scholarly journals Unveiling the planet population at birth

2021 ◽  
Vol 503 (1) ◽  
pp. 1526-1542 ◽  
Author(s):  
James G Rogers ◽  
James E Owen
Keyword(s):  
Mass Distribution ◽  
Mass Fraction ◽  
Additional Mass ◽  
Core Mass ◽  
Water Ice ◽  
The Core ◽  
Core Composition ◽  
Peak Mass ◽  
Core Accretion ◽  
Atmospheric Mass

ABSTRACT The radius distribution of small, close-in exoplanets has recently been shown to be bimodal. The photoevaporation model predicted this bimodality. In the photoevaporation scenario, some planets are completely stripped of their primordial H/He atmospheres, whereas others retain them. Comparisons between the photoevaporation model and observed planetary populations have the power to unveil details of the planet population inaccessible by standard observations, such as the core mass distribution and core composition. In this work, we present a hierarchical inference analysis on the distribution of close-in exoplanets using forward models of photoevaporation evolution. We use this model to constrain the planetary distributions for core composition, core mass, and initial atmospheric mass fraction. We find that the core-mass distribution is peaked, with a peak-mass of ∼4M⊕. The bulk core-composition is consistent with a rock/iron mixture that is ice-poor and ‘Earth-like’; the spread in core-composition is found to be narrow ($\lesssim 16{{\ \rm per\ cent}}$ variation in iron-mass fraction at the 2σ level) and consistent with zero. This result favours core formation in a water/ice poor environment. We find the majority of planets accreted a H/He envelope with a typical mass fraction of $\sim 4{{\ \rm per\ cent}}$; only a small fraction did not accrete large amounts of H/He and were ‘born-rocky’. We find four times as many super-Earths were formed through photoevaporation, as formed without a large H/He atmosphere. Finally, we find core-accretion theory overpredicts the amount of H/He cores would have accreted by a factor of ∼5, pointing to additional mass-loss mechanisms (e.g. ‘boil-off’) or modifications to core-accretion theory.

Planetesimal Capture by an Evolving Giant Gaseous Protoplanet

2012 ◽  
Vol 8 (S293) ◽  
pp. 263-269
Author(s):  
Morris Podolak ◽  
Nader Haghighipour
Keyword(s):  
Mass Distribution ◽  
Total Mass ◽  
Size Composition ◽  
Giant Planets ◽  
The Core ◽  
Last Stage ◽  
Core Accretion ◽  
Gaseous Envelope ◽  
Gas Drag ◽  
Probability Of Capture

AbstractBoth the core-accretion and disk-instability models suggest that at the last stage of the formation of a gas-giant, the core of this object is surrounded by an extended gaseous envelope. At this stage, while the envelope is contracting, planetesimals from the protoplanetary disk may be scattered into the protoplanets atmosphere and deposit some or all of their materials as they interact with the gas. We have carried out extensive simulations of approximately 104 planetesimals interacting with a envelope of a Jupiter-mass protoplanet including effects of gas drag, heating, and the effect of the protoplanets extended mass distribution. Simulations have been carried out for different radii and compositions of planetesimals so that all three processes occur to different degrees. We present the results of our simulations and discuss their implications for the enrichment of ices in giant planets. We also present statistics for the probability of capture (i.e. total mass-deposition) of planetesimals as a function of their size, composition, and closest approach to the center of the protoplanetary body.

scholarly journals Sculpting the valley in the radius distribution of small exoplanets as a by-product of planet formation: the core-powered mass-loss mechanism

2019 ◽  
Vol 487 (1) ◽  
pp. 24-33 ◽  
Author(s):  
Akash Gupta ◽  
Hilke E Schlichting
Keyword(s):  
Mass Loss ◽  
Thermal Evolution ◽  
Relative Magnitude ◽  
Occurrence Rate ◽  
Loss Mechanism ◽  
Water Ice ◽  
The Core ◽  
Planetary Cores ◽  
Short Period ◽  
Atmospheric Mass

ABSTRACT Recent observations revealed a bimodal radius distribution of small, short-period exoplanets with a paucity in their occurrence, a radius ‘valley’, around 1.5–2.0 R⊕. In this work, we investigate the effect of a planet’s own cooling luminosity on its thermal evolution and atmospheric mass loss (core-powered mass-loss) and determine its observational consequences for the radius distribution of small, close-in exoplanets. Using simple analytical descriptions and numerical simulations, we demonstrate that planetary evolution based on the core-powered mass-loss mechanism alone (i.e. without any photoevaporation) can produce the observed valley in the radius distribution. Our results match the valley’s location, shape and slope in planet radius–orbital period parameter space, and the relative magnitudes of the planet occurrence rate above and below the valley. We find that the slope of the valley is, to first order, dictated by the atmospheric mass-loss time-scale at the Bondi radius and given by d logRp/d logP ≃ 1/(3(1 − β)) that evaluates to −0.11 for β ≃ 4, where Mc/M⊕ = (Rc/R⊕)β(ρc∗/ρ⊕)β/3 is the mass–radius relation of the core. This choice for β yields good agreement with observations and attests to the significance of internal compression for massive planetary cores. We further find that the location of the valley scales as $\rho _{\rm c*}^{-4/9}$ and that the observed planet population must have predominantly rocky cores with typical water–ice fractions of less than ${\sim } 20{{\, \rm per\, cent}}$. Furthermore, we show that the relative magnitude of the planet occurrence rate above and below the valley is sensitive to the details of the planet-mass distribution but that the location of the valley is not.

