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.


INTRODUCTION
Open Clusters(OCs) in the Milky Way are the collection of stars formed from the same molecular cloud and gravitationally bound together, Thus, sharing similar specific characteristics, e.g.age, distance, reddening, metal abundance, etc. OCs provide an ideal laboratory for studying star formation and evolution.Recent studies based on Kepler data show that nearly 50% of stars host planets (Zhu & Dong 2021).Since most stars form in clusters (Lada & Lada 2003), many exoplanets are formed in cluster environments.Then the majority of stars will eventually become field stars as clusters are dissociated.Detecting exoplanets in OCs can provide an ideal sample for studying planet formation and evolution.
The first planet in OCs, tau b, was detected by Sato et al. (2007) via Radial Velocity.Kepler-66b and Kepler-67b are the first cluster planets discovered by transit (Meibom et al. 2013).Thanks to Kepler/K2 and TESS, tens of planets in clusters have been discovered, and the number is growing.There are several programs focusing on planets in star clusters, especially young exoplanets.Zodiacal Exoplanets In Time (ZEIT) collaboration uses K2 data to monitor young open clusters and associations in the ecliptic plane and found planets in the Hyades, Praesepe, Upper Sco, and Taurus (Mann et al. 2016a(Mann et al. ,b, 2017(Mann et al. , 2018;;Rizzuto et al. 2017;Gaidos et al. 2017;Vanderburg et al. 2018;Rizzuto et al. 2018).With the help of enable extensive follow-up observations, The TESS Hunt for Young and Maturing Exoplanets (THYME) collaboration has reported on planets in Upper Sco (Rizzuto et al. 2020), the Tuc-Hor association (Newton et al. 2019), the Ursa Major moving group (Mann et al. 2020), and the Pisces Eridanus stream (Newton et al. 2021).Bouma et al. (2019Bouma et al. ( , 2020) ) begun a Cluster Difference Imaging Photometric Survey(CDIPS) to discover giant transiting planets with known ages, and to provide light curves suitable for studies in stellar astrophysics.Nardiello et al. 2019Nardiello et al. , 2020;;Nardiello 2020;Nardiello et al. 2021 use a PSF-based Approach to TESS High-quality data of star clusters (PATHOS) and find 90 planet candidates.
Hitherto, there are many surveys and projects focusing on the young planets in clusters, but the number of reported planets in clusters is limited and is not enough to support statistical work, ∼ 30 according to Nardiello et al. (2021).To enlarge the number of planets in open clusters, both expanding the number of cluster members and identifying new clusters are available in Gaia Era.
The Gaia DR2/EDR3 catalog (Gaia Collaboration et al. 2018;Lindegren et al. 2021) presents more than 1.3 billion stars with unprecedented high-precision astrometric and photometric data, greatly improving the reliability of stellar membership determination and characterization of a large sample of stellar groups including star clusters, association, and other comoving groups.The recent analysis of Gaia Data has greatly expanded our knowledge of stellar groups (e.g., Cantat-Gaudin et al. 2018;Kounkel & Covey 2019;Kerr et al. 2021).In previous knowledge, a star cluster is a set of stars that are gravitationally bound to one another (Portegies Zwart et al. 2010).However, the recent discovery of stars in diffuse regions reminds us that we need to extend the original definition of star clusters.Because these stars in diffuse regions, i.e. not gravitational bound, are proved to have the same age as core cluster members through analyses of color-absolute magnitude diagrams (CAMDs; Kounkel & Covey 2019;Meingast & Alves 2019;Bouma et al. 2021).On top of that, these stars in diffuse regions also share a similar distribution with core cluster members in stellar rotation periods (Bouma et al. 2021) and chemical abundances (Arancibia-Silva et al. 2020;Hawkins et al. 2020).Therefore, these stars in diffuse regions are probably coeval.In this series of papers, we extend the definition of open clusters to those stars in diffuse regions, i.e. comoving groups, diffuse streams, tidal tails, etc., not only the core cluster members.Thus, the number of stars in open clusters can be extremely enlarged.
There are many previous works that identified new OCs in the Milky Way using different algorithms, e.g.Cantat-Gaudin et al. (2018) applied the UPMASK algorithm to select cluster members and provided an updated catalog of 1229 OCs; Cantat-Gaudin & Anders (2020) found 582 new cluster candidates located in the low galactic latitude area using an algorithm named Density-Based Spatial Clustering of Applications with Noise(DBSCAN), and etc.Using Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN, McInnes et al. 2017), Kounkel & Covey (2019) systematically clustered Gaia DR2 data within 1 kpc and identified 1640 populations containing a total of 288,370 stars.In their recent work, Kounkel et al. (2020) (hereafter K2020), they extended the distance from 1 to 3 kpc and identified 8292 comoving groups consisting of 987,376 stars.
Utilizing the enlarged stellar population in clusters, the UPiC (Understanding Planetary Formation and Evolution in Star Clusters) project focuses on the planets in open clusters, including association and other comoving groups.We are trying to find evidence that how planets form and evolve in cluster environments.Lots of works have shown that both dynamical (Spurzem et al. 2009;Liu et al. 2013;Cai et al. 2017;Hamers & Tremaine 2017;Rodet et al. 2021;Li et al. 2023) and radiation (Johnstone et al. 1998;Matsuyama et al. 2003;Dai et al. 2018;Winter et al. 2018) environments in clusters can influence the planet's formation and evolution.As the initial work of UPiC, this paper collects the largest transiting planet sample in open clusters and aims to analyze the correlation between the planetary radius and cluster ages, which is crucial for planet formation timescales.For example, (Szabó & Kiss 2011;Beaugé & Nesvorný 2013;Mazeh et al. 2016) discovered the hot Neptune desert in planetary mass-period and radius-period distribution.The boundaries of the desert can be explained by photoevaporation and high-e migration Owen & Lai (2018).These two mechanisms have different timescales.Thus, the age of the planets can distinguish different mechanisms and help us understand the time-evolution of planet radius.
This paper is arranged as follows.In section 2, we describe methods, including data collection, age validation, and sample cut.In section 3, we use these refined data to study planet radius -age diagram and estimate the evolution of three different planet populations.In section 4, we discuss how the statistical results constrain the planet formation mechanisms, including high-e migration and photoevaporation.Last, we summarize and discuss our major conclusions in section 5.

