Single planet formation regime in the high-ionization environment:Possible origin of hot Jupiters and super-Earths

We studied the particle growth in a protoplanetary disk in a high-ionization environment and found that icy planet formation is inactive for a disk with an ionization rate 100 times higher than that of the present Solar System. In particular, in the case of M 〈 10^（-7.4）M_☉yr^（-1）, only rocky planet formation occurs. In such a case, all the solid materials in the disk drift inward, eventually reach the inner MRI front,and accumulate there. They form a dense, thin sub-disk of solid particles, which undergoes gravitational instability to form rocky planetesimals. The planetesimals rapidly grow into a planet through pebble accretion. Consequently, rocky planets tend to be much larger than planets formed through other regimes（tandem planet formation regime and dispersed planet formation regime）, in which icy planet formation actively takes place. These rocky planets may evolve into hot Jupiters if they grow fast enough to the critical core mass of the runaway gas accretion before the dispersal of the disk gas, or they may evolve into super-Earths if the gas dispersed sufficiently early.

The origin of high eccentricity planets:The dispersed planet formation regime for weakly magnetized disks

In the tandem planet formation regime,planets form at two distinct sites where solid particles are densely accumulated due to the on/off state of the magnetorotational instability（MRI）.We found that tandem planet formation can reproduce the solid component distribution of the Solar System and tends to produce a smaller number of large planets through continuous pebble flow into the planet formation sites.In the present paper,we investigate the dependence of tandem planet formation on the vertical magnetic field of the protoplanetary disk.We calculated two cases of BZ 3.4 × 10^-3 G and BZ = 3.4 × 10^-5 G at 100 AU as well as the canonical case of BZ = 3.4 × 10^-4 G.We found that tandem planet formation holds up well in the case of the strong magnetic field（BZ 3.4 × 10^-3 G）.On the other hand,in the case of a weak magnetic field（BZ= 3.4 × 10^-5 G） at 100 AU,a new regime of planetary growth is realized：the planets grow independently at different places in the dispersed area of the MRl-suppressed region of r-8-30 AU at a lower accretion rate of M 〈 10^-7.4M⊙yr^-1.We call this the ＂dispersed planet formation＂ regime.This may lead to a system with a larger number of smaller planets that gain high eccentricity through mutual collisions.

Tandem planet formation for solar system-like planetary systems

We present a new united theory of planet formation,which includes magneto-rotational instability（MRl） and porous aggregation of solid particles in a consistent way.We show that the ＂tandem planet formation＂ regime is likely to result in solar system-like planetary systems.In the tandem planet formation regime,planetesimals form at two distinct sites：the outer and inner edges of the MRl suppressed region.The former is likely to be the source of the outer gas giants,and the latter is the source for the inner volatile-free rocky planets.Our study spans disks with a various range of accretion rates,and we find that tandem planet formation can occur for M = 10^7.3- 10^-6.9Myr^-1.The rocky planets form between 0.4-2 AU,while the icy planets form between 6-30 All;no planets form in 2-6 AU region for any accretion rate.This is consistent with the gap in the solid component distribution in the solar system,which has only a relatively small Mars and a very small amount of material in the main asteroid belt from 2-6 AU.The tandem regime is consistent with the idea that the Earth was initially formed as a completely volatile-free planet.Water and other volatile elements came later through the accretion of icy material by occasional inward scattering from the outer regions.Reactions between reductive minerals,such as schreibersite（Fe-jP）,and water are essential to supply energy and nutrients for primitive life on Earth.

A tale of planet formation: from dust to planets

The characterization of exoplanets and their birth protoplanetary disks has enormously advanced in the last decade.Benefitting from that,our global understanding of the planet formation processes has been substantially improved.In this review,we first summarize the cutting-edge states of the exoplanet and disk observations.We further present a comprehensive panoptic view of modern core accretion planet formation scenarios,including dust growth and radial drift,planetesimal formation by the streaming instability,core growth by planetesimal accretion and pebble accretion.We discuss the key concepts and physical processes in each growth stage and elaborate on the connections between theoretical studies and observational revelations.Finally,we point out the critical questions and future directions of planet formation studies.

