The radius of a giant planet is a key physical property. It encapsulates the outcome of its mass, composition, and thermal state, serving as a critical link between observations and the theory of planetary interiors. While traditional interior models assume distinct core-envelope structures, recent gravity measurements of Jupiter and Saturn reveal complex interiors with deep composition gradients. Here, we combine an analytic framework with numerical evolution simulations to elucidate how internal structures with composition gradients affect the planetary radius. We demonstrate that the spatial redistribution of heavy elements does not inherently alter the planetary size; rather, it is the resulting difference in total entropy over time that drives observable radius variations. We show that this mechanism naturally establishes two distinct evolutionary regimes. During the first few gigayears of evolution, composition gradients trap thermal energy deep within the interior, significantly affecting the planetary evolution and internal structure. However, as the planet cools and contracts, this ``thermal memory'' fades and the total entropy no longer depends on the primordial conditions. Consequently, the planetary radius decouples from the internal distribution of heavy elements, becoming solely a function of the total mass and bulk composition. Our results present the physical origin of the mass-radius-composition relation and suggest that the use of simplified interior models for giant exoplanets is legitimate only after the planet has surpassed this evolutionary threshold. Our analysis establishes a thermodynamic constraint on the planetary structure: while composition gradients can temporarily modulate cooling, they cannot permanently sustain radius inflation, as the addition of heavy elements, regardless of their distribution, inevitably leads to planetary contraction.
Applying the survival function analysis to the planet radius distribution of the Kepler exoplanet candidates, we have identified two natural divisions of planet radius at 4 Earth radii and 10 Earth radii. These divisions place constraints on planet formation and interior structure model. The division at 4 Earth radii separates small exoplanets from large exoplanets above. When combined with the recently-discovered radius gap at 2 Earth radii, it supports the treatment of planets 2-4 Earth radii as a separate group, likely water worlds. Thus, for planets around solar-type FGK main-sequence star…
Applying the survival function analysis to the planet radius distribution of the Kepler confirmed/candidate planets, we have identified two natural divisions of planet radius at 4 Earth radii and 10 Earth radii. These divisions place constraints on planet formation and interior structure model. The division at 4 Earth radii separates small exoplanets from large exoplanets above. When combined with the recently-discovered radius gap at 2 Earth radii, it supports the treatment of planets 2-4 Earth radii as a separate group, likely water worlds. For planets around solar-type FGK main-sequence sta…
We carry out an independent search of Kepler photometry for small transiting planets with sizes 0.5--8.0 times that of Earth and orbital periods between 5 and 50 days, with the goal of measuring the fraction of stars harboring such planets. We use a new transit search algorithm, TERRA, optimized to detect small planets. We restrict our stellar sample to include the 12,000 stars having the lowest photometric noise in the Kepler survey. We report 129 planet candidates having radii less than 6 Earth-radii found in 3 years of Kepler photometry. Forty-seven of these candidates are not in Batalha et…
The migration of the giant planets due to the scattering of planetesimals causes powerful resonances to move through the asteroid belt and the terrestrial planet region. Exactly when and how the giant planets migrated is not well known. In this paper we present results of an investigation of the formation of the terrestrial planets during and after the migration of the giant planets. The latter is assumed to have occurred immediately after the dissipation of the nebular disk -- i.e. "early" with respect to the timing of the Late Heavy Bombardment (LHB). The presumed cause of our modeled early …
Exoplanetary systems host giant planets on substantially non-circular, close-in orbits. We propose that these eccentricities arise in a phase of giant impacts, analogous to the final stage of Solar System assembly that formed Earth's Moon. In this scenario, the planets scatter each other and collide, with corresponding mass growth as they merge. We numerically integrate an ensemble of systems with varying total planet mass, allowing for collisional growth, to show that (1) the high-eccentricity giants observed today may have formed preferentially in systems of higher initial total planet mass,…
The detection of many extrasolar gas giants with high eccentricities indicates that dynamical instabilities in planetary systems are common. These instabilities can alter the orbits of gas giants as well as the orbits of terrestrial planets and therefore eject or move a habitable planet out of the habitable zone. In this work 423 simulations with 153 different hypothetical planetary systems with gas giants and terrestrial planets have been modelled to explore the orbital stability of habitable planets. The initial parameter variations include the number, distances and masses of the giant plane…
