arXiv subjects

Hui-Gen Liu

Publications and source records attributed to Hui-Gen Liu.

At least 19 recordsLinked to original sources

arXiv2026

Flare-driven habitability: Expanding life's potential around low-mass stars

The traditional definition of the circumstellar habitable zone (HZ) focuses on liquid water, but neglects the crucial role of ultraviolet (UV) radiation in prebiotic chemistry. Low-mass stars typically emit insufficient UV radiation for photochemistry throughout the liquid water HZs during quiescent states. However, frequent flares can provide substantial UV fluxes, potentially fostering habitable conditions. We refine the concept of a UV habitable zone (UV-HZ) by incorporating a temperature-dependent model for RNA precursor synthesis. Furthermore, we explore a parameterized spectral energy distribution model and adopt an empirical flare frequency distribution for flares on different stars to quantify their UV contribution. Applying this framework to different flaring stars, we find the UV-HZ around low-mass stars can extend to inner regions, and overlap with the traditional HZ in wide ranges. Apply the analysis to 9 planets around Kepler flaring stars, three planets are located within both the refined UV-HZ and liquid water habitable zone (LW-HZ) without causing ozone depletion. Our findings highlight the significant role of flares in expanding the potential for life around low-mass stars, offering a revised perspective on exoplanet habitability criteria.

astro-ph.EP↗

arXiv2026

An Adolescent and Near-Resonant Planetary System Near the End of Photoevaporation

Young exoplanets provide vital insights into the early dynamical and atmospheric evolution of planetary systems. Many multi-planet systems younger than 100 Myr exhibit mean-motion resonances, likely established through convergent disk migration. Over time, however, these resonant chains are often disrupted, mirroring the Nice model proposed for the Solar System. We present a detailed characterization of the ~200-Myr-old TOI-2076 system, which contains four sub-Neptune planets between 1.4 and 3.5 Earth radii. We demonstrate that its planets are near but not locked in mean-motion resonances, making the system dynamically fragile. The four planets have comparable core masses but display a monotonic increase in hydrogen and helium (H/He) envelope mass fractions (stripped-1%-5%-5%) with decreasing stellar insolation. This trend is consistent with atmospheric mass-loss due to photoevaporation, which predicts that the envelopes of irradiated planets either erode completely or stabilize at a residual level of ~1% by mass within the first few hundred million years, with more distant, less-irradiated planets retaining most of primordial envelopes. Additionally, previous detections of metastable helium outflows rule out a pure water-world scenario for TOI-2076 planets. Our finding provides direct observational evidence that the dynamical and atmospheric reshaping of compact planetary systems begin early, offering an empirical anchor for models of their long-term evolution.

astro-ph.EP↗

arXiv2026

TOI-4495: A Pair of Aligned, Near-Resonant Sub-Neptunes that Likely Experienced Overstable Migration

We report the discovery of a sub-Neptune and a Neptune-like planet ($R_b = 2.48^{+0.14}_{-0.10}\,R_\oplus$, $R_c = 4.03^{+0.23}_{-0.15}\,R_\oplus$) orbiting the F-type star TOI-4495. The planets have orbital periods of 2.567 days and 5.185 days, lying close to a 2:1 mean-motion resonance (MMR). Our photodynamical analysis of the TESS light curves constrains the planetary masses to $M_b = 7.7 \pm 1.4\,M_\oplus$ and $M_c = 23.2 \pm 4.7\,M_\oplus$. The measured masses and radii indicate the presence of volatile-rich gaseous envelopes on both planets. The Rossiter-McLaughlin effect and the Doppler shadow of TOI-4495 c reveal a well-aligned orbit with a projected stellar obliquity of $\lambda = -2.3^{+8.3}_{-7.8}\,\mathrm{deg}$. Combined with the low mutual inclination constrained by the photodynamical analysis ($\Delta I < 8.7\,\mathrm{deg}$), the planetary orbits are likely coplanar and aligned with the host star's spin axis. We show that the planets are near, but not in, the 2:1 MMR, with a circulating resonant angle. We also find substantial free eccentricity for the inner planet, TOI-4495 b ($e_b = 0.078^{+0.020}_{-0.013}$). Given the observed proximity to the 2:1 resonance and the more massive outer planet, TOI-4495 b and c are particularly susceptible to resonant overstability, which can convert resonantly excited eccentricity into free eccentricity. However, additional mechanisms (e.g., planetesimal scattering) may be required to further excite the eccentricity by $\sim 4\%$. To prevent tidal damping from reducing the eccentricity below the observed level over the star's lifetime (1.9 Gyr), the reduced tidal quality factor of TOI-4495 b must be $Q' \gtrsim 10^5$, consistent with the presence of a thick envelope on the planet.