Delay of planet formation at large radius and the outward decrease in mass and gas content of Jovian planets

A prominent observation of the solar system is that the mass and gas content of Jovian planets decrease outward with orbital radius, except that, in terms of these properties, Neptune is almost the same as Uranus. In previous studies, the solar nebula was assumed to preexist and the formation process of the solar nebula was not considered. It was therefore assumed that planet formation at different radii started at the same time in the solar nebula. We show that planet formation at different radii does not start at the same time and is delayed at large radii. We suggest that this delay might be one of the factors that causes the outward decrease in the masses of Jovian planets. The nebula starts to form from its inner part because of the inside-out collapse of its progenitorial molecular cloud core. The nebula then expands outward due to viscosity. Material first reaches a small radius and then reaches a larger radius, so planet formation is delayed at the large radius. The later the material reaches a planet＇s location, the less time it has to gain mass and gas content. Hence, the delay tends to cause the outward decrease in mass and gas content of Jovian planets. Our nebula model shows that the material reaches Jupiter, Saturn, Uranus and Neptune at t = 0.40, 0.57, 1.50 and 6.29 × 10^6 yr, respectively. We discuss the effects of time delay on the masses of Jovian planets in the framework of the core accretion model of planet formation. Saturn＇s formation is not delayed by much time relative to Jupiter so that they both reach the rapid gas accretion phase and become gas giants. However, the delay in formation of Uranus and Neptune is long and might be one of the factors that cause them not to reach the rapid gas accretion phase before the gas nebula is dispersed. Saturn has less time to go through the rapid gas accretion, so Saturn＇s mass and gas content are significantly less than those of Jupiter.

Gap formation in a self-gravitating disk and the associated migration of the embedded giant planet

We present the results of our recent study on the interactions between a giant planet and a self-gravitating gas disk. We investigate how the disk＇s self-gravity affects the gap formation process and the migration of the giant planet. Two series of 1-D and 2-D hydrodynamic simulations are performed. We select several surface densities and focus on the gravitationally stable region. To obtain more reliable gravity torques exerted on the planet, a refined treatment of the disk＇s gravity is adopted in the vicinity of the planet. Our results indicate that the net effect of the disk＇s self- gravity on the gap formation process depends on the surface density of the disk. We notice that there are two critical values, ∑I and ∑n. When the surface density of the disk is lower than the first one,∑0 〈 ∑I, the effect of self-gravity suppresses the formation of a gap. When ∑0 〉 ∑I, the self-gravity of the gas tends to benefit the gap formation process and enlarges the width/depth of the gap. According to our 1-D and 2-D simulations, we estimate the first critical surface density to be ∑I ≈ 0.8 MMSN. This effect increases until the surface density reaches the second critical value ∑n- When ∑0 〉 ∑n, the gravitational turbulence in the disk becomes dominant and the gap formation process is suppressed again. Our 2-D simulations show that this critical surface density is around 3.5 MMSN. We also study the associated orbital evolution of a giant planet. Under the effect of the disk＇s self-gravity, the migration rate of the giant planet increases when the disk is dominated by gravitational turbulence. We show that the migration timescale correlates with the effective viscosity and can be up to 104 yr.

Relation between Mass and Radius of Exoplanets Distinguished by their Density

The formation of the solar system has been studied since the 18th century and received a boost in 1995 with the discovery of the first exoplanet,51 Pegasi b.The investigations increased the number of confirmed planets to about5400 to date.The possible internal structure and composition of these planets can be inferred from the relationship between planet mass and radius,M-R.We have analyzed the M-R relation of a selected sample of iron-rock and ice-gas planets using a fractal approach to their densities.The application of fractal theory is particularly useful to define the physical meaning of the proportionality constant and the exponent in an empirical M-R power law in exoplanets,but this does not necessarily mean that they have an internal fractal structure.The M-R relations based on this sample are M=(1.46±0.08)R^(2.6±0.2)for the rocky population(3.6≤ρ≤14.3 g cm^(-3)),with 1.5≤M≤39M_(⊕),and M=(0.27±0.04)R^(2.7±0.2)for ice-gas planets(0.3≤ρ≤2.1 g cm^(-3))with 5.1≤M≤639 M_(⊕)(or■2 M_(J))and orbital periods greater than 10 days.Both M-R relations have in their density range a great predictive power for the determination of the mass of exoplanets and even for the largest icy moons of the solar system.The average fractal dimension of these planets is D=2.6±0.1,indicating that these objects likely have a similar degree of heterogeneity in their densities and a nearly similar composition in each sample.The M-R diagram shows a"gap"between ice-gas and iron-rock planets.This gap is a direct consequence of the density range of these two samples.We empirically propose an upper mass limit of about 100 M_(⊕),so that an M-R relation for ice-gas planets in a narrow density range is defined by M∝R^(3).

