Most, if not all, sun-like stars host one or more planets, making multi-planetary systems commonplace in our galaxy. We utilize hundreds of multi-planet simulations to explore the origin of such systems, focusing on their orbital architecture. The first set of simulations assumes in-situ assembly of planetary embryos, while the second explores planetary migration. After applying observational biases to the simulations, we compare them to 250+ observed multi-planetary systems, including 13 systems with planets in the habitable zone. For all of the systems, we calculate two of the so-called statistical measures: the mass concentration ($S_{c}$) and orbital spacing ($S_{s}$). After analytic and empirical analyses, we find that the measures are related to first-order with a power law: $S_{c} \sim S_{s}^β$. The in-situ systems exhibit steeper power-law relations relative to the migration systems. We show that different formation scenarios cover different regions in the $S_{s} - S_{c}$ diagram with some overlap. Furthermore, we discover that observed systems with $S_{s} < 30$ are likely dominated by the migration scenario, while those with $S_{s} \geq 30$ are likely dominated by the in-situ scenario. We apply these criteria to determine that a majority (62%) of observed multi-planetary systems formed via migration, whereas most systems with currently observed habitable planets formed via in-situ assembly. This work provides methods of leveraging the statistical measures ($S_{s}$ and $S_{c}$) to disentangle the formation history of observed multi-planetary systems based on their present-day architectures.
Most water in the universe may be superionic, and its thermodynamic and transport properties are crucial for planetary science but difficult to probe experimentally or theoretically. We use machine learning and free energy methods to overcome the limitations of quantum mechanical simulations, and characterize hydrogen diffusion, superionic transitions, and phase behaviors of water at extreme conditions. We predict that a close-packed superionic phase with mixed stacking is stable over a wide temperature and pressure range, while a body-centered cubic phase is only thermodynamically stable in a…
The recent Kepler discovery of KOI-152 reveals a system of three hot super-Earth candidates that are in or near a 4:2:1 mean motion resonance. It is unlikely that they formed in situ, the planets probably underwent orbital migration during the formation and evolution process. The small semimajor axes of the three planets suggest that migration stopped at the inner edge of the primordial gas disk. In this paper we focus on the influence of migration halting mechanisms, including migration "dead zones", and inner truncation by the stellar magnetic field. We show that the stellar accretion rate, …
Magnetised exoplanets are expected to emit at radio frequencies analogously to the radio auroral emission of Earth and Jupiter. We predict the radio emission from V830 Tau b, the youngest (2 Myr) detected exoplanet to date. We model the host star wind using 3DMHD simulations that take into account its surface magnetism. With this, we constrain the local conditions around V830 Tau b that we use to then compute its radio emission. We estimate average radio flux densities of 6 to 24mJy, depending on the assumed radius of the planet (one or two Rjupiter). These radio fluxes are present peaks that …
We study tidal dissipation in stars with masses in the range $0.1-1.6 M_\odot$ throughout their evolution, including turbulent effective viscosity acting on equilibrium tides and inertial waves in convection zones, and internal gravity waves in radiation zones. We consider a range of stellar evolutionary models and incorporate the frequency-dependent effective viscosity acting on equilibrium tides based on the latest simulations. We compare the tidal flow and dissipation obtained with the conventional equilibrium tide, which is strictly invalid in convection zones, finding that the latter typi…
Free-floating (or rogue) planets are planets that are liberated (or ejected) from their host systems. Although simulations predict their existence in substantial numbers, direct observational evidence for free-floating planets with masses below ~5 MJup is still lacking. Several cycle-1 observing programs with JWST aim to hunt for them in four different star-forming clusters. These surveys are designed to be sensitive to masses of 1-15 MJup (assuming a hot-start formation), which corresponds to spectral types of early L to late T for the ages of these clusters. If the existing simulations are n…
Twinkle Twinkle Little Star, Roman Sees Where You Are: Predicting Exoplanet Transit Yields in the Rosette Nebula with the Nancy Grace Roman Space Telescope
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；University of Michigan（密歇根大学）；Massachusetts Institute of Technology（麻省理工学院）
Secular oscillations in multi-planet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This "secular chaos" readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets' properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-…
A planetary atmosphere is the outer gas layer of a planet. Besides its scientific significance among the first and most accessible planetary layers observed from space, it is closely connected with planetary formation and evolution, surface and interior processes, and habitability of planets. Current theories of the planetary atmosphere were primarily obtained through the studies of eight large planets, Pluto and three large moons (Io, Titan, and Triton) in the Solar System. Outside the Solar System, more than four thousand extra-solar planets (exoplanets) and two thousand brown dwarfs have be…
