Planetary Mass Research Articles

Direct detectability of tidally heated exomoons by photometric orbital modulation

Aims. We investigate whether volcanic exomoons can be detected in thermal wavelength light curves due to their phase variability along their orbit. The method we use is based on the photometric signal variability that volcanic features or hotspots would cause in infrared (IR) wavelengths, when they are inhomogeneously distributed on the surface of a tidally heated exomoon (THEM). Methods. We simulated satellites of various sizes around an isolated planet and modeled the system’s variability in two IR wavelengths, taking into account photon shot noise. The moon’s periodic signal as it orbits the planet introduces a peak in the frequency space of the system’s time-variable flux. We investigated the THEM and system properties that would make a moon stand out in the frequency space of its host’s variable flux. Results. The moon’s signal can produce a prominent feature in its host’s flux periodogram at shorter IR wavelengths for hotspots with temperatures similar to the ones seen on the Jovian moon, Io, while the same moon would not be identifiable in longer IR wavelengths. By comparing observations at two different wavelengths, we are able to disentangle the signal of an exomoon with transiting and non-transiting orbital inclinations from the planet’s signal in the frequency domain for system distances up to ~10 pc for Mars-sized exomoons and even further for Earth-sized ones. Conclusions. This method enlarges the parameter space of detectable exomoons around isolated planetary mass objects and directly imaged exoplanets, as it is sensitive to Io- to Earth-sized exomoons with hot volcanic features for a wide range of non-transiting orbital inclinations. Exomoon transits and the detection of outgassed volcanic molecules can subsequently confirm a putative detection.

Influence of Orbit and Mass Constraints on Reflected Light Characterization of Directly Imaged Rocky Exoplanets

Survey strategies for upcoming exoplanet direct imaging missions have considered varying assumptions of prior knowledge. Precursor radial velocity surveys could have detected nearby exo-Earths and provided prior orbit and mass constraints. Alternatively, a direct imaging mission performing astrometry could yield constraints on the orbit and phase angle of target planets. Understanding the impact of prior mass and orbit information on planetary characterization is crucial for efficiently recognizing habitable exoplanets. To address this question, we use a reflected-light retrieval tool to infer the atmospheric and bulk properties of directly imaged Earth-analogs while considering varying levels of prior information and signal-to-noise ratio (S/N). Because of the strong correlation between the orbit-related parameters and the planetary radius, prior information on the orbital distance and planetary phase angle yield much tighter constraints on the planetary radius: from Rp=2.95−1.95+2.69R⊕ without prior knowledge, to Rp=1.01−0.19+0.33R⊕ with prior determination of the orbit for S/N = 20 in the visible/near-infrared spectral range, thus allowing size determination from reflected light observations. However, additional knowledge of planet mass does not notably enhance radius ( Rp=0.98−0.14+0.17R⊕ ) or atmospheric characterization. Also, prior knowledge of the mass alone does not yield a tight radius constraint ( Rp=1.64−0.80+1.29R⊕ ) nor improves atmospheric composition inference. By contrast, because of its sensitivity to gas column abundance, detecting a Rayleigh scattering slope or bounding Rayleigh opacity helps to refine gas mixing ratio inferences without requiring prior mass knowledge. Overall, apart from radius determination, increasing the S/N is more beneficial than additional prior observations.

Stellar X-Ray Activity and Habitability Revealed by the ROSAT Sky Survey

Using the homogeneous X-ray catalog from ROSAT observations, we conducted a comprehensive investigation into stellar X-ray activity–rotation relations for both single and binary stars. Generally, the relation for single stars consists of two distinct regions: a weak decay region, indicating a continued dependence of the magnetic dynamo on stellar rotation rather than a saturation regime with constant activity, and a rapid decay region, where X-ray activity is strongly correlated with the Rossby number. Detailed analysis reveals more fine structures within the relation: in the extremely fast-rotating regime, a decrease in X-ray activity was observed with increasing rotation rate, referred to as supersaturation, while in the extremely slow-rotating region, the relation flattens, mainly due to the scattering of F stars. This scattering may result from intrinsic variability in stellar activities over one stellar cycle or the presence of different dynamo mechanisms. Binaries exhibit a similar relation to that of single stars while the limited sample size prevented the identification of fine structures in the relation for binaries. We calculated the mass-loss rates of planetary atmospheres triggered by X-ray emissions from host stars. Our findings indicate that for an Earthlike planet within the stellar habitable zone, it would easily lose its entire primordial H/He envelope (equating to about 1% of the planetary mass).

