The stellar atmospheric parameters and physical properties of stars in the Kepler Input Catalog (KIC) are of great significance for the study of exoplanets, stellar activity, and asteroseismology. However, despite extensive effort over the past decades, accurate spectroscopic estimates of these parameters are available for only about half of the stars in the full KIC. In our work, by training relationships between photometric colors and spectroscopic stellar parameters from Gaia DR3, the Kepler-INT Survey, Large Sky Area Multi-Object Fiber Spectroscopic Telescope DR10, and Galactic Evolution Experiment at Apache Point Observatory DR17, we have obtained atmospheric parameter estimates for over 195,000 stars, accounting for 97% of the total sample of KIC stars. We obtain 1
As the most powerful and successful exoplanet explorer to date, the Kepler/K2 mission (W. J. Borucki et al. 2010;S. B. Howell et al. 2014) has discovered more than 3300 exoplanets, over half of the currently confirmed exoplanets. The extremely precise and short-cadence (~1 minute) light curves obtained from Kepler/K2 have revolutionized the field of asteroseismology. These data have facilitated the detection of solar-like oscillations in over 500 main-sequence and subgiant stars (W. J. Chaplin et al. 2014), as well as for more than 20,000 red giants (e.g., D. Stello et al. 2013;J. Yu et al. 2016). This extensive data set has enabled accurate modeling of the fundamental properties of these stars across nearly the entire low-mass Hertzsprung-Russell (H-R) diagram (D. Huber & K. Zwintz 2020). There are also 75 exoplanets confirmed from Kepler's archival data, demonstrating the enduring impact and vitality of this space mission.
During its first 4 yr of operations, Kepler made long-term observations of the Kepler field, a 116 deg 2 area of sky located between the constellations Cygnus and Lyra. To guide these observations, a catalog of some 200,000 stars, known as the Kepler Input Catalog (KIC; T. M. Brown et al. 2011), was determined in advance. Observations of this area accumulated a large amount of photometric data over temporal baselines on the order of years, which have not only greatly advanced the field of exoplanet search and characterization but also provided an important basis for research in many other fields, including stellar activity, asteroseismology, and the study of star clusters (R. L. Gilliland et al. 2010;T. Shibayama et al. 2013;A. McQuillan et al. 2014; W. J. Borucki 2016).
The fundamental stellar parameters of stars play a important role in refining our understanding of stellar theoretical models and evolution. In order to construct the appropriate stellar models to constrain their evolution, the physical properties of stars, in particular the metallicity, are essential input parameters (C. A. Tremonti et al. 2004;A. Bressan et al. 2012). The situation is similar for the estimation of stellar ages and masses; a precise metallicity estimate of a star is required. After determining the stellar age, the age-rotation relation can be analyzed to a high level of precision (V. Witzke et al. 2020;K. Masuda 2022). The metallicity also deeply influences the stellar atmosphere and structure, as well as the relationship between stellar activity and metallicity (C. Karoff et al. 2018; V. See et al. 2023;V. Loaiza-Tacuri et al. 2024).
The nature of the exoplanet(s) associated with a star is expected to be related to the physical properties of the host. Both the probability that a star hosts a planet and the type of the planet are influenced by the elemental abundances of the protoplanetary disk (G. Gonzalez 1997; J. A. Johnson et al. 2010;E. A. Petigura et al. 2018; K. M. Boley et al. 2024). Furthermore, the radius gap, a region that shows a deficit of planet occupation in the planet radius-mass map (at around 1.9 R ⊕ ), is also thought to be influenced by the host star's metallicity, mass, and age (E. D. Lopez & J. J. Fortney 2013; J. E. Owen & Y. Wu 2017; K. K. Hardegree-Ullman et al. 2020; R. Burn et al. 2024; S. Yun et al. 2024).
However, we still lack full information on the fundamental stellar parameters of KIC stars, particularly metallicity, which is crucial for accurately determining other parameters as mentioned above. Attempts to obtain this information continued throughout the Kepler mission, both before and after. Prior to the launch of the Kepler satellite, the atmospheric parameters of KIC stars were estimated through the use of broadband photometry. For example, T. M. Brown et al. (2011) provided estimates of the metallicity, effective temperature, surface gravity, and extinction toward KIC stars using a Bayesian posterior estimation method based on this photometry. However, the stellar parameters predicted by this method differ significantly from those obtained from both low-resolution (e.g., S. Dong et al. 2014) and high-resolution spectroscopic studies with the Keck telescope (e.g., J. A. Johnson et al. 2017).
The Kepler Stellar Properties Catalog (D. Huber et al. 2014) provided revised stellar parameters for 138,600 targets in Quarters 1-16 (Q1-Q16), using colors, proper motions, spectroscopy, parallaxes, and Galactic population synthesis models. However, only 7% of stars in this catalog had spectroscopic information at that time. Applying similar methods, S. Mathur et al. (2017) provided stellar parameters for 197,096 targets in Quarters 1-17 (Q1-Q17). Again, spectroscopic parameters were available for no more than 10% of sample stars. Most recently, this group (T. A. Berger 2020) provided a catalog for 186,301 Kepler stars, with fundamental properties (including stellar ages) homogeneously estimated from isochrone fitting using broadband photometry, and Gaia Data Release 2 parallaxes, as well as spectroscopic metallicities if available. Compared to previous versions, the fraction of stars with spectroscopic information has increased to approximately 35% (about 66,000 stars), less than half of the number of KIC stars.