We study the masses and radii of 65 exoplanets smaller than 4 Earth radii with orbital periods shorter than 100 days. We calculate the weighted mean densities of planets in bins of 0.5 Earth radii and identify a density maximum of 7.6 g/cc at 1.4 Earth radii. Planets with radii up to R = 1.5 Earth radii increase in density with increasing radius. Above 1.5 Earth radii, planet density rapidly decreases with increasing radius, indicating that these planets have a large fraction of volatiles by volume overlying a rocky core. Including the solar system terrestrial planets with the exoplanets below…
In this chapter we summarize current knowledge of the internal structure of giant planets. We concentrate on the importance of heavy elements and their role in determining the planetary composition and internal structure, in planet formation, and during the planetary long-term evolution. We briefly discuss how internal structure models are derived, present the possible structures of the outer planets in the Solar System, and summarise giant planet formation and evolution. Finally, we introduce giant exoplanets and discuss how they can be used to better understand giant planets as a class of pl…
The most irradiated transiting hot Jupiters are characterized by anomalously inflated radii, sometimes exceeding Jupiter's size by more than 60%. While different theoretical explanations have been applied, none of them provide a universal resolution to this observation, despite significant progress in the past years. We refine the photometric transit light curve analysis of 115 Kepler giant planet candidates based on public Q0-Q2 photometry. We find that 14% of them are likely false positives, based on their secondary eclipse depth. We report on planet radii vs. stellar flux. We find an increa…
The orbital distributions of currently observed extrasolar giant planets allow marginally stable orbits for hypothetical, terrestrial planets. In this paper, we propose that many of these systems may not have additional planets on these "stable" orbits, since past dynamical instability among giant planets could have removed them. We numerically investigate the effects of early evolution of multiple giant planets on the orbital stability of the inner, sub-Neptune-like planets which are modeled as test particles, and determine their dynamically unstable region. Previous studies have shown that t…
Evidence of mutually inclined planetary orbits has been reported for giant planets these last years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and investigate whether it can possibly lead to the existence of inclined terrestrial planets. We have performed 126 simulations of the late-stage planetary accretion in eccentric and inclined giant planet systems. The physical and orbital parameters of the giant planet systems result from n-body simulations of three giant planets in the late stage of the gas disc, under …
Giant planet migration is an important phenomenon in the evolution of planetary systems. Recent works have shown that giant planet growth and migration can shape the asteroid belt, but these works have not considered interactions between planetesimals. We have calculated the evolution of planetesimal disks, including planetesimal-planetesimal collisions, during gas giant growth and migration. The numbers, locations, and impact velocities of these collisions depend on the specific growth and migration path. We find that giant planet growth alone has little effect on impact velocities, and most …
We present a systematic evaluation of the agreement between the observed radii of 90 well-characterized transiting extrasolar giant planets and their corresponding model radii. Our model radii are drawn from previously published calculations of core-less giant planets that have attained their asymptotic radii, and which have been tabulated for a range of planet masses and equilibrium temperatures. (We report a two-dimensional polynomial fitting function that accurately represents the models). As expected, the model radii provide a statistically significant improvement over a null hypothesis th…
The giant planets of the solar system likely played a large role in shaping the architecture of the terrestrial planets. Using an updated collision model, we conduct a suite of high resolution N-body integrations to probe the relationship between giant planet mass, and terrestrial planet formation and system architecture. We vary the mass of the planets that reside at Jupiter's and Saturn's orbit and examine the effects on the interior terrestrial system. We find a correlation between the mass of the exterior giant planets and the collision history of the resulting planets, which holds implica…