HD 110067 c has an aligned orbit

Planetary systems in mean motion resonances hold a special place among the planetary population. They allow us to study planet formation in great detail as dissipative processes are thought to have played an important role in their existence. Additionally, planetary masses in bright resonant systems can be independently measured via both radial velocities and transit timing variations. In principle, they also allow us to quickly determine the inclination of all planets in the system since, for the system to be stable, they are likely all in coplanar orbits. To describe the full dynamical state of the system, we also need the stellar obliquity, which provides the orbital alignment of a planet with respect to the spin of its host star and can be measured thanks to the Rossiter–McLaughlin effect. It was recently discovered that HD 110067 harbors a system of six sub-Neptunes in resonant chain orbits. We here analyze an ESPRESSO high-resolution spectroscopic time series of HD 110067 during the transit of planet c. We find the orbit of HD 110067 c to be well aligned, with a sky-projected obliquity of λ =6+24-26 deg. This result indicates that the current architecture of the system was reached through convergent migration without any major disruptive events. Finally, we report transit-timing variation in this system as we find a significant offset of 19 ± 4 min in the center of the transit compared to the published ephemeris.

Keck and Hubble Observations Show that MOA-2008-BLG-379Lb is a Super-Jupiter Orbiting an M Dwarf

We present high angular resolution imaging that detects the MOA-2008-BLG-379L exoplanet host star using Keck adaptive optics and the Hubble Space Telescope. These observations reveal host star and planet masses of M host = 0.434 ± 0.065 M ⊙ and m p = 2.44 ± 0.49 M Jupiter. They are located at a distance of D L = 3.44 ± 0.53 kpc, with a projected separation of 2.70 ± 0.42 au. These results contribute to our determination of exoplanet host star masses for the Suzuki et al. statistical sample, which will determine the dependence of the planet occurrence rate on the mass and distance of the host stars. We also present a detailed discussion of the image-constrained modeling version of the eesunhong light-curve modeling code that applies high angular resolution image constraints to the light-curve modeling process. This code increases modeling efficiency by a large factor by excluding models that are inconsistent with the high angular resolution images. The analysis of this and other events from the Suzuki et al. statistical sample reveals the importance of including higher-order effects, such as microlensing parallax and planetary orbital motion, even when these features are not required to fit the light-curve data. The inclusion of these effects may be needed to obtain accurate estimates of the uncertainty of other microlensing parameters that affect the inferred properties of exoplanet microlens systems. This will be important for the exoplanet microlensing survey of the Roman Space Telescope, which will use both light-curve photometry and high angular resolution imaging to characterize planetary microlens systems.

TOI-2374 b and TOI-3071 b: two metal-rich sub-Saturns well within the Neptunian desert

ABSTRACT We report the discovery of two transiting planets detected by the Transiting Exoplanet Survey Satellite (TESS), TOI-2374 b and TOI-3071 b, orbiting a K5V and an F8V star, respectively, with periods of 4.31 and 1.27 d, respectively. We confirm and characterize these two planets with a variety of ground-based and follow-up observations, including photometry, precise radial velocity monitoring and high-resolution imaging. The planetary and orbital parameters were derived from a joint analysis of the radial velocities and photometric data. We found that the two planets have masses of (57 ± 4) M⊕ or (0.18 ± 0.01) MJ, and (68 ± 4) M⊕ or (0.21 ± 0.01) MJ, respectively, and they have radii of (6.8 ± 0.3) R⊕ or (0.61 ± 0.03) RJ and (7.2 ± 0.5) R⊕ or (0.64 ± 0.05) RJ, respectively. These parameters correspond to sub-Saturns within the Neptunian desert, both planets being hot and highly irradiated, with Teq ≈ 745 K and Teq ≈ 1812 K, respectively, assuming a Bond albedo of 0.5. TOI-3071 b has the hottest equilibrium temperature of all known planets with masses between 10 and 300 M⊕ and radii less than 1.5 RJ. By applying gas giant evolution models we found that both planets, especially TOI-3071 b, are very metal-rich. This challenges standard formation models which generally predict lower heavy-element masses for planets with similar characteristics. We studied the evolution of the planets’ atmospheres under photoevaporation and concluded that both are stable against evaporation due to their large masses and likely high metallicities in their gaseous envelopes.