Another major effort for obtaining stellar parameters for KIC stars are large-scale spectroscopic surveys, including the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST)-Kepler Survey (P. De Cat et al. 2015; W. Zong et al. 2018;J.-N. Fu et al. 2020;J. Fu et al. 2022), the Galactic Evolution Experiment at Apache Point Observatory (APO-GEE)-Kepler Survey (M. H. Pinsonneault et al. 2014;M. Pinsonneault et al. 2018), and the California-Kepler Survey (CKS; J. A. Johnson et al. 2017;E. A. Petigura et al. 2017E. A. Petigura et al. , 2018)). As shown in Table 1, these three surveys have obtained stellar parameters for 78,141, 23,198, and 1716 stars by crossmatching their data releases with the KIC. Despite these extensive efforts, the total number of stars with spectroscopically measured atmospheric parameters is 85,986, still less than 50% of the number of KIC stars.
More recently, stellar atmospheric and other physical parameters have been derived using narrow-or medium-band photometric surveys, particularly those in the near-ultraviolet bands (e.g., H. Yuan et al. 2015b;Y. Huang et al. 2019Y. Huang et al. , 2022Y. Huang et al. , 2023Y. Huang et al. , 2024;;A. Chiti et al. 2021). The precision is comparable to that achieved from low-or medium-resolution spectroscopy. In recent decades, the Kepler field has been observed using near-ultraviolet bands, such as the Kepler-INT Survey (KIS; S. Greiss et al. 2012aGreiss et al. , 2012b)), or through the use of Gaia XP spectra. Parameter-sensitive narrow-or mediumband photometric colors (e.g., the well-known Strömgren filter system) can be readily integrated from the flux-calibrated lowresolution spectra (LRS) of the latter survey. In this work, we aim to determine stellar parameters for all KIC stars using narrow-or medium-band photometric colors from these surveys, with spectroscopic labels from the LAMOST serving as training data. The paper is structured as follows: Section 2 describes the data. Section 3 presents the 3D extinction map toward the Kepler field. Atmospheric parameters are determined in Section 4, while physical parameters are estimated in Section 5. Finally, Sections 6 and 7 provide a discussion and a summary.
The Kepler field, a 116 deg 2 region situated between Cygnus and Lyra, is centered at celestial coordinates (α, δ) = (290 o , 45 o ) and Galactic coordinates (l, b) = (76 o , 14 o ) (T. M. Brown et al. 2011) and has attracted a multitude of surveys. In this work, we primarily employed data from Gaia Data Release 3, KIS Data Release 2, Large Sky Area Multi-Object Fiber Spectroscopic Telescope Data Release 10, and Apache Point Observatory Galactic Evolution Experiment Data Release 17, supplemented with distance estimates sourced from the catalog by C. A. L. Bailer-Jones et al. (2021).
The Gaia third data release (DR3; Gaia Collaboration et al. 2023), derived from observations over a 35-month period, not only includes low-resolution (R = λ/Δλ ~50) BP/RP (XP) spectra for around 220 million sources, predominantly those with magnitudes brighter than G < 17.65 (well calibrated both internally and externally by J. M. Carrasco et al. 2021, F. De Angeli et al. 2023, and P. Montegriffo 2023, respectively), but also offers the most precise photometric data (G, BP, RP) to date for approximately 1.8 billion stars (Gaia Collaboration et al. 2021a, 2021b;M. Riello 2021). This provides the high-quality photometric and slitless spectroscopic data essential for conducting our study.
Based on the Gaia XP spectra, we further synthesized Strömgren photometry for the vby bands using the generation function provided by the Python package GaiaXPy (D. Ruz-Mieres & zuzannakr 2022).
The Kepler field is observed by the KIS (S. Greiss et al. 2012aGreiss et al. , 2012b)), which employs the Isaac Newton Telescope (INT) to collect photometric data. The KIS second data release (DR2) includes U-, g-, r-, i-, and Hα-band photometry for 14.5 million stars, spanning a 113 deg 2 area of the Kepler field. In particular, the near-violet U-band photometry in KIS DR2 is crucial for the analysis presented in this work.
