The observed exoplanet population features a gap in the radius distribution that separates the smaller super-Earths ($\lesssim$1.7 Earth radii) from the larger sub-Neptunes ($\sim$1.7--4 Earth radii). While mass loss theories can explain many of the observed features of this radius valley, it is difficult to reconcile them with potentially rising population of terrestrials beyond orbital periods of $\sim$30 days. We investigate the ability of gas accretion during the gas-poor phase of disk evolution to reproduce both the location of the observed radius gap and the existence of long-period terrestrial planets. Updating the analytic scaling relations of gas accretion rate accounting for the shrinking of the bound radius by hydrodynamic effects and deriving a more realistic disk temperature profile, we find that the late-stage gas accretion alone is able to carve out the observed radius gap, with slopes $R_{\rm gap} \propto P^{-0.096}$ and $R_{\rm gap} \propto M_\star^{0.15}$ for top-heavy; and $R_{\rm gap} \propto P^{-0.089}$ and $R_{\rm gap} \propto M_\star^{0.22}$ for bottom-heavy core mass distributions, in good agreement with observations. The general morphology of the primordial radius gap is stable against a range of disk gas density and disk accretion rate with the latter affecting mostly the population of large planets ($\gtrsim$3--4$R_\oplus$). The peaks and valleys in the radius distribution were likely set in place primordially while post-formation mass loss further tunes the exoplanetary population. We provide potential observational tests that may be possible with TESS, PLATO and Roman Space Telescope.
The hot Saturn population exhibits a boundary in mass-radius space, such that no planets are observed at a density less than $\sim$0.1 g cm$^{-3}$. Yet, planet interior structure models can readily construct such objects as the natural result of radius inflation. Here, we investigate the role XUV-driven mass-loss plays in sculpting the density boundary by constructing interior structure models that include radius inflation, photoevaporative mass loss and a simple prescription of Roche lobe overflow. We demonstrate that planets puffier than $\sim$0.1 g cm$^{-3}$ experience a runaway mass loss c…
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…
Recent observations revealed a bimodal radius distribution of small, short-period exoplanets with a paucity in their occurrence, a radius `valley', around $1.5-2.0$ $R_\oplus$. In this work, we investigate the effect of a planet's own cooling luminosity on its thermal evolution and atmospheric mass-loss (core-powered mass-loss) and determine its observational consequences for the radius distribution of small, close-in exoplanets. Using simple analytical descriptions and numerical simulations, we demonstrate that planetary evolution based on the core-powered mass-loss mechanism alone (i.e., wit…
The EUV/X-ray photoevaporation and core-powered mass-loss models are both capable of reproducing the bimodality in the sizes of small, close-in exoplanets observed by the \textit{Kepler} space mission, often referred to as the "radius gap". However, it is unclear which of these two mechanisms dominates the atmospheric mass-loss which is likely sculpting the radius gap. In this work, we propose a new method of differentiating between the two models, which relies on analysing the radius gap in 3D parameter space. Using models for both mechanisms, and by performing synthetic transit surveys we pr…
In recent years, analyzing the bimodality in the size distribution of small planets, i.e., the `radius valley', has given us unprecedented insight into the planet formation process. Here we explore the properties of the radius valley for low mass stars, assuming that the core-powered mass-loss is the dominant process shaping the small exoplanet population. We show that the slope of radius valley in the planet size-orbital period space, to first-order, does not vary with stellar mass and has a negative slope of $\text{d log}R_p/\text{d log}P \simeq -0.11$ even for stars as small as 0.1 $M_\odot…
Long-Term Evolution of Close-in Sub-Neptunes and Outer Planetary Embryos: Atmospheric Mass Loss and Origin of Planets Inside and Outside the Radius Gap
Shanghai Jiao Tong University（上海交通大学）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大李政道研究所）
We construct models of the structural evolution of super-Earth- and mini-Neptune-type exoplanets with hydrogen-helium envelopes, incorporating radiative cooling and XUV-driven mass loss. We conduct a parameter study of these models, focusing on initial mass, radius, and envelope mass fractions, as well as orbital distance, metallicity, and the specific prescription for mass loss. From these calculations, we investigate how the observed masses and radii of exoplanets today relate to the distribution of their initial conditions. Orbital distance and initial envelope mass fraction are the most im…
We use models of coupled thermal evolution and photo-evaporative mass loss to understand the formation and evolution of the Kepler-36 system. We show that the large contrast in mean planetary density observed by Carter et al. (2012) can be explained as a natural consequence of photo-evaporation from planets that formed with similar initial compositions. However, rather than being due to differences in XUV irradiation between the planets, we find that this contrast is due to the difference in the masses of the planets' rock/iron cores and the impact that this has on mass loss evolution. We expl…
