On the low-mass planethood criterion

2008

We propose a quantitative concept for the lower planetary boundary, requiring that a planet must keep its atmosphere in vacuum. The solution-set framework of Pečnik and Wuchterl (2005) enabled a clear and quantitative criterion for the discrimination of a planet and a minor body. Using a simple isothermal core-envelope model, we apply the proposed planetary criterion to the large bodies in the Solar System.

Proceedings of the National Academy of Sciences, 2014

Small planets, 1-4x the size of Earth, are extremely common around Sun-like stars, and surprisingly so, as they are missing in our solar system. Recent detections have yielded enough information about this class of exoplanets to begin characterizing their occurrence rates, orbits, masses, densities, and internal structures. The Kepler mission finds the smallest planets to be most common, as 26% of Sun-like stars have small, 1-2 R ⊕ planets with orbital periods under 100 days, and 11% have 1-2 R ⊕ planets that receive 1-4x the incident stellar flux that warms our Earth. These Earth-size planets are sprinkled uniformly with orbital distance (logarithmically) out to 0.4 AU, and probably beyond. Mass measurements for 33 transiting planets of 1-4 R ⊕ show that the smallest of them, R < 1.5 R ⊕ , have the density expected for rocky planets. Their densities increase with increasing radius, likely caused by gravitational compression. Including solar system planets yields a relation: ρ = 2.32 + 3.19R/R ⊕ [g cm −3 ]. Larger planets, in the radius range 1.5-4.0 R ⊕ , have densities that decline with increasing radius, revealing increasing amounts of lowdensity material (H and He or ices) in an envelope surrounding a rocky core, befitting the appellation "mini-Neptunes." Planets of ∼ 1.5 R ⊕ have the highest densities, averaging near 10 g cm −3 . The gas giant planets occur preferentially around stars that are rich in heavy elements, while rocky planets occur around stars having a range of heavy element abundances. One explanation is that the fast formation of rocky cores in protoplanetary disks enriched in heavy elements permits the gravitational accumulation of gas before it vanishes, forming giant planets. But models of the formation of 1-4 R ⊕ planets remain uncertain. Defining habitable zones remains difficult, without benefit of either detections of life elsewhere or an understanding of life's biochemical origins.

Monthly Notices of the Royal Astronomical Society, 2011

With planets orbiting stars, a planetary mass function should not be seen as a low-mass extension of the stellar mass function, but a proper formalism needs to take care of the fact that the statistical properties of planet populations are linked to the properties of their respective host stars. This can be accounted for by describing planet populations by means of a differential planetary mass-radius-orbit function, which together with the fraction of stars with given properties that are orbited by planets and the stellar mass function allows to derive all statistics for any considered sample. These fundamental functions provide a framework for comparing statistics that result from different observing techniques and campaigns which all have their very specific selection procedures and detection efficiencies. Moreover, recent results both from gravitational microlensing campaigns and radial-velocity surveys of stars indicate that planets tend to cluster in systems rather than being the lonely child of their respective parent star. While planetary multiplicity in an observed system becomes obvious with the detection of several planets, its quantitative assessment however comes with the challenge to exclude the presence of further planets. Current exoplanet samples begin to give us first hints at the population statistics, whereas pictures of planet parameter space in its full complexity call for samples that are 2-4 orders of magnitude larger. In order to derive meaningful statistics however, planet detection campaigns need to be designed in such a way that well-defined fully-deterministic target selection, monitoring, and detection criteria are applied. The probabilistic nature of gravitational microlensing makes this technique an illustrative example of all the encountered challenges and uncertainties.

Progress in Physics, 2014

J.Wheeler's geometrodynamic concept have been used, in which space continuum is considered as a topologically non-unitary coherent surface admitting the existence of transitions of the input-output kind between distant regions of the space in an additional dimension. This model assumes the existence of closed structures (micro-and macrocontours) formed due to the balance between main interactions: gravitational, electric, magnetic, and inertial forces. It is such macrocontours that have been demonstrated to form-independently of their material basisthe essential structure of objects at various levels of organization of matter. On the basis of this concept in this paper basic regularities acting during formation planetary systems have been obtained. The existence of two sharply different types of planetary systems has been determined. The dependencies linking the masses of the planets, the diameters of the planets, the orbital radii of the planet, and the mass of the central body have been deduced. Formation of low-density planets was explained. The possibility of formation Earth-like planets near brown dwarfs has been grounded. The minimum mass of the planet, which may arise in the planetary system, has been defined.