Table 1 KIC Stars in Large-scale/Dedicated Spectroscopic Surveys Catalog/Survey Number KIC 200,038 LAMOST DR10 79,015 APOGEE DR17 23,198 CKS DR1 and DR2 1716 KIC stars with spectroscopic parameters 86,482 2.3. LAMOST DR10 LAMOST features a unique quasi-meridian reflecting Schmidt design outfitted with 4000 optical fibers, covering a 20 deg 2 field of view. Its 10th data release (DR10) provides an extensive collection of tens of millions of low-resolution (R ~1800) spectra across the optical spectrum from 3800 to 9000 Å. For estimation of the primary stellar atmospheric parameters (effective temperature T eff , surface gravity log g, and metallicity [Fe/H]), the project relies on the LAMOST Stellar Parameter Pipeline for AFGK stars (LASP; Y. Wu et al. 2011; Y. Wu et al. 2014) and LAMOST Stellar Parameter Pipeline for M stars (LASPM; B. Du et al. 2021). 2.4. APOGEE DR17 APOGEE, as a part of the Sloan Digital Sky Survey (SDSS-III) initiative, aimed to comprehensively address galaxy formation by conducting an unprecedented large-scale survey with detailed chemical and kinematic analysis. The APOGEE Stellar Parameter and Chemical Abundances Pipeline (ASP-CAP; A. E. Garcìa Pérez et al. 2016) delivers high-precision estimates of stellar parameters, including effective T eff , surface gravity log g, and metallicity [Fe/H]. APOGEE DR17 published stellar atmosphere parameters for about 0.73 million stars, achieving measurement precision of typically 2%, 0.1 dex, and 0.05 dex for T eff , log g, and [Fe/H], respectively. In this work, we utilized both photometric and spectroscopic data to estimate the atmospheric parameters of KIC stars. To achieve this, we crossmatched the KIC with data from the aforementioned surveys. After crossmatching, we found 199,571 stars with Gaia DR3 ultra-wide-band photometry, 197,157 stars with Gaia DR3 XP spectra, and 190,604 stars with KIS DR2 photometry. For spectroscopic data, we found 23,198 stars observed by APOGEE and 79,015 observed by LAMOST, as summarized in Table 1. To incorporate extinction values from the map derived in Section 3, we required distance estimates for the KIC stars. Crossmatching with C. A. L. Bailer-Jones et al. (2021) provided distance information for 197,064 stars. All crossmatching processes were conducted using TopCat (M. B. Taylor 2005), employing the best-matching model and a 3″ matching radius. 3. Construction of a 3D Dust Map for the Kepler Field with the "Star-pair" Method
In this study, the D. J. Schlegel et al. (1998) dust map E (B -V ) is not utilized for reddening correction, due to its inadequacies at low Galactic latitudes and the presence of spatially dependent errors, as reported in recent work by Sun et al. (2022). Instead, the 3D dust map for the Kepler field, derived through the straightforward "star-pair" (SP) method (H. B. Yuan et al. 2013; see their Section 5 for more details), is employed.
The central idea behind the SP method is that stars with similar atmospheric parameters-metallicity, effective temperature, and surface gravity-exhibit analogous intrinsic colors. The SP method typically involves defining the relationship between the intrinsic colors and the physical quantities using a sample of low-extinction stars, which is then applied to the entire sample to obtain E(BP -RP).
A detailed description of the SP method with the Gaia DR3 photometry color BP -RP and LAMOST DR10 spectroscopic stellar parameters is as follows.
1. We combine the Gaia DR3 photometric data with the spectroscopic data from LAMOST DR10, as well as the C. A.
L. Bailer-Jones et al. (2021) distance catalog, with a crossmatching radius of 3″. A reference sample, constituting 1,037,145 stars, is selected with the following constraints: (1) signal-to-noise ratio for the g band (SNR g ) of the LAMOST spectra greater than 20; (2) Galactic latitude higher than 40 o ; (3) the 3D dust map from G. M. Green et al. (2019), represented as E(B -V ) G19 , is less than 0.01; and (4) C. A. L. Bailer-Jones et al. (2021) relative distance error less than 30%, in order to avoid poorly constrained distance information. 2. To construct the Kepler field target sample, we combine the Gaia DR3 photometric data with the spectroscopic data from LAMOST DR10, as well as the C. A. L. Bailer-Jones et al. (2021) distance catalog, with a crossmatching radius of 3″. The target sample includes 126,277 stars that meet the following constraints: (1) SNR g of the LAMOST spectra more than 20, (2) located in the sky area where R.A. ranges from 279 o to 302 o and decl. ranges from 36 o to 52 o , and (3) C. A. L. Bailer-Jones et al. (2021) relative distance error less than 30%. 3. The BP -RP is adopted from the Gaia BP and RP bands;
the intrinsic color (BP -RP) 0 can be estimated from
To obtain the reddening value, E(BP -RP), a transformation is performed as shown in the following equation:
where R BP/RP is the reddening coefficient with respect to E(B -V ) G19 for the BP and RP bands, respectively, which can be calculated with
where R V represents the total-to-selective extinction ratio, defined as
Here, instead of fixing it at 3.1, we use the actual measurements from R. Zhang et al. (2023) for each target. The A BP/RP and A V are the reddening values in the BP/RP and V bands, respectively. The reddening ratio of A BP/RP /A V is taken from S. Wang & X. Chen (2019).
