Planetary evolution with atmospheric photoevaporation I. Analytical derivation and numerical study of the evaporation valley and transition from super-Earths to sub-Neptunes
Observations have revealed in the Kepler data a depleted region separating smaller super-Earths from larger sub-Neptunes. This can be explained as an evaporation valley between planets with and without H/He that is caused by atmospheric escape. First, we conduct numerical simulations of the evolution of close-in low-mass planets with H/He undergoing escape. Second, we develop an analytical model for the valley locus. We find that the bottom of the valley quantified by the radius of the largest stripped core $R_{\rm b}$ at a given orbital distance depends only weakly on post-formation H/He mass. The reason is that a high initial H/He mass means that there is more gas to evaporate, but also that the planet density is lower, increasing loss. Regarding stellar $L_{\rm XUV}$, $R_{\rm b}$ scales as $L_{\rm XUV}^{0.135}$. The same weak dependency applies to the efficiency factor $\varepsilon$ of energy-limited evaporation. As found numerically and analytically, $R_{\rm b}$ varies as function of orbital period $P$ for a constant $\varepsilon$ as $P^{-2 p_{\rm c}/3}\approx P^{-0.18}$ where $M \propto R^{p_{\rm c}}$ is the mass-radius relation of solid cores. $R_{\rm b}$ is about 1.7 $R_{\oplus}$ at a 10-day orbit for an Earth-like composition, increasing linearly with ice mass fraction. The numerical results are explained very well with the analytical model where complete evaporation occurs if the temporal integral over the stellar XUV irradiation absorbed by the planet is larger than binding energy of the envelope in the gravitational potential of the core. The weak dependency on primordial H/He mass, $L_{\rm XUV}$ and $\varepsilon$ explains why observationally the valley is visible, and why theoretically models find similar results. At the same time, given the large observed spread of $L_{\rm XUV}$, the dependency on it is still strong enough to explain why the valley is not completely empty.
Short-period sub-Neptunes with substantial volatile envelopes are among the most common type of known exoplanets. However, recent studies of the Kepler population have suggested a dearth of sub-Neptunes on highly irradiated orbits, where they are vulnerable to atmospheric photoevaporation. Physically, we expect this "photoevaporation desert" to depend on the total lifetime X-ray and extreme ultraviolet flux, the main drivers of atmospheric escape. In this work, we study the demographics of sub-Neptunes as a function of lifetime exposure to high energy radiation and host star mass. We find that…
Transit surveys indicate that there is a deficit of Neptune-sized planets on close-in orbits. If this ``Neptune desert' is entirely cleared out by atmospheric mass loss, then planets at its upper edge should only be marginally stable against photoevaporation, exhibiting strong outflow signatures in tracers like the metastable helium triplet. We test this hypothesis by carrying out a 12-night photometric survey of the metastable helium feature with Palomar/WIRC, targeting seven gas-giant planets orbiting K-type host stars. Eight nights of data are analyzed here for the first time along with rea…
The mass-period or radius-period distribution of close-in exoplanets shows a paucity of intermediate mass/size (sub-Jovian) planets with periods ~< 3 days. We show that this sub-Jovian desert can be explained by the photoevaporation of highly irradiated sub-Neptunes and the tidal disruption barrier for gas giants undergoing high-eccentricity migration. The distinctive triangular shape of the sub-Jovain desert result from the fact that photoevaporation is more effective closer to the host star, and that in order for a gas giant to tidally circularise closer to the star without tidal disruption …
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 …
The observational detection of a localized reduction in the small planet occurrence rate, sometimes termed a 'gap', is an exciting discovery because of the implications for planet evolutionary history. This gap appears to define a transition region in which sub-Neptune planets are believed to have lost their H/He envelope, potentially by photoevaporation or core powered mass loss, and have thus been transformed into bare cores terrestrial planets. Here we investigate the transition between sub-Neptunes and super-Earths using a real sample of observed small close-in planets and applying envelop…