Gravitational wave emission from close-in strange quark planets around strange stars with magnetic interactions

ABSTRACT According to the strange quark matter hypothesis, strange planets may exist, which are planetary mass objects composed of almost equal numbers of up, down, and strange quarks. A strange planet can revolve around its host strange star in a very close-in orbit. When it finally merges with the host, strong gravitational wave emissions will be generated. Here, the gravitational waveforms are derived for the merging process, taking into account the effects of the strange star’s magnetic field on the dynamics. Effects of the inclination angle are also considered. Templates of the gravitational waveforms are derived. It is found that the magnetic interactions significantly speed up the merging process. Coalescence events of such strange planetary systems occurring in our Galaxy as well as in local galaxies can be effectively detected by current and future gravitational experiments, which may hopefully provide a new method to test the strange quark matter hypothesis and probe the magnetic field of compact stars.

TESS Giants Transiting Giants. IV. A Low-density Hot Neptune Orbiting a Red Giant Star

Hot Neptunes, gaseous planets smaller than Saturn (∼3–8 R ⊕) with orbital periods less than 10 days, are rare. Models predict this is due to high-energy stellar irradiation stripping planetary atmospheres over time, often leaving behind only rocky planetary cores. Using our TESS full-frame-image pipeline giants in conjunction with Keck/HIRES radial velocity measurements, we present the discovery of TIC365102760 b, a 6.2 R ⊕(0.55 R J), 19.2 M ⊕(0.060 M J) planet transiting a red giant star every 4.21285 days. The old age and high equilibrium temperature yet remarkably low density of this planet ( ρp=0.58−0.20+0.30ρJ ) suggest that its gaseous envelope should have been stripped by high-energy stellar irradiation billions of years ago. The present-day planet mass and radius suggest the atmospheric stripping was slower than predicted. Unexpectedly low stellar activity and/or late-stage planet inflation could be responsible for the observed properties of this system. Further studies of this system with more precise photometry in multiple passbands will be capable of revealing more details of this planet’s atmosphere.

Populating the Milky Way

Context. Stellar populations and their distribution differ widely across the Galaxy, which is likely to affect planet demographics. Our local neighbourhood is dominated by young, metal-rich stars in the galactic thin disc, while the stellar halo and galactic bulge host a large fraction of older, metal-poor stars. Aims. We study the impact of these variations on planet populations in different regions of the Galaxy by combining a high-resolution galaxy formation simulation with state-of-the-art planet population synthesis models. Methods. We constructed a population model to estimate occurrence rates of different planet types, based on the New Generation Planet Population Synthesis (NGPPS). We applied this model to a simulated Milky Way (MW) analogue in the HESTIA galaxy formation simulation. We studied the planet occurrence rate in the metal-rich regions of the inner Galaxy, namely, in the galactic bulge and thin disc. We compared these result with the frequencies in the more distant, metal-poor region such as the thick disc and stellar halo. Results. We find that the planet demographics in the central, metal-rich regions of the MW analogue differ strongly from the planet populations in the more distant, metal-poor regions. The occurrence rate of giant planets (>300 M⊕) is 10–20 times larger in the thin disc compared to the thick disc, driven by the low amounts of solid material available for planet formation around metal-poor stars. Similarly, low-mass Earth-like planets around Sun-like stars are most abundant in the thick disc, being 1.5 times more frequent than in the thin disc. Moreover, low-mass planets are expected to be abundant throughout the galaxy, from the central regions to the outer halo, due to their formation processes being less dependent on stellar metallicity. The planet populations differ more strongly around Sun-like stars compared to dwarfs with masses 0.3–0.5 M⊙, caused by a weaker correlation between [Fe/H] metallicity and planet mass. However, it is important to note that the occurrence rates of low-mass planets are still uncertain, making our findings strongly model-dependent. Massive planets are more comprehensively understood and our findings are more robust. Nonetheless, other systematic effects have the potential to alter the giant planet population that we have not addressed in this study. We discuss some of these limitations and offer further directions for future research.