For each target star, the reference stars are selected from the reference sample as those having values of T eff , log g, and [Fe/H] that differ from those of the target by less than 130 K, 0.06 dex, and 0.06 dex, respectively. The box sizes for selecting reference stars are empirically determined to ensure both a sufficient number of stars and a clear relationship between intrinsic color and atmospheric parameters within the box range. The extinction values for the target stars E(BP -RP) are measured from the difference between the observed color BP -RP and intrinsic color (BP -RP) 0 . The latter is derived both assuming that the intrinsic colors of the target and its control stars vary linearly with T eff , g log , and [Fe/H] and based on the random forest machine learning fitting technique (L. Breiman 2001). From comparison with the results of the above two techniques, the outcome of the random forest approach has been selected as the final result.
to all KIC stars, it is required to interpolate the discrete reddening values we have obtained. We subdivided the Kepler field into a grid of ¢ ¢ 10 10 squares, assuming that the stars within each grid share the same line of sight. For the stars in each grid square, we employed two interpolation techniques: cubic function fitting and Gaussian error function fitting. We then derived continuous color-excess values. Among these two interpolation strategies, the method demonstrating superior goodness of fit, as measured by the coefficient of determination, was adopted as the final choice.
Finally, we constructed a 3D extinction map with an angular resolution of 10′ and a distance resolution of 20 pc in the Kepler field, as shown in Figure 1. As a first check, the extinction values E(BP -RP) yielded by the SP method are directly compared with those from E(B -V ) G19 (see Figure A1). Generally, they are very consistent with each other, with a negligible offset and a moderate scatter of 0.037 mag. We further assess the accuracy of reddening derived from the SP technique using member stars of open clusters, where extinction values are assumed to be constant. In the Kepler field, there are four open clusters: NGC 6811, NGC 6819, NGC 6866, and NGC 6791. Using positions, distances, and proper motions from Gaia DR3 (following the methods in Y. Huang et al. 2019;X.-Y. Li et al. 2023), we selected member stars of these four open clusters according to their mean positions, distances, and proper motions reported in C. A. L. Bailer-Jones et al. (2021), and E. L. Hunt & S. Reffert (2023). The extinction distributions E(B -V ) for the member stars, derived both from our SP technique and from G. M. Green et al. (2019), are shown in Figure A2. It is evident that the SP technique produces narrower distributions for all four clusters, indicating that the internal precision of the SP method is significantly higher than that of G. M. Green et al. (2019). Typically, the scatter in the extinction distributions obtained using the SP technique is significantly smaller than 0.01 mag, whereas the scatter from G. M. Green et al. (2019) exceeds 0.025 mag. The median extinction values for the member stars of all four clusters are consistent with those reported in the literature (see Table A1; K. Janes et al. 2013;B. J. Anthony-Twarog et al. 2014;D. Bossini et al. 2019).
Multiband photometric data, particularly if narrowband filters are involved, provide an extremely efficient means to estimate stellar atmospheric parameters, as has been recognized for over half a century. For example, B. Strömgren (1963) Fan et al. 2023). We here will adopt the same technique to derive metallicity, effective temperature, and surface gravity for KIC stars from the KIS and synthesized Strömgren photometry from Gaia XP spectra.
To derive photometric metallicity, we use stars in common with the LAMOST-KIC data set as our training set. In total, there are over 77,000 KIC stars observed by LAMOST with g-band SNR 20. Using these training stars, we aim to establish relationships between spectroscopic metallicity and stellar colors taken from either the KIS or Strömgren photometry synthesized from Gaia XP spectra. Generally, the relationships are trained separately for dwarf and giant stars. To achieve better precision, we here train the relationships across five luminosity classes, including giants with (BP -RP) 0 < 1.8, main-sequence stars with (BP -RP) 0 < 1.8, binaries, turnoff stars, and blue stars with (BP -RP) 0 < 0.4, based on their positions in the color-absolute magnitude diagram (see Figure 2). We note that the cuts to select these classes are empirically determined.
To show the sensitivities of KIS U and Strömgren (U -BP) 0 and [m 1 ] ≡ (vb) 0 -(by) 0 change with the BP for typical FGK-type stars.foot_1 Instead of using two-dimensional polynomial functions, as employed by previous studies (e.g., H. Yuan et al. 2015b; Y. Huang et al. 2022), we adopt the random forest machine learning method to model the relations [Fe/H] = f ((U -BP) 0 , (BP -RP) 0 ) and [Fe/H] = f ([m 1 ], (BP -RP) 0 ) separately for the five luminosity classes.
After establishing the metallicity-color relations through training, we applied them to the entire KIC stellar sample to derive their photometric metallicities. In total, we derived photometric metallicities for 179,413 KIC stars using the model trained with KIS photometry and for 189,727 stars using the model trained on Gaia XP spectral-synthesis-generated photometric data. Overall, this yields metallicity estimates for 191,551 stars, representing 95% of the total KIC stellar sample. First, as an internal check, the metallicity estimated from KIS is compared to that derived from the synthesized Strömgren photometry in Figure 4. No offset is found between the estimates from the two relations, with a minimal scatter of only 0.12 dex. This suggests an intrinsic precision of 0.08 dex, assuming equal contributions to the scatter from both relations.