The effects of viscosity on circumplanetary disks

The effects of viscosity on the circumplanetary disks residing in the vicinity of protoplanets are investigated through two-dimensional hydrodynamical simulations with the shearing sheet model. We find that viscosity can considerably affect properties of the circumplanetary disk when the mass of the protoplanet Mp ~ 33 Me, where Me is the Earth＇s mass. However, effects of viscosity on the circumplanetary disk are negligibly small when the mass of the protoplanet Mp 〉 33 Me. We find that when Mp ~ 33 Me, viscosity can markedly disrupt the spiral structure of the gas around the planet and smoothly distribute the gas, which weakens the torques exerted on the protoplanet. Thus, viscosity can slow the migration speed of a protoplanet. After including viscosity, the size of the circumplanetary disk can be decreased by a factor of 〉~ 20%. Viscosity helps to transport gas into the circumplanetary disk from the differentially rotating circumstellar disk. The mass of the circumplanetary disk can be increased by a factor of 50% after viscosity is taken into account when Mp ~ 33 Me. Effects of viscosity on the formation of planets and satellites are briefly discussed.

Long-term effects of main-body's obliquity on satellite formation perturbed by third-body gravity in elliptical and inclined orbit

A new non-simplified model of formation flying is derived in the presence of an oblate main- body and third-body perturbation. In the proposed model, considering the perturbation of the third- body in an inclined orbit, the effect of obliquity （axial tilt） of the main-body is becoming important and has been propounded in the absolute motion of a reference satellite and the relative motion of a follower satellite. From a new point of view, J2 perturbed relative motion equations and considering a disturbing body in an elliptic inclined three dimensional orbit, are derived using Lagrangian mechanics based on accurate introduced perturbed reference satellite motion. To validate the accuracy of the model presented in this study, an auxiliary model was constructed as the Main-body Center based Relative Motion （MCRM） model. Finally, the importance of the main-body＇s obliquity is demonstrated by several examples related to the Earth-Moon system in relative motion and lunar satellite formation keeping. The main-body＇s obliquity has a remarkable effect on formation keeping in the examined in-track and projected circular orbit （PCO） formations.

Astrophysical Applications of a Variant to Kepler’s Third Law

It is verified that the Nebula Hypothesis is applicable to the Solar System by way of a straightforward generalization of Kepler’s third law which also confirms that angular momentum transport is achieved by way of the self-gravity of the protoplanetary disk itself as it coalesces into planetesimals. The masses of the planets may then be approximately determined (within 10% error, for three planets) by way of this methodology, using the radius as well as the rate of rotation of the particular planet being considered. This would only be possible, not only in light of the Nebula Hypothesis, but also due to angular momentum transport (as these three planets most ideally express the expectations of angular momentum conservation from the protoplanetary disk). Also in this regard, the rotation of the Sun at its equator is discussed as it is found to be closely related to the planetary issue as it pertains to the evolution and structure of the body. A modified technique from that used in planetary study is then applied to the Galaxy for the purpose of the calculation of dark matter mass, presupposes treating the Galaxy as a homogeneous sphere (of dark matter) that is rotating. The model provides clear evidence of not only flat rotation-curves, but also the lack of centrifugal ejection of stars from galaxies as well as the configuration of the arms of spiral galaxies, along with a sound basis for black hole creation at the center of spiral galaxies.

The study of Mg isotope compositions of terrestrial rocks and meteorites

The study of Mg isotopes has been carried out for about 40 years since 1970 s. With analytical progress, the study is not only limited to the excess of ^26Mg due to decay of short-lived ^26Al in primitive meteorites, also extended to mass-dependent fractionation of Mg isotopes in meteorites and terrestrial rocks. This paper reviews recent development in Mg isotope researches.