The migration of planetary cores embedded in a protoplanetary disk is an important mechanism within planet-formation theory, relevant for the architecture of planetary systems. Consequently, planet migration is actively discussed, yet often results of independent theoretical or numerical studies are unconstrained due to the lack of observational diagnostics designed in light of planet migration. In this work we follow the idea of inferring the migration behavior of embedded planets by means of the characteristic radial structures that they imprint in the disk's dust density distribution. We ru…
We constrain the planetary atmospheric mass fraction at the time of the dispersal of the protoplanetary disk and the evolution of the stellar rotation rate for a dozen multi-planet systems that host sub-Neptunes and/or super-Earths. We employ a custom-developed Python code that we have dubbed Pasta (Planetary Atmospheres and Stellar roTation rAtes), which runs within a Bayesian framework to model the atmospheric evolution of exoplanets. The code combines MESA stellar evolutionary tracks, a model describing planetary structures, a model relating stellar rotation and activity level, and a model …
Models of planetary core growth by either planetesimal or pebble accretion are traditionally disconnected from the models of dust evolution and formation of the first gravitationally-bound planetesimals. The state-of-the-art models typically start with massive planetary cores already present. We aim to study the formation and growth of planetary cores in a pressure bump, motivated by the annular structures observed in protoplanetary disks, starting with sub-micron-sized dust grains. We connect the models of dust coagulation and drift, planetesimal formation in the streaming instability, gravit…
We investigate whether any multi-planet systems among Kepler candidates (2011 February release) can harbor additional terrestrial-mass planets or smaller bodies. We apply the "packed planetary systems" hypothesis that suggests all planetary systems are filled to capacity, and use a Hill stability criterion to identify eight 2-planet systems with significant gaps between the innermost and outermost planets. For each of these systems, we perform long-term numerical integrations of 10^7 years to investigate the stability of 4000-8000 test particles injected into the gaps. We map out stability reg…
Planetary-scale collisions are common during the last stages of formation of solid planets, including the Solar system terrestrial planets. The problem of growing planets has been divided into studying the gravitational interaction of embryos relevant in million year timescales and treated with N-body codes and the collision between objects with a timescale of hours to days and treated with smoothed-particle hydrodynamics. These are now being coupled with simple parameterized models. We set out to investigate if machine learning techniques can offer a better solution by predicting the outcome …
The requirement that planetary systems be dynamically stable is often used to vet new discoveries or set limits on unconstrained masses or orbital elements. This is typically carried out via computationally expensive N-body simulations. We show that characterizing the complicated and multi-dimensional stability boundary of tightly packed systems is amenable to machine learning methods. We find that training an XGBoost machine learning algorithm on physically motivated features yields an accurate classifier of stability in packed systems. On the stability timescale investigated ($10^7$ orbits),…
We study the phase curves for the planets of our Solar System; which, is considered as a non-compact planetary system. We focus on modeling the small variations of the light curve, based on the three photometric effects: reflection, ellipsoidal, and Doppler beaming. Theoretical predictions for these photometric variations are proposed, as if a hypothetical external observer would measure them. In contrast to similar studies of multi-planetary systems, the physical and geometrical parameters for each planet of the Solar System are well-known. Therefore, we can evaluate with accuracy the mathema…
The tilt of a planet's spin axis off its orbital axis ("obliquity") is a basic physical characteristic that plays a central role in determining the planet's global circulation and energy redistribution. Moreover, recent studies have also highlighted the importance of obliquities in sculpting not only the physical features of exoplanets but also their orbital architectures. It is therefore of key importance to identify and characterize the dominant processes of excitation of non-zero axial tilts. Here we highlight a simple mechanism that operates early on and is likely fundamental for many extr…
Understanding Exoplanet Habitability: A Bayesian ML Framework for Predicting Atmospheric Absorption Spectra
1 Department of Information Science, University at Albany, Albany, NY 12222, USA 2 Department of Physics, University at Albany, Albany, NY 12222, USA 3 NASA Goddard Institute for Space Studies, New York, NY 10025, USA 4 Theoretical Astrophysics, Department of Physics \& Astronomy, Uppsala University, 75105 Uppsala, Sweden
We analyze the long-term tidal evolution of a single-planet system through the use of numerical simulations and averaged equations giving the variations of semi-major axis and eccentricity of the relative orbit. For different types of planets, we compute the variations due to the planetary and stellar tides. Then, we calculate the critical value of the eccentricity for which the stellar tide becomes dominant over the planetary tide. The timescales for orbital decay and circularization are also discussed and compared.