The presence of giant planets influences potentially habitable worlds in numerous ways. Massive celestial neighbors can facilitate the formation of planetary cores and modify the influx of asteroids and comets towards Earth-analogs later on. Furthermore, giant planets can indirectly change the climate of terrestrial worlds by gravitationally altering their orbits. Investigating 147 well characterized exoplanetary systems known to date that host a main sequence star and a giant planet we show that the presence of 'giant neighbors' can reduce a terrestrial planet's chances to remain habitable, e…
The radius of an exoplanet may be affected by various factors, including irradiation, planet mass and heavy element content. A significant number of transiting exoplanets have now been discovered for which the mass, radius, semi-major axis, host star metallicity and stellar effective temperature are known. We use multivariate regression models to determine the dependence of planetary radius on planetary equilibrium temperature T_eq, planetary mass M_p, stellar metallicity [Fe/H], orbital semi-major axis a, and tidal heating rate H_tidal, for 119 transiting planets in three distinct mass regime…
In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant pla…
According to planetary interior models, some giant planets contain large metal masses with large metal-mass fractions. HD 149026b and TOI-849b are characteristic examples of these giant planets. It has been suggested that the envelope mass loss during giant impacts plays a key role in the formation of such giant planets. The aim of the present letter is to propose a mechanism that can explain the origin of such giant planets. We investigate the formation of giant planets in a rapidly dissipating disk using N-body simulations that consider pebble accretion. The results show that although the pe…
Many features of the outer solar system are replicated in numerical simulations if the giant planets undergo an orbital instability that ejects one or more ice giants. During this instability, Jupiter and Saturn's orbits diverge, crossing their 2:1 mean motion resonance (MMR), and this resonance-crossing can excite the terrestrial planet orbits. Using a large ensemble of simulations of this giant planet instability, we directly model the evolution of the terrestrial planet orbits during this process, paying special attention to systems that reproduce the basic features of the outer planets. In…
We review the interior structure and evolution of Jupiter, Saturn, Uranus and Neptune, and extrasolar giant planets with particular emphasis on constraining their global composition.
In the paper, we have discussed the problem of the existence of the metallic hydrogen in the superconducting state inside the cold giant planet. We have shown that the {\it cold} planet represents the final state of the thermal evolution of free-floating giant planet.
Approximately half of the extrasolar planets (exoplanets) with radii less than four Earth radii are in orbits with short periods. Despite their sheer abundance, the compositions of such planets are largely unknown. The available evidence suggests that they range in composition from small, high-density rocky planets to low-density planets consisting of rocky cores surrounded by thick hydrogen and helium gas envelopes. Understanding the transition from the gaseous planets to Earth-like rocky worlds is important to estimate the number of potentially habitable planets in our Galaxy and provide con…
We discuss the interior structure and composition of giant planets, and how this structure changes as these planets cool and contract over time. Here we define giant planets as those that have an observable hydrogen-helium envelope, which includes Jupiter-like planets, which are predominantly H/He gas, and Neptune-like planets which are predominantly composed of elements heavier than H/He. We describe the equations of state of planetary materials and the construction of static structural models and thermal evolution models. We apply these models to transiting planets close to their parent star…
Constraining the planetary composition is essential for exoplanetary characterization. In this paper, we use a statistical analysis to determine the characteristic maximum (threshold) radii for various compositions for exoplanets with masses up to 25 Earth masses (M$_\oplus$). We confirm that most planets with radii larger than 1.6 Earth radius (R$_\oplus$) are not rocky, and must consist of lighter elements, as found by previous studies. We find that planets with radii above 2.6 R$_\oplus$ cannot be pure-water worlds, and must contain significant amounts of hydrogen and helium (H-He). We find…
In the standard model of core accretion, the cores of the giant planets form by the accretion of planetesimals. In this scenario, the evolution of the planetesimal population plays an important role in the formation of massive cores. Recently, we studied the role of planetesimal fragmentation in the in situ formation of a giant planet. However, the exchange of angular momentum between the planet and the gaseous disk causes the migration of the planet in the disk. In this new work, we incorporate the migration of the planet and globally study the role of planet migration in the formation of a m…