Data collection
There are many works that use Gaia data to identify new OCs.If we combine all the catalogs of star clusters, we can definitely get more OCs, so as the stars in OCs.However, data selection criteria and clustering algorithms vary in different works, which will increase the inhomogeneity of the combined catalog.Therefore, to maximize the number of stars in OCs and make the sample as homogeneous as possible, we adopt the catalog from K2020, the largest catalog of stars with age estimations in comoving groups.K2020 identified 8292 comoving groups within 3 kpc and galactic latitude |b| < 30 • by applying the unsupervised machine learning algorithm HDBSCAN on Gaia DR2's 5D data.We use the stellar catalog of K2020 to cross-match with the host stars of confirmed transiting planets and planet candidates.In this section, we use planets/candidates from Kepler, K2, and TESS.Since we are concerned about the radius of planets, we do not consider planets detected via the Radial Velocity method.The following subsections will briefly introduce how we select the planets and cut the planet sample to exclude some observation biases.

K2020 cross-matching with confirmed exoplanets
The number of confirmed planets from the NASA exoplanets archive 1 is 5347 up to now (05/2023).After cross-matching with K2020, we find 76 confirmed planets in clusters.To study the planet size-age distribution, we select 51 transiting planets with known planet radii.
The properties of planets and their host stars, e.g.planet radius, orbital periods, effective temperature, surface gravity, and stellar mass are adopted from the table of NASA exoplanets archive.We adopt the age of the host stars from K2020 temporarily, which is completed.The adopted ages from K2020 will be validated via comparison in subsection 2.2.

K2020 cross-matching with KOIs
The number of KOIs from Kepler DR25 (Thompson et al. 2018) is 8445, including confirmed planets and candidates.After cross-matching with K2020, we find 98 KOIs in clusters.Since some of these KOIs may be False Positives, such as eclipsing binaries in the background of the targets, or physically bound to them which can mimic the photometric signal of a transiting planet.Then, we exclude the sources flagged as False Positive.There are 26 confirmed planets and 17 planet candidates in clusters for Kepler sources.Here, we use the Gaia-Kepler Stellar Properties Catalog (Berger et al. 2020) to update and obtain the accurate and precise properties of these 43 selected KOIs and their host stars.The age information is also adopted from K2020.

K2020 cross-matching with K2
1 https://exoplanetarchive.ipac.caltech.eduFor K2 sources, we use the catalog of K2 including both confirmed planets and candidates from the NASA exoplanet archive to cross-match with K2020.We get only 25 matching sources.After excluding 9 candidates flagged as "FALSE POSITIVE", we obtain 9 confirmed planets and 7 planet candidates with planet radius measurements.The properties of planets and planets' host stars are taken from the NASA exoplanet archive.The age information is taken from K2020.

K2020 cross-matching with TOIs
Up to 05/2023, there are 6586 TOIs detected by TESS.After cross-matching with K2020, there are 116 TOIs left.There are many False Positives in TOIs (Gan et al. 2023).Thus, we select the TOIs carefully.Firstly, we exclude some sources flagged as "FA", "APC", and "FP", which means false alarm, ambiguous planet candidate, and false positive respectively.After exclusion, 68 TOIs are left.Besides, based on publicly available observational notes on ExoFOP2 , we also remove some TOIs with comments like "centroid offset3 ", "V-shaped", "Likely eclipsing binary(EB)", and "oddeven".For example, the comment of TOI 1376.01 is "centroid offset on TIC 190743999 in spoc-s56".So after removing these TOIs, we finally select 42 TOIs, i.e. 12 confirmed planets and 30 candidates.The properties of these 42 selected TOIs and their host stars are taken from the table of TOIs.The age information is taken from K2020.
2.1.5.other sources K2020 focuses on the stars with galactic latitude |b| < 30 • .Actually, there are many other clusters out of such range, and so do the planets in clusters.We add the planets and planet candidates in the PATHOS project to include more planets at higher galactic latitudes.Table 6 of PATHOS -IV (Nardiello et al. 2021), provides 33 confirmed planets in clusters.Although 11 confirmed planets are repeated selected planets in section 2.1.1,14 of them are with |b| > 30 • , and 8 of them are uncross-matched with K2020.Additionally, the PATHOS project has found 90 planet candidates in clusters, which are not included in TOI completely.After cross-matching with K2020, we get the age information of 40 planet candidates with |b| < 30 • .Here, we do not include the candidates of the PATHOS project with |b| > 30 • , because they do not have the age measurements.Nardiello et al. (2021) provide false positive Note-Due to the space limitation, we only show the first 10 rows of the table.Here, "OName" shows the name of the parental cluster, "Group" shows the corresponding group number in K2020, "Flag" shows the name of the mission that detects the planets, and "Validation" shows whether this planet/candidate has the convincing age estimation (i.e."YES", "NO", and "Excluded").After the cross-matching, we check the catalog of transiting planets in clusters and exclude the repeated planets.Finally, there are 73 confirmed planets and 84 planet candidates in 86 clusters.Table 1 shows all these planets in 133 planetary systems.Planets detected by different missions are flagged as "Kepler", "K2", "TESS", and "other".Here, "other" means sources detected by other facilities, e.g.CoRoT (Léger et al. 2009) and ground-based telescopes.This is the largest catalog of the planets and planet candidates in star clusters.
Due to space constraints, we only list 10 sources in Table 1.The whole table can be downloaded from the web: https://github.com/astrodyz/UPiC

