Search

The existence of high-$\alpha$ stars with inferred ages < 6 Gyr has been confirmed recently with large spectroscopic and photometric surveys. However, stellar mergers or binary interactions can induce properties associated with young ages, such as high mass, rapid rotation, or high activity, even in old populations. Literature studies have confirmed that at least some of these apparently young stars are old merger products. However, none have ruled out the possibility of genuinely young high-$\alpha$ stars. Because cool GKM dwarfs spin down, rapid rotation can be used to indicate youth. In this paper, we provide strong evidence that truly young high-$\alpha$ stars exist by studying high-$\alpha$ rotators in the Kepler and K2 field with abundance measurements from GALAH and APOGEE. After excluding close binaries using radial velocity (RV) measurements from Gaia DR3 and multi-epoch RVs from APOGEE, we find a total of 70 high-$\alpha$ rapid rotators with periods ~10-30 days, 29 of which have lithium measurements from GALAH, indicating that they have not gone through past mass transfer or stellar merger events. We identify 10 young high-$\alpha$ candidates with no signs of merger-induced mixing or close companions. One clear example is a G dwarf with a measurable rotation and an age of 1.98$^{+0.12}_{-0.28}$ Gyr that is likely a single star with multiple RV measurements from APOGEE, has significant lithium detection from GALAH (A(Li) = 1.79), and has no signs of planet engulfment., Comment: 21 pages, 13 figures, submitted to AJ

The solar-type subgiant $\beta$ Hyi has long been studied as an old analog of the Sun. Although the rotation period has never been measured directly, it was estimated to be near 27 days. As a southern hemisphere target it was not monitored by long-term stellar activity surveys, but archival International Ultraviolet Explorer data revealed a 12 year activity cycle. Previous ground-based asteroseismology suggested that the star is slightly more massive and substantially larger and older than the Sun, so the similarity of both the rotation rate and the activity cycle period to solar values is perplexing. We use two months of precise time-series photometry from the Transiting Exoplanet Survey Satellite (TESS) to detect solar-like oscillations in $\beta$ Hyi and determine the fundamental stellar properties from asteroseismic modeling. We also obtain a direct measurement of the rotation period, which was previously estimated from an ultraviolet activity-rotation relation. We then use rotational evolution modeling to predict the rotation period expected from either standard spin-down or weakened magnetic braking (WMB). We conclude that the rotation period of $\beta$ Hyi is consistent with WMB, and that changes in stellar structure on the subgiant branch can reinvigorate the large-scale dynamo and briefly sustain magnetic activity cycles. Our results support the existence of a "born-again" dynamo in evolved subgiants -- previously suggested to explain the cycle in 94 Aqr Aa -- which can best be understood within the WMB scenario., Comment: ApJ accepted. 8 pages including 6 figures and 2 tables

Characterizing outer companions to hot Jupiters plays a crucial role in deciphering their origins. We present the discovery of a long-period giant planet, HD 118203 c ($m_{c}=11.79^{+0.69}_{-0.63}\ \mathrm{M_{J}}$, $a_{c}=6.28^{+0.10}_{-0.11}$ AU) exterior to a close-in eccentric hot Jupiter HD 118203 b ($P_{b}=6.135\ \mathrm{days}$, $m_{b}=2.14\pm{0.12}\ \mathrm{M_{J}}$, $r_{b}=1.14\pm{0.029}\ \mathrm{R_{J}}$, $e_{b}=0.31\pm{0.007}$) based on twenty-year radial velocities. Using Rossiter-McLaughlin (RM) observations from the Keck Planet Finder (KPF), we measured a low sky-projected spin-orbit angle $\lambda_{b}=-11^{\circ}.7^{+7.6}_{-10.0}$ for HD 118203 b and detected stellar oscillations in the host star, confirming its evolved status. Combining the RM observation with the stellar inclination measurement, we constrained the true spin-orbit angle of HD 118203 b as $\Psi_{b}<33^{\circ}.5\ (2\sigma)$, indicating the orbit normal of the hot Jupiter nearly aligned with the stellar spin axis. Furthermore, by combining radial velocities and Hipparcos-Gaia astrometric acceleration, we constrained the line-of-sight mutual inclination between the hot Jupiter and the outer planet to be $9^{\circ}.8^{+16.2}_{-9.3}$ at $2\sigma$ level. HD 118203 is one of first hot Jupiter systems where both the true spin-orbit angle of the hot Jupiter and the mutual inclination between inner and outer planets have been determined. Our results are consistent with a system-wide alignment, with low mutual inclinations between the outer giant planet, the inner hot Jupiter, and the host star. This alignment, along with the moderate eccentricity of HD 118203 c, implies that the system may have undergone coplanar high-eccentricity tidal migration. Under this framework, our dynamical analysis suggests an initial semi-major axis of 0.3 to 3.2 AU for the proto-hot Jupiter., Comment: 30 pages, 12 figures, accepted by AJ