We present the mass-density relationship (log M - log rho) for objects with masses ranging from planets (M ~ 0.01 M_Jup) through stars (M > 0.08 M_Sun). This relationship shows three distinct regions separated by a change in slope in log M -- log rho plane. In particular, objects with masses in the range 0.3 M_Jup to 60 M_Jup follow a tight linear relationship with no distinguishing feature to separate the low mass end (giant planets) from the high mass end (brown dwarfs). The distinction between giant planets and brown dwarfs thus seems arbitrary. We propose a new definition of giant planets …
Giant planets are tens to thousands of times as massive as the Earth, and many times as large. Most of their volumes are occupied by hydrogen and helium, the primary constituents of the protostellar disks from which they formed. Significantly, the solar system giants are also highly enriched in heavier elements relative to the Sun, indicating that solid material participated in their assembly. Giant planets account for most of the mass of our planetary system and of those extrasolar planetary systems in which they are present. Therefore, giant planets are primary actors in determining the orbi…
Planet-planet scattering best explains the eccentricity distribution of extrasolar giant planets. Past literature showed that the orbits of planets evolve due to planet-planet scattering. This work studies the spin evolution of planets in planet-planet scattering in 2-planet systems. Spin can evolve dramatically due to spin-orbit coupling made possible by the evolving spin and orbital precession during the planet-planet scattering phase. The main source of torque to planet spin is the stellar torque, and the total planet-plane torque contribution is negligible. As a consequence of the evolutio…
Hot Jupiters are giant planets on orbits a few hundredths of an AU. They do not share their system with low-mass close-in planets, despite these latter being exceedingly common. Two migration channels for hot Jupiters have been proposed: through a protoplanetary gas disc or by tidal circularisation of highly-eccentric planets. We show that highly-eccentric giant planets that will become hot Jupiters clear out any low-mass inner planets in the system, explaining the observed lack of such companions to hot Jupiters. A less common outcome of the interaction is that the giant planet is ejected by …
We herein develop a new simple model for giant planet formation, which predicts the final mass of a giant planet born in a given disk, by adding the disk mass loss due to photoevaporation and a new type II migration formula to our previous model. The proposed model provides some interesting results. First, it gives universal evolution tracks in the diagram of planetary mass and orbital radius, which clarifies how giant planets migrate at growth in the runaway gas accretion stage. Giant planets with a few Jupiter masses or less suffer only a slight radial migration in the runaway gas accretion …
In the standard scenario of planet formation, terrestrial planets and the cores of the giant planets are formed by accretion of planetesimals. As planetary embryos grow the planetesimal velocity dispersion increases due to gravitational excitations produced by embryos. The increase of planetesimal relative velocities causes the fragmentation of them due to mutual collisions. We study the role of planetesimal fragmentation on giant planet formation. We analyze how planetesimal fragmentation modifies the growth of giant planet's cores for a wide range of planetesimal sizes and disk masses. We in…
The large number of detected giant exoplanets offers the opportunity to improve our understanding of the formation mechanism, evolution, and interior structure of gas giant planets. The two main models for giant planet formation are core accretion and disk instability. There are substantial differences between these formation models, including formation timescale, favorable formation location, ideal disk properties for planetary formation, early evolution, planetary composition, etc. First, we summarize the two models including their substantial differences, advantages, and disadvantages, and …
We propose a pebble-driven planet formation scenario to form giant planets with high multiplicity and large orbital distances in the early gas disk phase. We perform N-body simulations to investigate the growth and migration of low-mass protoplanets in the disk with inner viscously heated and outer stellar irradiated regions. The key feature of this model is that the giant planet cores grow rapidly by a combination of pebble accretion and planet-planet collisions. This consequently speeds up their gas accretion. Because of efficient growth, the planet transitions from rapid type I migration to…
(abridged) We have obtained precise radial velocities for a sample of 373 G and K type giants at Lick Observatory regularly over more than 12 years. Planets have been identified around 15 giant stars; an additional 20 giant stars host planet candidates. We investigate the occurrence rate of substellar companions around giant stars as a function of stellar mass and metallicity. We probe the stellar mass range from about 1 to beyond 3 M_Sun, which is not being explored by main-sequence samples. We fit the giant planet occurrence rate as a function of stellar mass and metallicity with a Gaussian …