Age validation
Since we focus on the age-size distribution of planets in clusters, the accuracy, and precision of age measurements are essential.In this section, we will compare the age measurement of stars from He et al. (2022) (hereafter He2020), K2020, and the table of the NASA exoplanet archive to illustrate whether the age estimation in K2020 is robust.Kounkel et al. (2020) adopted a neural network called Auriga to robustly estimate the ages of the individual groups they identified.The uncertainty of log(Age) of comoving groups within 1 kpc in K2020 is similar to Kounkel & Covey (2019), i.e. ∼ 0.15 dex.In He2022, they use the isochrone fitting to derive the ages of 886 nearby clusters and candidates within 1.2 kpc.
Although Kounkel et al. (2020) discuss the contamination and demonstrate that the vast majority of the age are well consistent with the results of isochrone fitting, the age estimation in K2020 may still have some systematic biases compared to He2022.On top of that, the difference in identifying clusters may also influence the final age estimation.K2020 used unsupervised machine learning HDBSCAN to identify clusters, while He2022 used DBSCAN.HDBSCAN has a better performance on the data with different density structures than DB-SCAN, i.e. prefer to reveal more fine structures.Therefore, both the age estimation and the cluster membership identification will lead to systematic biases.
Then, we cross-matched the catalog of K2020 and He2022 to present whether the bias of age estimation in K2020 is non-negligible compared to other age sources.In panel (a) of Figure 1, red hollow dots are the 36 planets/candidates in 22 clusters that both have the age estimation in K2020 and He2022.Only one planet candidate has a large difference of age estimation, out of the 3 sigma limit, i.e. the PATHOS 64 in King-6.Therefore, we assume that the majority of the age estimation in K2020 is relatively robust.To validate the ages of this cluster, we refer to the ages from other previous works.In K2020, the estimation of the age of King-6 is 204 +91 −63 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 Log 10 [age/yr] K2020   Myr which is consistent with the previous result of Ann et al. ( 2002)(250±50 Myr), while in He2022, the age of King-6 is 44 Myr without uncertainty.Thus, we adopt 204 +91 −63 Myr as the final age of King-6.Additionally, we also compare the age of the K2020 and the NASA exoplanet archives.In panel (b) of Figure 1, there are 29 planet host stars(44 planets) in our catalog with both ages from K2020 and NASA exoplanet archives.Eleven host stars are out of the 3 sigma limit in the age measurement, i.e.CoRoT-22, HATS-47, HD 110113, KELT-20, Kepler-1062, Kepler-1118, Kepler-1502, Kepler-411, Kepler-968, TOI-1937 A, and TOI-4145 A. All the ages of these planets' host stars from NASA exoplanet archives are much larger than the ages from K2020.E.g. the age of CoRoT-22 is 3.3±2.0Gyr in Moutou et al. (2014), while in K2020 is 339± 100 Myr; the age of HATS-47 in Hardegree-Ullman et al. ( 2020) is 8.10 +2.90 −4.30Gyr, while in K2020 is 589 +243 −171 Myr; the age HD 110113 Osborn et al. ( 2021) is 4.0± 0.5 Gyr, while in K2020 is 645 +245 −178 Myr.Because the individual age estimation of these stars depends on the models and methods, which are inhomogeneous in the NASA exoplanet archive.Strictly, we use different ways to validate the ages of the eleven host stars.
Firstly, some stars may have several(≥ 3) age measurements, which we can evaluate through majority voting.For instance, the age estimation of KELT-20 is ≤0.6 Gyr according to Lund et al. (2017).However, according to Talens et al. (2018),   Myr, respectively).We speculate HATS-47HD 110113, Kepler-1062, and Kepler 968 may be the contaminating stars in star cluster identification.They may be field stars having similar kinematic properties compare to the comoving stellar groups in their proximity coincidently.Therefore, we exclude these three potential contaminating sources in cluster identification.We also remove HATS-47 because it does not have a convincing age measurement.
Thirdly, for CoRoT-22, Kepler-1502, TOI-1937 A b, and TOI-4145 A b which have inconsistent age measurements and lack of stellar rotation measurements, we can hardly validate their age.Additionally, Yee et al. (2023) suspects that TOI-1937 A and TOI-4145 A may be the field star because of the poorly constrained cluster membership identification.Therefore, we directly exclude these four systems.
To sum up, we validate the age measurement of 70 planets/candidates in star clusters, obtain more convinced ages of three host stars via either literature or the new gyrochronological relation, and exclude eight planetary systems without convincing age estimations.If we assume those eight host stars are field stars, the contamination rate of our catalog is about 6%, which is consistent with that in Kounkel & Covey (2019), i.e., 5%-10%.

Sample cut
In section 2.2, we obtain 63 planets and 84 planet candidates in star clusters with relatively robust age estimation.We aim to obtain the planet radius evolution, i.e. planet radius-age distribution.The accuracy of planet radius and age measurement will significantly influence our results.Therefore, we need to do the sample cut to minimize the influence of observational biases.
Here, we list the steps of sample cut in Table 2. Without the mass measurement, we can hardly determine whether the planet candidates are planets or brown dwarfs.Planet candidates with large radii are unlikely planets.Thus, we exclude 23 planets/candidates, with R p > 2.5 R J (the same criteria described in Nardiello et al. (2021)).Brown dwarfs with larger masses can induce the motion of the photon center.Berger et al. (2020) suggest that stars with high re-normalized unitweight error (RUWE>1.4), are likely to be binaries.Thus, we adopt the criteria, RUWE<1.4,to exclude 9 planet candidates in potential binary systems.
Since planets with poor radius measurements may contaminate the results, we exclude 7 samples with relative radius errors larger than 50%.Due to the precision of TESS and the stellar noise of young stars, small planets detected by TESS and planets around young stars are less complete.Thus, we need to constrain the lower limits of the planet radius to exclude the bias of completeness.As shown in Appendix A, planets with radius R p > 2R ⊕ and period P < 20 days are considered to be detectable (SNR>7.1)via both Kepler and TESS.Thus, we cut the sample via R p > 2R ⊕ and P < 20 days.
After the sample cut, there are 66 planets/candidates left.In the next section, we mainly use the sample to do the analysis.

