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 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.

scholarly journals Empirical models of Jupiter’s interior from Juno data

2018 ◽  
Vol 613 ◽  
pp. A32 ◽  
Author(s):  
Dongdong Ni
Keyword(s):  
Gravity Field ◽  
Equations Of State ◽  
Moment Of Inertia ◽  
Radial Density ◽  
Love Number ◽  
Core Mass ◽  
The Core ◽  
Theoretical Approaches ◽  
Radial Density Profile ◽  
History Of

Context. The Juno spacecraft has significantly improved the accuracy of gravitational harmonic coefficients J4, J6 and J8 during its first two perijoves. However, there are still differences in the interior model predictions of core mass and envelope metallicity because of the uncertainties in the hydrogen-helium equations of state. New theoretical approaches or observational data are hence required in order to further constrain the interior models of Jupiter. A well constrained interior model of Jupiter is helpful for understanding not only the dynamic flows in the interior, but also the formation history of giant planets. Aims. We present the radial density profiles of Jupiter fitted to the Juno gravity field observations. Also, we aim to investigate our ability to constrain the core properties of Jupiter using its moment of inertia and tidal Love number k2 which could be accessible by the Juno spacecraft. Methods. In this work, the radial density profile was constrained by the Juno gravity field data within the empirical two-layer model in which the equations of state are not needed as an input model parameter. Different two-layer models are constructed in terms of core properties. The dependence of the calculated moment of inertia and tidal Love number k2 on the core properties was investigated in order to discern their abilities to further constrain the internal structure of Jupiter. Results. The calculated normalized moment of inertia (NMOI) ranges from 0.2749 to 0.2762, in reasonable agreement with the other predictions. There is a good correlation between the NMOI value and the core properties including masses and radii. Therefore, measurements of NMOI by Juno can be used to constrain both the core mass and size of Jupiter’s two-layer interior models. For the tidal Love number k2, the degeneracy of k2 is found and analyzed within the two-layer interior model. In spite of this, measurements of k2 can still be used to further constrain the core mass and size of Jupiter’s two-layer interior models.

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 Search for the Star-Planet Interaction

2011 ◽  
Vol 7 (S282) ◽  
pp. 125-126
Author(s):  
Tereza Krejčová ◽  
Ján Budaj ◽  
Július Koza
Keyword(s):  
Orbital Period ◽  
Equivalent Width ◽  
Extrasolar Planets ◽  
Sudden Change ◽  
Qualitative Change ◽  
Significant Evidence ◽  
Orbital Parameters ◽  
The Core ◽  
Orbital Periods ◽  
Stellar Chromosphere

AbstractWe analyse the chromospherical activity of stars with extrasolar planets and search for a possible correlation between the equivalent width of the core of the Ca II K line and orbital parameters of the planet. We found statistically significant evidence that the equivalent width of the Ca II K line reversal, which originates in the stellar chromosphere, depends on the orbital period Porb of the exoplanet. Planets orbiting stars with Teff < 5 500 K and with Porb < 20 days generally have much stronger emission than planets at similar temperatures but at longer orbital periods. Porb = 20 days marks a sudden change in behaviour, which might be associated with a qualitative change in the star-planet interaction.

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 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 &gt; 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.

scholarly journals Full exploration of the giant planet population around β Pictoris

2018 ◽  
Vol 612 ◽  
pp. A108 ◽  
Author(s):  
A.-M. Lagrange ◽  
M. Keppler ◽  
N. Meunier ◽  
J. Lannier ◽  
H. Beust ◽  
...  
Keyword(s):  
Extrasolar Planets ◽  
Giant Planet ◽  
Young Stars ◽  
Giant Planets ◽  
Close Orbit ◽  
Wide Range ◽  
Detection Probabilities ◽  
Solar Type ◽  
Formation And Evolution ◽  
The One

Context. The search for extrasolar planets has been limited so far to close orbit (typ. ≤5 au) planets around mature solar-type stars on the one hand, and to planets on wide orbits (≥10 au) around young stars on the other hand. To get a better view of the full giant planet population, we have started a survey to search for giant planets around a sample of carefully selected young stars. Aims. This paper aims at exploring the giant planet population around one of our targets, β Pictoris, over a wide range of separations. With a disk and a planet already known, the β Pictoris system is indeed a very precious system for studies of planetary formation and evolution, as well as of planet–disk interactions. Methods. We analyse more than 2000 HARPS high-resolution spectra taken over 13 years as well as NaCo images recorded between 2003 and 2016. We combine these data to compute the detection probabilities of planets throughout the disk, from a fraction of au to a few dozen au. Results. We exclude the presence of planets more massive than 3 MJup closer than 1 au and further than 10 au, with a 90% probability. 15+ MJup companions are excluded throughout the disk except between 3 and 5 au with a 90% probability. In this region, we exclude companions with masses larger than 18 (resp. 30) MJup with probabilities of 60 (resp. 90) %.

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