Several models have been introduced in order to explain the radius distribution in exoplanet radii observed by Fulton et al. (2017) with one peak at $\rm \sim 1.3 R_{\oplus} $ the other at $\rm \sim 2.4 R_{\oplus} $ and the minimum at $\rm \sim 1.75R_{\oplus} $. In this paper we focus on the hypothesis that the exoplanet size distribution is caused by stellar XUV-induced atmospheric loss. We evolve $10^{6}$ synthetic exoplanets by exposing them to XUV irradiation from synthetic ZAMS stars. For each planet we set a different interior composition which ranged from $\rm 100 \: wt\%$ Fe (very dense) through $\rm 100 \: wt\%$ $\rm MgSiO_{3}$ (average density) and to $\rm 100 \: wt\%$ $\rm H_{2}O$ ice (low density) with varying hydrogen envelop sizes which varied from $\rm 0 \: wt\%$ (a negligible envelop) to $\rm 100 \: wt\%$ (a negligible core). Our simulations were able to replicate the bimodal distribution in exoplanet radii. We argue that in order to reproduce the distribution by Fulton et al. (2017) it is mandatory for there to be a paucity of exoplanets with masses above $\rm \sim 8M_{\oplus}$. Furthermore, our best-fit result predicts an initial flat distribution in exoplanet occurrence for $\rm M_{P} \lesssim 8M_{\oplus}$ with a strong deficiency for planets with $\rm \lesssim 3M_{\oplus}$. Our results are consistent with the $\rm \sim 1.3R_{\oplus}$ radius peak mostly encompassing denuded exoplanets whilst the $\rm \sim 2.4R_{\oplus}$ radius peak mainly comprising exoplanets with large hydrogen envelops
We study the evolution of six exoplanetary systems with the stellar evolutionary code MESA and conclude that they will likely spin-up the envelope of their parent stars on the red giant branch (RGB) or later on the asymptotic giant branch (AGB) to the degree that the mass loss process might become non-spherical. We choose six observed exoplanetary systems where the semi-major axis is ~1-2AU, and use the binary mode of MESA to follow the evolution of the systems. In four systems the star engulfs the planet on the RGB, and in two systems on the AGB, and the systems enter a common envelope evolut…
We assume that the strong convection during core helium flash of low mass red giant branch (RBG) stars excite waves that propagate to the envelope, and find that the energy that these waves deposit in the envelope causes envelope expansion and brightening. We base our assumption and the estimate of the wave energy on studies that explored such a process due to the vigorous core convection of massive stars just before they experience a core collapse supernova explosion. Using the stellar evolutionary code MESA we find that the wave energy causes an expansion within few years by tens to hundreds…
The James Webb Space Telescope (JWST) will measure exoplanet transmission and eclipse spectroscopy at un-precedented precisions to better understand planet structure, dynamics, chemistry and formation. These are essential tools on the march towards biosignature searches on potentially habitable planets. We explore a range of exoplanet atmospheric conditions and forecast the expected results with JWST. We take realistic CHIMERA models that match existing Spitzer and HST results and simulate the spectra achievable with the JWST MIRI + NIRCam Guaranteed Time Observations (GTO) survey. We then ret…
The observed distribution of radii for exoplanets shows a bimodal form that can be explained by mass-loss from planetary atmospheres due to high energy radiation emitted by their host stars. The location of the minimum of this radius distribution depends on the mass-radius relation, which in turn depends on the composition of planetary cores. Current studies suggest that super-Earth and mini-Neptune planets have iron-rich and hence largely Earth-like composition cores. This paper explores how non-zero planetary magnetic fields can decrease the expected mass-loss rates from these planets. These…