scholarly journals How cores grow by pebble accretion

2018 ◽  
Vol 611 ◽  
pp. A65 ◽  
Author(s):  
M. G. Brouwers ◽  
A. Vazan ◽  
C. W. Ormel
Keyword(s):  
Second Phase ◽  
Temperature Dependent ◽  
Core Mass ◽  
The Core ◽  
Third Phase ◽  
The Mean ◽  
Inner Region ◽  
Core Accretion ◽  
Mean Molecular Weight ◽  
Ablated Mass

Context. Planet formation by pebble accretion is an alternative to planetesimal-driven core accretion. In this scenario, planets grow by the accretion of cm- to m-sized pebbles instead of km-sized planetesimals. One of the main differences with planetesimal-driven core accretion is the increased thermal ablation experienced by pebbles. This can provide early enrichment to the planet’s envelope, which influences its subsequent evolution and changes the process of core growth. Aims. We aim to predict core masses and envelope compositions of planets that form by pebble accretion and compare mass deposition of pebbles to planetesimals. Specifically, we calculate the core mass where pebbles completely evaporate and are absorbed before reaching the core, which signifies the end of direct core growth. Methods. We model the early growth of a protoplanet by calculating the structure of its envelope, taking into account the fate of impacting pebbles or planetesimals. The region where high-Z material can exist in vapor form is determined by the temperature-dependent vapor pressure. We include enrichment effects by locally modifying the mean molecular weight of the envelope. Results. In the pebble case, three phases of core growth can be identified. In the first phase (Mcore < 0.23–0.39 M⊕), pebbles impact the core without significant ablation. During the second phase (Mcore < 0.5M⊕), ablation becomes increasingly severe. A layer of high-Z vapor starts to form around the core that absorbs a small fraction of the ablated mass. The rest of the material either rains out to the core or instead mixes outwards, slowing core growth. In the third phase (Mcore > 0.5M⊕), the high-Z inner region expands outwards, absorbing an increasing fraction of the ablated material as vapor. Rainout ends before the core mass reaches 0.6 M⊕, terminating direct core growth. In the case of icy H2O pebbles, this happens before 0.1 M⊕. Conclusions. Our results indicate that pebble accretion can directly form rocky cores up to only 0.6 M⊕, and is unable to form similarly sized icy cores. Subsequent core growth can proceed indirectly when the planet cools, provided it is able to retain its high-Z material.

scholarly journals Luminosity functions of Planetary Nebulae

1997 ◽  
Vol 180 ◽  
pp. 413-413
Author(s):  
Marcelle Tremblay ◽  
Sun Kwok
Keyword(s):  
Mass Distribution ◽  
Planetary Nebula ◽  
Luminosity Function ◽  
Planetary Nebulae ◽  
Core Mass ◽  
The Core ◽  
Luminosity Functions

Planetary nebulae have recently been shown to be useful as standard candles (Ciardullo et al. 1989, ApJ, 339, 53; Jacoby 1989, ApJ, 339, 39). Distances to many galaxies have been determined by fitting a planetary nebula luminosity function (PNLF) to observations of the OIII 5007å line of PNe. Here, the effect of the core mass distribution on the determination of the luminosity function is investigated and a technique for interpolating between model evolutionary tracks is discussed.

scholarly journals Reconsideration of mass-distribution models

2014 ◽  
pp. 23-28
Author(s):  
S. Ninkovic
Keyword(s):  
Mass Distribution ◽  
Mass Fraction ◽  
Total Mass ◽  
Density Ratio ◽  
Distribution Model ◽  
Extended Model ◽  
Core Radius ◽  
Distribution Models ◽  
The Core ◽  
Fraction Versus

