arXiv subjects

Di-Chang Chen

Publications and source records attributed to Di-Chang Chen.

17 recordsLinked to original sources

arXiv2026

A Systematic Gaia--ZTF Search for Short-Period Blue Compact-Binary Candidates

We present a catalog of 147 short-period (10.34--106.46~min) blue compact-binary candidates, identified by combining Gaia DR3 astrometry and photometry with ZTF DR23 light curves via a Gaia selection, period searches, and machine-learning morphology ranking. Of these, 111 lack prior compact-binary classifications. Multiwavelength data (DESI DR1, GALEX, AllWISE) reveal a heterogeneous sample: on the Gaia colour--magnitude diagram, 52 sources lie on the white-dwarf locus, 69 in the hot-subdwarf region, and 26 are intermediate. Among 26 sources with DESI spectra, only about one third follow the white-dwarf cooling sequence; the rest are more luminous blue stars with white-dwarf-like low-resolution spectra. We highlight a prioritized subset of new white-dwarf-locus candidates for follow-up, including ten with periods below 40~min and none with existing radial-velocity data. Under fiducial binary assumptions, 17 of these newly identified white-dwarf-locus candidates would exceed the adopted LISA signal-to-noise threshold (led by a 37~pc white dwarf), with the count depending on chirp mass (9 for $0.15\,M_\odot$, 17 for $0.3\,M_\odot$, 21 for $0.6\,M_\odot$), assuming orbital modulation. However, for most of the white-dwarf-locus sample, observed modulation amplitudes exceed any plausible ellipsoidal signal by three to five orders of magnitude, implying that rotating magnetic or chemically inhomogeneous single white dwarfs offer a viable alternative that ZTF photometry alone cannot rule out---the catalog includes at least one confirmed case. We release the full 147-source catalog, including periods, Gaia/spectroscopic classifications, harmonic/ellipsoidal diagnostics, and supplementary tables of fiducial GW estimates and UV--IR photometry.

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arXiv2026

Fates of the sub-stellar objects (FOSSO) II. Evidence for Suppression of Metal Pollution in White Dwarfs by Close Substellar Companions

Approximately 25--50\% of white dwarfs (WDs) exhibit metal absorption lines in their photospheres, interpreted as evidence of ongoing/recent accretion of planetary debris from remnant systems. Previous theoretical studies have suggested that massive, close-in substellar companion may prevent delivery of larger bodies via dynamical interactions, thereby reducing white-dwarf pollution. However, no conclusive observational evidence has yet been established to confirm such a protective effect. In this work, based on a sample of 17 white dwarf-substellar companion (1--75 $M_{\rm J}$) systems with reliable spectroscopic classifications, we find that white dwarfs hosting close substellar companions (orbital period $P < 5$ d) exhibit a metal-pollution fraction of $7.7^{+11.3}_{-4.0}\%$, which is suppressed by a factor of $5.75^{+3.24}_{-1.94}$ (corresponding to a protection efficiency of $87.2^{+3.4}_{-9.2}\%$) relative to single white dwarfs with a confidence level of 99.96\%. In contrast, white dwarfs with wider companions show a metal-pollution fraction of approximately $25.0^{+24.0}_{-12.8}\%$, comparable to that of single white dwarf systems. To interpret these results, we perform ensembles of N-body integrations and demonstrate that massive close-in substellar companions are capable of clearing 80\%--90\% of small-body contaminants. The good consistency between the observational statistics and dynamical simulations provides strong evidence for suppressed metal pollution in white dwarfs with close companions, and offers insights into the long-term dynamical evolution of WD remanent systems.