astro-ph.EP↗

arXiv2025

Understanding the Planetary Formation and Evolution in Star Clusters(UPiC)-II: Catalog of planets/candidates in Open Clusters and Moving Groups

Detecting planets in open clusters offers a unique opportunity to test planet formation theories in clustered environments. The precisely determined ages of young open clusters make their planets particularly valuable for tracing the early evolution of planetary systems. As the second paper of the UPiC project, this study focuses on stars in stellar groups that host transiting planets or planetary candidates. We categorize these stellar groups into Open Clusters (OCs) and Moving Groups (MGs) based on the Jacobi radius to investigate potential differences in their planetary systems. By cross-matching the latest star cluster catalogs with catalogs of transiting planets and candidates, we have compiled the most extensive catalog to date, containing 106 confirmed planets and 168 candidates within OCs and MGs. We refitted the structural parameters of these stellar groups and identified substructures using the \texttt{HDBSCAN} and Gaussian Mixture Model (GMM) algorithms. Our analysis reveals the density evolution of both MGs and OCs during their first Gyr. We find that MGs consistently exhibit a significantly higher planet fraction than OCs, regardless of sample selection, particularly for Hot Jupiters. Furthermore, exoplanet radii show a clear dichotomy at early stages: most sub-Jupiters evolve into Neptune-sized planets within 100 Myr, while super-Jupiters undergo only minimal contraction. These results suggest that young sub-Jupiters (\textless 100 Myr) represent puffy, Neptune-mass planets undergoing vigorous photoevaporation, whereas Jupiter-mass planets can maintain their atmospheres. We also report evidence for the early emergence of the hot-Neptune desert at 100 Myr in both OCs and MGs.

astro-ph.EP↗

arXiv2025

Introduction to the Chinese Space Station Survey Telescope (CSST)

The Chinese Space Station Survey Telescope (CSST) is an upcoming Stage-IV sky survey telescope, distinguished by its large field of view (FoV), high image quality, and multi-band observation capabilities. It can simultaneously conduct precise measurements of the Universe by performing multi-color photometric imaging and slitless spectroscopic surveys. The CSST is equipped with five scientific instruments, i.e. Multi-band Imaging and Slitless Spectroscopy Survey Camera (SC), Multi-Channel Imager (MCI), Integral Field Spectrograph (IFS), Cool Planet Imaging Coronagraph (CPI-C), and THz Spectrometer (TS). Using these instruments, CSST is expected to make significant contributions and discoveries across various astronomical fields, including cosmology, galaxies and active galactic nuclei (AGN), the Milky Way and nearby galaxies, stars, exoplanets, Solar System objects, astrometry, and transients and variable sources. This review aims to provide a comprehensive overview of the CSST instruments, observational capabilities, data products, and scientific potential.

astro-ph.IM↗

arXiv2025

The influence of stellar activity on detecting Earth-like planets via nulling interferometry

The direct imaging of Earth-like planets in solar neighbors is challenging. Both transit and radial velocity (RV) methods suffer from noise due to stellar activity. By choosing a typical configuration of an X array interferometer, we used theoretical formulas to calculate the intrinsic Poisson noise and the noise of stellar activities. Assuming a fixed array with no rotation and ignoring other systematic and astrophysical noises, we considered a single active region on a stellar disk, including both spots and flares with different parameters, for instance, the position, size, and temperature of the active regions. Then we simulated the S/N of Earth-like planets in HZ around G dwarf stars (solar-like) and M dwarfs (Proxima-like), with different stellar activities in the mid-infrared (MIR) band ( 7-12 $\mu$m). The noise attributed to stellar activity has much less influence than the Transit and RV method when detecting Earth-like planets around both G and M dwarfs. I.e. Stellar activity can hardly influence the detection of Earth-like planets around G dwarf stars. However, detecting Earth-like planets around M dwarfs, which are usually more active, can be significantly hindered. We also analyzed the uncertainty of the planet's location due to the deduced S/N. Consequently, we have determined the possibility of mistaking a planet in the HZ as being outside the HZ based on an erroneous S/N measurement. Selecting quiescent target stars or monitoring the light curves of stars would be a helpful way to get rid of contaminates associated with violent stellar activities.