Giant exoplanets orbiting close to their host stars have high temperatures because of the immense stellar irradiation which they receive. The extreme energy input leads to the expansion of the atmosphere and the escape of neutral hydrogen. A particularly intriguing case among the hot giant planets is KELT-9b -- an exoplanet orbiting very close to an early A-type star with the highest temperature (~4600 K at day-side) among all the exoplanets known so far. The atmospheric composition and dynamic of such a unique planet have been unknown. Here we report the first detection of an extended hot hyd…
Exoplanets orbiting M dwarfs present a valuable opportunity for their detection and atmospheric characterisation. This is evident from recent inferences of H$_2$O in such atmospheres, including that of the habitable-zone exoplanet K2-18b. With a bulk density between Earth and Neptune, K2-18b may be expected to possess a H/He envelope. However, the extent of such an envelope and the thermodynamic conditions of the interior remain unexplored. In the present work, we investigate the atmospheric and interior properties of K2-18b based on its bulk properties and its atmospheric transmission spectru…
Recent observations identify a valley in the radius distribution of small exoplanets, with planets in the range $1.5-2.0\,{\rm R}_{\oplus}$ significantly less common than somewhat smaller or larger planets. This valley may suggest a bimodal population of rocky planets that are either engulfed by massive gas envelopes that significantly enlarge their radius, or do not have detectable atmospheres at all. One explanation of such a bimodal distribution is atmospheric erosion by high-energy stellar photons. We investigate an alternative mechanism: the luminosity of the cooling rocky core, which can…
Insights into the Exoplanet Radius Valley from Host-Star Ages, Activity, Chemistry, and Birth Radius
School of Science, Hangzhou Dianzi University（杭州电子科技大学理学院）；National Astronomical Data Center Zhijiang Branch（国家天文台紫江分中心）；CAS Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台光学天文重点实验室）；Department of Astronomy, The Ohio State University（俄亥俄州立大学天文学系）；Center for Cosmology and Astroparticle Physics (CCAPP), The Ohio State University（俄亥俄州立大学宇宙学与高能粒子物理中心）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；School of Science, Xichang University（西昌学院理学院）
The photoevaporation model is one of the leading explanations for the evolution of small, close-in planets and the origin of the radius-valley. However, without planet mass measurements, it is challenging to test the photoevaporation scenario. Even if masses are available for individual planets, the host star's unknown EUV/X-ray history makes it difficult to assess the role of photoevaporation. We show that systems with multiple transiting planets are the best in which to rigorously test the photoevaporation model. By scaling one planet to another in a multi-transiting system, the host star's …
Recent astronomical observations obtained with the Kepler and TESS missions and their related ground-based follow-ups revealed an abundance of exoplanets with a size intermediate between Earth and Neptune. A low occurrence rate of planets has been identified at around twice the size of Earth, known as the exoplanet radius gap or radius valley. We explore the geometry of this gap in the mass-radius diagram, with the help of a Mathematica plotting tool developed with the capability of manipulating exoplanet data in multidimensional parameter space, and with the help of visualized water equations…
The radius-period distribution of exoplanets has been characterized by the \textit{Kepler} survey, and the empirical mass-radius relation by the subset of \textit{Kepler} planets with mass measurements. We combine the two in order to constrain the joint mass-radius-period distribution of \textit{Kepler} transiting planets. We employ hierarchical Bayesian modeling and mixture models to formulate four models with varying complexity and fit these models to the data. We find that the most complex models that treat planets with significant gaseous envelopes, evaporated core planets, and intrinsical…