The limited completeness of the Kepler sample for planets with orbital periods $\gtrsim$ 1 yr leaves open the possibility that exoplanetary systems may host undetected giant planets. Should such planets exist, their dynamical interactions with the inner planets may prove vital in sculpting the final orbital configurations of these systems. Using an $N$-body code with additional forces to emulate the effects of a protoplanetary disc, we perform simulations of the assembly of compact systems of super-Earth-mass planets with unseen giant companions. The simulated systems are analogous to Kepler-1…
Probabilistic relationships between the mass and radius of planets are useful for a variety of purposes, including estimating the yields of planet discovery efforts and the radii of discovered planets given their masses. Previous work on giant planets often do not make the important distinction between cool and (inflated) hot giants. This can lead to needlessly large uncertainties and overestimated radii for the cooler objects. Using hierarchical bayesian modeling and the AIC model selection criterion, we identify an empirical mass-radius relationship for cool giant planets above 15 Earth mass…
Applying survival function analysis to the planet orbital period (P) and semi-major axis (a) distribution from the Kepler sample, we find that all exoplanets are uniformly distributed in (ln a) or (ln P), with an average inner cut-off of 0.05 AU to the host star. More specifically, this inner cut-off is 0.04 AU for rocky worlds (1-2 Earth radii) and 0.08 AU for water worlds (2-4 Earth radii). Moreover, the transitional planets (4-10 Earth radii) and gas giants (>10 Earth radii) have a change of slope of survival function at 0.4 AU from -1 to -1/2, suggesting a different statistical distributio…
Gas giants orbiting interior to the ice line are thought to have been displaced from their formation locations by processes that remain debated. Here we uncover several new metallicity trends, which together may indicate that two competing mechanisms deliver close-in giant planets: gentle disk migration, operating in environments with a range of metallicities, and violent planet-planet gravitational interactions, primarily triggered in metal-rich systems in which multiple giant planets can form. First, we show with 99.1% confidence that giant planets with semi-major axes between 0.1 and 1 AU o…
We have explored the evolution of a cold debris disk under the gravitational influence of dwarf planet sized objects (DPs), both in the presence and absence of an interior giant planet. Through detailed long-term numerical simulations, we demonstrate that, when the giant planet is not present, DPs can stir the eccentricities and inclinations of disk particles, in linear proportion to the total mass of the DPs; on the other hand, when the giant planet is included in the simulations, the stirring is approximately proportional to the mass squared. This creates two regimes: below a disk mass thres…
The two current models for giant planet formation are core accretion and disk instability. We discuss the core masses and overall planetary enrichment in heavy elements predicted by the two formation models, and show that both models could lead to a large range of final compositions. For example, both can form giant planets with nearly stellar compositions. However, low-mass giant planets, enriched in heavy elements compared to their host stars, are more easily explained by the core accretion model. The final structure of the planets, i.e., the distribution of heavy elements, is not firmly con…
Recent studies of solar system formation suggest that the solar system's giant planets formed and migrated in the protoplanetary disk to reach resonant orbits with all planets inside 15 AU from the Sun. After the gas disk's dispersal, Uranus and Neptune were likely scattered by gas giants, and approached their current orbits while dispersing the transplanetary disk of planetesimals, whose remains survived to this time in the region known as the Kuiper belt. Here we performed N-body integrations of the scattering phase between giant planets in an attempt to determine which initial states are pl…
Standard models of planet formation explain how planets form in axisymmetric, unperturbed disks in single star systems. However, it is possible that giant planets could have already formed when other planetary embryos start to grow. We investigate the dynamics of planetesimals under the perturbation of a giant planet in a gaseous disk. Our aim is to understand the effect of the planet's perturbation on the formation of giant planet cores outside the orbit of the planet. We calculate the orbital evolution of planetesimals ranging from $10^{13}$ to $10^{20}$g, with a Jupiter-mass planet located …
We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equat…