To check the accuracy of the derived photometric metallicity, we crossmatched and compared KIC with results from APOGEE DR17. Overall, the photometric metallicities estimated from KIS and Strömgren colors exhibit excellent agreement with those from APOGEE DR17, with negligible offsets and a very small scatter of around 0.10 dex (see Figures 5 and 6). However, we find that the photometric metallicities are slightly higher than those from APOGEE DR17, likely due to differences in the metallicity scales between LAMOST and APOGEE (Y. Huang et al. 2024). This consistency holds across all stellar types, except for blue stars, where the limited number of KIC-APOGEE common stars prevents a meaningful comparison (see Figures 5, 6, B1, and B2). The precision for main-sequence, turnoff, giant, and binary stars is 0.12, 0.10, 0.10, and 0.18 dex, respectively.
To further evaluate the accuracy of the photometric metallicities, our sample is crossmatched with wide binaries selected from Gaia DR2 (H.-J. Tian et al. 2020), which are expected to have identical metallicities owing to their identical birthplace and formation time. In total, 131 and 144 wide binaries are found to have photometric estimates of metallicity measured from KIS and Strömgren colors, respectively. As shown in Figure 7, the offsets are within 0.02 dex, with a scatter of approximately 0.15 dex, demonstrating the consistency of metallicities between stars in the same binary system.
In the previous subsection, we discussed the methodology for estimating the photometric metallicity for the great majority of the KIC stars. These photometric metallicities will serve as inputs to the training sets for subsequent steps in this work. First, we consider the effective temperature, T eff .
Figure 8 shows the T eff versus (by) color plots for giants and dwarfs (hereafter dwarfs represent main-sequence stars, turnoff stars, and blue stars). In this case, the photometry is synthetically generated from the Gaia XP spectra, the effective temperatures are taken from the LAMOST DR10 spectroscopic data, and the metallicities used to color code the legend are those obtained from the photometric fits described in Section 4.1. From inspection, similar to the color-color map, the stars are on distinct loci and are stratified because of their different metallicities. We obtain estimates of effective temperature with the following relationship:
Again, a random forest regressor machine learning method is adopted to train the T eff -color-[Fe/H] relation. APOGEE DR17 data, we adopted the photometric metallicity estimates from the method with higher accuracy for each type of star. For stars classed as dwarfs, the photometric metallicity estimates trained by KIS and Gaia photometry were adopted. For stars classed as binary or giant, we employed the photometric metallicities trained by synthetic photometry data from the Gaia XP spectra.
We then applied the trained relations to all three types of stars, resulting in effective temperature estimates for a total of 189,727 KIC stars. Figure 9 shows a comparison with the spectroscopic effective temperatures from CKS DR2 (E. A. Petigura et al. 2017Petigura et al. , 2018) ) and APOGEE DR17. For the giant sample, there is a tiny offset of only +4 K and a dispersion of 63 K when analyzing the difference of our photometric T eff minus APOGEE DR17. For the binaries, the offset is +110 K with a scatter of 247 K. For the dwarf sample, we compared our photometric T eff estimates with those from CKS DR2, rather than APOGEE DR17, as the latter's pipeline is primarily designed for giant stars. The results show a small offset of +17 K (this work minus CKS) with a scatter of 114 K.
We now consider surface gravity estimates for the KIC stars based on the photometric color and photometric metallicities. Figure 10 shows the log g-(U -BP) color plots for giant and dwarf stars. In this case, the photometry data are from KIS DR2 and Gaia DR3. The metallicities are from the result of photometric estimates as described in Section 4.1, and the surface gravities used for training are from the LAMOST DR10 spectroscopic data. The U-band photometry contains information about both the Balmer jump (which correlates with surface gravity) and metallicity. With the photometric metallicity fixed, the color (U -BP) 0 can be further used to constrain log g. As seen in the plots, the stars are stratified owing to their different values of log g. Once again, we employed a random forest regressor machine learning method to train the log g-color-[Fe/H] relations for different types of stars, following the same technical treatments as used for effective temperature (see Section 4.2). The total training set consists of 68,063 stars. From Figure 10, we note that, among the dwarf stars, some with low log g values, located at (U -BP) 0 ∼ 0.5 and [Fe/H] ∼ -0.6, do not conform to the overall log g gradient changes in the (U -BP) 0 -(BP -RP) 0 diagram. Upon further examination, we found that these stars are located at the boundary between turnoff stars and subgiant stars. Therefore, the discrepancy for these stars is possibly due to their stellar classification; they are better classified as giants than as dwarfs. We then applied the trained relations to all types of stars, obtaining surface gravity estimates for 189,727 KIC stars. Figure 11 shows a comparison between our method and the spectroscopic surface gravity estimates from CKS DR2 (for dwarf stars) and APOGEE DR17 (for giants and binaries). The result for dwarfs exhibits an offset of -0.01 dex (this work minus CKS DR2) and a dispersion of 0.14 dex. As for the result for giant stars compared with APOGEE DR17, the offset is +0.17 dex (this work minus APOGEE DR17) and the dispersion is 0.19 dex. For binaries, the offset is +0.03 dex (this work minus APOGEE DR17) and the dispersion is 0.09 dex. The moderate offset in surface gravity for giant stars is primarily due to the scale difference between LAMOST (used as the training set) and APOGEE. By comparing over 10,000 common stars between LAMOST and APOGEE, we detected a similar offset of approximately 0.14 dex in surface gravity for giant stars. g g log log phot APOGEE CKS , as a function of G magnitude. The red dashed lines in the bottom panels represent the zero level. The golden lines in the bottom panels represent the 1σ scatter. The color bar to the right of each panel codes the number density of stars in the panel.