Planet formation scenarios can be constrained by the ratio of the gaseous envelope mass relative to the solid core mass in the observed exoplanet populations. One-dimensional calculations find a critical (maximal) core mass for quasi-static envelopes to exist, suggesting that envelopes around more massive cores should collapse due to a `core-nucleated' instability. We study self-gravitating planetary envelopes via hydrodynamic simulations, progressively increasing the dimensionality of the problem. We characterize the core-nucleated instability and its non-linear evolution into runaway gas acc…
Dynamically Selected Mass-Radius Relationship for Low Mass Exoplanets
Mani L. Bhaumik Institute for Theoretical Physics Department of Physics & Astronomy, University of California Los Angeles（加州大学洛杉矶分校物理与天文学系曼尼·L·巴乌米克理论物理研究所）；Department of Physics & Astronomy, University of California Los Angeles（加州大学洛杉矶分校物理与天文学系）
In order to characterize giant exoplanets and better understand their origin, knowledge of how the planet's composition depends on its mass and stellar environment is required. In this work, we simulate the thermal evolution of gaseous planets and explore how various common model assumptions such as different equations of state, opacities, and heavy-element distributions affect the inferred radius and metallicity. We examine how the theoretical uncertainties translate into uncertainties in the inferred planetary radius and bulk metallicity. While we confirm the mass-metallicity trend previousl…
Among exoplanets, the small-size population constitutes the dominant one, with a diversity of properties and compositions ranging from rocky to gas dominated envelope. While a large fraction of them have masses and radii similar to or smaller than Neptune, yet none share common properties in term of orbital period and insulation with our ice giants. These exoplanets belong to multi-planet systems where planets are closely packed within the first tenth of AU and often exposed to strong irradiation from their host star. Their formation process, subsequent evolution, and fate are still debated an…
The interior composition of exoplanets is not observable, limiting our direct knowledge of their structure, composition, and dynamics. Recently described observational trends suggest that rocky exoplanets, that is, planets without significant volatile envelopes, are likely limited to $<$1.5 Earth radii. We show that given this likely upper limit in the radii of purely-rocky super-Earth exoplanets, the maximum expected core-mantle boundary pressure and adiabatic temperature is relatively moderate, 630 GPa and 5000 K, while the maximum central core pressure varies between 1.5 and 2.5 TPa. We fur…
Planets that reside close-in to their host star are subject to intense high-energy irradiation. Extreme-ultraviolet (EUV) and X-ray radiation (together, XUV) is thought to drive mass loss from planets with volatile envelopes. We present $\textit{XMM-Newton}$ observations of six nearby stars hosting transiting planets in tight orbits (with orbital period, $P_\text{orb} < 10\,$d), wherein we characterise the XUV emission from the stars and subsequent irradiation levels at the planets. In order to reconstruct the unobservable EUV emission, we derive a new set of relations from Solar $\textit{TIME…
Habitability of Terrestrial-Mass Planets in the HZ of M Dwarfs. I. H/He-Dominated Atmospheres
M矮星的普遍存在，加上相对容易探测到它们周围的地球质量行星，使它们成为寻找和描述“宜居带“（HZ）行星的主要目标。然而，开普勒发现，地球质量的系外行星通常具有大量的H/He包层，包括质量分数（$M_{env}/M_{core}$）$\gtrsim 1$ %。如果这些行星在Gyr时间尺度上保持这样的包络，即使在HZ内，它们也不会“适合居住”。由于M矮星的X射线/紫外线通量很强，我们研究是否有足够的包络质量可以被光蒸发掉，使这些行星变得适合居住。我们改进了以前的工作，通过使用流体动力学模型，占辐射冷却以及从流体动力学到弹道逃逸的过渡。采用一个包含恒星演化的M矮星XUV光谱模板，同时考虑蒸发和热演化，我们证明了：（1）质量损失是（大大）低于以前的估计，使用“能量有限”的形式主义和忽略过渡到金斯逃逸，（2）在HZ的内边缘，行星的核心质量$\lesssim 0.9$ M $_\oplus$，（3）在HZ的外缘，即使从地核到0.8 M $_\oplus$，蒸发也不能去除$\sim$ 1%H/He包层。因此，如果行星形成时有庞大的H/He包层，那么只有那些具有低质量核心的行星最终可能适合居住。核心$\gtrsim$ 1 M $_\oplus$，与$\gtrsim$ 1%的出生H/He信封，将不适合居住在M矮星的HZ。