Context: The current distribution of planet mass vs. incident stellar X-ray flux supports the idea that photoevaporation of the atmosphere may take place in close-in planets. Integrated effects have to be accounted for. A proper calculation of the mass loss rate due to photoevaporation requires to estimate the total irradiation from the whole XUV range. Aims: The purpose of this paper is to extend the analysis of the photoevaporation in planetary atmospheres from the accessible X-rays to the mostly unobserved EUV range by using the coronal models of stars to calculate the EUV contribution to t…
Short period planets are subject to intense energetic irradiations from their stars. It has been shown that this can lead to significant atmospheric mass-loss and create smaller mass planets. Here, we analyse whether the evaporation mechanism can affect the orbit of planets. The orbital evolution of a planet undergoing evaporation is derived analytically in a very general way. Analytical results are then compared with the period distribution of two classes of inner exoplanets: Jupiter-mass planets and Neptune-mass planets. These two populations have a very distinct period distribution, with a …
Despite the identification of a great number of Jupiter-like and Earth-like planets at close-in orbits, the number of "hot Neptunes" - the planets with 0.6-18 times of Neptune mass and orbital periods less than 3 days - turned out to be very small. The corresponding region in the mass-period distribution was assigned as the "short-period Neptunian desert". The common explanation of this fact is that the gaseous planet with few Neptune masses would not survive in the vicinity of host star due to intensive atmosphere outflow induced by heating from stellar radiation. To check this hypothesis we …
Planets are born from the gas and dust discs surrounding young stars. Energetic radiation from the central star can drive thermal outflows from the discs atmospheres, strongly affecting the evolution of the discs and the nascent planetary system. In this context several numerical models of varying complexity have been developed to study the process of disc photoevaporation from their central stars. We describe the numerical techniques, the results and the predictivity of current models and identify observational tests to constrain them.
There is growing evidence that the population of close-in planets discovered by the Kepler mission was sculpted by atmospheric loss, though the typical timescale for this evolution is not well-constrained. Among a highly complete sample of planet hosts of varying ages the age-dependence of the relative fraction of super-Earth and sub-Neptune detections can be used to constrain the rate at which some small planets lose their atmospheres. Using the California-Kepler Survey (CKS) sample, we find evidence that the ratio of super-Earth to sub-Neptune detections rises monotonically from 1-10 Gyr. Ou…
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…
Recent surveys have uncovered an exciting new population of ultra-short-period (USP) planets with orbital periods less than a day. These planets typically have radii <1.5 Earth radii, indicating that they likely have rocky compositions. This stands in contrast to the overall distribution of planets out to ~100 days, which is dominated by low-density sub-Neptunes above 2 Earth radii, which must have gaseous envelopes to explain their size. However, on ultra-short-period orbits, planets are bombarded by intense levels of photo-ionizing radiation and consequently gaseous sub-Neptunes are extremel…
Lyman-alpha (Lya) emission of neutral hydrogen (1215.67 Angström) is the main contributor to the ultraviolet flux of low-mass stars such as M dwarfs. It is also the main light source used in studies of the evaporating upper atmospheres of transiting extrasolar planets with ultraviolet transmission spectroscopy. However, there are very few observations of the Lya emissions of quiet M dwarfs, and none exist for those hosting exoplanets. Here, we present Lya observations of the hot-neptune host star GJ436 with the Hubble Space Telescope Imaging Spectrograph (HST/STIS). We detect bright emission i…
