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

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.

scholarly journals Heavy-metal Jupiters by major mergers: metallicity versus mass for giant planets

2020 ◽  
Vol 498 (1) ◽  
pp. 680-688 ◽  
Author(s):  
Sivan Ginzburg ◽  
Eugene Chiang
Keyword(s):  
Heavy Metal ◽  
Accretion Rate ◽  
Giant Planet ◽  
Giant Planets ◽  
Solid Core ◽  
Core Mass ◽  
The Core ◽  
Multiple Cores ◽  
Merger Rate ◽  
Gas Accretion

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.

Constraining planetary interiors with the Love number k2

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.

scholarly journals Uncertainty in Scatterometer-Derived Vorticity

2010 ◽  
Vol 27 (3) ◽  
pp. 594-603 ◽  
Author(s):  
Mark A. Bourassa ◽  
Kelly McBeth Ford
Keyword(s):  
Spatial Organization ◽  
Truncation Error ◽  
Random Errors ◽  
Observational Error ◽  
Worst Case ◽  
Truncation Errors ◽  
The Third ◽  
Representation Error ◽  
Observational Uncertainty ◽  
Observational Errors

Abstract A more versatile and robust technique is developed for determining area-averaged surface vorticity based on vector winds from swaths of remotely sensed wind vectors. This technique could also be applied to determine the curl of stress, and it could be applied to any gridded dataset of winds or stresses. The technique is discussed in detail and compared to two previous studies that focused on early development of tropical systems. Error characteristics of the technique are examined in detail. Specifically, three independent sources of error are explored: random observational error, truncation error, and representation error. Observational errors are due to random errors in the wind observations and determined as a worst-case estimate as a function of averaging spatial scale. The observational uncertainty in the Quick Scatterometer (QuikSCAT)-derived vorticity averaged for a roughly circular shape with a 100-km diameter, expressed as one standard deviation, is approximately 0.5 × 10−5 s−1 for the methodology described herein. Truncation error is associated with the assumption of linear changes between wind vectors. Uncertainty related to truncation has more spatial organization in QuikSCAT data than observational uncertainty. On 25- and 50-km scales, the truncation errors are very large. The third type of error, representation error, is due to the size of the area being averaged compared to values with 25-km length scales. This type of error is analogous to oversmoothing. Tropical and subtropical low pressure systems from three months of QuikSCAT observations are used to examine truncation and representation errors. Representation error results in a bias of approximately −1.5 × 10−5 s−1 for area-averaged vorticity calculated on a 100-km scale compared to vorticity calculated on a 25-km scale. The discussion of these errors will benefit future projects of this nature as well as future satellite missions.

scholarly journals Formation of the Giant Planets

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.

scholarly journals Blue Stragglers as Long-Lived Stars

1981 ◽  
Vol 93 ◽  
pp. 187-189
Author(s):  
J. Craig Wheeler ◽  
Michel Breger
Keyword(s):  
Main Sequence ◽  
Narrow Range ◽  
Core Region ◽  
Open Clusters ◽  
Apparent Mass ◽  
Core Mass ◽  
Hydrogen Burning ◽  
Blue Stragglers ◽  
The Core ◽  
Chandrasekhar Limit

The existence of blue stragglers in old open clusters with apparent mass more than twice the mass of the turnoff argues against simple binary mass transfer as the mechanism of their origin. The excess of blue stragglers to the red of the termination of the core hydrogen burning main sequence suggests that blue stragglers are not evolving normally. Stellar evolution models invoking mixing in an extended core region can account for the distribution of blue stragglers in the H-R diagram. Such models live longer, brightening and evolving further to the red before core hydrogen exhaustion than do normal stars. The distribution of blue stragglers in NGC 7789 is consistent with a range of mixed core mass fraction ~30–90 per cent and a narrow range in mass ~1.7–2.1 M⊙. Such evolution will result in a class of helium rich stars which have lived longer than normal and whose total mass exceeds the Chandrasekhar limit.

scholarly journals 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

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.

scholarly journals Chemical Enrichment and Central Star Properties

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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