Many observed giant planets lie on eccentric orbits. Such orbits could be the result of strong scatterings with other giant planets. The same dynamical instability that produces these scatterings may also cause habitable planets in interior orbits to become ejected, destroyed, or be transported out of the habitable zone. We say that a habitable planet has resilient habitability if it is able to avoid ejections and collisions and its orbit remains inside the habitable zone. Here we model the orbital evolution of rocky planets in planetary systems where giant planets become dynamically unstable.…
We present the discovery of planet-mass companions to two giant stars by the ongoing Penn State- Toruń Planet Search (PTPS) conducted with the 9.2 m Hobby-Eberly Telescope. The less massive of these stars, K5-giant BD+20 274, has a 4.2 MJ minimum mass planet orbiting the star at a 578-day period and a more distant, likely stellar-mass companion. The best currently available model of the planet orbiting the K0-giant HD 219415 points to a Jupiter-mass companion in a 5.7-year, eccentric orbit around the star, making it the longest period planet yet detected by our survey. This planet has an ampli…
We used {\sl \textup{ab initio}} molecular dynamics simulations to calculate the high-pressure melting temperatures of the three potential core components. The planetary adiabats were obtained by solving the hydrostatic equations in a three-layer model adjusted to reproduce the measured gravitational moments. Recently developed {\sl \textup{ab initio}} equations of state were used for the envelope and the core. We find that the cores of the giant and ice-giant planets of the solar system differ because the pressure-temperature conditions encountered in each object correspond to different regio…
The exoplanet mass radius diagram reveals that super Earths display a wide range of radii, and therefore mean densities, at a given mass. Using planet population synthesis models, we explore the key physical factors that shape this distribution: planets' solid core compositions, and their atmospheric structure. For the former, we use equilibrium disk chemistry models to track accreted minerals onto planetary cores throughout formation. For the latter, we track gas accretion during formation, and consider photoevaporation-driven atmospheric mass loss to determine what portion of accreted gas es…
Within the general framework of core-nucleated accretion theory of giant planet formation, the conglomeration of massive gaseous envelopes is facilitated by a transient period of rapid accumulation of nebular material. While the concurrent buildup of angular momentum is expected to leave newly formed planets spinning at near-breakup velocities, Jupiter and Saturn, as well as super-Jovian long-period extrasolar planets, are observed to rotate well below criticality. In this work, we demonstrate that the large luminosity of a young giant planet simultaneously leads to the generation of a strong …
Revealing the true nature of the gas giant planets in our Solar System is challenging. The masses of Jupiter and Saturn are about 318 and 95 Earth masses, respectively. While they mostly consist of hydrogen and helium, the total mass and distribution of the heavier elements, which reveal information on their origin, are still unknown. Recent accurate measurements of the gravitational fields of Jupiter and Saturn together with knowledge of the behavior of planetary materials at high pressures allow us to better constrain their interiors. Updated structure models of Jupiter and Saturn suggest th…
Hundreds of giant planets have been discovered so far and the quest of exo-Earths in giant planet systems has become intriguing. In this work, we aim to address the question of the possible long-term coexistence of a terrestrial companion on an orbit interior to a giant planet, and explore the extent of the stability regions for both non-resonant and resonant configurations. Our study focuses on the restricted three-body problem, where an inner terrestrial planet (massless body) moves under the gravitational attraction of a star and an outer massive planet on a circular or elliptic orbit. Usin…
We present a systematic search for transiting giant planets ($0.6 R_{\rm J} \leq R_{\rm P} \leq 2.0 R_{\rm J}$) orbiting nearby low-mass stars ($M_{*} \leq 0.71 M_{\odot}$). The formation of giant planets around low-mass stars is predicted to be rare by the core-accretion planet formation theory. We search 91,306 low-mass stars in the TESS 30 minute cadence photometry detecting fifteen giant planet candidates, including seven new planet candidates which were not known planets or identified as TOIs prior to our search. Our candidates present an exciting opportunity to improve our knowledge of t…
Frequency of detected giant planets is observed to increase rapidly with metallicity of the host star. This is usually interpreted as evidence in support of the Core Accretion (CA) theory, which assembles giant planets as a result of formation of a massive solid core. A strong positive planet-metallicity correlation for giant planets formed in the framework of Gravitational disc Instability (GI) model is found here. The key novelty of this work is "pebble accretion" onto GI fragments which has been recently demonstrated to accelerate contraction of GI fragments. Driven closer to the star by th…