Making use of the publicly available 1D photoionization hydrodynamics code ATES we set out to investigate the combined effects of planetary gravitational potential energy ($ϕ_p\equiv GM_p/R_p$) and stellar X-ray and Extreme Ultraviolet (XUV) irradiation ($F_{\rm XUV}$) on the evaporation efficiency ($η$) of moderately-to-highly irradiated gaseous planets, from sub-Neptunes through hot Jupiters. We show that the (known) existence of a threshold potential above which energy-limited escape (i.e., $η\simeq 1$) is unattainable can be inferred analytically. For $\log ϕ_p\gtrsim \log ϕ_p^{\rm thr}\ap…
A new piece of evidence supporting the photoevaporation-driven evolution model for low-mass, close-in exoplanets was recently presented by the California-Kepler-Survey. The radius distribution of the Kepler planets is shown to be bimodal, with a ``valley' separating two peaks at 1.3 and 2.6 Rearth. Such an ``evaporation-valley' had been predicted by numerical models previously. Here, we develop a minimal model to demonstrate that this valley results from the following fact: the timescale for envelope erosion is the longest for those planets with hydrogen/helium-rich envelopes that, while only …
Most Neptune-mass planets in close-in orbits (orbital periods less than a few days) present nonzero eccentricity, typically around 0.15. This is somehow unexpected, as these planets undergo strong tidal dissipation that should circularize their orbits in a time-scale shorter than the age of the system. In this paper we discuss some mechanisms that can oppose to bodily tides, namely, thermal atmospheric tides, evaporation of the atmosphere, and excitation from a distant companion. In the first two cases, the eccentricity can increase consistently, while in the last one, the eccentricity can onl…
We show that photoevaporation of small gaseous exoplanets ("mini-Neptunes") in the habitable zones of M dwarfs can remove several Earth masses of hydrogen and helium from these planets and transform them into potentially habitable worlds. We couple X-ray/extreme ultraviolet (XUV)-driven escape, thermal evolution, tidal evolution and orbital migration to explore the types of systems that may harbor such "habitable evaporated cores" (HECs). We find that HECs are most likely to form from planets with $\sim 1 M_\oplus$ solid cores with up to about 50% H/He by mass, though whether or not a given mi…
We investigate possible pathways for the formation of the low density Neptune-mass planet HAT-P-26b. We use two formation different models based on pebbles and planetesimals accretion, and includes gas accretion, disk migration and simple photoevaporation. The models tracks the atmospheric oxygen abundance, in addition to the orbital period, and mass of the forming planets, that we compare to HAT-P-26b. We find that pebbles accretion can explain this planet more naturally than planetesimals accretion that fails completely unless we artificially enhance the disk metallicity significantly. Pebbl…
Simulations show that the orbits of planets are readily disrupted in dense star-forming regions; planets can be exchanged between stars, become free-floating and then be captured by other stars. However, dense star-forming regions also tend to be populous, containing massive stars that emit photoionising radiation, which can evaporate the gas in protoplanetary discs. We analyse N-body simulations of star-forming regions containing Jovian-mass planets and determine the times when their orbits are altered, when they become free-floating, and when they are stolen or captured. Simultaneously, we p…
Several circumbinary planets have recently been discovered. The orbit of a planet around a binary stellar system poses several dynamic constraints. The effects that radiation from the host stars may have on the planet atmospheres must be considered. Because of the configuration of a close binary system, these stars have a high rotation rate, which causes a permanent state of high stellar activity and copious XUV radiation. The accumulated effects are stronger than for exoplanets around single stars, and cause a faster evaporation of their atmospheres. We evaluate the effects that stellar radia…
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…
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 $\text{d …
Since planet occurrence and primordial atmospheric retention probability increase with period, the occurrence-weighted median planets discovered by transit surveys may bear little resemblance to the low-occurrence, short-period planets sculpted by atmospheric escape ordinarily used to calibrate mass--radius relations and planet formation models. An occurrence-weighted mass--radius relation for the low-mass planets discovered so far by transit surveys orbiting solar-type stars requires both occurrence-weighted median Earth-mass and Neptune-mass planets to have a few percent of their masses in h…