2011

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 us 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 M - R diagram. This shape can be understood with basic concepts of the core accretion model.

Astronomy & Astrophysics, 2005

We present a model for the equilibrium of solid planetary cores embedded in a gaseous nebula. From this model we are able to extract an idealized roadmap of all hydrostatic states of the isothermal protoplanets. The complete classification of the isothermal protoplanetary equilibria should improve the understanding of the general problem of giant planet formation, within the framework of the nucleated instability hypothesis. We approximate the protoplanet as a spherically symmetric, isothermal, self-gravitating classical ideal gas envelope in equilibrium, around a rigid body of given mass and density, with the gaseous envelope required to fill the Hill-sphere. Starting only with a core of given mass and an envelope gas density at the core surface, the equilibria are calculated without prescribing the total protoplanetary mass or nebula density. The static critical core masses of the protoplanets for the typical orbits of 1, 5.2, and 30 AU, around a parent star of 1 solar mass are found to be 0.1524, 0.0948, and 0.0335 Earth masses, respectively, for standard nebula conditions (Kusaka et al. 1970). These values are much lower than currently admitted ones primarily because our model is isothermal and the envelope is in thermal equilibrium with the nebula. For a given core, multiple solutions (at least two) are found to fit into the same nebula. We extend the concept of the static critical core mass to the local and global critical core mass. We conclude that the 'global static critical core mass' marks the meeting point of all four qualitatively different envelope regions.

2017

Planetary systems, under suitable general assumptions, admit positive measure sets of "initial data" whose evolution gives rise to the planets revolving on nearly circular and nearly co-planar orbits around their star. This statement (or more primitive formulations) challenged astronomers, physicists and mathematicians for centuries. In this chapter we shall review the mathematical theory (with particular attention to recent developments) needed to prove the above statement.

Astronomical Journal, 2006

A planet is an end product of disk accretion around a primary star or substar. I quantify this definition by the degree to which a body dominates the other masses that share its orbital zone. Theoretical and observational measures of dynamical dominance reveal gaps of 4-5 orders of magnitude separating the eight planets of our solar system from the populations of asteroids and comets. The proposed definition dispenses with upper and lower mass limits for a planet. It reflects the tendency of disk evolution in a mature system to produce a small number of relatively large bodies (planets) in nonintersecting or resonant orbits, which prevents collisions between them.

EPJ Web of Conferences, 2011

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 us 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 M − R diagram. This shape can be understood with basic concepts of the core accretion model.

Astronomy and Astrophysics, 2005

We present a model for the equilibrium of solid planetary cores embedded in a gaseous nebula. From this model we are able to extract an idealized roadmap of all hydrostatic states of the isothermal protoplanets. The complete classification of the isothermal protoplanetary equilibria should improve the understanding of the general problem of giant planet formation, within the framework of the nucleated instability hypothesis. We approximate the protoplanet as a spherically symmetric, isothermal, self-gravitating classical ideal gas envelope in equilibrium, around a rigid body of given mass and density, with the gaseous envelope required to fill the Hill-sphere. Starting only with a core of given mass and an envelope gas density at the core surface, the equilibria are calculated without prescribing the total protoplanetary mass or nebula density. In this way, a variety of hydrostatic core-envelope equilibria has been obtained. Two types of envelope equilibria can be distinguished: uniform equilibrium, were the density of the envelope gas drops approximately an order of magnitude as the radial distance increases to the outer boundary, and compact equilibrium, having a small but very dense gas layer wrapped around the core and very low, exponentially decreasing gas density further out. The effect of the envelope mass on the planetary gravitational potential further discriminates the models into the self-gravitating and the non-self gravitating ones. The static critical core masses of the protoplanets for the typical orbits of 1, 5.2, and 30 AU, around a parent star of 1 solar mass (M ) are found to be 0.1524, 0.0948, and 0.0335 Earth masses (M ⊕ ), respectively, for standard nebula conditions ). These values are much lower than currently admitted ones primarily because our model is isothermal and the envelope is in thermal equilibrium with the nebula. Our solutions show a wide range of possible envelopes. For a given core, multiple solutions (at least two) are found to fit into the same nebula. Some of those solutions posses equal envelope mass. This variety is a consequence of the envelope's self-gravity. We extend the concept of the static critical core mass to the local and global critical core mass. Above the global critical mass, only compact solutions exist. We conclude that the "global static critical core mass" marks the meeting point of all four qualitatively different envelope regions.