The TESS mission delivers time-series photometry for millions of stars across the sky, offering a probe into stellar astrophysics, including rotation, on a population scale. However, light curve systematics related to the satellite's 13.7-day orbit have prevented stellar rotation searches for periods longer than 13 days, putting the majority of stars beyond reach. Machine learning methods have the ability to identify systematics and recover robust signals, enabling us to recover rotation periods up to 35 days for GK dwarfs and 80 days for M dwarfs. We present a catalog of 7245 rotation periods for cool dwarfs in the Southern Continuous Viewing Zone, estimated using convolutional neural networks. We find evidence for structure in the period distribution consistent with prior Kepler and K2 results, including a gap in 10--20-day cool star periods thought to arise from a change in stellar spin-down or activity. Using a combination of spectroscopic and gyrochronologic constraints, we fit stellar evolution models to estimate masses and ages for stars with rotation periods. We find strong correlations between the detectability of rotation in TESS and the effective temperature, age, and metallicity of the stars. Finally, we investigate the relationships between rotation and newly obtained spot filling fractions estimated from APOGEE spectra. Field star spot filling fractions are elevated in the same temperature and period regime where open clusters' magnetic braking stalls, lending support to an internal shear mechanism that can produce both phenomena., Comment: 36 pages, 22 figures, 7 tables, 3 appendices. Accepted to ApJ. Machine readable versions of Tables 5 and 6 included

When main-sequence stars expand into red giants, they are expected to engulf close-in planets. Until now, the absence of planets with short orbital periods around post-expansion, core-helium-burning red giants has been interpreted as evidence that short-period planets around Sun-like stars do not survive the giant expansion phase of their host stars. Here we present the discovery that the giant planet 8 Ursae Minoris b orbits a core-helium-burning red giant. At a distance of only 0.5 au from its host star, the planet would have been engulfed by its host star, which is predicted by standard single-star evolution to have previously expanded to a radius of 0.7 au. Given the brief lifetime of helium-burning giants, the nearly circular orbit of the planet is challenging to reconcile with scenarios in which the planet survives by having a distant orbit initially. Instead, the planet may have avoided engulfment through a stellar merger that either altered the evolution of the host star or produced 8 Ursae Minoris b as a second-generation planet. This system shows that core-helium-burning red giants can harbour close planets and provides evidence for the role of non-canonical stellar evolution in the extended survival of late-stage exoplanetary systems., Comment: Published in Nature on 28 June 2023. In press