The ubiquity of planets and diversity of planetary systems reveal planet formation encompass many complex and competing processes. In this series of papers, we develop and upgrade a population synthesis model as a tool to identify the dominant physical effects and to calibrate the range of physical conditions. Recent planet searches leads to the discovery of many multiple-planet systems. Any theoretical models of their origins must take into account dynamical interaction between emerging protoplanets. Here, we introduce a prescription to approximate the close encounters between multiple planet…
Planetary rotation rate is a key parameter in determining atmospheric circulation and hence the spatial pattern of clouds. Since clouds can exert a dominant control on planetary radiation balance, rotation rate could be critical for determining mean planetary climate. Here we investigate this idea using a three-dimensional general circulation model with a sophisticated cloud scheme. We find that slowly rotating planets (like Venus) can maintain an Earth-like climate at nearly twice the stellar flux as rapidly rotating planets (like Earth). This suggests that many exoplanets previously believed…
The relationship between mass and radius (M-R relation) is the key for inferring the planetary compositions and thus valuable for the studies of formation and migration models. However, the M-R relation alone is not enough for planetary characterization due to the dependence of it on other confounding variables. This paper provides a non-trivial extension of the M-R relation by including the incident flux as an additional variable. By using Bayesian hierarchical modeling (BHM) that leverages the flexibility of finite mixture models, a probabilistic mass-radius-flux relationship (M-R-F relation…
Early dynamical evolution of close-in planetary systems is shaped by an intricate combination of planetary gravitational interactions, orbital migration, and dissipative effects. While the process of convergent orbital migration is expected to routinely yield resonant planetary systems, previous analyses have shown that the semi-major axes of initially resonant pairs of planets will gradually diverge under the influence of long-term energy damping, producing an overabundance of planetary period ratios in slight excess of exact commensurability. While this feature is clearly evident in the orbi…
Recent isotopic studies of Martian meteorites by Dauphas & Pourmond (2011) have established that large (~ 3000 km radius) planetary embryos existed in the solar nebula at the same time that chondrules - millimeter-sized igneous inclusions found in meteorites - were forming. We model the formation of chondrules by passage through bow shocks around such a planetary embryo on an eccentric orbit. We numerically model the hydrodynamics of the flow, and find that such large bodies retain an atmosphere, with Kelvin-Helmholtz instabilities allowing mixing of this atmosphere with the gas and particles …
We have studied the possibility that a third circumbinary planet in the Kepler-47 planetary system be the source of the single unexplained transiting event reported during the discovery of these planets. We applied the MEGNO technique to identify regions in the phase space where a third planet can maintain quasi-periodic orbits, and assessed the long-term stability of the three-planet system by integrating the entire 5 bodies (binary + planets) for 10 Myr. We identified several stable regions between the two known planets as well as a region beyond the orbit of Kepler-47c where the orbit of th…
Rapid and Predictive Planet Population Synthesis Model (RAPPS) I. Upgraded model and resulting synthetic populations
Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）；UTokyo Organization for Planetary Space Science (UTOPS), University of Tokyo（东京大学地球行星科学宇宙科学研究机构（UTOPS））；Division of Science, National Astronomical Observatory of Japan（日本国立天文台理学院）；Astrobiology Center (ABC)（天体生物学中心）；Graduate Institute for Advanced Studies, SOKENDAI（SOKENDAI高等研究院）；Department of Earth and Planetary Science, University of Tokyo（东京大学地球行星科学系）
The proportions of oxygen, carbon and major rock-forming elements (e.g. Mg, Fe, Si) determine a planet's dominant mineralogy. Variation in a planet's mineralogy subsequently affects planetary mantle dynamics as well as any deep water or carbon cycle. Through thermodynamic models and high pressure diamond anvil cell experiments, we demonstrate the oxidation potential of C is above that of Fe at all pressures and temperatures indicative of 0.1 - 2 Earth-mass planets. This means that for a planet with (Mg+2Si+Fe+2C)/O > 1, excess C in the mantle will be in the form of diamond. We model the genera…
We present three-band simultaneous observations of a weak-line T-Tauri star CVSO~30 (PTFO~8-8695), which is one of the youngest objects having a candidate transiting planet. The data were obtained with the Multicolor Simultaneous Camera for studying Atmospheres of Transiting exoplanets (MuSCAT) on the 188 cm telescope at Okayama Astrophysical Observatory in Japan. We observed the fading event in the $g^{\prime}_2$-, $r^{\prime}_2$-, and $z_{\rm s,2}$-bands simultaneously. As a result, we find a significant wavelength dependence of fading depths of about 3.1\%, 1.7\%, 1.0\% for the $g^{\prime}_…
