Predictions on the core mass of Jupiter and of giant planets in general

ABSTRACT Some Jupiter-mass exoplanets contain ${\sim}100\, {\rm M}_{\hbox{$\oplus $}}$ of metals, well above the ${\sim}10\, {\rm M}_{\hbox{$\oplus $}}$ typically needed in a solid core to trigger giant planet formation by runaway gas accretion. We demonstrate that such ‘heavy-metal Jupiters’ can result from planetary mergers near ∼10 au. Multiple cores accreting gas at runaway rates gravitationally perturb one another on to crossing orbits such that the average merger rate equals the gas accretion rate. Concurrent mergers and gas accretion implies the core mass scales with the total planet mass as Mcore ∝ M1/5 – heavier planets harbour heavier cores, in agreement with the observed relation between total mass and metal mass. While the average gas giant merges about once to double its core, others may merge multiple times, as merger trees grow chaotically. We show that the dispersion of outcomes inherent in mergers can reproduce the large scatter in observed planet metallicities, assuming $3{-}30\, {\rm M}_{\hbox{$\oplus $}}$ pre-runaway cores. Mergers potentially correlate metallicity, eccentricity, and spin.

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Constraining planetary interiors with the Love number k2

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311020898 ◽

2010 ◽

Vol 6 (S276) ◽

pp. 482-484

Author(s):

Ulrike Kramm ◽

Nadine Nettelmann ◽

Ronald Redmer

Keyword(s):

Density Distribution ◽

Extrasolar Planets ◽

Giant Planets ◽

Love Number ◽

Core Mass ◽

Planetary Interiors ◽

Orbital Parameters ◽

First Order ◽

The Core ◽

Observable Parameter

AbstractFor the solar sytem giant planets the measurement of the gravitational moments J2 and J4 provided valuable information about the interior structure. However, for extrasolar planets the gravitational moments are not accessible. Nevertheless, an additional constraint for extrasolar planets can be obtained from the tidal Love number k2, which, to first order, is equivalent to J2. k2 quantifies the quadrupolic gravity field deformation at the surface of the planet in response to an external perturbing body and depends solely on the planet's internal density distribution. On the other hand, the inverse deduction of the density distribution of the planet from k2 is non-unique. The Love number k2 is a potentially observable parameter that can be obtained from tidally induced apsidal precession of close-in planets (Ragozzine & Wolf 2009) or from the orbital parameters of specific two-planet systems in apsidal alignment (Mardling 2007). We find that for a given k2, a precise value for the core mass cannot be derived. However, a maximum core mass can be inferred which equals the core mass predicted by homogeneous zero metallicity envelope models. Using the example of the extrasolar transiting planet HAT-P-13b we show to what extend planetary models can be constrained by taking into account the tidal Love number k2.

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Formation of the Giant Planets

Symposium - International Astronomical Union ◽

10.1017/s0074180900073812 ◽

1981 ◽

Vol 93 ◽

pp. 133-134

Author(s):

Hiroshi Mizuno

Keyword(s):

Radiative Transfer ◽

Solar Nebula ◽

Giant Planet ◽

Giant Planets ◽

Core Mass ◽

The Core ◽

Gaseous Envelope

The structure of a gaseous envelope surrounding a icy/rocky core is studied in consideration of radiative transfer. It is found that when the core grows beyond a critical core mass, the envelope cannot be in equilibrium and collapses onto the core to form a proto-giant planet. The results are as follows (for details, see Mizuno 1980).1) The critical core mass is smaller than that estimated by Perri and Cameron (1974) and Mizuno, Nakazawa and Hayashi (1978). 2) When the grain opacity in the envelope varies from 0 to 1 cm2/g, the critical core mass changes from ~2 to ~12 Earth's masses. 3) The critical core mass is independent of the region in the solar nebula.These are due to the existence of the radiative region in the envelope.

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On uncertainty of Jupiter's core mass due to observational errors

Proceedings of the International Astronomical Union ◽

10.1017/s1743921308016554 ◽

2007 ◽

Vol 3 (S249) ◽

pp. 163-166

Author(s):

Yasunori Hori ◽

Takayoshi Sano ◽

Masahiro Ikoma ◽

Shigeru Ida

Keyword(s):