The ages of solar-like stars have been at the center of many studies such as exoplanet characterization or Galactic-archaeology. While ages are usually computed from stellar evolution models, relations linking ages to other stellar properties, such as rotation and magnetic activity, have been investigated. With the large catalog of 55,232 rotation periods, $P_{\rm rot}$, and photometric magnetic activity index, $S_{\rm ph}$ from Kepler data, we have the opportunity to look for such magneto-gyro-chronology relations. Stellar ages are obtained with two stellar evolution codes that include treatment of angular momentum evolution, hence using $P_{\rm rot}$ as input in addition to classical atmospheric parameters. We explore two different ways of predicting stellar ages on three subsamples with spectroscopic observations: solar analogs, late-F and G dwarfs, and K dwarfs. We first perform a Bayesian analysis to derive relations between $S_{\rm ph}$ and ages between 1 and 5 Gyr, and other stellar properties. For late-F and G dwarfs, and K dwarfs, the multivariate regression favors the model with $P_{\rm rot}$ and $S_{\rm ph}$ with median differences of 0.1%.and 0.2% respectively. We also apply Machine Learning techniques with a Random Forest algorithm to predict ages up to 14 Gyr with the same set of input parameters. For late-F, G and K dwarfs together, predicted ages are on average within 5.3% of the model ages and improve to 3.1% when including $P_{\rm rot}$. These are very promising results for a quick age estimation for solar-like stars with photometric observations, especially with current and future space missions., Comment: 29 pages, 13 figures, including 8 pages of Appendix. Accepted for publication in ApJ

Despite multiple previous searches, no transiting planets have yet been identified within a globular cluster. This is believed to be due to a combination of factors: the low metallicities of most globular clusters suggests that there is significantly less planet-forming material per star in most globular clusters relative to the solar neighborhood, the high likelihood of dynamical interactions can also disrupt planetary orbits, and the data available for globular clusters is limited. However, transiting planets have been identified in open clusters, indicating that there may be planets in more massive clusters that have simply gone undetected, or that more massive clusters inhibit planet formation. Less than two degrees away from the nominal Galactic Bulge Time Domain Survey footprint, two globular clusters, NGC 6522 and NGC 6528, can be simultaneously observed by the Roman telescope during the Galactic Bulge Time Domain Survey. These clusters are comparable in mass (1-2 x 10$^5$ solar masses) and age (12 Gyr), but feature drastically different average metallicities: NGC 6522 has an average [Fe/H] $\sim$ -1.3, while NGC 6528 has an average [Fe/H] $\sim$ -0.1. If no transiting planets are detected in one season of time domain observations of these clusters, this would indicate a difference in planet occurrence among field stars and globular clusters at >3-$\sigma$ significance even after accounting for metallicity, which could be enhanced to >5-$\sigma$ significance with similar observations of another nearby field hosting a metal-rich globular cluster. Additionally, time domain observations of NGC 6522 and NGC 6528 will detect variable stars in both clusters, testing the connection between stellar variability and binary fraction to metallicity and cluster environment, as well as testing the dependence of exoplanet yields on stellar density and distance from the Galactic midplane., Comment: 7 pages, 3 figures

Radial velocity (RV) measurements of transiting multiplanet systems allow us to understand the densities and compositions of planets unlike those in the Solar System. Kepler-102, which consists of 5 tightly packed transiting planets, is a particularly interesting system since it includes a super-Earth (Kepler-102d) and a sub-Neptune-sized planet (Kepler-102e) for which masses can be measured using radial velocities. Previous work found a high density for Kepler-102d, suggesting a composition similar to that of Mercury, while Kepler-102e was found to have a density typical of sub-Neptune size planets; however, Kepler-102 is an active star, which can interfere with RV mass measurements. To better measure the mass of these two planets, we obtained 111 new RVs using Keck/HIRES and TNG/HARPS-N and modeled Kepler-102's activity using quasi-periodic Gaussian Process Regression. For Kepler-102d, we report a mass upper limit of M$_{d} < $5.3 M$_{\oplus}$ [95\% confidence], a best-fit mass of M$_{d}$=2.5 $\pm$ 1.4 M$_{\oplus}$, and a density of $\rho_{d}$=5.6 $\pm$ 3.2 g/cm$^{3}$ which is consistent with a rocky composition similar in density to the Earth. For Kepler-102e we report a mass of M$_{e}$=4.7 $\pm$ 1.7 M$_{\oplus}$ and a density of $\rho_{e}$=1.8 $\pm$ 0.7 g/cm$^{3}$. These measurements suggest that Kepler-102e has a rocky core with a thick gaseous envelope comprising 2-4% of the planet mass and 16-50% of its radius. Our study is yet another demonstration that accounting for stellar activity in stars with clear rotation signals can yield more accurate planet masses, enabling a more realistic interpretation of planet interiors., Comment: Accepted to AJ 11/08/2022