Random forest machine learning methods generally do not provide uncertainty estimates for the derived parameters of individual stars. To address this, we estimate the uncertainty of each parameter using the Monte Carlo (MC) method. The MC simulation accounts for both the uncertainties in the input quantities and the mapping relations defined by the random forest regressor.
Using [Fe/H] as an example, we train the color-[Fe/H] relations with the random forest algorithm 1000 times. In each iteration, we sample the photometric errors from KIS/Gaiasynthesized photometry and Gaia data, as well as the uncertainties in extinction. All these errors are assumed to follow a Gaussian distribution. We then apply each relation to all KIC stars, again sampling their photometric and extinction uncertainties under the assumption of Gaussian distributions. For each star, this process yields a distribution of photometric [Fe/H], with the dispersion serving as the uncertainty. Figure 12 shows an example of the final distribution of 1000 simulated photometric [Fe/H] estimates and dispersion. Following the same approach, we derive the uncertainties for photometric T eff and log g.
To validate the reliability of the uncertainty estimates, we compare our results with those from APOGEE DR17. First, we divide the stars into magnitude bins within the specified magnitude range. For each bin, we calculate the dispersion of the differences between our derived [Fe/H] and those from APOGEE DR17, treating this dispersion as the reference uncertainty for that group. Then, we compare these reference uncertainties with the mean uncertainties obtained from our method. As shown in the right panel of Figure 12, the uncertainties from the MC simulations are in excellent agreement with those with APOGEE DR17 uncertainties, with an offset of 0.01 dex and a dispersion of 0.04 dex, confirming the robustness of the uncertainty calculations.
In this section, we derive ages, masses, and radii of the KIC stars from isochrone fitting based on a Bayesian approach. The methods we apply are similar to those used by B. R. Jørgensen & L. Lindegren (2005) and Y. Huang et al. (2022). Essentially, we match the observed parameters with the theoretical results given by stellar evolution models and obtain these estimates from the models.
The observed parameters we employ are (1) the intrinsic color (BP -RP) 0 and G-band absolute magnitude of the KIC stars, corrected by our 3D extinction map; and (2) the stellar metallicities. For metallicity, we combined the spectroscopic metallicities from APOGEE and LAMOST, where available, along with the photometric metallicities obtained by our methods. For metallicities from different sources, we used the following criteria. For a given KIC star, if the APOGEE data have a metallicity that is obtained from a spectrum with SNR larger than 30, this metallicity is chosen. If this is not available and there is an available metallicity obtained from a LAMOST low-resolution spectrum whose g-band SNR is greater than 30, we select that estimate. If neither of these is available, we select the photometric metallicity using the same strategy employed for selecting data for the training set for models used to fit the T eff -color-[Fe/H] and log g-color-[Fe/H] relations, according to the assigned object type of the star.
For the stellar evolution models, we used the PARSEC isochrones (A. Bressan et al. 2012). For the ages and metallicities of the models, we divided the grid over the age ranging from 0.1 to 15.2 Gyr and [M/H] from -2.2 to +0.5. The step of the age grid is 0.2 Gyr for models with ages younger than 1.2 Gyr, and it is 0.5 Gyr for models whose ages are older than 1.2 Gyr. The step in [M/H] is 0.02 dex. This yields a grid of 1.38 × 10 6 stellar model points. The median value of this distribution is marked by a green dashed line, and the estimate by LAMOST is marked by a red dashed line. Right panel: comparison of the mean uncertainties derived from our MC method with those obtained from APOGEE DR17. The "STD" is estimated by calculating the dispersion of the metallicity difference between photometric method and APOGEE DR17 across various magnitude bins. We use 100 bins, evenly spaced between magnitudes 10 and 16. The red dashed line is the one-to-one line.
There remains the problem that the theoretical metallicities given by PARSEC are in the form of 2.
For the Bayesian estimation method, there are three parameters that decide stellar evolution: age τ, mass m, and metallicity Z. Thus, the posterior probability distribution function of the stellar parameters can be described as
where f 0 is the prior distribution of the parameters. In this work, we assumed that age and metallicity [M/H] follow a uniform distribution. For the mass, we assumed that it follows a powerlaw distribution given by E. E. Salpeter (1955):
The prior distributions are independent of each other. is the likelihood function of the parameters, which can be described as
Here χ 2 is defined as
where O represents observational parameters, including the Gband absolute magnitude, intrinsic (BP -RP) 0 color, and metallicity [M/H]. T are the theoretical values of those parameters given by the isochrone model under a specific set of parameters for τ, M, and Z.