Narrow Range ◽

Giant Planets ◽

Observational Error ◽

Core Mass ◽

The Core ◽

Observational Uncertainty ◽

Observational Errors ◽

Gas Giant ◽

Accurate Observation ◽

Juno Mission

AbstractThe origins of extrasolar gas giant planets have been discussed, based on our understanding of the gas giant planets in the solar system, Jupiter and Saturn. However, how Jupiter and Saturn formed is still uncertain because of the uncertainty in their interiors, especially the core mass (Mc). The uncertainty in Mc is partly due to those in observational data such as gravitational moments (J2n), equatorial radius (Req) and 1-bar temperatures (T1bar). New frontiers mission to Jupiter by NASA (JUNO) launched in 2011 is expected to reduce the observational errors. However, it is not necessarily clear yet which observational uncertainty dominates and how accurate observation is needed to constrain Mc enough to know the origin of Jupiter. Thus, modeling the interior of Jupiter, we evaluate each effect on Mc and required precision. We have found that the observational error of 5% in T1bar yields an error of several M⊕ in Mc. We have also found that the values of J6 of our successful models are confined in a narrow range compared to its observational error. This implies that comparison between the values of J6 of our successful models and the J6 value obtained from JUNO mission helps us to know whether the present theoretical model is valid.

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Formation of GW190521 from stellar evolution: the impact of the hydrogen-rich envelope, dredge-up and 12C(α, γ)16O rate on the pair-instability black hole mass gap

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3916 ◽

2020 ◽

Author(s):

Guglielmo Costa ◽

Alessandro Bressan ◽

Michela Mapelli ◽

Paola Marigo ◽

Giuliano Iorio ◽

...

Keyword(s):

Stellar Evolution ◽

Reaction Rate ◽

Primary Component ◽

Mass Reduction ◽

Black Hole Mass ◽

Core Mass ◽

The Core ◽

Mass Gap ◽

M Stars ◽

The Impact

Abstract Pair-instability (PI) is expected to open a gap in the mass spectrum of black holes (BHs) between ≈40 − 65 M⊙ and ≈120 M⊙. The existence of the mass gap is currently being challenged by the detection of GW190521, with a primary component mass of $85^{+21}_{-14}$ M⊙. Here, we investigate the main uncertainties on the PI mass gap: the 12C(α, γ)16O reaction rate and the H-rich envelope collapse. With the standard 12C(α, γ)16O rate, the lower edge of the mass gap can be 70 M⊙ if we allow for the collapse of the residual H-rich envelope at metallicity Z ≤ 0.0003. Adopting the uncertainties given by the starlib database, for models computed with the 12C(α, γ)16O rate −1 σ, we find that the PI mass gap ranges between ≈80 M⊙ and ≈150 M⊙. Stars with MZAMS > 110 M⊙ may experience a deep dredge-up episode during the core helium-burning phase, that extracts matter from the core enriching the envelope. As a consequence of the He-core mass reduction, a star with MZAMS = 160 M⊙ may avoid the PI and produce a BH of 150 M⊙. In the −2 σ case, the PI mass gap ranges from 92 M⊙ to 110 M⊙. Finally, in models computed with 12C(α, γ)16O −3 σ, the mass gap is completely removed by the dredge-up effect. The onset of this dredge-up is particularly sensitive to the assumed model for convection and mixing. The combined effect of H-rich envelope collapse and low 12C(α, γ)16O rate can lead to the formation of BHs with masses consistent with the primary component of GW190521.

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Derivation of the core mass-halo mass relation of fermionic and bosonic dark matter halos from an effective thermodynamical model

Physical Review D ◽

10.1103/physrevd.100.123506 ◽

2019 ◽

Vol 100 (12) ◽

Cited By ~ 6

Author(s):

Pierre-Henri Chavanis

Keyword(s):

Dark Matter ◽

Mass Relation ◽

Dark Matter Halos ◽

Core Mass ◽

The Core ◽

Thermodynamical Model

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Chemical Enrichment and Central Star Properties

Symposium - International Astronomical Union ◽

10.1017/s0074180900172468 ◽

1993 ◽

Vol 155 ◽

pp. 572-572

Author(s):

C.Y. Zhang

Keyword(s):

Planetary Nebulae ◽

Central Star ◽

Agb Stars ◽

Physical Processes ◽

Chemical Abundances ◽

Core Mass ◽

Chemical Enrichment ◽

The Core ◽

Stellar Temperature ◽

Independent Parameters

We have selected a sample of planetary nebulae, for which the core masses are determined using distance-independent parameters (Zhang and Kwok 1992). The chemical abundances of He, N, O, and C are taken from the literature for them. Relationships of the ratios of He/H, N/O, and C/O with various stellar parameters of planetary nebulae (PN), such as the core mass, the mass of the core plus the ionized nebular gas, the stellar age and temperature, are examined. It is found that the N/O increases with increasing mass, while the C/O first increases and then decreases with the core mass. No strong correlation seems to exist between the He/H and the core mass. A correlation of the N/O and He/H with the stellar temperature exists. The current dredge-up theory for the progenitor AGB stars cannot satisfactorily account for these patterns of chemical enrichment in PN. Furthermore, the correlations of the N/O and He/H with the stellar age and temperature indicate that besides the dredge-ups in the RG and AGB stages, physical processes that happen in the planetary nebula stage may also play a role in forming the observed patterns of chemical enrichment in the planetary nebulae.