Secular Dynamics of Compact Three-planet Systems

The secular Laplace–Lagrange orbital solution, decomposing eccentricities into a set of uniformly precessing eigenmodes, is a classical result that is typically solved numerically. However, in the limit where orbits are closely spaced, several simplifications make it possible to make analytical progress. We derive simple expressions for the eccentricity eigenmodes in a coplanar three-planet system where the middle planet is much less massive than its neighbors, and we show that these approximate the true eigenmodes of more general systems with three massive planets in various limits. These results provide intuition for the secular dynamics of real systems, and have applications for understanding the stability boundary for compact multiplanet systems.

Delivery of Dust Particles from Protoplanetary Disks onto Circumplanetary Disks of Giant Planets

The principal regular satellites of gas giants are thought to be formed by the accumulation of solid materials in circumplanetary disks (CPDs). While there has been significant progress in the study of satellite formation in CPDs, details of the supply of satellite building blocks to CPDs remain unclear. We perform the orbital integration of solid particles in the protoplanetary disk (PPD) approaching a planet, considering the gas drag force by using the results of three-dimensional hydrodynamical simulations of a local region around the planet. We investigate the planetary mass dependence of the capture positions and the capture rates of dust particles accreting onto the CPD. We also examine the degree of dust retention in the accreting gas onto the CPD, which is important for determining the ratio of the dust-to-gas inflow rates, a key parameter in satellite formation. We find that the degree of dust retention increases with increasing planetary mass for a given dust scale height in the PPD. In the case of a small planet (M p = 0.2M Jup), most particles with insufficient initial altitudes in the PPD are isolated from the gas in the accreting region. On the other hand, in the case of a massive planet (M p = 1M Jup), dust particles can be coupled to the vertically accreting gas, even when the dust scale height is about 10%–30% of the gas scale height. The results of this study can be used for models of dust delivery and satellite formation in the CPDs of gas giants of various masses, including exoplanets.

Enhancing Exoplanet Ephemerides by Leveraging Professional and Citizen Science Data: A Test Case with WASP-77 A b

We present an updated ephemeris, and physical parameters, for the exoplanet WASP-77 A b. In this effort, we combine 64 ground- and space-based transit observations, 6 space-based eclipse observations, and 32 radial velocity observations to produce this target's most precise orbital solution to date aiding in the planning of James Webb Space Telescope and Ariel observations and atmospheric studies. We report a new orbital period of 1.360029395 ± 5.7 × 10−8 days, a new mid-transit time of 2459957.337860 ± 4.3 × 10−5 Barycentric Julian Date in the Barycentric Dynamical Timescale (BJDTDB) and a new mid-eclipse time of 2459956.658192 ± 6.7 × 10−5 BJDTDB. Furthermore, the methods presented in this study reduce the uncertainties in the planet's mass 1.6654 ± 4.5 × 10−3 M Jup and orbital period 1.360029395 ± 5.7 × 10−8 days by factors of 15.1 and 10.9, respectively. Through a joint fit analysis comparison of transit data taken by space-based and citizen science-led initiatives, our study demonstrates the power of including data collected by citizen scientists compared to a fit of the space-based data alone. Additionally, by including a vast array of citizen science data from ExoClock, Exoplanet Transit Database, and Exoplanet Watch, we can increase our observational baseline and thus acquire better constraints on the forward propagation of our ephemeris than what is achievable with Transiting Exoplanet Survey Satellite data alone.