Current spectroscopic surveys are producing large catalogs of chemical abundances for stars of all types. The yttrium to magnesium ratio, [Y/Mg], has emerged as a candidate age indicator for solar twins in the local stellar neighborhood. However, it is unclear whether it is a viable age diagnostic for more diverse stellar types, so we investigate [Y/Mg] as an age indicator for the FGK-type planet host stars observed by $Kepler$. We find that the [Y/Mg] "Clock" is most precise for solar twins, with a [Y/Mg]/Age slope of $m$ = $-$0.0370 $\pm$ 0.0071 dex/Gyr and $\sigma_{\mathrm{Age}}$ = 2.6 Gyr. We attribute the lower precision compared to literature results to non-solar twins contaminating our solar twin sample and recommend a 1.5 Gyr systematic uncertainty for stellar ages derived with any [Y/Mg]-Age relation. We also analyzed the [Y/Mg] Clock as a function of $T_{\mathrm{eff}}$, $\log g$, and metallicity individually and find no strong trends, but compute statistically significant [Y/Mg]-Age relations for subsamples defined by ranges in $T_{\mathrm{eff}}$, $\log g$, and metallicity. Finally, we compare [Y/Mg] and rotation ages and find statistically similar trends as for isochrone ages, although we find that rotation ages perform better for GK dwarfs while isochrones perform better for FG subgiants. We conclude that the [Y/Mg] Clock is most precise for solar twins and analogs but is also a useful age diagnostic for FGK stars., Comment: 18 pages, 13 figures, 2 tables. Accepted by ApJ

Multi-planet systems are valuable arenas for investigating exoplanet architectures and comparing planetary siblings. TOI-1246 is one such system, with a moderately bright K dwarf ($\rm{V=11.6,~K=9.9}$) and four transiting sub-Neptunes identified by TESS with orbital periods of $4.31~\rm{d},~5.90~\rm{d},~18.66~\rm{d}$, and $~37.92~\rm{d}$. We collected 130 radial velocity observations with Keck/HIRES and TNG/HARPS-N to measure planet masses. We refit the 14 sectors of TESS photometry to refine planet radii ($\rm{2.97 \pm 0.06~R_\oplus},\rm{2.47 \pm 0.08~R_\oplus}, \rm{3.46 \pm 0.09~R_\oplus}$, $\rm{3.72 \pm 0.16~R_\oplus}$), and confirm the four planets. We find that TOI-1246 e is substantially more massive than the three inner planets ($\rm{8.1 \pm 1.1 M_\oplus}$, $\rm{8.8 \pm 1.2 M_\oplus}$, $\rm{5.3 \pm 1.7 M_\oplus}$, $\rm{14.8 \pm 2.3 M_\oplus}$). The two outer planets, TOI-1246 d and TOI-1246 e, lie near to the 2:1 resonance ($\rm{P_{e}/P_{d}=2.03}$) and exhibit transit timing variations. TOI-1246 is one of the brightest four-planet systems, making it amenable for continued observations. It is one of only six systems with measured masses and radii for all four transiting planets. The planet densities range from $\rm{0.70 \pm 0.24}$ to $3.21 \pm 0.44 \rm{g/cm^3}$, implying a range of bulk and atmospheric compositions. We also report a fifth planet candidate found in the RV data with a minimum mass of 25.6 $\pm$ 3.6 $\rm{M_\oplus}$. This planet candidate is exterior to TOI-1246 e with a candidate period of 93.8 d, and we discuss the implications if it is confirmed to be planetary in nature., Comment: Accepted at The Astronomical Journal; 33 pages, 10 figures