Planet Radius-Age Diagram
Figure 2 shows the planetary size -age distribution of 37 planets and 44 planet candidates in star clusters(15 planets/planet candidates with R p < 2 R ⊕ and 66 planets/planet candidates with 2 R ⊕ < R p < 2.5 R J ).
Here, we classify planets into three groups by size for the sake of simplicity: • Jovian planets, i.e. planets of 8 R ⊕ < R p < 2.5 R J .
There are only 5 Jovian planets younger than 100 Myr, while dozens beyond 100 Myr.So, it seems that there is a gap in the planet radius-age diagram for the Jovian planets younger than 100 Myr.Additionally, there may be another gap for Sub-Jupiters with ages between 50-200 Myr.Before 50 Myrs, there are several Sub-Jupiters, while between 50-200 Myr, the number of Sub-Jupiters declines to nearly none.On top of that, there are nearly no Sub-Neptunes between 50-100 Myr.
Therefore, it seems that all of the planets disappear between 50-100 Myr.However, due to the small number of planets/candidates(i.e. the large statistical error), whether the gap is real can not be easily demonstrated.In order to avoid observational bias, in the next subsection, we will take into the age error and the radius error of the planets to obtain the time-dependent relation for the proportion (instead of the number) of different-sized planets in star clusters.

The Evolution of Planet Radius
To investigate the time-dependent relation of different-sized planets in star clusters.We defined the proportions of planets with different sizes and ages.To determine the proportions and the uncertainties, we randomize the ages and radii of all the planets 100,000 times, assuming the Gaussian distribution.Then, we can obtain the proportions of each time, denoted as f i , via the formula: where N i is the number of planets in star clusters with different sizes, i.e.N SubN , N SubJ or N J corresponding to Sub-Neptunes, Sub-Jupiters, and Jovian planets in section 3.1, respectively.After calculating 100,000 times, we obtain the distribution of f i and adopt the lower lim-its, median values, and the upper limit, according to the 16, 50, and 84 percentiles of f i , respectively.The results are as shown in Figure 3.Note the age is cut by ≤ 1 Gyr because most of the selected planets/candidates in star clusters are younger than 1 Gyr(Figure 2).Panel To extend the evolution of planets/candidates older than 1 Gyr, we calculate the proportion of planets both in star clusters and around field stars, with different sizes.Here, we add ∼ 871 confirmed planets with age measurements from the NASA Exoplanet Archive.These confirmed planets share the same cut with planets/candidates in star clusters, i.e. 2R ⊕ < R p < 2.5R J , and P < 20 days.Using the same estimating procedures as those in Figure 3, we obtained the proportion varying with age, as shown in Figure 4.
In the panel (a) and (b) of Figure 4, the proportion of Jovian planets (red diamonds, f J ), Sub-Jupiters (blue squares, f SubJ ), and Sub-Neptunes (gray circles, f SubN ) show the similar time-dependent relation within 1 Gyr to that in Figure 3. I.e.f J reaches maximum between 100 and 200 Myr, f SubJ rapidly declines around 100 Myr, and f SubN increases after 100 Myr.Because Figure 4 has a longer time span than Figure 3, there are more substructures in Figure 4.For example, all of panels in Figure 4 show a tiny bump of f J around 2 Gyr, which is anti-correlated with f SubN , i.e. a small dip of f SubN around 2 Gyr.These two timescales, i.e. 100 Myr and 2 Gyr (gray shadow regions), may correspond to different planet formation environments (see discussion in 4.2).Because the majority of planets younger than 300 Myr are in star clusters, while most of the planets older than 1 Gyr are around field stars.
To illustrate that our results are robust, we should exclude the influence of some other stellar parameters.For example, some of the planet host stars are very hot, i.e.T eff > 7500 K, especially for the candidates detected by TESS.For main-sequence stars, hotter stars usually have larger stellar radii than cooler ones.Therefore, the transit method tends to find larger planet candidates around hotter stars.In panel (c), we add another criterion for planets/candidates in star clusters and around field stars, i.e.T eff < 7500 K.Although the proportion of Jovian planets f J around 200 Myr is smaller than that in panel (b) because of the additional sample cut, f J still continuously increases between 100 and 400 Myr, i.e., the peak moves backward to around 400 Myr.The proportion of f SubJ rapidly decreases around 100 Myr, then remain at ∼ 0.1 after 100 Myr, which is similar to that in panel (b).f SubN does not show an obvious increasing/decreasing after 100 Myr.
The widely used definition of Hot Jupiters(HJs) is Jupiter-sized planets within 10 days Dawson & Johnson (2018).Here, in panel (d), as a comparison, we also show the results of the conventional hot planets within 10 days.For Jovian planets and sub-Jupiters, panel (d) shows similar results to panel (b).Therefore, in the following, we call the Jovian planets within 20 days as HJs for simplicity (if without additional annotation).For sub-Neptunes, the increasing tendency after 100 Myr is ambiguous.
In panel (e), we show the results of the time-dependent relation of planet radius for planets within 200 days.Because including some warm planets, the increment of f J around 100 Myr in panel (e) becomes less than that in panel (b).As the majority of the warm planets are sub-Neptunes, f SubN in panel (e) is systematically higher than that in panel (b) after 100 Myr.In turn, the f J in panel (e) is systematically lower than that in panel (b) after 100 Myr.The time-dependent relation of f SubJ in panel (e) is similar to other panels.
In Figure 4, we can not find an obvious increase trend of the proportion of sub-Neptunes within 1 Gyr as shown in Figure 3.Because it seems sensitive to the parameter cut.To summarize this section, we obtain the timedependent relation of planet radius for planets/candidates in star clusters and around both cluster members and field stars, i.e.
• The proportion of Jovian planets f J increases around 100 Myr and reaches maximum between 100 Myr and 200 Myr, which is mainly attributed to the HJs in star clusters.The tiny bump of f J around 2 Gyr is attributed to the HJs around field stars.
• The proportion of Sub-Jupiters f SubJ declines rapidly around 100 Myr, then remains at a low value.The declination of f SubJ is mainly attributed to the hot Sub-Jupiters in star clusters.