The mass-distribution model proposed by Kuzmin and Veltmann (1973) is revisited. It is subdivided into two models which have a common case. Only one of them is subject of the present study. The study is focused on the relation between the density ratio (the central one to that corresponding to the core radius) and the total-mass fraction within the core radius. The latter one is an increasing function of the former one, but it cannot exceed one quarter, which takes place when the density ratio tends to infinity. Therefore, the model is extended by representing the density as a sum of two components. The extension results into possibility of having a correspondence between the infinite density ratio and 100% total-mass fraction. The number of parameters in the extended model exceeds that of the original model. Due to this, in the extended model, the correspondence between the density ratio and total-mass fraction is no longer one-to-one; several values of the total-mass fraction can correspond to the same value for the density ratio. In this way, the extended model could explain the contingency of having two, or more, groups of real stellar systems (subsystems) in the diagram total-mass fraction versus density ratio.

scholarly journals Evolution and Mass Distribution of Central Stars of Planetary Nebulae

1983 ◽  
Vol 103 ◽  
pp. 359-371 ◽  
Author(s):  
D. Schoenberner ◽  
V. Weidemann
Keyword(s):  
Mass Distribution ◽  
Theoretical Calculations ◽  
Planetary Nebulae ◽  
Birth Rates ◽  
Core Mass ◽  
The Core ◽  
Average Factor ◽  
Red Giant ◽  
Central Stars ◽  
Hr Diagram

Considerable progress has been made in our understanding of the evolution of the central stars of planetary nebulae (NPN) compared to the situation five years ago at the Ithaca Symposium where Shaviv (1978) and Paczynski (1978) reviewed the subject. Shaviv stressed the necessity to start theoretical calculations with realistic initial models but doubted - in view of the loops in the HR diagram made by flashing stars - if the Harman-Seaton sequence could be taken as a single evolutionary sequence. Paczynski pointed out how strongly the theoretical rate of evolution depends on the stellar mass - a result which had appeared in his earlier calculations (1971) - and expected the existence of more flashing NPN's of the FG Sagittae type among the luminous (L > 104 L⊙) central stars, for which the core mass luminosity relation (Mc > 0.7 M⊙) combined with the core mass interpulse time relation predicts fairly short (2.10 yrs) intervals between flashing events. Weidemann, however, at the Symposium and shortly thereafter (1977a) concluded in view of the lower effective temperature derived by Pottasch et al. (1978) and the observed narrow mass distribution of white dwarfs around a 0.6 Mo. combined with the theoretical predicted horizontal tracks from the red giant branch towards the NPN region at a luminosity given by the core mass luminosity relation that the high luminosity part (and also the “upturn”) of the Harman-Seaton sequence does not exist. He also proposed an increase in the distances by an average factor of 1.3 compared to the Seaton/Webster (Seaton, 1968) or Cahn/Kaler (1971) scale in order to bring the observed NPN on the 0.6 M⊙ track in the HR diagram and to lower the NPN birth rates to a value compatible with white dwarf birth rates.

scholarly journals On the importance of including devolatilized stellar abundances in determining the composition of rocky exoplanets

2021 ◽  
Author(s):  
Fabian Seidler ◽  
Haiyang Wang ◽  
Sascha Quanz
Keyword(s):  
Mass Fraction ◽  
Terrestrial Planets ◽  
Chemical Compositions ◽  
Posterior Distributions ◽  
Stellar Abundances ◽  
Core Mass ◽  
The Core ◽  
Planetary Mass ◽  
Before And After ◽  
Mass Fractions

&lt;p&gt;Since stars and their planets form from the same molecular clouds, stellar chemical composition can be informative, to first order, of planetary bulk chemistry. An important feature of terrestrial planets compared to their host stars is the depletion of volatiles, the most important being oxygen. Previous studies on planet interiors focus on the mass and radius constraints and/or the host stellar refractory elements (e.g. Fe, Si and Mg), neglecting devolatilisation and its impact on the final picture of planet mineralogy and structure. This work assesses to what extent the devolatilised stellar abundances reflect rocky planetary composition.&amp;#160;&amp;#160;&lt;/p&gt;&lt;p&gt;We firstly test how the uncertainties associated with planetary mass and radius would affect the modelling results of core mass fraction &amp;#8211; an important interior parameter. To do so, we choose the Sun-like star Kepler-21 (stellar abundance uncertainties &lt;0.05 dex) as a case study and assume it hosts an Earth-mass-and-radius planet in its habitable zone. We then assign different levels of uncertainties to the mass and radius of the hypothetical planet, ranging from 0.1% to 20%. We find that with increasing uncertainty level, the modelling result of core mass fraction constrained by the devolatilised stellar abundances and mass and radius becomes identical with the core mass fraction constrained purely by the devolatilised stellar abundances. This reveals the increased modelling degeneracy with growing uncertainties in mass and radius measurements, but also the strong constraints placed by using the devolatilised stellar abundances.&lt;/p&gt;&lt;p&gt;We further investigate a sample of 12 confirmed exoplanets, which are all less than 10 Earth masses and 2 Earth radii &amp;#8211; i.e. potentially terrestrial planets or super-Earths &amp;#8211; and with the measured uncertainties in mass and radius respectively less than 35% and 10%. By comparing the prior and posterior distributions of mass and radius before and after introducing the devolatilised stellar abundances as another prior, we find that the posterior distributions of all samples, but 55 Cnc e and Kepler-107 c, can be sampled within the 2&amp;#963; ranges of the prior distributions. For the two exceptional cases, it means that the devolatilised stellar abundances and the measured mass and radius are not compatible within the level of 2&amp;#963;.&lt;/p&gt;&lt;p&gt;We also find a diverse distribution of the core mass fractions of the sample from 0% (i.e. coreless) up to 40%, which are consistent at the 2&amp;#963; level &amp;#61472;with the core mass fractions purely constrained by mass and radius measurements (except Kepler-107 c and 55 Cnc e),&amp;#160; but are significantly constrained by adding the devolatilized stellar abundances. In contrast, the previous study for the similar sample shows nearly constant core mass fractions of ~ 30% based on the unaltered stellar abundances and by assuming 100% Fe sunk into the core (i.e. free of consideration of the oxidation state of the planets). We emphasise that to break the degeneracies of terrestrial-type exoplanet interior modelling, we must use well the currently available observables including planetary mass and radius and host stellar chemical compositions, but they must be viewed through the lens of planet formation&amp;#160; and the resulting devolatilization.&lt;/p&gt;