Using sedimentary and eclipse-based measurements of the lunar recession velocity, we derive a new local-Universe measurement of the Hubble constant ($H_0$) from the recession rate of Earth's Moon. Taking into account the effects of tides, we find a value of $H_{0}$ = 63.01 $\pm$ 1.79 km s$^{-1}$ Mpc$^{-1}$, which is in approximate agreement with the Planck space mission's measurement using the cosmic microwave background (CMB) and base $\Lambda$CDM. Our new measurement represents the first ever model-independent, single-step measurement of the Universe's current expansion rate. This is also the first major local Universe measurement of $H_0$ which is below the measurement from Planck. Importantly, it is robust to the systematic errors that may be present in other $H_0$ measurements using other cosmological probes such as type Ia supernovae, baryon acoustic oscillations, or lensed quasars. Our work provides key evidence towards the notion that the existing Hubble tension may indeed be a result of systematic uncertainties in the local distance ladder., Comment: Main result can be seen in Figure 1

Stellar rotation is a complex function of mass, metallicity, and age and can be altered by binarity. To understand the importance of these parameters in main sequence stars, we have assembled a sample of observations that spans a range of these parameters using a combination of observations from The Transiting Exoplanet Survey Satellite (TESS) and the Kepler Space Telescope. We find that while we can measure rotation periods and identify other classes of stellar variability (e.g., pulsations) from TESS lightcurves, instrument systematics prevent the detection of rotation signals longer than the TESS orbital period of 13.7 days. Due to this detection limit, we also utilize rotation periods constrained using rotational velocities measured by the APOGEE spectroscopic survey and radii estimated using the Gaia mission for both TESS and Kepler stars. From these rotation periods, we 1) find we can track rotational evolution along discrete mass tracks as a function of stellar age, 2) find we are unable to recover trends between rotation and metallicity that were observed by previous studies, and 3) note that our sample reveals that wide binary companions do not affect rotation, while close binary companions cause stars to exhibit more rapid rotation than single stars., Comment: 19 pages, 13 figures, Accepted for publication in the Astrophysical Journal

We present the discovery of two nearly identically-sized sub-Neptune transiting planets orbiting HD 63935, a bright ($V=8.6$ mag), sun-like ($T_{eff}=5560K$) star at 49 pc. TESS identified the first planet, HD 63935 b (TOI-509.01), in Sectors 7 and 34. We identified the second signal (HD 63935 c) in Keck HIRES and Lick APF radial velocity data as part of our followup campaign. It was subsequently confirmed with TESS photometry in Sector 34 as TOI-509.02. Our analysis of the photometric and radial velocity data yields a robust detection of both planets with periods of $9.0600 \pm 0.007$ and $21.40 \pm 0.0019$ days, radii of $2.99 \pm 0.14$ and $2.90 \pm 0.13$ $R_\oplus$, and masses of $10.8 \pm 1.8$ and $11.1 \pm 2.4$ $M_\oplus$. We calculate densities for planets b and c consistent with a few percent of the planet mass in hydrogen/helium envelopes. We also describe our survey's efforts to choose the best targets for JWST atmospheric followup. These efforts suggest that HD 63935 b will have the most clearly visible atmosphere of its class. It is the best target for transmission spectroscopy (ranked by Transmission Spectroscopy Metric, a proxy for atmospheric observability) in the so-far uncharacterized parameter space comprising sub-Neptune-sized (2.6 $R_\oplus$ $<$ $R_p$ $<$ 4 $R_\oplus$), moderately-irradiated (100 $F_\oplus$ $<$ $F_p$ $<$ 1000 $F_\oplus$) planets around G-stars. Planet c is also a viable target for transmission spectroscopy, and given the indistinguishable masses and radii of the two planets, the system serves as a natural laboratory for examining the processes that shape the evolution of sub-Neptune planets., Comment: 22 pages, 12 figures, published in AJ