CONSTRAINTS OF HOT GIANT PLANETS FORMATION TIMESCALE
Based on the statistical results above, we try to explain or constrain the timescales of hot giant planets' formation mechanisms in star clusters.Here, the hot giant planets mean HJs and hot Sub-Jupiters (or hot Neptunes).
There are several formation scenarios of HJ, i.e. insitu formation when disk mass is large, or ex-situ formation then undergoing disk migration or high-e migration.The time scales of the first two HJ formation scenarios are mainly limited by the lifetime of the gas disk, which is typically ∼10 Myr.Therefore, if the in-situ formation and disk migration are the dominant channels of HJ formation, the number of HJs will not significantly change after 10 Myrs.However, Figure 3 and 4 show that the proportion of HJs(f J ) has an obvious increment around ∼ 100 Myrs, which is probably attributed to the high-e migration.
Note, we do not exclude the possibility of HJs forming through the in-situ formation and disk migration.However, with a lack of clusters younger than 10 Myr, we can hardly constrain the in-situ formation mechanism and the fraction of such planets.
In the following discussion, we mainly focus on the increment of f J and the rapid declination of f SubJ around 100 Myrs in star clusters.More specifically, in section 4.1, we estimate the timescales of flyby-induced high-e migrations in star clusters, using typical parameters.In section 4.2, we try to explain the tiny bump of HJs, as well as the small dip of sub-Neptune.The Hot-Neptune desert is also discussed in section 4.3.

Flybys induced high-e migration in open clusters within 200 Myr
Recently, several observation works have shown environments in clusters can influence planet formation and evolution (Winter et al. 2020;Dai et al. 2021).In star clusters, especially dense clusters, close stellar flybys may occur frequently.A series of theoretical works have shown that the HJ formation can be triggered by stellar flybys in star clusters (Wang et al. 2020(Wang et al. , 2022;;Li et al. 2020;Rodet et al. 2021;Li et al. 2023).Similar to previous works, we consider hierarchical planet systems with both Jovian planets and an out companion (e.g. a cold giant planet, sub-stellar, or stellar companion).The high-e migrations of the Jovian planet induced by flybys can be described as follows.During a close flyby event, a flyby star exchanges the angular momentum with the outer companion and excites its eccentricity and inclinations.Consequently, the eccentricities of the Jovian planets will be highly excited through the von Zeipel- Lidov-Kozai mechanism (ZKL, von Zeipel 1910;Kozai 1962;Lidov 1962).Finally, tidal circularization leads to the inward migration of the Jovian planet.
There are three factors determining the formation timescale of HJs under flybys-induced high-e migration in star clusters, i.e. the timescale of the close flyby (τ flyby ), the ZLK mechanism (τ ZKL ), and the tidal circularization (τ tidal ).Roquette et al. (2021) demonstrates that an effective stellar flyby means flyby with small periastron q, which can trigger the ZKL oscillation successfully, and subsequently excite the high-eccentricity of the innerJovian planet.Here, we combine the equation ( 17),(18), and (19) in Roquette et al. (2021), to get an estimation of τ flyby , the timescale of an effective flyby, i.e., Gyr, (2) where n * is stellar density in clusters, M tot is the total mass of the hierarchical three-body system, a out is the semi-major axis of the outer companion, and σ * is the velocity dispersion of star clusters.Here, we assume a solar-Jupiter system plus a solar-like companion, i.e.M tot ∼ 2 M .Other parameter setting are as follows, n * = 10 4 stars pc −3 , a out = 50 AU, and σ * = 1 km/s.The setting of σ * =1 km/s and a out = 50 AU are the same as Rodet et al. (2021).For stellar density n * , some earlier works (e.g.Adams 2010;Malmberg et al. 2011;Craig & Krumholz 2013) assume that high stellar density can only exist in the high-mass clusters.However, the recent work Pfalzner & Govind (2021) revealed that low-mass clusters share a similar stellar density around 10 4 pc −3 as high-mass clusters (e.g. the central area of the Orion nebula cluster) at least in the early stage of cluster evolution.Therefore, we set the typical density of star clusters to 10 4 stars pc −3 .Then, the timescale of an effective flyby τ flyby is about 100 Myr, The ZLK timescale(τ ZKL ) can be estimated as Wang et al. (2022): where P in is the orbital period of the inner Jovian planet, M tot,in is the total mass of the Sun-Jupiter system, M out is the mass of outer companion, and the e out is the eccentricity of the outer companion.If we assume that the inner Jupiter form outside the water ice line (around 2.7 AU), i.e. a in ≥ 2.7 AU and P in ≥ 4.4 yr, the typical ZLK timescale τ ZKL is 0.3 Myr, which is much shorter than τ flyby .
According to Figure 2 in Rodet et al. (2021), an effective flyby can successfully lead to the high-eccentric orbit of the inner planet, typically larger than 0.99.For HJs in star clusters, the median value of the orbital period is around 3 days, which corresponds to 0.04 AU around a Solar-like star.If we set the final semi-major axis (a f = 2q in , Owen & Lai 2018) after tidal circularization of a Jovian planet as 0.04 AU, the periastron of the inner planet q in is about 0.02 au.According to Figure 1 or Equation 5in Wang et al. (2022), the typical tidal dissipation timescale of such a system is 100 Myr.Therefore, the typical formation timescale of HJs (τ HJC ) through flyby-induced high-e migration is 200 Myr under our parameter settings.Due to the uncertainty of the mass of outer companions, τ HJC may move backward to several hundreds of Myr.Dawson & Johnson (2018) provides that the occurrence rate of HJs is 0.5-1%, which is ten times of estimation by Roquette et al. (2021).Interestingly, if we adopt the new stellar density value in Pfalzner & Govind (2021) (i.e.n * = 10 4 pc −3 ), the observed HJs can be successfully explained by flyby-induced high eccentricity migration in star clusters.This may indicate that the flyby-induced high-e migration is the dominant formation scenario of HJ in star clusters.As described of the high-e migration, Jupiter-sized planets (i.e.warm-Jupiters and cold-Jupiters) may migrate inward and become HJs.Therefore it also results in the decline of warm-Jupiters and cold-Jupiters after ∼100 Myr.In Figure 5, we show the planetary radius-age distribution of 107 planets/candidates within 200 days in star clusters.There are 7 young Warm-Jupiters in clusters(WJ, 20 < P < 200 days, age < 100 Myr, green circles).However, there are no WJs in clusters with ages between 100 Myr and 1000 Myr.This may be another hint of the flyby-induced high-e migration in star clusters.Note there are dozens of WJs with age measurements from the NASA exoplanet archive (20 < P < 200 days, 8R ⊕ < R p < 2.5R J , blue diamonds in Figure 5).The majority of these WJs around field stars are older than 1 Gyr.The absence of WJs between 100-1000 Myr may indicate that WJs are hardly sustained in cluster environments, i.e. such relatively dense environments prefer the formation of HJs.However, due to the small number of warm plants in star clusters, we need more observation data.