astro-ph.EP↗

arXiv2024

Photo-dynamical Analysis of Circumbinary Multi-planet system TOI-1338: a Fully Coplanar Configuration with a Puffy Planet

TOI-1338 is the first circumbinary planet system discovered by TESS. It has one transiting planet at P$\sim$95 day and an outer non-transiting planet at P$\sim$215 day complemented by RV observation. Here we present a global photo-dynamical modeling of the TOI-1338 system that self-consistently accounts for the mutual gravitational interactions between all known bodies in the system. As a result, the three-dimensional architecture of the system can be established by comparing the model with additional data from TESS Extended Mission and published HARPS/ESPRESSO radial velocity data. We report an inconsistency of binary RV signal between HARPS and ESPRESSO, which could be due to the contamination of the secondary star. According to stability analysis, the RV data via ESPRESSO is preferred. Our results are summarized as follows: (1) the inner transiting planet is extremely coplanar to the binary plane $\Delta I_b \sim 0.12 ^\circ$, making it a permanently transiting circumbinary planet at any nodal precession phases. We updated the future transit ephemerides with improved precisions. (2) The outer planet, despite its non-transiting nature, is also coplanar with the binary plane by $\Delta I_c=9.1^{+6.0 \circ}_{-4.8}$ (22$^\circ$ for 99\% upper limit). (3) The inner planet could have a density of $0.137 \pm 0.026$ g/cm$^{-3}$. With a TESS magnitude of 11.45, TOI-1338 b is an optimal circumbinary planet for ground-based follow-up and transit spectroscopy.

astro-ph.EP↗

arXiv2023

The Accretion History of EX Lup: A Century of Bursts, Outbursts, and Quiescence

EX Lup is the archetype for the class of young stars that undergoes repeated accretion outbursts of $\sim 5$ mag at optical wavelengths and that last for months. Despite extensive monitoring that dates back 130 years, the accretion history of EX Lup remains mostly qualitative and has large uncertainties. We assess historical accretion rates of EX Lup by applying correlations between optical brightness and accretion, developed on multi-band magnitude photometry of the $\sim 2$ mag optical burst in 2022. Two distinct classes of bursts occur: major outbursts ($\Delta V\sim5$ mag) have year-long durations, are rare, reach accretion rates of $\dot{M}_{\rm acc}\sim10^{-7}~M_\odot~{\rm yr^{-1}}$ at peak, and have a total accreted mass of around 0.1 Earth masses. The characteristic bursts ($\Delta V\sim2$ mag) have durations of $\sim 2-3$ months, are more common, reach accretion rates of $\dot{M}_{\rm acc}\sim10^{-8}~M_\odot~{\rm yr^{-1}}$ at peak, and have a total accreted mass of around $10^{-3}$ Earth masses. The distribution of total accreted mass in the full set of bursts is poorly described by a power law, which suggests different driving causes behind the major outburst and characteristic bursts. The total mass accreted during two classes of bursts is around two times the masses accreted during quiescence. Our analysis of the light curves reveals a color-dependent time lag in the 2022 post-burst light curve, attributed to the presence of both hot and cool spots on the stellar surface.

astro-ph.SR↗

arXiv2023

Understanding the Planetary Formation and Evolution in Star Clusters(UPiC)-I: Evidence of Hot Giant Exoplanets Formation Timescales

Planets in young star clusters could shed light on planet formation and evolution since star clusters can provide accurate age estimation. However, the number of transiting planets detected in clusters was only $\sim 30$, too small for statistical analysis. Thanks to the unprecedented high-precision astrometric data provided by Gaia DR2 and Gaia DR3, many new Open Clusters(OCs) and comoving groups have been identified. The UPiC project aims to find observational evidence and interpret how planet form and evolve in cluster environments. In this work, we cross-match the stellar catalogs of new OCs and comoving groups with confirmed planets and candidates. We carefully remove false positives and obtain the biggest catalog of planets in star clusters up to now, which consists of 73 confirmed planets and 84 planet candidates. After age validation, we obtain the radius--age diagram of these planets/candidates. We find an increment of the fraction of Hot Jupiters(HJs) around 100 Myr and attribute the increment to the flyby-induced high-e migration in star clusters. An additional small bump of the fraction of HJs after 1 Gyr is detected, which indicates the formation timescale of HJ around field stars is much larger than that in star clusters. Thus, stellar environments play important roles in the formation of HJs. The hot-Neptune desert occurs around 100 Myr in our sample. A combination of photoevaporation and high-e migration may sculpt the hot-Neptune desert in clusters.