Long-period modulation of the classical T Tauri star CI Tau

Context. Detecting planets within protoplanetary disks around young stars is essential for understanding planet formation and evolution. However, planet detection using the radial velocity method faces challenges due to the strong stellar activity in these early stages. Aims. We detect long-term periodicities in photometric and spectroscopic time series of the classical T Tauri star (CTTS) CI Tau, and retrieve evidence for inner embedded planets in its disk. Methods. The study conducted photometric and spectroscopic analyses using K2 and Las Cumbres Observatory Global Network light curves, and high-resolution spectra from ESPaDOnS and SPIRou. We focused our radial velocity analysis on a wavelength domain less affected by spot activity. To account for spot effects, a quasi-periodic Gaussian process model was applied to K2 light curve, ESPaDOnS, and SPIRou radial velocity data. Additionally, a detailed bisector analysis on cross-correlation functions was carried out to understand the cause of long-term periodicity. Results. We detect coherent periods at ~6.6d, 9d, ~11.5d, ~14.2d, and ~25.2d, the last of which is seen consistently across all datasets. Bisector analysis of the cross-correlation functions provides strong hints for combined activity-induced and Doppler reflex signals in the radial velocities at a period of 25.2 d. Our analysis suggests that this periodicity is best explained by the presence of a 3.6 ± 0.3 MJup eccentric (e ~ 0.58) planet at a semi-major axis of 0.17 au. Conclusions. We report the detection of a massive inner planet in CI Tau. Our study outlines the difficulty of searching for disk-embedded planets in the inner 0.1 au of young and active systems. When searching for planets in actively accreting stars such as CI Tau, we demonstrate that the primary limitation is stellar activity rather than the precision of RV measurements provided by the instrument.

Characterisation of the TOI-421 planetary system using CHEOPS, TESS, and archival radial velocity data

Context. The TOI-421 planetary system contains two sub-Neptune-type planets (Pb ~ 5.2 days, Teq,b ~ 900 K, and Pc ~ 16.1 days, Teq,c ~ 650 K) and is a prime target to study the formation and evolution of planets and their atmospheres. The inner planet is especially interesting as the existence of a hydrogen-dominated atmosphere at its orbital separation cannot be explained by current formation models without previous orbital migration. Aims. We aim to improve the system parameters to further use them to model the interior structure and simulate the atmospheric evolution of both planets, to finally gain insights into their formation and evolution. We also investigate the possibility of detecting transit timing variations (TTVs). Methods. We jointly analysed photometric data of three TESS sectors and six CHEOPS visits as well as 156 radial velocity data points to retrieve improved planetary parameters. We also searched for TTVs and modelled the interior structure of the planets. Finally, we simulated the evolution of the primordial H-He atmospheres of the planets using two different modelling frameworks. Results. We determine the planetary radii and masses of TOI-421 b and c to be Rb = 2.64 ± 0.08 R⊕, Mb = 6.7 ± 0.6 M⊕, Rc = 5.09 ± 0.07 R⊕, and Mc = 14.1 ± 1.4 M⊕. Using these results we retrieved average planetary densities of ρb = 0.37 ± 0.05ρ⊕ and ρc = 0.107 ± 0.012 ρ⊕. We do not detect any statistically significant TTV signals. Assuming the presence of a hydrogen-dominated atmosphere, the interior structure modelling results in both planets having extensive envelopes. While the modelling of the atmospheric evolution predicts for TOI-421 b to have lost any primordial atmosphere that it could have accreted at its current orbital position, TOI-421 c could have started out with an initial atmospheric mass fraction somewhere between 10 and 35%. Conclusions. We conclude that the low observed mean density of TOI-421 b can only be explained by either a bias in the measured planetary parameters (e.g. driven by high-altitude clouds) and/or in the context of orbital migration. We also find that the results of atmospheric evolution models are strongly dependent on the employed planetary structure model.