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arXiv2026

Sub-Neptunes Show a Stronger Correlation with Cold Jupiters than Super-Earths Especially in Metal-rich Systems

Correlations between the inner small planets and cold giants encodes the formation and evolution of planetary systems. It remains unclear if the correlation differs on the two sides of the radius valley. In this work, we compute the conditional frequency of cold Jupiters in systems with only inner sub-Neptunes $P(\rm CJ|SN)$ and those with only inner super-Earths $P(\rm CJ|SE)$. We find that, around transiting sample around metal-rich stars, $P(\rm CJ|SN, [Fe/H]>0)$ and $P(\rm CJ|SE, [Fe/H]>0)$ are $42.6^{+10.6}_{-9.9}\%$ and $14.5^{+12.7}_{-6.9}\%$. Comparing with the field giant frequency ($14.3^{+2.0}_{-1.8}\%$), we show that inner sub-Neptunes and cold Jupiters exhibit a significant positive correlation for metal-rich systems with a confidence level of 99.95\%, whereas this correlation is absent for systems with super-Earths. We also consider a homogeneous Kepler-Keck subsample and derive similar results, with $P(\rm CJ|SN, [Fe/H]>0)$ of $45.8^{+18.6}_{-16.3}\%$ and $P(\rm CJ|SE, [Fe/H]>0)$ of $13.3^{+17.0}_{-6.8}\%$. Radial velocity sample shows consistent results, with metal-rich systems hosting massive inner planets exhibiting a strong positive correlation (confidence level of 99.11\%) with outer cold Jupiters ($P(\rm CJ|M_{p}>10M_\oplus, [Fe/H]>0) = 34.6^{+11.0}_{-9.1}\%$). These results can be naturally understood since metal-rich disks are expected to more efficiently produce both outer cold Jupiters and inner planets with larger radii and masses. Our findings highlight the critical role of stellar metallicity in shaping planetary architectures, particularly for large/massive planets.

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arXiv2026

Inversion of Hydrogen-rich Atmosphere and Water Content for GJ 486b

GJ~486b is a close-in planet orbiting an M dwarf and is therefore expected to have undergone strong atmospheric escape. Motivated by theoretical and observational studies on the constraints of its water and atmosphere, we investigate which combinations of an primordial hydrogen-rich atmosphere and water inventory could fit the current water content implied by bulk density measurements. We model the atmosphere escape using VPLanet, following the loss of an initial hydrogen-rich atmosphere and the subsequent escape of a water-dominated atmosphere. By scanning a broad parameter space across different stellar ages, we invert for the initial hydrogen-rich atmospheric mass and water inventory consistent with the current constraints. Our results reveal a strong degeneracy between the water reservoir and the initial hydrogen-rich atmosphere. Even a modest hydrogen-rich atmosphere can significantly delay early escape of the water and reduce the water inventory required to reproduce the current water content. We also find that the inferred initial conditions are also strongly age dependent. Incorporating a planet formation dataset as a prior, we derive a probabilistic constraint on the host star age, yielding an expected age of $2.90^{+2.47}_{-2.27}$~Gyr, which is consistent with the results obtained from other methods to determine M dwarf ages.

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arXiv2026

How a Close-in Planet Protects its White Dwarf Host from Pollution

Approximately 25-50% of white dwarfs (WDs) exhibit metal absorption lines in their photospheres, which are attributed to accretion from their remnant planetary systems. Although white dwarfs with detected planetary systems are more likely to show photospheric pollution, one notable exception - WD 1856+534 - hosts a close-in giant planet yet exhibits no detectable photospheric metal pollution. Previous studies have proposed that massive, close-in planets can block inward transport of small particles driven by radiative forces (e.g., Poynting-Robertson drag and the Yarkovsky effect). However, it remains unclear whether the close-in planet can similarly prevent delivery of larger bodies via dynamical interactions. We aim to quantify the protective influence of close-in planets on white-dwarf pollution by asteroids approaching on near-parabolic orbits, and to explore the planetary masses and orbital separations required to provide effective protection. We perform ensembles of short-term N-body integrations, sampling a range of planet masses and orbital separations and initializing asteroids on highly eccentric orbits with periapses near the WD Roche radius, in order to measure scattering, capture, and ejection outcomes and quantify the planet's shielding efficiency. For WD1856+534b-like configurations (a_p = 0.02 au), giant planets with masses greater than 0.5 Jupiter masses are sufficient to clear over 80% of highly eccentric small-body contaminants. The effectiveness of the protective effect diminishes with decreasing planetary mass and increasing semi-major axis. These findings help explain why some white dwarfs that host close-in giant planets do not show the photospheric metal pollution commonly observed in other systems.