astro-ph.EP↗

arXiv2023

Correcting Stellar Flare Frequency Distributions Detected by TESS and Kepler

The habitability of planets is closely connected with the stellar activity, mainly the frequency of flares and the distribution of flare energy. Kepler and TESS find many flaring stars are detected via precise time-domain photometric data, and the frequency and energy distribution of stellar flares on different types of stars are studied statistically. However, the completeness and observational bias of detected flare events from different missions (e.g. Kepler and TESS) vary a lot. We use a unified data processing and detection method for flares events based on the light curve from Kepler and TESS. Then we perform injection and recovery tests in the original light curve of each star for each flare event to correct the completeness and energy of flares. Three samples of flaring stars are selected from Kepler and TESS, with rotating periods from 1 to $\sim$ 5 days. Adopting a hot-blackbody assumption, our results show that the cumulative flare frequency distributions (FFDs) of the same stars in Kepler and TESS bands tend to be consistent after correction, revealing a more natural flaring frequency and energy distribution. Our results also extend the low-energy limit in cumulative FFD fitting to $10^{31.5-33}$ erg on different types of stars. For solar-type stars, the average power-law index of cumulative FFD ($α_{\rm cum}$) is $-0.84$, which indicates that low-energy flares contribute less to the total flare energy. With a piecewise correlation between $α_{\rm cum}$ and $T_{\rm eff}$, $α_{\rm cum}$ first rises with $T_{\rm eff}$ from M2 to K1 stars, then slightly decreases for stars hotter than K1.

astro-ph.SR↗

arXiv2022

ET White Paper: To Find the First Earth 2.0

We propose to develop a wide-field and ultra-high-precision photometric survey mission, temporarily named "Earth 2.0 (ET)". This mission is designed to measure, for the first time, the occurrence rate and the orbital distributions of Earth-sized planets. ET consists of seven 30cm telescopes, to be launched to the Earth-Sun's L2 point. Six of these are transit telescopes with a field of view of 500 square degrees. Staring in the direction that encompasses the original Kepler field for four continuous years, this monitoring will return tens of thousands of transiting planets, including the elusive Earth twins orbiting solar-type stars. The seventh telescope is a 30cm microlensing telescope that will monitor an area of 4 square degrees toward the galactic bulge. This, combined with simultaneous ground-based KMTNet observations, will measure masses for hundreds of long-period and free-floating planets. Together, the transit and the microlensing telescopes will revolutionize our understandings of terrestrial planets across a large swath of orbital distances and free space. In addition, the survey data will also facilitate studies in the fields of asteroseismology, Galactic archeology, time-domain sciences, and black holes in binaries.

astro-ph.IM↗

arXiv2022

Revisiting the Full Sets of Orbital Parameters for the XO-3 System: No evidence for Temporal Variation of the Spin-Orbit Angle

We present 12 new transit light curves and 16 new out-of-transit radial velocity measurements for the XO-3 system. By modelling our newly collected measurements together with archival photometric and Doppler velocimetric data, we confirmed the unusual configuration of the XO-3 system, which contains a massive planet ($M_P=11.92^{+0.59}_{-0.63} M_J$) on a relatively eccentric ($e=0.2853^{+0.0027}_{-0.0026}$) and short-period ($3.19152 \pm 0.00145\,$day) orbit around a massive star ($M_*=1.219^{+0.090}_{-0.095} M_{\odot}$). Furthermore, we find no strong evidence for a temporal change of either $V\sin i_{*}$ (and by extension, the stellar spin vector of XO-3), or the transit profile (and thus orbital angular momentum vector of XO-3b). We conclude that the discrepancy in previous Rossiter-McLaughlin measurements ($70.0^{\circ} \pm 15.0^{\circ}$ (Hebrard et al. 2008); $37.3^{\circ} \pm 3.7^{\circ}$ (Winn et al. 2009); $37.3^{\circ} \pm 3.0^{\circ}$ (Hirano et al. 2011)) may have stemmed from systematic noise sources.