At present, microlensing light curves from different telescopes and filters are photometrically aligned by fitting them to a common model. We present a second method based on photometry of common field stars. If two spectral responses are similar (or the color of the source is known) then this technique can resolve important ambiguities that frequently arise when predicting the future course of the event, and that occasionally persist even when the event is over. Or if the spectral responses are different, it can be used to derive the color of the source when that is unknown. We present the es…
Planetary population synthesis is a tool to understand the physics of planetary system formation. It builds on a model that includes a multitude of physical processes. The outcome can be statistically compared with exoplanet observations. Here, we review the population synthesis method and then use one population to explore how different planetary system architectures emerge and which conditions lead to their formation. The systems can be classified into four main architectures: Class I of near-in situ compositionally ordered terrestrial and ice planets, Class II of migrated sub-Neptunes, Clas…
Revealing the mechanisms shaping the architecture of planetary systems is crucial for our understanding of their formation and evolution. In this context, it has been recently proposed that stellar clustering might be the key in shaping the orbital architecture of exoplanets. The main goal of this work is to explore the factors that shape the orbits of planets. We used a homogeneous sample of relatively young FGK dwarf stars with RV detected planets and tested the hypothesis that their association to phase space (position-velocity) over-densities ('cluster' stars) and under-densities ('field' …
The preference for the axial dipole in planetary dynamos is investigated through the analysis of wave motions in spherical dynamo models. Our study focuses on the role of slow magnetostrophic waves, which are generated from localized balances between the Lorentz, Coriolis and buoyancy (MAC) forces. Since the slow waves are known to intensify with increasing field strength, simulations in which the field grows from a small seed towards saturation are useful in understanding the role of these waves in dynamo action. Axial group velocity measurements in the energy-containing scales show that fast…
The TRAPPIST-1 system provides an exquisite laboratory for advancing our understanding exoplanetary atmospheres, compositions, dynamics and architectures. A remarkable aspect of TRAPPIST-1 is that it represents the longest known resonance chain, where all seven planets share near mean motion resonances with their neighbors. Prior to the measurement of 1h's period, Luger et al. (2017) showed that six possible and highly precise periods for 1h were expected, assuming it also participated in the resonant chain. We show here that combining this argument with a Titius-Bode law fit of the inner six …
Recent ALMA observations have identified a variety of dust gaps in protoplanetary disks, which are commonly interpreted to be generated by unobserved planets. Predicting mass of such embedded planets is of fundamental importance in comparing those disk architectures with the observed diversity of exoplanets. The prediction, however, depends on the assumption that whether the same gap structure exists in the dust component alone or in the gas component as well. We assume a planet can only open a gap in the gas component when its mass exceeds the pebble isolation mass by considering the core acc…
Early analyses of exoplanet statistics from the Kepler Mission revealed that a model population of multiple-planet systems with low mutual inclinations (${\sim1^{\circ}-2^{\circ}}$) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. This so-called "Kepler dichotomy" signals the existence of a sub-population of multi-planet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically expl…
Detailed observational characterization of transiting exoplanet systems has revealed that the spin-axes of massive (M > ~1.2 solar masses) stars often exhibit substantial misalignments with respect to the orbits of the planets they host. Conversely, lower-mass stars tend to only have limited obliquities. A similar trend has recently emerged within the observational dataset of young stars' magnetic field strengths: massive T-Tauri stars tend to have dipole fields that are ~10 times weaker than their less-massive counterparts. Here we show that the associated dependence of magnetic star-disk tor…
At least 30\% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use N-body simulations including a model for gas-assisted pebble accretion and disk--planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes ($\lesssim15M_{\oplus}$) and super-massive planetary cores potentially able to become gas giant planets ($\gtrsim15M_{\oplus}$). Simulations with moderate pebble fluxes grow multiple super-Ear…
The rapid growth in the number of known exoplanets has revealed the existence of several distinct planetary populations in the observed mass-period diagram. Two of the most surprising are, (1) the concentration of gas giants around 1AU and (2) the accumulation of a large number of low-mass planets with tight orbits, also known as super-Earths and hot Neptunes. We have recently shown that protoplanetary disks have multiple planet traps that are characterized by orbital radii in the disks and halt rapid type I planetary migration. By coupling planet traps with the standard core accretion scenari…