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arXiv2025

Planets Across Space and Time (PAST). VIII : Kinematic Characterization and Identification of Radial Velocity Variables for the LAMOST-Gaia-TESS Stars

The Transiting Exoplanet Survey Satellite (TESS) has discovered over 6700 nearby exoplanets candidates using the transit method through its all-sky survey. Characterizing the kinematic properties and identifying variable stars for the TESS stellar sample is crucial for revealing the correlations between the properties of planetary systems and the properties of stars (e.g., Galactic components, age, chemistry, dynamics, radiation). Based on data from TESS, Gaia DR3, and LAMOST DR10, we present a catalog of kinematic properties (i.e., Galactic positions, velocities, orbits, Galactic components, and kinematic age) as well as other basic stellar parameters for $\sim 660,000$ TESS stars. Our analysis of the kinematic catalog reveals that stars belonging to different Galactic components (i.e., thin disk, thick disk, halo and 12 streams in the disk) display distinctive kinematic and chemical properties. We also find that hot planets with period less then 10 days in the TESS sample favor thin disk stars compared to thick disk stars, consistent with previous studies. Furthermore, using the LAMOST multiple-epoch observations, we identify 41,445 stars exhibiting significant radial velocity variations, among which 7,846 are classified as binary stars. By fitting the radial velocity curves, we further derive orbital parameters (e.g., mass ratio, orbital period and eccentricity) for 297 binaries. The observed decreasing orbital eccentricity with shorting period reveals evidence of tidal circularization. The catalogs constructed in this work have laid a solid foundation for future work on the formation and evolution of stellar and planetary systems in different Galactic environments.

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arXiv2025

Planet Across Space and Time (PAST). VII. The origin and tidal evolution of hot Jupiters constrained by a broken age-frequency relation

The discovery of hot Jupiters has challenged the classical planet formation theory. Although various formation mechanisms have been proposed, the dominant channel and relative contributions remain unclear. Furthermore, hot Jupiters offer a unique opportunity to test tidal theory and measure the fundamental tidal quality factor, which is yet to be well-constrained. In this work, based on a hot Jupiter sample around single Sun-like stars with kinematic properties, {we find that the declining trend of their frequency is broken with a ridge at about 2 Gyr, providing direct evidence that hot Jupiters are formed with multiple origins of different timescales. By fitting with the theoretical expectations, we provide a constraint of tidal factor for Sun-like stars, which aligns well with the detected number of hot Jupiters with orbital decay. Moreover, we simultaneously constrain the relative importance of different channels: although the majority of hot Jupiters are formed early, within several tenths of Gyr via 'Early' models (e.g., in-situ formation, disk migration, planet-planet scattering and Kozai-Lidov interaction), a significant portion (about 40%) should be formed late on a relatively long timescale extending up to several Gyr mainly via the secular chaos mechanism, further supported by the obliquity distribution of 'late-arrived' hot Jupiters. Our findings provide a unified framework that reconciles hot Jupiter demographics and long-term evolution with multichannel formation.

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arXiv2025

The New Generation Planetary Population Synthesis (NGPPS) VIII. Impact of host star metallicity on planet occurrence rates, orbital periods, eccentricities, and radius valley morphology

The dust-to-gas ratio in the protoplanetary disk, which is likely imprinted into the host star metallicity, is a property that plays a crucial role during planet formation. We aim at constraining planet formation and evolution processes by statistically analysing planetary systems generated by the Generation III Bern model, comparing with the correlations derived from observational samples. Using synthetic planets biased to observational completeness, we find that (1) the occurrence rates of large giant planets and Neptune-size planets are positively correlated with [Fe/H], while small sub-Earths exhibit an anti-correlation. In between, for sub-Neptune and super-Earth, the occurrence rate first increases and then decreases with increasing [Fe/H] with an inflection point at 0.1 dex. (2) Planets with orbital periods shorter than ten days are more likely to be found around stars with higher metallicity, and this tendency weakens with increasing planet radius. (3) Both giant planets and small planets exhibit a positive correlation between the eccentricity and [Fe/H], which could be explained by the self-excitation and perturbation of outer giant planets. (4) The radius valley deepens and becomes more prominent with increasing [Fe/H], accompanied by a lower super-Earth-to-sub-Neptune ratio. Furthermore, the average radius of the planets above the valley increases with [Fe/H]. Our nominal model successfully reproduces many observed correlations with stellar metallicity, supporting the description of physical processes and parameters included in the Bern model. However, the dependences of orbital eccentricity and period on [Fe/H] predicted by the synthetic population is however significantly weaker than observed. This discrepancy suggests that long-term dynamical interactions between planets, along with the impact of binaries/companions, can drive the system towards a dynamically hotter state.