High-e migration of HJs around field stars beyond 1 Gyr
In Figure 4, we find a tiny bump of proportion of Jovian planets f J around 2 Gyr, which is anti-correlated with f SubN , i.e. a small dip of f SubN around 2 Gyr.
High-e migration can explain the anti-correlation.During the inward migration of the Jovian planet, the inner planets can be ejected from the system due to the planet-planet interaction (Mustill et al. 2015).I.e.HJs after high-e migration are usually lonely (Steffen et al. 2012;Hord et al. 2021).Thus, the proportion of smaller planets, e.g.Sub-Neptunes and Super-Earths, have a declination.
Due to tidal dissipation during the high-e migration, the eccentricity of the HJs will decrease with time.Therefore, if the tiny bump in the proportion of Jovian planets f J around 2 Gyr is attributed to the HJs that form through high-e migration, we may also see a small bump in the eccentricity-age diagram around 2 Gyr.To test this conjecture, in the following, we select 336 HJs both having eccentricity and age measurements from the NASA exoplanet archive.We constrain the period of the HJs to be shorter than 20 days and the relative uncertainty of planet radii is no more than 50%.Figure 6 shows the eccentricity-age distribution of the 289 HJs.In Panel (a) red dots shows the median eccentricity of each age bin changing with age.The error bar is calculated according to the 16 and 84 percentiles of the eccentricities of each age bin.Because the majority of the HJs have low eccentricity, the median eccentricity of each age bin is nearly a zero constant, i.e. unchanging with age.
However, red dots have larger error bars in the older region.It seems that the number of HJs with high eccentricity increases beyond 1 Gyr.Therefore, we calculate the relative ratio of High-eccentricity HJs in each age bin, as shown in panel (b) of Figure 6.Similar to the previous analysis, this ratio is calculated with the assumption of the Gaussian distribution of age and eccentricity of each HJ.We find that both the ratio of HJs with e > 0.1 and e > 0.2 rapidly increase beyond 1 Gyrs, i.e. the difference between the two data points before and after 1 Gyr is 2 σ and 12 σ, respectively.After reaching the maximum of around 2 Gyr, the ratio of HJs with high-eccentricity declines with age due to the tidal dissipation as expected.Therefore, the eccentricity evolution also supports the high-e migration for these HJs older than 1 Gyr.
Because HJs around field stars are the dominant population beyond 1 Gyr, as shown in Figure 2, we can conclude that the bump of f J around 2 Gyr is likely due to the formation of HJs around field stars through high-e migration.Since the timescale of 2 Gyr is ten times longer than the formation timescale of HJs through flyby-induced high-e migration in star clusters (τ HJC 200 Myr).We explain the large differences via the different environments of stellar density.The HJs form around field stars after 1 Gyr, which escape the cluster environments at the early stage (< 100 Myr).Because the less dense dynamical environments lead to longer flyby timescale, the trigger time of high-e migration is probably much longer than that in cluster environments.

Formation of Hot Neptune desert around 100 Myr
Several previous works find the hot Neptune desert in planetary mass-period distribution and radius-period distribution, i.e.Szabó & Kiss (2011); Beaugé & Nesvorný (2013); Mazeh et al. (2016).In Figure 4, we find that the proportion of the Sub-Jupiters within 20 days, f SubJ , rapidly declines around 100 Myr, then remains at the low value.The declination is correlated to the hot Neptune desert and may indicate the formation timescale of such desert.
However, the Sub-Jupiters classified via radius and period independently, are not in the hot-Neptune desert exactly.According to Mazeh et al. (2016), the borders of the desert are period-dependent.I.e. at large radii, the planet's radius decreases with increasing period, while at small radii, the radius increases with increasing period (the dashed lines in Figure 7).Using the same region with Mazeh et al. (2016), we compare the timedependent ratio of the number of planets inside and outside the hot Neptune desert, to constrain the formation timescale of the hot Neptune desert.In Figure 7, we show 107 planets/candidates in star clusters and 1991 other confirmed planets around field stars in the radius-period plane.We divide the planets/candidates in star clusters within 20 days into two groups.One is planets younger than 100 Myr (red circles).The other is planets older than 100 Myr (green diamonds).
We calculate the ratio of the number of planets inside and outside the hot Neptune desert, i.e.N in /N out , for both the younger and older groups.Then, we use the Monte Carlo simulation to get a distribution of N in /N out under the assumption of the Gaussian distribution of planet radius, period, and age.The error of N in /N out is adopted according to the 16 and 84 percentiles of the ratio distribution.We find that the younger group have much higher N in /N out (0.80 +0.20  −0.19 ) than older groups (0.19 +0.03  −0.03 ) in nearly 3.0 σ confidence level.If we add a planet radius cut for detection completeness, i.e.R p > 2R ⊕ (horizontal shadow line), the result is similar.I.e. the younger group has higher N in /N out (0.67 +0.17 −0.13 ) than older group (0.18 +0.03 −0.01 ) in 3.67 σ confidence level.Alternatively, if we use 300 Myr to distinguish the younger and older group, the difference of N in /N out between the young and old group will decrease, which is smaller than the 100-Myr case.I.e. the difference between the median value of the young group's N in /N out (0.48 +0.07  −0.05 ), and old group's N in /N out (0.31 +0.04  −0.04 ).Therefore, we can conclude that the rapid declination of f SubJ around 100 Myr corresponds to the formation of the hot-Neptune desert around 100 Myr.Owen & Lai (2018) explains two boundaries of the hot-Neptune desert in a combination of photoevaporation and high-e migration.For the lower boundary, photoevaporation functions effectively in the first several hundred of million years and will trigger the atmospheric mass loss of Neptune-sized planets, which is consistent with the formation timescale we obtained.If the highe migration sculpts the lower boundary, the formation timescale will be much larger than 100 Myr, because the hot-Neptunes usually experience longer tidal circularization ( 1 Gyr).We prefer that photoevaporation sculpts the lower boundary of the hot-Neptune desert around 100 Myr.
For the upper boundary, photoevaporation seems not a suitable explanation.Because several works show that the massive planets(M p > 0.5 M J ) can resist photoevaporation even at extremely short periods (e.g.Owen & Jackson 2012;Tripathi et al. 2015;Owen & Alvarez 2016).Therefore, photoevaporation will predict a lower upper boundary(Figure 4 in Owen & Lai (2018)).However, in some specific cases, the rapid declination of the radius of giant planets may explain the upper boundary of the Hot-Neptune desert.E.g.Thorngren et al. (2023) developed a model including radius inflation, photoevaporative mass loss, and Roche lobe overflow, which can trigger a runaway mass loss of a puff hot Saturn around 400 Myr.Because the desert already existed around 100 Myr, we do not consider such a mechanism as the dominant.
High-e migration can deliver Jovian planets from the outer region to the inner orbit.Then, the subsequent decay due to stellar tides will further sculpt the upper boundary.More specifically, both the tidal circularization timescale (planetary tides) and tidal decay timescale (stellar tides) decrease with increasing planetary radius or mass.As described in section 4.1, the typical formation timescale of HJs in clusters is 200 Myr, which is consistent with the formation timescale of the Hot-Neptune desert.Therefore, flyby-induced highe migration could sculpt the upper boundary of the hot-Neptune desert in clusters.
The formation timescale of the Hot-Neptune desert in star clusters is around 100 Myr.When it comes to field stars, the formation timescale of the Hot-Neptune desert may move backward to several Gyr because of the relatively slow high-e migration for HJs around field stars.However, due to the limited sample of young planets around field stars, we do not find any evidence.
Because the scenario of flyby-induced high-e migration can not only explain the increment of f J around 100 Myr, but may also sculpt the upper boundary of the Hot-Neptune desert around 100 Myr.Therefore, we prefer to the scenario of flyby-induced high-e migration, i.e. a combination of photoevaporation and flybyinduced high-e migration could sculpt the hot-Neptune desert around 100 Myr.