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Simulations of the IMF in Clusters

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311000317 ◽

2010 ◽

Vol 6 (S270) ◽

pp. 151-158

Author(s):

Ralph E. Pudritz

Keyword(s):

Equations Of State ◽

Stellar Dynamics ◽

Mass Function ◽

Initial Mass Function ◽

Core Mass ◽

Numerical Work ◽

Computational Approaches ◽

The Core ◽

The Imf

AbstractWe review computational approaches to understanding the origin of the Initial Mass Function (IMF) during the formation of star clusters. We examine the role of turbulence, gravity and accretion, equations of state, and magnetic fields in producing the distribution of core masses - the Core Mass Function (CMF). Observations show that the CMF is similar in form to the IMF. We focus on feedback processes such as stellar dynamics, radiation, and outflows can reduce the accreted mass to give rise to the IMF. Numerical work suggests that filamentary accretion may play a key role in the origin of the IMF.

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Envelopes of embedded super-Earths – II. Three-dimensional isothermal simulations

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1870 ◽

2019 ◽

Vol 488 (2) ◽

pp. 2365-2379 ◽

Cited By ~ 6

Author(s):

William Béthune ◽

Roman R Rafikov

Keyword(s):

Three Dimensional ◽

Polar Axis ◽

High Mass ◽

Gas Flows ◽

Core Mass ◽

Material Recycling ◽

The Core ◽

Planetary Cores ◽

Mass Circulation ◽

Runaway Growth

ABSTRACT Massive planetary cores embedded in protoplanetary discs are believed to accrete extended atmospheres, providing a pathway to forming gas giants and gas-rich super-Earths. The properties of these atmospheres strongly depend on the nature of the coupling between the atmosphere and the surrounding disc. We examine the formation of gaseous envelopes around massive planetary cores via three-dimensional inviscid and isothermal hydrodynamic simulations. We focus the changes in the envelope properties as the core mass varies from low (subthermal) to high (superthermal) values, a regime relevant to close-in super-Earths. We show that global envelope properties such as the amount of rotational support or turbulent mixing are mostly sensitive to the ratio of the Bondi radius of the core to its physical size. High-mass cores are fed by supersonic inflows arriving along the polar axis and shocking on the densest parts of the envelope, driving turbulence, and mass accretion. Gas flows out of the core’s Hill sphere in the equatorial plane, describing a global mass circulation through the envelope. The shell of shocked gas atop the core surface delimits regions of slow (inside) and fast (outside) material recycling by gas from the surrounding disc. While recycling hinders the runaway growth towards gas giants, the inner regions of protoplanetary atmospheres, more immune to mixing, may remain bound to the planet.

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Clouds, cores, and stars in the nearest molecular complexes

Symposium - International Astronomical Union ◽

10.1017/s0074180900239569 ◽

1991 ◽

Vol 147 ◽

pp. 221-228

Author(s):

P. C. Myers

Keyword(s):

Column Density ◽

Velocity Dispersion ◽

Molecular Complexes ◽

Star Cluster ◽

The Sun ◽

Core Size ◽

Core Mass ◽

The Core ◽

Internal Motions ◽

Over Time

The properties and structure of six molecular complexes within 500 pc of the Sun are described and compared. They are generally organized into elongated filaments which appear connected to less elongated, more massive clouds. Their prominent star clusters tend to be located in the massive clouds rather than in the filaments. The complexes have similar structure, but big differences in scale, from a few pc to some 30 pc. They show a pattern of regional virial equilibrium, where the massive, centrally located clouds are close to virial equilibrium, while the less massive filaments and other small clouds have too little mass to bind their observed internal motions. Complexes can be ranked according to increasing size, mass, core mass, and the mass and number of the associated stars: they range from Lupus to Taurus to Ophiuchus to Perseus to Orion B to Orion A. The cores in nearby complexes tend to have maps which are elongated, rather than round. The core size, velocity dispersion, and column density of most cores are consistent with virial equilibrium. Cores in Orion tend to exceed cores in Taurus in their line width, size, temperature, mass, and in the mass of the associated star, if any. Stars in Orion tend to be more numerous and more massive than in Taurus, while those in Taurus tend to be more numerous and more massive than in Lupus. The mass of a core tends to increase with the mass of the cloud where it is found, with the mass of the star cluster with which it is associated, and with its proximity to a star cluster. These properties suggest that complexes and their constituent cores and clusters develop together over time, perhaps according to the depth of the gravitational well of the complex.

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