With this procedure we can obtain the posterior probability distribution function (pdf), denoted as ( | ) t P M Z , , , for the parameter of interest. The parameters to be determined include stellar mass, age, surface gravity, and radius. For each parameter, we then calculate the pdf for each star using our Bayesian approach. The final estimate of each parameter for a given star is taken as the median of the resulting posterior pdf, with its uncertainty defined as half the difference between the 84th and 16th percentile values of the posterior pdf. The estimated physical parameters are then compared with independent measurements to assess their accuracy.
The resulting log g values are compared with those from APOGEE DR17 and LAMOST DR10. As shown in Figure 13, the values from isochrone fitting are consistent with the spectroscopic measurements. The mean offsets are only -0.03 dex (isochrone fitting minus APOGEE) and -0.06 dex (isochrone fitting minus LAMOST), with small scatters of 0.14 and 0.17 dex, respectively. These comparisons indicate that our log g estimates from isochrone fitting are more accurate than those derived from stellar colors, as described above.
To validate our age and mass estimates, we crossmatched our results with those from J. L. Sanders & P. Das (2018, hereafter SD18), which provides a catalog of stellar ages and g g log log isochrone fitting APOGEE LAMOST , as a function of G magnitude. The red dashed lines in the bottom panels represent the zero level. The golden lines in the bottom panels represents the 1σ scatter. The color bar to the right of each panel codes the number density of stars in the panel.
masses for approximately 3 million stars, derived from spectroscopic data from existing surveys combined with Gaia parallax measurements.
First, the stellar masses are compared with those from SD18 in Figure 14. Overall, the consistency is very good, with a mean offset of -0.06 M e (our values minus those of SD18) and a scatter of 0.10 M e . Note that giant stars are excluded from this comparison, as their mass estimates are highly sensitive to the uncertain parameter of mass loss, for which we adopted a constant value of η Reimers = 0.2, following the recommendation in PARSEC. We will later assess the masses of giant stars using asteroseismic estimates. Second, we compare our stellar ages with those from SD18, as shown in Figure 14. Only turnoff stars are included in this comparison, as their ages can be reliably constrained through isochrone fitting. The relative age ratio (τ ISO -τ SD18 )/(τ ISO ) shows a mean offset of +10%, with a dispersion around 19%. To further evaluate the precision of isochrone-derived ages, we selected members of open clusters using the method described in Section 3. Figure 15 shows the age distributions for member stars of four open clusters in the Kepler field. The median values of these distributions are close to those reported by other independent studies (L. N. Brewer et al. 2016;E. L. Sandquist et al. 2016;D. Bossini et al. 2019;K. Brogaard et al. 2021; see Table A1).
As previously described, CKS is a high-resolution spectroscopic survey designed to determine the properties of exoplanets and their host stars in the Kepler field. Observations conducted with the Keck telescope have provided atmospheric parameters and other characteristics for approximately 1700 exoplanet-host stars. Using the Keck spectra, E. A. Petigura et al. (2017Petigura et al. ( , 2018) ) derived the stellar atmospheric parameters (effective temperature, surface gravity, and metallicity) for the exoplanet-host stars. Based on these parameters, J. A. Johnson et al. (2017) further determined the masses and radii of these stars.
As shown in Figure 16, the isochrone-derived log g is in excellent agreement with that of CKS, with no offset and a minimal scatter of 0.12 dex. Both stellar mass and radius from isochrone fitting are also in very close agreement with CKS results. The offsets are negligible, with no offset for radius and only -0.03 M e (our values minus those of CKS) for mass. The scatter is just 0.07 M e for mass and 0.05 R e for radius.
Asteroseismology is an important technique in the field of stellar parameter measurement, as it enables precise estimates of mass, radius, and surface gravity. Here we compare our results with those from the Apache Point Observatory Galactic Evolution Experiment and the Kepler Asteroseismic Science Consortium (APOKASC; M. H. Pinsonneault et al. 2014Pinsonneault et al. , 2018)). The APOKASC catalog provides stellar parameters derived by combining asteroseismic data (such as frequency spacing Δμ and maximum oscillation frequency m max , from which mass and radius can be estimated) from the Kepler Asteroseismic Science Consortium (KASC) with spectroscopic data (such as T eff , [Fe/H]) from APOGEE.
We compared our isochrone-derived log g, mass, and radius with those from APOKASC. As shown in Figure 17, all parameters estimated from isochrone fitting exhibit good agreement with APOKASC results. For log g, the mean offset is only -0.01 dex (our result minus APOKASC), with a dispersion of 0.11 dex. For stellar radius, there is an offset of 0.01 R e , and the scatter is only 0.73 R e . For stellar mass, a slight offset of -0.05M e (our result minus APOKASC) is observed, with a moderate scatter of 0.14 M e . This offset and dispersion are at least partly due to uncertainties in the massloss parameter for red giant stars.