We consider the evaporation of close in planets by the star's intrinsic EUV and X-ray radiation. We calculate evaporation rates by solving the hydrodynamical problem for planetary evaporation including heating from both X-ray and EUV radiation. We show that most close-in planets (a<0.1 AU) are evaporating hydrodynamically, with the evaporation occurring in two distinct regimes: X-ray driven, in which the X-ray heated flow contains a sonic point, and EUV driven, in which the X-ray region is entirely sub-sonic. The mass-loss rates scale as L_X/a^2 for X-ray driven evaporation, and as Phi_*^{1/2}…
We report the discovery in TESS data and validation of HD 56414 b (a.k.a. TOI-1228 b), a Neptune-size ($R_{\rm p} = 3.71 \pm 0.20\, R_\oplus$) planet with a 29-day orbital period transiting a young (Age = $420 \pm 140$ Myr) A-type star in the TESS southern continuous viewing zone. HD 56414 is one of the hottest stars ($T_{\rm eff} = 8500 \pm 150 \, {\rm K}$) to host a known sub-Jovian planet. HD 56414 b lies on the boundary of the hot Neptune desert in planet radius -- bolometric insolation flux space, suggesting that the planet may be experiencing mass loss. To explore this, we apply a photoe…
The role of stellar age in the measured properties and occurrence rates of exoplanets is not well understood. This is in part due to a paucity of known young planets and the uncertainties in age-dating for most exoplanet host stars. Exoplanets with well-constrained ages, particularly those which are young, are useful as benchmarks for studies aiming to constrain the evolutionary timescales relevant for planets. Such timescales may concern orbital migration, gravitational contraction, or atmospheric photo-evaporation, among other mechanisms. Here we report the discovery of an adolescent transit…
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…
Extrasolar planets with sizes between that of the Earth and Neptune ($R_{\rm p}=1{-}4~{\rm R}_\oplus$) have a bimodal radius distribution. This 'planet radius valley' separates compact, rocky super-Earths ($R_{\rm p}=1.0{-}1.8~{\rm R}_\oplus$) from larger sub-Neptunes ($R_{\rm p}=1.8{-}3.5~{\rm R}_\oplus$) hosting a gaseous hydrogen-helium envelope around their rocky core. Various hypotheses for this radius valley have been put forward, which all rely on physics internal to the planetary system: photoevaporation by the host star, long-term mass loss driven by the cooling planetary core, or the…
One of the most significant advances by NASA's ${\mathit Kepler}$ Mission was the discovery of an abundant new population of highly irradiated planets with sizes between the Earth and Neptune. Subsequent analysis showed that at ~1.5 Earth radii there is a transition from a population of predominantly rocky super-Earths to non-rocky sub-Neptunes, which must have substantial volatile envelopes. Determining the origin of these highly irradiated rocky planets will be critical to our understanding of low-mass planet formation and the frequency of potentially habitable Earth-like planets. These shor…
The interiors of giant planets remain poorly understood. Even for the planets in the Solar System, difficulties in observation lead to large uncertainties in the properties of planetary cores. Exoplanets that have undergone rare evolutionary processes provide a route to understanding planetary interiors. Planets found in and near the typically barren hot-Neptune 'desert' (a region in mass-radius space that contains few planets) have proved to be particularly valuable in this regard. These planets include HD149026b, which is thought to have an unusually massive core, and recent discoveries such…
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…
In the presence of a magnetic field and weakly ionizing winds, ohmic dissipation is expected to take place in the envelopes of Jovian and lower-mass planets alike. While the process has been investigated on the former, there have been no studies done on mini-Neptunes so far. From structure and thermal evolution models, we determine that the required energy deposition for halting the contraction of mini-Neptunes increases with planetary mass and envelope fraction. Scaled to the insolation power, the ohmic heating needed is small $\sim10^{-5}$ -- orders of magnitude lower than for exo-Jupiters $…