astro-ph.EP↗

arXiv2021

Transiting Exoplanet Monitoring Project (TEMP). VI. The Homogeneous Refinement of System Parameters for 39 Transiting Hot Jupiters with 127 New Light Curves

We present 127 new transit light curves for 39 hot Jupiter systems, obtained over the span of five years by two ground-based telescopes. A homogeneous analysis of these newly collected light curves together with archived spectroscopic, photometric, and Doppler velocimetric data using EXOFASTv2 leads to a significant improvement in the physical and orbital parameters of each system. All of our stellar radii are constrained to accuracies of better than 3\%. The planetary radii for 37 of our 39 targets are determined to accuracies of better than $5\%$. Compared to our results, the literature eccentricities are preferentially overestimated due to the Lucy-Sweeney bias. Our new photometric observations therefore allow for significant improvement in the orbital ephemerides of each system. Our correction of the future transit window amounts to a change exceeding $10\,{\rm min}$ for ten targets at the time of JWST's launch, including a $72\,{\rm min}$ change for WASP-56. The measured transit mid-times for both literature light curves and our new photometry show no significant deviations from the updated linear ephemerides, ruling out in each system the presence of companion planets with masses greater than $0.39 - 5.0\, rm M_{\oplus}$, $1.23 - 14.36\, \rm M_{\oplus}$, $1.65 - 21.18\, \rm M_{\oplus}$, and $0.69 - 6.75\, \rm M_{\oplus}$ near the 1:2, 2:3, 3:2, and 2:1 resonances with the hot Jupiters , respectively, at a confidence level of $\pm 1\,σ$. The absence of resonant companion planets in the hot Jupiter systems is inconsistent with the conventional expectation from disk migration.

astro-ph.EP↗

arXiv2021

Follow-up photometry in another band benefits reducing \emph{Kepler}'s false positive rates

Kepler Mission's single-band photometry suffers from astrophysical false positives, the most common of background eclipsing binaries (BEBs) and companion transiting planets (CTPs). Multi-color photometry can reveal the color-dependent depth feature of false positives and thus exclude them. In this work, we aim to estimate the fraction of false positives that are unable to be classified by Kepler alone but can be identified with their color-dependent depth feature if a reference band (z, Ks and TESS) were adopted in follow-up observation. We build up physics-based blend models to simulate multi-band signals of false positives. Nearly 65-95% of the BEBs and more than 80% of the CTPs that host a Jupiter-size planet will show detectable depth variations if the reference band can achieve a Kepler-like precision. Ks band is most effective in eliminating BEBs exhibiting any depth sizes, while z and TESS band prefer to identify giant candidates and their identification rates are more sensitive to photometric precision. Provided the radius distribution of planets transiting the secondary star in binary systems, we derive formalism to calculate the overall identification rate for CTPs. By comparing the likelihood distribution of the double-band depth ratio for BEB and planet models, we calculate the false positive probability (FPP) for typical Kepler candidates. Additionally, we show that the FPP calculation helps distinguish the planet candidate's host star in an unresolved binary system. The analysis framework of this paper can be easily adapted to predict the multi-color photometry yield for other transit surveys, especially for TESS.

astro-ph.EP↗

arXiv2021

Planet Occurrence Rate Correlated to Stellar Dynamical History: Evidence from Kepler and Gaia

The dynamical history of stars influences the formation and evolution of planets significantly. To explore the influence of dynamical history on planet formation and evolution from observations, we assume that stars who experienced significantly different dynamical histories tend to have different relative velocities. Utilizing the accurate Gaia-Kepler Stellar Properties Catalog, we select single main-sequence stars and divide these stars into three groups according to their relative velocities, i.e. high-V, medium-V, and low-V stars. After considering the known biases from Kepler data and adopting prior and posterior correction to minimize the influence of stellar properties on planet occurrence rate, we find that high-V stars have a lower occurrence rate of super-Earths and sub-Neptunes (1--4 R$_{\rm \oplus}$, P<100 days) and higher occurrence rate of sub-Earth (0.5--1 R$_{ \oplus}$, P<30 days) than low-V stars. Additionally, high-V stars have a lower occurrence rate of hot Jupiter sized planets (4--20 R$_{\oplus}$, P<10 days) and a slightly higher occurrence rate of warm or cold Jupiter sized planets (4--20 R$_{\oplus}$, 10<P<400 days). After investigating the multiplicity and eccentricity, we find that high-V planet hosts prefer a higher fraction of multi-planets systems and lower average eccentricity, which is consistent with the eccentricity-multiplicity dichotomy of Kepler planetary systems. All these statistical results favor the scenario that the high-V stars with large relative velocity may experience fewer gravitational events, while the low-V stars may be influenced by stellar clustering significantly.

