the synthetic mass-radius diagram. This shape can be understood with basic concepts of the core accretion model.

THE SPARSEST CLUSTERS WITH O STARS

There is much debate on how high-mass star formation varies with environment, and whether the sparsest star-forming environments are capable of forming massive stars. To address this issue, we have observed eight apparently isolated OB stars in the SMC using HST's Advanced Camera for Surveys. Five of these objects appear as isolated stars, two of which are confirmed to be runaways. The remaining three objects are found to exist in sparse clusters, with <10 companion stars revealed, having masses of 1-4 solar mass. Stochastic effects dominate in these sparse clusters, so we perform Monte Carlo simulations to explore how our observations fit within the framework of empirical, galactic cluster properties. We generate clusters using a simplistic -2 power-law distribution for either the number of stars per cluster (N_*) or cluster mass (M_cl). These clusters are then populated with stars randomly chosen from a Kroupa IMF. We find that simulations with cluster lower-mass limits of M_cl,lo >20 solar mass and N_*,lo >40 match best with observations of SMC and Galactic OB star populations. We examine the mass ratio of the second-most massive and most massive stars (m_max,2/m_max), finding that our observations all exist below the 20th percentile of our simulated clusters. However, all of our observed clusters lie within the parameter space spanned by the simulated clusters, although some are in the lowest 5th percentile frequency. These results suggest that clusters are built stochastically by randomly sampling stars from a universal IMF with a fixed stellar upper-mass limit. In particular, we see no evidence to suggest a m_max - M_cl relation. Our results may be more consistent with core accretion models of star formation than with competitive accretion models, and they are inconsistent with the proposed steepening of the integrated galaxy IMF (IGIMF).

METALLICITIES OF PLANET-HOSTING STARS: A SAMPLE OF GIANTS AND SUBGIANTS

This work presents a homogeneous derivation of atmospheric parameters and iron abundances for a sample of giant and subgiant stars which host giant planets, as well as a control sample of subgiant stars not known to host giant planets. The analysis is done using the same technique as for our previous analysis of a large sample of planet-hosting and control sample dwarf stars. A comparison between the distributions of [Fe/H] in planet-hosting main-sequence stars, subgiants, and giants within these samples finds that the main-sequence stars and subgiants have the same mean metallicity of <[Fe/H]> \simeq +0.11 dex, while the giant sample is typically more metal poor, having an average metallicity of <[Fe/H]> = -0.06 dex. The fact that the subgiants have the same average metallicities as the dwarfs indicates that significant accretion of solid metal-rich material onto the planet-hosting stars has not taken place, as such material would be diluted in the evolution from dwarf to subgiant. The lower metallicity found for the planet-hosting giant stars in comparison with the planet-hosting dwarfs and subgiants is interpreted as being related to the underlying stellar mass, with giants having larger masses and thus, on average larger-mass protoplanetary disks. In core accretion models of planet formation, larger disk masses can contain the critical amount of metals necessary to form giant planets even at lower metallicities.

Composition of massive giant planets

AbstractThe two current models for giant planet formation are core accretion and disk instability. We discuss the core masses and overall planetary enrichment in heavy elements predicted by the two formation models, and show that both models could lead to a large range of final compositions. For example, both can form giant planets with nearly stellar compositions. However, low-mass giant planets, enriched in heavy elements compared to their host stars, are more easily explained by the core accretion model. The final structure of the planets, i.e., the distribution of heavy elements, is not firmly constrained in either formation model.