Using the methods described above, we have obtained physical parameter estimates for around 190,000 KIC stars. However, around 10,000 KIC stars still lack these estimates. An examination of the H-R diagram (see Figure 18) reveals that most of the stars without parameter estimates are cool dwarfs and giants with (BP -RP) 0 1.8, as well as hot subdwarfs and white dwarfs. These stars were excluded from the training process owing to the challenges in obtaining reliable parameter estimates for them. Additionally, a small number of mainsequence and turnoff stars lack parameter estimates because they do not have Gaia XP spectra or KIS photometry observations.
To obtain parameters for as many KIC stars as possible, we trained the photometric parameter relations for M-type stars using a method similar to that described in Section 4. Recently, LAMOST DR10 released stellar atmospheric parameters for both M dwarf and giant stars using the LASPM pipeline (B. Du et al. 2021). We crossmatched our sample of cool stars with (BP -RP) 0 1.8 against the LAMOST M dwarf and giant catalog, finding over 1500 stars (582 dwarfs and 981 giants). Using the same training methods described in Section 4, we derived relationships between atmospheric parameters and synthesized Strömgren photometry for both M dwarfs and giants. These relationships were then applied to over 5200 cool stars to estimate their missing atmospheric parameters. To assess the precision of our estimates, we crossmatched these stars with APOGEE DR17, finding around 100 M dwarfs and 1000 M giants in common. The comparisons indicate moderate offsets across all atmospheric parameters, with typical values around 0.10 dex for [M/H], 120 K for T eff , and 0.10 dex for log g. The dispersions are 0.20 dex for both log g and [M/H] and relatively low for T eff , at about 60 K. Due to the limited accuracy of the parameters (large offsets and dispersion), we do not proceed with isochrone-based estimates of physical parameters derived from these stellar atmospheric parameters.
In the final tables, we present data from two separate stellar catalogs: one for AFGK stars and another for M-type stars. A detailed description of the catalogs is provided in Table C1. The updated KIC parameter catalogs are publicly available on Zenodo at doi:10.5281/zenodo.14546166.
If one wishes to use the data from these tables, please take note of the following points:
1. Parameters of M-type Stars. Due to the relatively small size of the training set and limited data available for comparison and verification, the reliability of M-type star parameters is lower compared to that of AFGK stars. Caution is advised when using these values for further analysis. 2. Stellar Classification. The classification of stellar types on the H-R diagram in this paper is based on empirical methods. Some mixtures may occur at the classification boundaries, particularly between main-sequence stars and binary stars. 3. Isochrone Fitting. While the isochrone-fitting method provides reliable mass and age estimates for turnoff stars and subgiant stars, there is greater uncertainty for other stellar types. These uncertainties should be carefully taken into account during analysis. 4. Surface Gravity. In this work, stellar surface gravity was estimated using both stellar colors and isochrone fitting.
Based on various checks, the accuracy of the isochronefitting method is significantly better than that derived from stellar colors. Therefore, when surface gravity estimates are available from both methods, we recommend using the values obtained from isochrone fitting.
In this work, we have made three main improvements to the KIC: (1) established a high-precision 3D extinction map of the Kepler field, (2) obtained atmospheric parameter estimates for 97% of KIC stars using photometric data from KIS and Gaia XP, and (3) derived stellar mass, radius, surface gravity, and age estimates for these KIC stars based on their atmospheric parameters and stellar evolution models. Details of these improvements are outlined below.
1. First, we determined the extinction for stars in the Kepler field using the SP method and constructed a 3D extinction map for this region. By analyzing members of four well-known open clusters within the Kepler field, we found that this new 3D extinction map provides more accurate reddening values than those from the commonly used map by G. M. Green et al. (2019). 2. By training a relationship between the photometric colors from KIS DR2, the ultra-wide-band photometric colors from Gaia DR3, the photometric colors synthetically generated from the Gaia XP spectra, and the spectral stellar parameters from LAMOST DR10, we obtained atmospheric parameter estimates for about 195,000 stars, accounting for 97% of the total number of the KIC stars. We achieved uncertainties of 0.12 dex on [Fe/H], 100 K on T eff , and 0.2 dex on log g. 3. Using the PARSEC stellar evolution model, we estimated the masses, radii, surface gravities, and ages of KIC stars based on their atmospheric parameters and photometric data. We then compared our mass and age estimates with values from the literature, especially stars with mass, radius, and surface gravity measurements from asteroseismology data. These comparisons indicate that our estimates achieve precisions of 0.07 M e in mass, 0.05 R e in radius, and 0.12 dex in surface gravity for dwarf stars and 0.14 M e in mass, 0.73 R e in radius, and 0.11 dex in surface gravity for giant stars.
We summarize the methodology for each parameter estimate in Table 3. These results are expected to be valuable for future research on exoplanet-host stars, exoplanet habitability, and asteroseismology studies.
The Astrophysical Journal Supplement Series, 277:6 (20pp), 2025 March Zhang et al.
Here the reddening coefficients of the U and Strömgren bands are all taken from http://svo2.cab.inta-csic.es/theory/fps/.