Direct and statistical observational evidences suggest that photoevaporation is important in eroding the atmosphere of sub-Neptune planets. We construct full hydrodynamic simulations, coupled with consistent thermochemistry and ray-tracing radiative transfer, to understand the physics of atmospheric photoevaporation caused by high energy photons from the host star. We identify a region on the parameter space where a hydrostatic atmosphere cannot be balanced by any plausible interplanetary pressure, so that the atmosphere is particularly susceptible to loss by Parker wind. This region may lead …
We use Keck/NIRSPEC to survey a sample of of young ($<$1 Gyr), short period mini Neptunes orbiting nearby K dwargs to measure their mass loss via the metastable helium line. We detect helium absorption from all four of the targets in our initial sample. The first detection, around TOI 560b, was announced in a previous paper. We now announce three additional detections around TOI 1430.01, 2076b, and TOI 1683.01. All four planets show an average in-transit excess absorption of 0.7--1.0%. However, the outflows differ in their kinematic properties. TOI 1430b exhibits pre-ingress absorption, while …
The recent development of a new minimum mass solar nebula, under the assumption that the giant planets formed in the compact configuration of the Nice model, has shed new light on planet formation in the solar system. Desch previously found that a steady state protoplanetary disk with an outer boundary truncated by photoevaporation by an external massive star would have a steep surface density profile. In a completely novel way, we have adapted numerical methods for solving propagating phase change problems to astrophysical disks. We find that a one-dimensional time-dependent disk model that s…
Many exoplanets have been discovered with radii of 1-4 Earth radii, between that of Earth and Neptune. A number of these are known to have densities consistent with solid compositions, while others are "sub-Neptunes" likely to have significant hydrogen-helium envelopes. Future surveys will no doubt significantly expand these populations. In order to understand how the measured masses and radii of such planets can inform their structures and compositions, we construct models both for solid layered planets and for planets with solid cores and gaseous envelopes, exploring a range of core masses, …
Understanding the dynamics and kinematics of out-flowing atmospheres of hot and warm exoplanets is crucial to understanding the origins and evolutionary history of the exoplanets near the evaporation desert. Recently, ground based measurements of the meta-stable Helium atom's resonant absorption at 10830 Å~has become a powerful probe of the base environment which is driving the outflow of exoplanet atmospheres. We report evidence for the He I 10830 Å~in absorption (equivalent width $\sim$ $0.012 \pm 0.002$ Å) in the exosphere of a warm Neptune orbiting the M-dwarf GJ 3470, during three transit…
We report the detection and characterization of the transiting sub-Neptune TOI-1759 b, using photometric time-series from TESS and near infrared spectropolarimetric data from SPIRou on the CFHT. TOI-1759 b orbits a moderately active M0V star with an orbital period of $18.849975\pm0.000006$ d, and we measure a planetary radius and mass of $3.06\pm0.22$ R$_\oplus$ and $6.8\pm2.0$ M$_\oplus$. Radial velocities were extracted from the SPIRou spectra using both the CCF and the LBL methods, optimizing the velocity measurements in the near infrared domain. We analyzed the broadband SED of the star an…
An Adolescent and Near-Resonant Planetary System Near the End of Photoevaporation
Nanjing University（南京大学）；University of Hawai‘i（夏威夷大学）；Florida Institute of Technology（佛罗里达理工学院）；Tsinghua University（清华大学）；University of California Los Angeles（加州大学洛杉矶分校）；California Institute of Technology（加州理工学院）；University of California, San Diego（加州大学圣地亚哥分校）
Super-Earths and sub-Neptunes are commonly thought to have accreted hydrogen/helium envelopes, consisting of a few to ten percent of their total mass, from the primordial gas disk. Subsequently, hydrodynamic escape driven by core-powered mass-loss and/or photo-evaporation likely stripped much of these primordial envelopes from the lower-mass and closer-in planets to form the super-Earth population. In this work we show that after undergoing core-powered mass-loss, some super-Earths can retain small residual H/He envelopes. This retention is possible because, for significantly depleted atmosphe…