Molecular nitrogen is the most commonly assumed background gas that supports habitability on rocky planets. Despite its chemical inertness, nitrogen molecule is broken by lightning, hot volcanic vents, and bolide impacts, and can be converted into soluble nitrogen compounds and then sequestered in the ocean. The very stability of nitrogen, and that of nitrogen-based habitability, is thus called into question. Here we determine the lifetime of molecular nitrogen vis-a-vis aqueous sequestration, by developing a novel model that couples atmospheric photochemistry and oceanic chemistry. We find th…
Continued observational characterization of transiting planets that reside in close proximity to their host stars has shown that a substantial fraction of such objects posses orbits that are inclined with respect to the spin axes of their stars. Mounting evidence for the wide-spread nature of this phenomenon has challenged the conventional notion that large-scale orbital transport occurs during the early epochs of planet formation and is accomplished via planet-disk interactions. However, recent work has shown that the excitation of spin-orbit misalignment between protoplanetary nebulae and th…
The geometric arrangement of planet and moon orbits into a regularly spaced pattern of distances is the result of a self-organizing system. The positive feedback mechanism that operates a self-organizing system is accomplished by harmonic orbit resonances, leading to long-term stable planet and moon orbits in solar or stellar systems. The distance pattern of planets was originally described by the empirical Titius-Bode law, and by a generalized version with a constant geometric progression factor (corresponding to logarithmic spacing). We find that the orbital periods $T_i$ and planet distance…
This paper considers the dynamics of scattering of planetesimals or planetary embryos by a planet on a circumstellar orbit. We classify six regions in the planet's mass versus semimajor axis parameter space according to the dominant outcome for scattered objects: ejected, accreted, remaining, escaping, Oort Cloud, depleted Oort Cloud. We use these outcomes to consider which planetary system architectures maximise the observability of specific signatures, given that signatures should be detected first around systems with optimal architectures (if such systems exist in nature). Giant impact debr…
Symplectic integrators have made it possible to study the long-term evolution of planetary systems with direct N-body simulations. In this paper we reassess the accuracy of such simulations by running a convergence test on 20Myr integrations of the Solar System using various symplectic integrators. We find that the specific choice of metric for determining a simulation's accuracy is important. Only looking at metrics related to integrals of motions such as the energy error can overestimate the accuracy of a method. As one specific example, we show that symplectic correctors do not improve the …
Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural networks can assist us in exploring the fundamental laws of classical mechanics from data of planetary motion. Firstly, we predict the orbits of planets in the geocentric system using the gate recurrent unit, one of the common neural networks. We find that the precision of the prediction is obviously improved when the information of the Sun is included in the tr…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a mass…
Pairwise collisions between terrestrial embryos are the dominant means of accretion during the last stage of planet formation. Hence, their realistic treatment in N-body studies is critical to accurately model the formation of terrestrial planets and to develop interpretations of telescopic and spacecraft observations. In this work, we compare the effects of two collision prescriptions on the core-mantle differentiation of terrestrial planets: a model in which collisions are always completely accretionary (``perfect merging'') and a more realistic model based on neural networks that has been t…
Fast inward migration of planetary cores is a common problem in the current planet formation paradigm. Even though dust is ubiquitous in protoplanetary disks, its dynamical role in the migration history of planetary embryos has not been assessed. In this Letter, we show that the scattered pebble-flow induced by a low-mass planetary embryo leads to an asymmetric dust-density distribution that is able to exert a net torque. By analyzing a large suite of multifluid hydrodynamical simulations addressing the interaction between the disk and a low-mass planet on a fixed circular orbit, and neglectin…
Over 300 extrasolar planets have been found since 1992, showing that planetary systems are common and exhibit an outstanding variety of characteristics. As the number of detections grows and as models of planet formation progress to account for the existence of these new worlds, statistical studies and confrontations of observation with theory allow to progressively unravel the key processes underlying planet formation. In this chapter we review the dominant contribution of Doppler spectroscopy to the present discoveries and to our general understanding of planetary systems. We also emphasize …
Exoplanets Prediction in Multi-Planetary Systems and Determining the Correlation Between the Parameters of Planets and Host Stars Using Artificial Intelligence