scholarly journals Unveiling the Planet Population at Birth

2020 ◽  
Author(s):  
James Rogers ◽  
James Owen
Keyword(s):  
Mass Loss ◽  
Mass Fraction ◽  
Planet Formation ◽  
Evolution Model ◽  
Inference Model ◽  
Core Mass ◽  
Core Composition ◽  
New Information ◽  
Loss Mechanisms

&lt;p&gt;Recent Kepler data has shown that the radius distribution of small, close-in exoplanets is bimodal. Such bimodality was expected from photoevaporation models of close-in super-Earths, where some planets are stripped of their primordial H/He atmospheres, whilst others retain them. We present a hierarchical inference model on the distribution of Kepler planets using the photoevaporation evolution model. This approach is used to place key constraints on the planetary distributions for core composition, core mass and initial envelope mass-fraction, as well as test other models of planet evolution such as core-powered mass-loss. This new information has interesting implications on planet formation models and also hints at additional atmopsheric mass-loss mechanisms.&lt;/p&gt;

scholarly journals Planetary evolution with atmospheric photoevaporation

2020 ◽  
Vol 638 ◽  
pp. A52 ◽  
Author(s):  
C. Mordasini
Keyword(s):  
Analytical Model ◽  
Orbital Period ◽  
Core Mass ◽  
X Ray ◽  
Planetary Evolution ◽  
Atmospheric Escape ◽  
The Core ◽  
Core Composition ◽  
Low Mass ◽  
Gas Accretion

Context. Observations have revealed in the Kepler data a depleted region separating smaller super-Earths from larger sub-Neptunes. This can be explained as an evaporation valley between planets with and without H/He that is caused by atmospheric escape. Aims. We want to analytically derive the valley’s locus and understand how it depends on planetary properties and stellar X-ray and ultraviolet (XUV) luminosity. We also want to derive constraints for planet formation models. Methods. First, we conducted numerical simulations of the evolution of close-in low-mass planets with H/He undergoing escape. We performed parameter studies with grids in core mass and orbital separation, and we varied the postformation H/He mass, the strength of evaporation, and the atmospheric and core composition. Second, we developed an analytical model for the valley locus. Results. We find that the bottom of the valley quantified by the radius of the largest stripped core, Rbare, at a given orbital distance depends only weakly on postformation H/He mass. The reason is that a high initial H/He mass means that more gas needs to evaporate, but also that the planet density is lower, increasing mass loss. Regarding the stellar XUV-luminosity, Rbare is found to scale as LXUV0.135. The same weak dependency applies to the efficiency factor ε of energy-limited evaporation. As found numerically and analytically, Rbare varies a function of orbital period P for a constant ε as P−2pc∕3 ≈ P−0.18, where Mc ∝ Rcpc is the mass-radius relation of solid cores. We note that Rbare is about 1.7 R⊕ at a ten-day orbital period for an Earth-like composition. Conclusions. The numerical results are explained very well with the analytical model where complete evaporation occurs if the temporal integral over the stellar XUV irradiation that is absorbed by the planet is larger than the binding energy of the envelope in the gravitational potential of the core. The weak dependency on the postformation H/He means that the valley does not strongly constrain gas accretion during formation. But the weak dependency on primordial H/He mass, stellar LXUV, and ε could be the reason why the valley is so clearly visible observationally, and why various models find similar results theoretically. At the same time, given the large observed spread of LXUV, the dependency on it is still strong enough to explain why the valley is not completely empty.

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