astro-ph.EP↗

arXiv2018

A power law decay evolution scenario for polluted single white dwarfs

Planetary systems can survive the stellar evolution, as evidenced by the atmospheric metal pollution and dusty disks of single white dwarfs. Recent observations show that 1 to 4 percent of single white dwarfs are accompanied by dusty disks, while the occurrence rate of metal pollution is about 25 to 50 percent . The dusty disks and metal pollution have been associated with accretion of remnant planetary systems around white dwarfs, yet the relation between these two phenomena is still unclear. Here we suggest an evolutionary scenario to link the two observational phenomena. By analyzing a sample of metal polluted white dwarfs, we find that the mass accretion rate onto the white dwarf generally follows a broken power law decay, which matches well with the theoretical prediction, if assuming dust accretion is primarily driven by Poynting-Robertson drag and the dust source is primarily delivered via dynamically falling asteroids perturbed by a Jovian planet. The presence of disks is mainly at the early stage (about 0.1 to 0.7 billion years) of the whole process of metal pollution, which is detectable until about 8 billion years, naturally explaining the fraction (about 2-16 percent) of metal-polluted white dwarfs having dusty disks. The success of this scenario also implies that the configuration of an asteroid belt with an outer gas giant might be common around stars of several solar masses.

astro-ph.EP↗

arXiv2018

Photo-evaporation of proto-planetary gas discs due to flybys of external single stars in different orbits

During the evolution of proto-planetary disc, photo-evaporations of both central and external stars play important roles. Considering the complicated radiation surroundings in the clusters, where the star formed, the proto-planetary discs survive in different lifetimes due to flyby events. In this paper, we mainly focus on the disc around a T Tauri star, which encounters with another main-sequence star with different temperatures in hyperbolic orbits with different peri-center distances, eccentricities and inclinations. We find the criterion for gap-opening due to photo-evaporation of central star after the flyby event. A gap is opened in the late stage of gas disc, and induce that the gap only influence the planet formation and migration limitedly. If the flyby orbit has a moderate value of peri-center distance, which weakly depends on the eccentricity and inclination, the external photo-evaporation lead to a maximum mass loss during the flyby event. Flyby stars in orbits with smaller eccentricities or larger inclinations induce larger mass loss. Adopting a simple multiple flyby models, we conclude that in open clusters, gas discs usually survive in typical lifetimes between 1 and 10 Myr, except there are many massive stars in dense open clusters. In globular clusters, discs disperse very quickly and hardly produce the gas giant planets. The fast-depleted discs are probably responsible for the null detection of giant planets in globular clusters.

astro-ph.EP↗

arXiv2018

Transiting Exoplanet Monitoring Project (TEMP). I. Refined System Parameters and Transit Timing Variations of HAT-P-29b

We report the photometry of six transits of the hot Jupiter HAT-P-29b obtained from 2013 October to 2015 January. We analyze the new light curves, in combination with the published photometric, and Doppler velocimetric, and spectroscopic measurements, finding an updated orbital ephemeris for the HAT-P-29 system, $T_{\rm C}[0]= 2456170.5494(15)\,[\rm{BJD_{TDB}}]$ and $P=5.723390(13) \,{\rm days}$. It is $17.63\,{\rm s}$ ($4.0\,σ$) longer than the previously published value, amounting to errors exceeding $2.5\,\rm{hrs}$ at the time of writing (on UTC 2018 June 1). The measured transit mid-times for HAT-P-29b show no compelling evidence of timing anomalies from a linear model, which rules out the presence of a perturbers with masses greater than $0.6$, $0.7$, $0.5$, and $0.4\,{\rm M_\oplus}$ near the $1:2$, $2:3$, $3:2$, and $2:1$ resonances with HAT-P-29b, respectively.

astro-ph.EP↗