A fading radius valley towards M dwarfs, a persistent density valley across stellar types

The radius valley separating super-Earths from mini-Neptunes is a fundamental benchmark for theories of planet formation and evolution. Observations show that the location of the radius valley decreases with decreasing stellar mass and with increasing orbital period. Here, we build on our previous pebble-based formation model. Combined with photoevaporation after disc dispersal, it has allowed us to unveil the radius valley as a separator between rocky and water-worlds. In this study, we expand our model for a range of stellar masses spanning from 0.1 to 1.5 M⊙. We find that the location of the radius valley is well described by a power-law in stellar mass as Rvalley = 1.8197 M⋆0.14(+0.02/−0.01), which is in excellent agreement with observations. We also find very good agreement with the dependence of the radius valley on orbital period, both for FGK and M dwarfs. Additionally, we note that the radius valley gets filled towards low stellar masses, particularly at 0.1–0.4 M⊙, yielding a rather flat slope in Rvalley − Porb. This is the result of orbital migration occurring at lower planet mass for less massive stars, which allows for low-mass water-worlds to reach the inner regions of the system, blurring the separation in mass (and size) between rocky and water worlds. Furthermore, we find that for planetary equilibrium temperatures above 400 K, the water in the volatile layer exists fully in the form of steam, puffing the planet radius up (as compared to the radii of condensed-water worlds). This produces an increase in planet radii of ∼30% at 1 M⊕ and of ∼15% at 5 M⊕ compared to condensed-water worlds. As with Sun-like stars, we find that pebble accretion leaves its imprint on the overall exoplanet population as a depletion of planets with intermediate compositions (i.e. water mass fractions of ∼0 − 20%), carving an planet-depleted diagonal band in the mass-radius (MR) diagrams. This band is better visualised when plotting the planet’s mean density in terms of an Earth-like composition. This change in coordinates causes the valley to emerge for all the stellar mass cases.

Comparison of Machine-learning and Bayesian Inferences for the Interior of Rocky Exoplanets with Large Compositional Diversity

In previous work, we demonstrated that machine-learning techniques based on mixture density networks (MDNs) are successful in inferring the interior structure of rocky exoplanets with large compositional diversity. In this study, we compare the performance of a well-trained MDN model with the conventional Bayesian inversion method based on the Markov chain Monte Carlo (MCMC) method, under the same observable constraints. Considering that MCMC inversion is generally performed with the prior knowledge of planetary mass, radius, and bulk molar ratios of Fe/Mg and Si/Mg, we regenerate a substantial data set of interior structure data for rocky exoplanets and train a new MDN model with inputs of planetary mass, radius, Fe/Mg, and Si/Mg. It has been found that the well-trained MDN model has comparable performance to that of the MCMC method but requires significantly less computation time. The MDN model presents a practical alternative to the traditional MCMC method, surpassing the latter with minimal requirements for specialized knowledge, faster prediction, and greater adaptability. The developed MDN model is made publicly available on GitHub for the broader scientific community’s utilization. With the advent of the James Webb Space Telescope, we are ushering in a new epoch in exoplanetary explorations. In this evolving landscape, the MDN model stands out as a valuable asset, particularly for its ability to rapidly assimilate and interpret new data, thereby substantially advancing our understanding of the interior and habitability of exoplanetary systems.

The interplay between forming planets and photoevaporating discs

Context. Disc winds and planet–disc interactions are two crucial mechanisms that define the structure, evolution, and dispersal of protoplanetary discs. While winds are capable of removing material from discs, eventually leading to their dispersal, massive planets can shape their disc by creating sub-structures such as gaps and spiral arms. Aims. We studied the interplay between an X-ray photoevaporative disc wind and the sub-structures generated due to planet–disc interactions to determine how their mutual interactions affect the disc’s and the planet’s evolution. Methods. We performed 3D hydrodynamic simulations of viscous discs (α = 6.9 × 10−4) that host a Jupiter-like planet and undergo X-ray photoevaporation. We traced the gas flows within the disc and wind and measured the rate of accretion onto the planet, as well as the gravitational torque that is acting on it. Results. Our results show that the planetary gap removes the wind’s pressure support, allowing wind material to fall back into the gap. This opens new pathways for material from the inner disc (and part of the outer disc) to be redistributed through the wind towards the gap. Consequently, the gap becomes shallower and the flow of mass across the gap in both directions is significantly increased, as is the planet’s mass-accretion rate (by factors of ≈5 and ≈2, respectively). Moreover, the wind-driven redistribution results in a denser inner disc and a less dense outer disc, which, combined with the recycling of a significant portion of the inner wind, leads to longer lifetimes for the inner disc, contrary to the expectation in a planet-induced photoevaporation scenario that has been proposed in the past.