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arXiv2025

Planets Across Space and Time (PAST). VI. Age Dependence of the Occurrence and Architecture of Ultra-Short-Period Planet Systems

Ultra-short-period (USP) planets, with orbital periods shorter than one day, represent a unique class of exoplanets whose origin remains puzzling. Determining their age distribution and temporal evolution is vital for uncovering their formation and evolutionary pathways. Using a sample of over 1,000 short-period planets around Sun-like stars, we find that the host stars of USP planets are relatively older and have a higher prevalence in the Galactic thick disk compared to stars hosting other short-period planets. Furthermore, we find that the occurrence of USP planets increases with stellar age and uncover evidence indicating that USP planetary system architectures evolve on Gyr timescales. This includes a distinct dip-pileup in period distributions around ~1 day and an expansion of orbital spacings with time. In addition, younger USP planet systems are observed to have fewer multiple transiting planets, implying fewer nearby companions and/or larger mutual orbital inclinations. Our findings suggest that USP planets continuously form through inward migration driven by tidal dissipation over Gyr timescales, and that younger and older USP planets may have originated via different specific tidal migration pathways.

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arXiv2024

C3PO III: On the Lithium Signatures Following Planet Engulfment by Stars

Planet engulfment has been identified as one of the mechanisms for enhancing lithium abundance in stars. However, comprehensive investigations into lithium signatures following such events remain limited. Stars born together, sharing a common origin and stellar characteristics, provide a unique opportunity to study these signatures and compare lithium abundances. We demonstrate that the distinctive signature of planet engulfment in lithium abundance is only discernible among highly similar stellar twins. We present lithium abundance measurements for 125 co-moving pairs of stars, representing the largest sample to date with a single, homogeneous assessment of high-precision lithium abundance. While lithium abundance enhancements in pairs showing planet engulfment signatures are within 0.35 dex, we find that even at fixed stellar parameters (temperature and age), the intrinsic scatter in lithium abundance is typically 0.35 dex for G/F dwarfs and can be as large as 0.6 dex for older and cooler stars due to internal stellar evolution processes. Since the planet engulfment signature from lithium can be masked by stellar intrinsic scatter, our findings raise questions about relying solely on lithium as an indicator for planet engulfment or attributing lithium-richness in stars primarily to planet engulfment events.

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arXiv2024

Constraints on the formation history and composition of Kepler planets from their distribution of orbital period ratios

The Kepler high-precision planetary sample has revealed a radius valley, separating compact super-Earths from sub-Neptunes with lower density. Super-Earths are generally assumed to be rocky planets that were probably born in-situ, while the composition and origin of sub-Neptunes remains debated. To provide more constraints on the formation history and composition, based on the planetary sample of Kepler multiple planet systems, we derive the distributions of orbital period ratios of sub-Neptune and super-Earth planet pairs and calculate the normalised fraction of near-first-order mean motion resonances. Using synthetic planetary systems generated by the Generation III Bern Model, we also obtain theoretical predictions of period ratio distributions of planet pairs of different compositions and origins. We find that actual Kepler sub-Neptune pairs show a normalised fraction smaller (larger) than the model predictions for water-rich (water-poor) pairs with confidence levels of about two sigma. The derived normalised fraction of actual Kepler Super-Earth pairs is generally consistent with that of water-poor model planet pairs but significantly smaller than that of synthetic water-rich planet pairs. Based on the distributions of orbital period ratios, we conclude that orbital migration has been more important for sub-Neptunes than for super-Earths, suggesting a partial ex situ formation of the former and an origin of the radius valley caused in part by distinct formation pathways. However, the model comparisons also show that sub-Neptunes in actual Kepler multiple systems are not likely to be all water-rich/ex situ planets but a mixture of the two (in situ/ex situ) pathways. Whereas, Kepler super-Earth planets are predominantly composed by of water-poor planets that were born inside the ice line, likely through a series of giant impacts without large scale migration.