CONCLUSION & DISCUSSION
Planets in young star clusters could help us understand the planet's formation and evolution because of the accurate age estimation.In section 2, we collect the largest catalog of 73 planets and 84 candidates in star clusters by cross-matching with K2020 and planets/candidates from the NASA exoplanet archive.We validate the age estimation of 70 planets/candidates in star clusters, obtain more convinced ages of three host stars via either literature or the new gyrochronological relation, and exclude eight planetary systems with no robust age estimations.
In section 3, we use this catalog to study the planet radius -age relation.The main statistical results are as follows: • The proportion of Jovian planets f J increases around 100 Myr and reaches maximum between 100 Myr and 200 Myr, which is mainly attributed to the HJs in star clusters.The bump of f J around 2 Gyr is attributed to the HJs around field stars.
• The proportion of Sub-Jupiters f SubJ declines rapidly around 100 Myr, then remains at a low value.The declination of f SubJ is mainly attributed to the hot Sub-Jupiters in star clusters.
After discussing several possible scenarios to explain the results, we give two constraints on the hot giant exoplanet formation timescales in section 4: • HJs likely form through flyby-induced high-e migration in star clusters within 200 Myr.
• A combination of photoevaporation and flybyinduced high-e migration in star clusters can sculpt the hot-Neptune desert around 100 Myr.
We find that flyby-induced high-e migration may be the dominant formation channel of HJs in star clusters.As described in section 4.1, those HJs in star clusters will accompany an outer companion, which is an effective angular momentum transmitter during a close flyby event.Therefore, we hope to discover some outer companions beyond these HJs with the Radial Velocity observations from ground-based telescopes and the astrometric data from the future data release of Gaia.
Different from HJs in star clusters, HJs around field stars may have much longer formation timescale (∼ 2 Gyr), which can be attributed to the different dynamical environments (section 4.2).
Note in this paper, we mainly focus on the ZLK mechanism to excite the high eccentricity of the inner Jovian planet.Actually, other mechanisms such as planetplanet scattering can trigger the high-eccentric orbit too.Wang et al. (2020) demonstrates that a very small fraction of HJs can form from the fly-induced planet-planet scattering channel, i.e.ZLK mechanism may be the dominant scenario of eccentricity excitation.However, we could not exclude the possibility of planet-planet scattering.One way to distinguish these two mechanisms definitely is the stellar obliquity, the angle between a planet's orbital axis and its host star's spin axis.ZLK mechanism predicts a bimodal stellar obliquity distribution, concentrated at 40 • and 140 • (e.g.Fabrycky & Tremaine 2007).While the planet-planet scattering after a convergent disk migration predicts a concentration of stellar obliquity around 90 • (Nagasawa & Ida 2011).
Additionally, a hint from the absence of WJs around field stars between 100 Myr and 1000 Myr also supports the scenario of flyby-induced high-e migration (section 4.1).However, this absence may be due to the observation bias.For instance, TESS prefers to discover HJs instead of WJs, because of the relatively short time span.
In the future, with the extended mission of TESS, the Earth 2.0 mission (ET2.0,Ge et al. 2022), the Chinese Space Station Telescope (CSST, Zhan 2011; Gong et al. 2019), and PLATO (Rauer et al. 2014), we hope to detect more young planets both in star clusters and around field stars.The subsequent astrometry data from Gaia and the follow-up Radial-Velocity observation (including the Rossiter-McLaughlin effect) from ground-based telescopes can also provide more information about warm planets and even outer companions.A larger sample of planets in clusters will benefit us to test different formation scenarios of HJs, as well as hot-Neptune deserts.In young clusters, stars are more active and may hide the transiting events, especially for small planets.Thus, the detection of small planets in young clusters is uncompleted.To study the selection effects, we try to derive the empirical relations between SNR and stellar age for planets of different sizes.Then, we can select suitable criteria of planet radius to cut our samples.
The calculation of SNR of a transiting planet is calculated as follows: SNR = δn 0.5 σ * (t dur ) (A1) where δ = (R p /R * ) is the transit depth of the star and n is the transit number.σ * is the stellar photometric noise.The transit duration time t dur is given by: where P is the planet's orbital period and a is the semi-major axis.In the calculation of SNR, we assume that host stars are solar-like (i.e.M * = 1M and R * = 1R ) and set P =20 days (because most of our select planets in star clusters are within 20 days).The same as the assumption of the Mulders et al. (2015) to assume that the stellar noise change with time as a simple power law distribution: where we normalize the noise (σ LC ) at the period in the long cadence, 1765.5 s (t LC ).ind CDPP is the power law index.We use Combined Differential Photometric Precision (CDPP, Christiansen et al. 2012)  For a rough calculation, we assume that the stars observed by Kepler and TESS are similar, i.e. the stellar noise evolution is similar.The major difference in SNR of planets of different sizes lies in the observation time t obs which determines the transit numbers.Here, the observation time of the Kepler stars is ∼ 1450 days and TESS is roughly two observation sectors, i.e. ∼ 54 days.
Figure A1 shows the calculated SNR of planets changing with age.Red, orange, and black hollow dots and dashed lines present the results of planets of different sizes (i.e. 1 R ⊕ , 2 R ⊕ , and 2.5 R ⊕ ) for TESS.The purple hollow dots and dashed line show the result of planets of 1 R ⊕ for Kepler.Since the data from Chen et al. (2021) does not provide the CDPP of stars younger than 300 Myr, we simply extend the relationship to 10 Myr through a log-linear exploration.The blue horizontal line is the SNR of 7.1 above which we consider TESS or Kepler can detect planets.To sum up, planets with a radius larger than 2 R ⊕ can be detected both by TESS and Kepler.Thus, in section 2.2, we focus on the planets with a radius larger than 2 R ⊕ to exclude the uncompleted detection due to the stellar noise of young stars.