X-Ray Irradiation of the Giant Planet Orbiting the T Tauri Star TAP 26

We present new Chandra X-ray observations of TAP 26, a ≈17 Myr old magnetically active weak-lined T Tauri star that has been reported to host a massive planet in a ≈10.8 day orbit. At a separation of a = 0.097 au the planet will be exposed to intense X-ray and UV radiation from the star. The first observation caught the star in a state of elevated X-ray emission with variability on a timescale of a few hours and an X-ray temperature kT x ≈ 2–4 keV. Two subsequent observations 5–10 days later showed slow variability and a lower X-ray flux and temperature (kT x ≈ 1 keV). We characterize the X-ray emission and estimate the X-ray ionization and heating rates that will need to be incorporated into realistic models of the planet’s atmosphere.

Planet Formation by Gas-assisted Accretion of Small Solids

We compute the accretion efficiency of small solids, with radii 1 cm ≤ R s ≤ 10 m, on planets embedded in gaseous disks. Planets have masses 3 ≤ M p ≤ 20 Earth masses (M ⊕) and orbit within 10 au of a solar mass star. Disk thermodynamics is modeled via 3D radiation-hydrodynamics calculations that typically resolve the planetary envelopes. Both icy and rocky solids are considered, explicitly modeling their thermodynamic evolution. The maximum efficiencies of 1 ≤ R s ≤ 100 cm particles are generally ≲10%, whereas 10 m solids tend to accrete efficiently or be segregated beyond the planet’s orbit. A simplified approach is applied to compute the accretion efficiency of small cores, with masses M p ≤ 1 M ⊕ and without envelopes, for which efficiencies are approximately proportional to Mp2/3 . The mass flux of solids, estimated from unperturbed drag-induced drift velocities, provides typical accretion rates dM p /dt ≲ 10−5 M ⊕ yr−1. In representative disk models with an initial gas-to-dust mass ratio of 70–100 and total mass of 0.05–0.06 M ⊙, the solids’ accretion falls below 10−6 M ⊕ yr−1 after 1–1.5 Myr. The derived accretion rates, as functions of time and planet mass, are applied to formation calculations that compute dust opacity self-consistently with the delivery of solids to the envelope. Assuming dust-to-solid coagulation times of ≈0.3 Myr and disk lifetimes of ≈3.5 Myr, heavy-element inventories in the range 3–7 M ⊕ require that ≈90–150 M ⊕ of solids cross the planet’s orbit. The formation calculations encompass a variety of outcomes, from planets a few times M ⊕, predominantly composed of heavy elements, to giant planets. The peak luminosities during the epoch of the solids’ accretion range from ≈10−7 to ≈10−6 L ⊙.

Measurement of Dependence of Microlensing Planet Frequency on the Host Star Mass and Galactocentric Distance by Using a Galactic Model

We measure the dependence of planet frequency on host star mass, M L, and distance from the Galactic center, R L, using a sample of planets discovered by gravitational microlensing. We compare the two-dimensional distribution of the lens-source proper motion, μ rel, and the Einstein radius crossing time, t E, measured for 22 planetary events from Suzuki et al. with the distribution expected from Galactic model. Assuming that the planet-hosting probability of a star is proportional to MLmRLr , we calculate the likelihood distribution of (m,r). We estimate that r=0.10−0.37+0.51 and m=0.50−0.70+0.90 under the assumption that the planet-hosting probability is independent of the mass ratio. We also divide the planet sample into subsamples based on their mass ratio, q, and estimate that m=−0.08−0.65+0.95 for q < 10−3 and 1.25−1.14+1.07 for q > 10−3. Although uncertainties are still large, this result implies a possibility that, in orbits beyond the snowline, massive planets are more likely to exist around more massive stars whereas low-mass planets exist regardless of their host star mass.