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arXiv2023

Planets Across Space and Time (PAST). V. The evolution of hot Jupiters revealed by the age distribution of their host stars

The unexpected discovery of hot Jupiters challenged the classical theory of planet formation inspired by our solar system. Until now, the origin and evolution of hot Jupiters are still uncertain. Determining their age distribution and temporal evolution can provide more clues into the mechanism of their formation and subsequent evolution. Using a sample of 383 giant planets around Sun-like stars collected from the kinematic catalogs of the Planets Across Space and Time (PAST) project, we find that hot Jupiters are preferentially hosted by relatively younger stars in the Galactic thin disk. We subsequently find that the frequency of hot Jupiters declines with age. In contrast, the frequency of warm/cold Jupiters shows no significant dependence on age. Such a trend is expected from the tidal evolution of hot Jupiters' orbits, and our result offers supporting evidence using a large sample. We also perform a joint analysis on the planet frequencies in the stellar age-metallicity plane. The result suggests that the frequencies of hot Jupiters and warm/cold Jupiters, after removing the age dependence are both correlated with stellar metallicities. Moreover, we show that the above correlations can explain the bulk of the discrepancy in hot Jupiter frequencies inferred from the transit and radial velocity (RV) surveys, given that RV targets tend to be more metal-rich and younger than transits.

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arXiv2023

Planets Across Space and Time (PAST) IV: The Occurrence and Architecture of Kepler Planetary Systems as a Function of Kinematic Age Revealed by the LAMOST-Gaia-Kepler Sample

One of the fundamental questions in astronomy is how planetary systems form and evolve. Measuring the planetary occurrence and architecture as a function of time directly addresses this question. In the fourth paper of the Planets Across Space and Time (PAST) series, we investigate the occurrence and architecture of Kepler planetary systems as a function of kinematic age by using the LAMOST-Gaia-Kepler sample. To isolate the age effect, other stellar properties (e.g., metallicity) have been controlled. We find the following results. (1) The fraction of stars with Kepler-like planets ($F_{\text{Kep}}$) is about 50% for all stars; no significant trend is found between $F_{\text{Kep}}$ and age. (2) The average planet multiplicity ($\bar{N}_p$) exhibits a decreasing trend (~2$σ$ significance) with age. It decreases from $\bar{N}_p$~3 for stars younger than 1 Gyr to $\bar{N}_p$~1.8 for stars about 8 Gyr. (3) The number of planets per star ($η=F_{\text{Kep}}\times\bar{N}_p$) also shows a decreasing trend (~2-3$σ$ significance). It decreases from $η$~1.6-1.7 for young stars to $η$~1.0 for old stars. (4) The mutual orbital inclination of the planets ($σ_{i,k}$) increases from $1.2^{+1.4}_{-0.5}$ to $3.5^{+8.1}_{-2.3}$ as stars aging from 0.5 to 8 Gyr with a best fit of $\log{σ_{i,k}}=0.2+0.4\times\log{\frac{\text{Age}}{\text{1Gyr}}}$. Interestingly, the Solar System also fits such a trend. The nearly independence of $F_{\text{Kep}}$~50% on age implies that planet formation is robust and stable across the Galaxy history. The age dependence of $\bar{N}_p$ and $σ_{i,k}$ demonstrates planetary architecture is evolving, and planetary systems generally become dynamically hotter with fewer planets as they age.