The inner solar system cratering record and the evolution of impactor populations

We review previously published and newly obtained crater size-frequency distributions in the inner solar system. These data indicate that the Moon and the ter- restrial planets have been bombarded by two populations of objects. Population 1, dominating at early times, had nearly the same size distribution as the present-day asteroid belt, and produced heavily cratered surfaces with a complex, multi-sloped crater size-frequency distribution. Population 2, dominating since about 3.8-3.7 Gyr, had the same size distribution as near-Earth objects （NEOs） and a much lower im- pact flux, and produced a crater size distribution characterized by a differential -3 single-slope power law in the crater diameter range 0.02 km to 100 km. Taken to- gether with the results from a large body of work on age-dating of lunar and meteorite samples and theoretical work in solar system dynamics, a plausible interpretation of these data is as follows. The NEO population is the source of Population 2 and it has been in near-steady state over the past ～ 3.7-3.8 Gyr; these objects are derived from the main asteroid belt by size-dependent non-gravitational effects that favor the ejection of smaller asteroids. However, Population 1 was composed of main belt as- teroids ejected from their source region in a size-independent manner, possibly by means of gravitational resonance sweeping during orbit migration of giant planets; this caused the so-called Late Heavy Bombardment （LHB）. The LHB began some time before ～3.9 Gyr, peaked and declined rapidly over the next ～ 100 to 300 Myr, and possibly more slowly from about 3.8-3.7 Gyr to ～2 Gyr. A third crater population （Population S） consisted of secondary impact craters that can dominate the cratering record at small diameters.

A physical interpretation of the Titius-Bode rule and its connection to the closed orbits of Bertrand's theorem

We consider the geometric Titius-Bode rule for the semimajor axes of planetary orbits. We derive an equivalent rule for the midpoints of the segments between consecutive orbits along the radial direction and we interpret it physically in terms of the work done in the gravitational field of the Sun by particles whose orbits are perturbed around each planetary orbit. On such energetic grounds, it is not surprising that some exoplanets in multiple-planet extrasolar systems obey the same relation. However,it is surprising that this simple interpretation of the Titius-Bode rule also reveals new properties of the bound closed orbits predicted by Bertrand’s theorem, which has been known since 1873.

Millimeter gap contrast as a probe for turbulence level in protoplanetary disks

Turbulent motions are believed to regulate angular momentum transport and influence dust evolution in protoplanetary disks.Measuring the strength of turbulence is challenging through gas line observations because of the requirement for high spatial and spectral resolution data,and an exquisite determination of the temperature.In this work,taking the well-known HD 163296 disk as an example,we investigated the contrast of gaps identified in high angular resolution continuum images as a probe for the level of turbulence.With self-consistent radiative transfer models,we simultaneously analyzed the radial brightness profiles along the disk major and minor axes,and the azimuthal brightness profiles of the B67 and B100 rings.By fitting all the gap contrasts measured from these profiles,we constrained the gas-to-dust scale height ratioΛto be 3.0^(+0.3)_(−0.8),1.2^(+0.1)_(−0.1),and≥6.5 for the D48,B67,and B100 regions,respectively.The varying gas-to-dust scale height ratios indicate that the degree of dust settling changes with radius.The inferred values forΛtranslate into a turbulence level of α_(turb)<3×10^(−3) in the D48 and B100 regions,which is consistent with previous upper limits set by gas line observations.However,turbulent motions in the B67 ring are strong with α_(turb)∼1.2×10^(−2).Due to the degeneracy betweenΛand the depth of dust surface density drops,the turbulence strength in the D86 gap region is not constrained.

Modeling the arc and ring structures in the HD 143006 disk

Rings and asymmetries in protoplanetary disks are considered as signposts of ongoing planet formation.In this work,we con-duct three-dimensional radiative transfer simulations to model the intriguing disk around HD143006 that has three dust rings and a bright arc.A complex geometric configuration,with a misaligned inner disk,is assumed to account for the asymmetric structures.The two-dimensional surface density is constructed by iteratively fitting the ALMA data.We find that the dust tem-perature displays a notable discontinuity at the boundary of the misalignment.The ring masses range from 0.6 to 16 M⊕that are systematically lower than those inferred in the younger HL Tau disk.The arc occupies nearly 20%of the total dust mass.Such a high mass fraction of dust grains concentrated in a local region is consistent with the mechanism of dust trapping into vortices.Assuming a gas-to-dust mass ratio of 30 that is constant throughout the disk,the dense and cold arc is close to the threshold of being gravitationally unstable,with the Toomre parameter Q∼1.3.Nevertheless,our estimate of Q relies on the assumption for the unknown gas-to-dust mass ratio.Adopting a lower gas-to-dust mass ratio would increase the inferred Q value.Follow-up high resolution observations of dust and gas lines are needed to clarify the origin of the substructures.