The instability in protoplanetary disks due to gas-dust friction and self-gravity of gas and dust is investigated by linear analysis. In the case where the dust to gas ratio is enhanced and turbulence is week, the instability grows, even in gravitationally stable disks, on a timescale of order $10^{4- 5}$yr at a radius of order 100AU. If we ignore the dynamical feedback from dust grains in the gas equation of motion, the instability reduces to the so-called "secular gravitational instability", which was investigated previously as an instability of dust in a fixed background gas flow. In this w…
We calculate the mass loss driven by MHD waves from hot Jupiters by using MHD simulations in one-dimensional flux tubes. If a gaseous planet has magnetic field, MHD waves are excited by turbulence at the surface, dissipate at the upper atmosphere, and drive gas outflows. Our calculation shows that mass loss rates are comparable to the observed mass loss rates of hot Jupiters, therefore it is suggested that gas flow driven by MHD waves can plays an important role in the mass loss from gaseous planets. The mass loss rate varies dramatically with radius and mass of a planet: a gaseous planet with…
We search for evidence of the cause of the exoplanet radius gap, i.e. the dearth of planets with radii near $1.8\ R_\oplus$. If the cause was photoevaporation, the radius gap should trend with proxies for the early-life high-energy emission of planet-hosting stars. If, alternatively, the cause was core-powered mass loss, no such trends should exist. Critically, spurious trends between the radius gap and stellar properties arise from an underlying correlation with instellation. After accounting for this underlying correlation, we find no trends remain between the radius gap and stellar mass or …
Characterizing the bulk compositions of transiting exoplanets within the M dwarf radius valley offers a unique means to establish whether the radius valley emerges from an atmospheric mass loss process or is imprinted by planet formation itself. We present the confirmation of such a planet orbiting an early M dwarf ($T_{\rm mag} = 11.0294 \pm 0.0074, M_s = 0.513 \pm 0.012\ M_\odot, R_s = 0.515 \pm 0.015\ R_\odot, T_{\rm eff} =3690\pm 50 K$): TOI-1695 b ($P = 3.13$ days, $R_p = 1.90^{+0.16}_{-0.14}\ R_\oplus$). TOI-1695 b's radius and orbital period situate the planet between model predictions …
The dearth of planets with sizes around 1.8 $\mathrm{R_\oplus}$ is a key demographic feature discovered by the $Kepler$ mission. Two theories have emerged as potential explanations for this valley: photoevaporation and core-powered mass-loss. However, Rogers et al. (2021) shows that differentiating between the two theories is possible using the three-dimensional parameter space of planet radius, incident flux, and stellar mass. We use homogeneously-derived stellar and planetary parameters to measure the $Kepler$ exoplanet radius gap in this three-dimensional space. We compute the slope of the …
We present a uniform analysis of the atmospheric escape rate of Neptune-like planets with estimated radius and mass (restricted to $M_{\rm p}<30\,M_{\oplus}$). For each planet we compute the restricted Jeans escape parameter, $Λ$, for a hydrogen atom evaluated at the planetary mass, radius, and equilibrium temperature. Values of $Λ\lesssim20$ suggest extremely high mass-loss rates. We identify 27 planets (out of 167) that are simultaneously consistent with hydrogen-dominated atmospheres and are expected to exhibit extreme mass-loss rates. We further estimate the mass-loss rates ($L_{\rm hy}$) …
Recent progress in transit photometry opened a new window to the interior of super-Earths. From measured radii and masses, we can infer planetary internal compositions. It has been recently revealed that super-Earths are diverse in composition. Such a diversity is thought to arise from diversity in volatile content. The stability of the volatile components is to be examined, because hot super-Earths undergo photo-evaporative mass loss. While several studies investigated the impact of photo-evaporative mass loss on hydrogen-helium envelopes, there are few studies as to the impact on water-vapor…
Recent studies have shown that atmospheric mass-loss powered by the cooling luminosity of a planet's core can explain the observed radius valley separating super-Earths and sub-Neptunes, even without photoevaporation. In this work, we investigate the dependence of this core-powered mass-loss mechanism on stellar mass ($M_\ast$), metallicity ($Z_\ast$) and age ($τ_\ast$). Without making any changes to the underlying planet population, we find that the core-powered mass-loss model yields a shift in the radius valley to larger planet sizes around more massive stars with a slope given by $\text{d …
\textit{Kepler} showed a paucity of planets with radii of 1.5 - 2 $\mathrm R_{\oplus}$ around solar mass stars but this radius-gap has not been well studied for low-mass star planets. Energy-driven escape models like photoevaporation and core-powered mass-loss predict opposing transition regimes between rocky and non-rocky planets when compared to models depicting planets forming in gas-poor environments. Here we present transit observations of three super-Earth sized planets in the radius-gap around low-mass stars using high-dispersion InfraRed Doppler (IRD) spectrograph on the Subaru 8.2m te…
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}$. This radius valley separates two classes of planets -- usually referred to as "super-Earths" and "mini-Neptunes" -- and its origin remains debated. One model proposes that super-Earths are the outcome of photo-evaporation or core-powered mass-loss stripping the primordial atmospheres of the mini-Neptunes. A contrasting model interprets the radius valley as a dichotomy in the bulk compositions, where sup…