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arXiv2022

Planets Across Space and Time (PAST). III. Morphology of the Planetary Radius Valley as a Function of Stellar Age and Metallicity in the Galactic Context Revealed by the LAMOST-Gaia-Kepler Sample

The radius valley, a dip in the radius distribution of exoplanets at ~1.9 Earth radii separates compact rocky Super-Earths and Sub-Neptunes with lower density. Various hypotheses have been put forward to explain the radius valley. Characterizing the radius valley morphology and its correlation to stellar properties will provide crucial observation constraints on its origin mechanism and deepen the understanding of planet formation and evolution. In this paper, the third part of the Planets Across the Space and Time (PAST) series, using the LAMOST-Gaia-Kepler catalog, we perform a systematical investigation into how the radius valley morphology varies in the Galactic context, i.e., thin/thick galactic disks, stellar age and metallicity abundance ([Fe/H] and [alpha/Fe]). We find that (1) The valley becomes more prominent with the increase of both age and [Fe/H]. (2) The number ratio of super-Earths to sub-Neptunes monotonically increases with age but decreases with [Fe/H] and [alpha/Fe]. (3) The average radius of planets above the valley (2.1-6 Earth radii) decreases with age but increases with [Fe/H]. (4) In contrast, the average radius of planets below the valley (R < 1.7 Earth radii) is broadly independent on age and metallicity. Our results demonstrate that the valley morphology as well as the whole planetary radius distribution evolves on a long timescale of giga-years, and metallicities (not only Fe but also other metal elements, e.g., Mg, Si, Ca, Ti) play important roles in planet formation and in the long term planetary evolution.

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arXiv2021

Planets Across Space and Time (PAST). II: Catalog and Analyses of the LAMOST-Gaia-Kepler Stellar Kinematic Properties

The Kepler telescope has discovered over 4,000 planets (candidates) by searching ? 200,000 stars over a wide range of distance (order of kpc) in our Galaxy. Characterizing the kinematic properties (e.g., Galactic component membership and kinematic age) of these Kepler targets (including the planet (candidate) hosts) is the first step towards studying Kepler planets in the Galactic context, which will reveal fresh insights into planet formation and evolution. In this paper, the second part of the Planets Across the Space and Time (PAST) series, by combining the data from LAMOST and Gaia and then applying the revised kinematic methods from PAST I, we present a catalog of kinematic properties(i.e., Galactic positions, velocities, and the relative membership probabilities among the thin disk, thick disk, Hercules stream, and the halo) as well as other basic stellar parameters for 35,835 Kepler stars. Further analyses of the LAMOST-Gaia-Kepler catalog demonstrate that our derived kinematic age reveals the expected stellar activity-age trend. Furthermore, we find that the fraction of thin(thick) disk stars increases (decreases) with the transiting planet multiplicity (Np = 0, 1, 2 and 3+) and the kinematic age decreases with Np, which could be a consequence of the dynamical evolution of planetary architecture with age. The LAMOST-Gaia-Kepler catalog will be useful for future studies on the correlations between the exoplanet distributions and the stellar Galactic environments as well as ages.

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arXiv2021

Planets Across Space and Time (PAST). I. Characterizing the Memberships of Galactic Components and Stellar Ages: Revisiting the Kinematic Methods and Applying to Planet Host Stars

Over 4,000 exoplanets have been identified and thousands of candidates are to be confirmed. The relations between the characteristics of these planetary systems and the kinematics, Galactic components, and ages of their host stars have yet to be well explored. Aiming to addressing these questions, we conduct a research project, dubbed as PAST (Planets Across Space and Time). To do this, one of the key steps is to accurately characterize the planet host stars. In this paper, the Paper I of the PAST series, we revisit the kinematic method for classification of Galactic components and extend the applicable range of velocity ellipsoid from about 100 pc to 1, 500 pc from the sun in order to cover most known planet hosts. Furthermore, we revisit the Age-Velocity dispersion Relation (AVR), which allows us to derive kinematic age with a typical uncertainty of 10-20% for an ensemble of stars. Applying the above revised methods, we present a catalog of kinematic properties (i.e. Galactic positions, velocities, the relative membership probabilities among the thin disk, thick disk, Hercules stream, and the halo) as well as other basic stellar parameters for 2,174 host stars of 2,872 planets by combining data from Gaia, LAMOST, APOGEE, RAVE, and the NASA exoplanet archive. The revised kinematic method and AVR as well as the stellar catalog of kinematic properties and ages lay foundation for future studies on exoplanets from two dimensions of space and time in the Galactic context.

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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.

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