Exoplanets smaller than Neptune are common around red dwarf stars (M dwarfs), with those that transit their host star constituting the bulk of known temperate worlds amenable for atmospheric characterization. We analyze the masses and radii of all known small transiting planets around M dwarfs, identifying three populations: rocky, water-rich, and gas-rich. Our results are inconsistent with the previously known bimodal radius distribution arising from atmospheric loss of a hydrogen/helium envelope. Instead, we propose that a density gap separates rocky from water-rich exoplanets. Formation mod…
Water worlds have been hypothesized as an alternative to photo-evaporation in order to explain the gap in the radius distribution of Kepler exoplanets. We explore water worlds within the framework of a joint mass-radius-period distribution of planets fit to a sample of transiting Kepler exoplanets, a subset of which have radial velocity mass measurements. We employ hierarchical Bayesian modeling to create a range of ten mixture models that include multiple compositional subpopulations of exoplanets. We model these subpopulations - including planets with gaseous envelopes, evaporated rocky core…
The initial physical conditions of Kepler-36 b & c
开普勒行星系由两颗距离相似（0.115和0.128 AU）的系外行星组成，它们的密度截然不同。内行星的密度与地球的成分一致，而外行星的密度极低，因此它必须包含大量的H/He包层。如果它们的电流密度代表它们在形成时的组成，则这种密度差异将对任何形成机制造成问题。然而，这两颗行星的距离足够近，在过去经历了显着的蒸发。我们约束的核心质量，核心成分，初始的质量，和初始冷却时间的每个行星蒸发模型的条件下，他们现在的质量和半径，从开普勒测光和过境时间分析推断。内行星是一个蒸发剥离的核心，而外行星由于其较高的核心质量而保留了一些最初的外壳。因此，这两颗行星可能有类似的形成路径，内侧行星的初始质量分数为$\lesssim 10\%$，核心质量为$\sim4.4$ M $_\oplus$，而外侧行星的初始质量分数为15-30\%，核心质量为$\sim7.3$ M $_\oplus$。最后，我们的研究结果表明，外行星有一个很长的（$\gtrsim30$百万年）初始冷却时间，比从简单的时间尺度参数天真地预测要长得多。较长的初始冷却时间可能是一个戏剧性的早期冷却事件，如最近提出的“蒸发”过程的证据。
The radii and orbital periods of 4000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. Yet an important question about the composition of planets ran…
Measurements of exoplanetary masses and radii have revealed a population of massive super-Earths --- planets sufficiently large that, according to one dimensional models, they should have turned into gas giants. To better understand the origin of these objects, we carry out hydrodynamical simulations of planetary cores embedded in a nascent protoplanetary disk. In this first paper of a series, to gain intuition as well as to develop useful diagnostics, we focus on two-dimensional simulations of the flow around protoplanetary cores. We use the pluto code to study isothermal and adiabatic envelo…
Planets intermediate in size between the Earth and Neptune, and orbiting closer to their host stars than Mercury does the Sun, are the most common type of planet revealed by exoplanet surveys over the last quarter century. Results from NASA's Kepler mission have revealed a bimodality in the radius distribution of these objects, with a relative underabundance of planets between 1.5 and 2.0 $R_{\oplus}$. This bimodality suggests that sub-Neptunes are mostly rocky planets that were born with primary atmospheres a few percent by mass accreted from the protoplanetary nebula. Planets above the radiu…
The size distribution of exoplanets is a bimodal division into two groups: Rocky planet (<2 Earth radii) and water-rich planet (>2 Earth radii) with or without gaseous envelope.
The size frequency distribution of exoplanet radii between 1 and 4$R_{\oplus}$ is bimodal with peaks at $\sim$1.4 $R_{\oplus}$ and $\sim$2.4 $R_{\oplus}$, and a valley at $\sim$1.8$R_{\oplus}$. This radius valley separates two classes of planets -- usually referred to as "super-Earths" and "mini-Neptunes" -- and its origin remains debated. One model proposes that super-Earths are the outcome of photo-evaporation or core-powered mass-loss stripping the primordial atmospheres of the mini-Neptunes. A contrasting model interprets the radius valley as a dichotomy in the bulk compositions, where sup…
We explore the application of machine learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number $k_2$. We create a dataset of 900$\:$000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from…
Architectures of Exoplanetary Systems. IV: A Multi-planet Model for Reproducing the Radius Valley and Intra-system Size Similarity of Planets around Kepler's FGK Dwarfs
NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Penn State University（宾夕法尼亚州立大学）