The observed distribution of radii for exoplanets shows a bimodal form that can be explained by mass-loss from planetary atmospheres due to high energy radiation emitted by their host stars. The location of the minimum of this radius distribution depends on the mass-radius relation, which in turn depends on the composition of planetary cores. Current studies suggest that super-Earth and mini-Neptune planets have iron-rich and hence largely Earth-like composition cores. This paper explores how non-zero planetary magnetic fields can decrease the expected mass-loss rates from these planets. These…
A significant fraction of super-Earths and sub-Neptunes are thought to experience an extreme loss of volatiles because of atmospheric evaporation in the early stages of their life. Though the mechanisms behind the extreme mass loss are not fully understood, two contenders have been widely discussed: photoevaporation from X-ray and ultraviolet irradiation and core powered mass loss. Here, it is shown that both mechanisms occur but with different timescales, and that atmospheric loss can take place over three regimes. In the first regime, a planet has very high internal temperatures arising from…
Architectures of Exoplanetary Systems. IV: A Multi-planet Model for Reproducing the Radius Valley and Intra-system Size Similarity of Planets around Kepler's FGK Dwarfs
NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Penn State University（宾夕法尼亚州立大学）
For the hot exoplanets CoRoT-24b and CoRoT-24c, observations have provided transit radii R$_{\rm T}$ of 3.7$\pm$0.4 R$_{\oplus}$ and 4.9$\pm$0.5 R$_{\oplus}$, and masses of $\le$5.7 M$_{\oplus}$ and 28$\pm$11 M$_{\oplus}$, respectively. We study their upper atmosphere structure and escape applying an hydrodynamic model. Assuming R$_{\rm T} \approx$ R$_{\rm PL}$, where R$_{\rm PL}$ is the planetary radius at the pressure of 100 mbar, we obtained for CoRoT-24b unrealistically high thermally-driven hydrodynamic escape rates. This is due to the planet's high temperature and low gravity, independen…
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 …
The detected exoplanet population displays a dearth of planets with sizes of about two Earth radii, the so-called radius gap. This is interpreted as an evolutionary effect driven by a variety of possible atmospheric mass loss processes of exoplanets. For mass loss driven by an exoplanet's irradiation by stellar X-ray and extreme-UV photons, the time evolution of the stellar magnetic activity is important. It is known from observations of open stellar clusters that stars of the same age and mass do not all follow the same time evolution of activity-induced X-ray and extreme-UV luminosities. Her…
Multi-planet systems orbiting M dwarfs provide valuable tests of theories of small planet formation and evolution. K2-3 is an early M dwarf hosting three small exoplanets (1.5-2.0 Earth radii) at distances of 0.07-0.20 AU. We measure the high-energy spectrum of K2-3 with HST/COS and XMM-Newton, and use empirically-driven estimates of Ly-alpha and extreme ultraviolet flux. We use EXOFASTv2 to jointly fit radial velocity, transit, and SED data. This constrains the K2-3 planet radii to 4% uncertainty and the masses of K2-3b and c to 13% and 30%, respectively; K2-3d is not detected in RV measureme…
We present calculations of the occurrence rate of small close-in planets around low mass dwarf stars using the known planet populations from the $Kepler$ and $K2$ missions. Applying completeness corrections clearly reveals the radius valley in the maximum a-posteriori occurrence rates as a function of orbital separation and planet radius. We measure the slope of the valley to be $r_{p,\text{valley}} \propto F^{-0.060\pm 0.025}$ which bears the opposite sign from that measured around Sun-like stars thus suggesting that thermally driven atmospheric mass loss may not dominate the evolution of pla…
We develop PLATYPOS (PLAneTarY PhOtoevaporation Simulator), a python code to perform planetary photoevaporative mass-loss calculations for close-in planets with hydrogen-helium envelopes atop Earth-like rocky cores. With physical and model parameters as input, PLATYPOS calculates the atmospheric mass loss and with it the radius evolution of a planet over time, taking into account also the thermal cooling and subsequent radius evolution of the planet. In particular, we implement different stellar activity evolution tracks over time. Our setup allows for a prediction of whether a planet can hold…
We show that, for a low-mass planet that orbits its host star within a few tenths of an AU (like the majority of the {\it Kepler} planets), the atmosphere it was able to accumulate while embedded in the proto-planetary disk may not survive unscathed after the disk disperses. This gas envelope, if more massive than a few percent of the core (with a mass below $10 M_\oplus$), has a cooling time that is much longer than the time-scale on which the planet exits the disk. As such, it could not have contracted significantly from its original size, of order the Bondi radius. So a newly exposed proto-…
Revisiting the exoplanet radius valley with host stars from SWEET-Cat
Kyambogo University（坎博戈大学）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理学研究所）；Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto（波尔图大学空间与天体物理研究所）；Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto（波尔图大学理学院物理与天文系）；Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系研究所）
