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The empirical relations between rotation period, chromospheric activity, and age can be used to estimate stellar age. To calibrate these relations, we present a catalog, including the masses and ages of 52,321 FGK dwarfs, 47,489 chromospheric activity index $logR^{+}_{HK}$, 6,077 rotation period $P_{rot}$ and variability amplitude $S_{ph}$, based on data from LAMOST DR7, Kepler and Gaia DR3. We find a pronounced correlation among $P_{rot}$, age, and [Fe/H] throughout the main-sequence phase for F dwarfs. However, the decrease of $logR^{+}_{HK}$ over time is not significant except for those with [Fe/H] $<$ $-$0.1. For G dwarfs, both $P_{rot}$ and $logR^{+}_{HK}$ are reliable age probes in the ranges $\sim$ 2-11 Gyr and $\sim$ 2-13 Gyr, respectively. K dwarfs exhibit a prominent decrease in $logR^{+}_{HK}$ within the age range of $\sim$ 3-13 Gyr when the relation of $P_{rot}-\tau$ is invalid. These relations are very important for promptly estimating the age of a vast number of stars, thus serving as a powerful tool in advancing the fields of exoplanet properties, stellar evolution, and Galactic-archaeology.

Based on all 2-minute cadence $TESS$ light curves from Sector 1 to 60, we provide a catalog of 8,651 solar-like oscillators, including frequency at maximum power ($\nu_{\rm max}$, with its median precision, $\sigma$=5.39\%), large frequency separation ($\Delta\nu$, $\sigma$=6.22\%), seismically derived masses, radii, and surface gravity. In this sample, we have detected 2,173 new oscillators and added 4,373 new $\Delta\nu$ measurements. Our seismic parameters are consistent with those from $Kepler$, $K2$, and previous $TESS$ data. The median fractional residual in $\nu_{\rm max}$ is $1.63\%$ with a scatter of $14.75\%$, and in $\Delta\nu$ it is $0.11\%$ with a scatter of $10.76\%$. We have detected 476 solar-like oscillators with $\nu_{\rm max}$ exceeding the $Nyquist$ frequency of $Kepler$ long-cadence data during the evolutionary phases of sub-giant and the base of the red-giant branch, which provide a valuable resource for understanding angular momentum transport.

We present the discoveries of two giant planets orbiting the red giant branch (RGB) star HD 112570 and the red clump (RC) star HD 154391, based on the radial velocity (RV) measurements from Xinglong station and Okayama Astrophysical Observatory (OAO). Spectroscopic and asteroseismic analyses suggest that HD 112570 has a mass of $1.15\pm0.12\,M_{\odot}$, a radius of $9.85\pm0.23\,R_{\odot}$, a metallicity [Fe/H] of $-0.46\pm0.1$ and a ${\rm log}\,g$ of $2.47\pm0.1$. With the joint analysis of RV and Hipparcos-Gaia astrometry, we obtain a dynamical mass of $M_{\rm p}={3.42}_{-0.84}^{+1.4}\ M_{\rm Jup}$, a period of $P={2615}_{-77}^{+85}$ days and a moderate eccentricity of $e={0.20}_{-0.14}^{+0.16}$ for the Jovian planet HD 112570 b. For HD 154391, it has a mass of $2.07\pm0.03\,M_{\odot}$, a radius of $8.56\pm0.05\,R_{\odot}$, a metallicity [Fe/H] of $0.07\pm0.1$ and a ${\rm log}\,g$ of $2.86\pm0.1$. The super-Jupiter HD 154391 b has a mass of $M_{\rm p}={9.1}_{-1.9}^{+2.8}\ M_{\rm Jup}$, a period of $P={5163}_{-57}^{+60}$ days and an eccentricity of $e={0.20}_{-0.04}^{+0.04}$. We found HD 154391 b has one of the longest orbital period among those ever discovered orbiting evolved stars, which may provide a valuable case in our understanding of planetary formation at wider orbits. Moreover, while a mass gap at $4\,M_{\rm Jup}$ seems to be present in the population of giant stars, there appears to be no significant differences in the distribution of metallicity among giant planets with masses above or below this threshold. Finally, The origin of the abnormal accumulation near 2 au for planets around large evolved stars ($R_{\star}>21\,R_{\odot}$), remains unclear., Comment: 26 pages, 18 figures, 8 tables, Accepted for publication in The Astronomical Journal

Using data from the Gaia Data Release 3 (Gaia DR3) and Kepler/K2, we present a catalog of 16 open clusters with ages ranging from 4 to 4000 Myr, which provides detailed information on membership, binary systems, and rotation. We assess the memberships in 5D phase space, and estimate the basic parameters of each cluster. Among the 20,160 members, there are 4,381 stars identified as binary candidates and 49 stars as blue straggler stars. The fraction of binaries vary in each cluster, and the range between 9% to 44%. We obtain the rotation periods of 5,467 members, of which 4,304 are determined in this work. To establish a benchmark for the rotation-age-color relation, we construct color-period diagrams. We find that the rotational features of binaries are similar to that of single stars, while features for binaries are more scattered in the rotation period. Moreover, the morphology of the color-period relationship is already established for Upper Scorpius at the age of 19 Myr, and some stars of varying spectral types (i.e. FG-, K-, and M-type) show different spin-down rates after the age of ~110 Myr. By incorporating the effects of stalled spin-down into our analysis, we develop an empirical rotation-age-color relation, which is valid with ages between 700 - 4000 Myr and colors corresponding to a range of 0.5 < (G_BP-G_RP)0 < 2.5 mag., Comment: 21 pages, 17 figures, accepted for publication in ApJS

Varying oxygen abundance could impact the modeling-inferred ages. This work aims to estimate the ages of dwarfs considering observed oxygen abundance. To characterize 67,503 LAMOST and 4,006 GALAH FGK-type dwarf stars, we construct a grid of stellar models which take into account oxygen abundance as an independent model input. Compared with ages determined with commonly-used $\alpha$-enhanced models, we find a difference of $\sim$9% on average when the observed oxygen abundance is considered. The age differences between the two types of models are correlated to [Fe/H] and [O/$\alpha$], and they are relatively significant on stars with [Fe/H] $\lesssim$ -0.6 dex. Generally, varying 0.2 dex in [O/$\alpha$] will alter the age estimates of metal-rich (-0.2 $<$ [Fe/H] $<$ 0.2) stars by $\sim$10%, and relatively metal-poor (-1 $<$ [Fe/H] $<$ -0.2) stars by $\sim$15%. Of the low-O stars with [Fe/H] $<$ 0.1 dex and [O/$\alpha$] $\sim$ -0.2 dex, many have fractional age differences of $\geq$ 10%, and even reach up to 27%. The fractional age difference of high-O stars with [O/$\alpha$] $\sim$ 0.4 dex reaches up to -33% to -42% at [Fe/H] $\lesssim$ -0.6 dex. We also analyze the chemical properties of these stars. We find a decreasing trend of [Fe/H] with age from 7.5-9 Gyr to 5-6.5 Gyr for the stars from the LAMOST and GALAH. The [O/Fe] of these stars increases with decreasing age from 7.5-9 Gyr to 3-4 Gyr, indicating that the younger population is more O-rich., Comment: 18 pages, 12 figures, accepted for publication in ApJS