Figure 1 .
Figure 1.The comparison of age estimation from different catalogs.Panel (a) uses data from the cross-matching catalog of K2020 and He2022.Panel (b) uses data from K2020 and the NASA exoplanet archive.Gray shadows are 1-sigma and 3-sigma areas considering the average uncertainty of age estimation of comoving groups within 1kpc in K2020.A black solid diagonal line is plotted for reference.

Figure 3 .
Figure 3.The time-dependent relation of the proportions of planets(in star clusters) of different sizes.Different colors show planets of different sizes.Panel (a) and (b) are different in numbers of age bins, i.e. 4 age bins between 10 to 1000 Myr under log scale in panel (a), and 8 age bins in panel (b).

Figure 4 .
Figure 4.The time-dependent relation of the proportions of planets(both in star clusters and probably around field stars) of different sizes.Different colors show planets of different sizes.Panel (a) and (b) are different in the number of age bins, i.e. 6 age bins between 10 to 10000 Myr under log scale in panel (a), and 12 age bins in panel (b).We add a cut of effective temperature in panel (c) and an additional period cut in panel (d), i.e.P < 10 days.For panel (e), we show the result for planets with P < 200 days as a comparison.Two shadow regions around 100 Myr and 2 Gyr are over-plotted to emphasize two typical timescales.

Figure 5 .
Figure 5.The planetary radius -age distribution of 107 planets/candidates (within 200 days, red squares and green circles) in clusters and 1991 confirmed planets (within 200 days, gray dots) around field stars.Here, we also show the 39 warm Jupiters around field stars with age measurements from the NASA exoplanet archive (20 < P < 200 days, blue diamonds).

Figure 6 .
Figure 6.The eccentricity-age relation of HJs.We select 336 known HJs (P < 20 days, σR p /Rp < 0.5) with age and eccentricity measurements.Panel (a) shows the entire sample in the eccentricity-age diagram.Panel (b) represents the ratio of high-eccentricity HJs changing with age.The blue and purple dots are the ratio of HJs with e > 0.1 and e > 0.2 changing with age, respectively.The shadow region is over-plotted to emphasize the peak of the ratio.
' confidence interval for a Poisson parameter Figure B1 shows the time-dependent relation of the proportions of planets of different sizes, adopted Poisson error.The error bar, i.e. standard confidence interval related to a Poisson parameter, is calculated through the chi-square distribution.Panel (a) includes planets/candidates in star clusters, consistent with the results of Figure 3, although with more significant uncertainties.Panel (b) includes planets/candidates in star clusters and around field stars, consistent with the results of Figure 4. I.e. the f J increases before 100 Myr and then decreases around 1-2 Gyr.

Table 1 .
Planets in clusters Morton et al. (2016)on of Kepler-1118 fromMorton et al. (2016)(4.07Gyr) is nearly ten times of that in K2020(490 +155 −118 Myr).We strengthen that Morton et al. set the age prior to 1-15 Gyr, which means the stellar age in their catalog is artificially larger than 1 Gyr.As the host cluster of Kepler-1118, NGC 6866 has the age of 705± 140 Myr from Janes et al. (2014)).Therefore, we adopt the age in K2020 forKELT-20 and Kepler-1118.Secondly, if stars do not have independent and consistent age measurements, we estimate the age via the gyrochronological relation.Kepler-411 is a special case that three age measurements are significantly different.

Table 2 .
Sample Cut of Planets/Candidates in clusters The planetary radius -age distribution of 37 planets and 44 planet candidates in star clusters(Table2).Different colors show the planets in clusters detected by different missions.Red, yellow, blue, and purple symbols are planets/candidates detected by different missions, i.e.Kepler, K2, TESS, and other ground-based telescopes, respectively.The gray dots are confirmed transiting planets whose host stars have age measurements.
Mazeh et al. (2016) planets in planets radiusperiod plane.Red dots are hot and young planets in star clusters(P < 20 days, age < 100 Myr).While black dots are hot and old planets in star clusters (P < 20 days, age > 100 Myr).Orange squares are planets in clusters with periods beyond 20 days.Two black dashed lines are boundaries of the Hot Neptune desert described inMazeh et al. (2016).The gray line of P=20 days and the gray line of Rp=2 R⊕ are over-plotted as reference.
Chen et al. (2021)which characterizes the noise level in Kepler lightcurves.Then, using the stellar kinematic age fromChen et al. (2021), we can obtain ind CDPP -age relation and SNR-age relation.