We present the identification of the COCONUTS-2 system, composed of the M3 dwarf L 34-26 and the T9 dwarf WISEPA J075108.79$-$763449.6. Given their common proper motions and parallaxes, these two field objects constitute a physically bound pair with a projected separation of 594$"$ (6471 au). The primary star COCONUTS-2A has strong stellar activity (H$\alpha$, X-ray, and UV emission) and is rapidly rotating ($P_{\rm rot} = 2.83$ days), from which we estimate an age of 150-800 Myr. Comparing equatorial rotational velocity derived from the TESS light curve to spectroscopic $v\sin{i}$, we find COCONUTS-2A has a nearly edge-on inclination. The wide exoplanet COCONUTS-2b has an effective temperature of $T_{\rm eff}=434 \pm 9$ K, a surface gravity of $\log{g} = 4.11^{+0.11}_{-0.18}$ dex, and a mass of $M=6.3^{+1.5}_{-1.9}$ $M_{\rm Jup}$ based on hot-start evolutionary models, leading to a $0.016^{+0.004}_{-0.005}$ mass ratio for the COCONUTS-2 system. COCONUTS-2b is the second coldest (after WD 0806$-$661B) and the second widest (after TYC 9486-927-1 b) exoplanet imaged to date. Comparison of COCONUTS-2b's infrared photometry with ultracool model atmospheres suggests the presence of both condensate clouds and non-equilibrium chemistry in its photosphere. Similar to 51 Eri b, COCONUTS-2b has a sufficiently low luminosity ($\log{(L_{\rm bol}/L_{\odot})} = -6.384 \pm 0.028$ dex) to be consistent with the cold-start process that may form gas-giant (exo)planets, though its large separation means such formation would not have occurred in situ. Finally, at a distance of 10.9 pc, COCONUTS-2b is the nearest imaged exoplanet to Earth known to date., Comment: Accepted for publication in ApJ Letters

We used a convolutional neural network to infer stellar rotation periods from a set of synthetic light curves simulated with realistic spot evolution patterns. We convolved these simulated light curves with real TESS light curves containing minimal intrinsic astrophysical variability to allow the network to learn TESS systematics and estimate rotation periods despite them. In addition to periods, we predict uncertainties via heteroskedastic regression to estimate the credibility of the period predictions. In the most credible half of the test data, we recover 10%-accurate periods for 46% of the targets, and 20%-accurate periods for 69% of the targets. Using our trained network, we successfully recover periods of real stars with literature rotation measurements, even past the 13.7-day limit generally encountered by TESS rotation searches using conventional period-finding techniques. Our method also demonstrates resistance to half-period aliases. We present the neural network and simulated training data, and introduce the software butterpy used to synthesize the light curves using realistic star spot evolution., Comment: 18 pages, 7 figures, 3 tables. Submitted to AAS Journals. For a brief video explaining this paper, see https://youtu.be/JNmMzHshyY0 . The code to simulate star spot evolution and light curves, butterpy, is available at https://github.com/zclaytor/butterpy

Asteroseismology of bright stars has become increasingly important as a method to determine fundamental properties (in particular ages) of stars. The Kepler Space Telescope initiated a revolution by detecting oscillations in more than 500 main-sequence and subgiant stars. However, most Kepler stars are faint, and therefore have limited constraints from independent methods such as long-baseline interferometry. Here, we present the discovery of solar-like oscillations in $\alpha$ Men A, a naked-eye (V=5.1) G7 dwarf in TESS's Southern Continuous Viewing Zone. Using a combination of astrometry, spectroscopy, and asteroseismology, we precisely characterize the solar analog alpha Men A (Teff = 5569 +/- 62 K, R = 0.960 +/- 0.016 Rsun, M = 0.964 +/- 0.045 Msun). To characterize the fully convective M dwarf companion, we derive empirical relations to estimate mass, radius, and temperature given the absolute Gaia magnitude and metallicity, yielding M = 0.169 +/- 0.006, R = 0.19 +/- 0.01 and Teff = 3054 +/- 44 K. Our asteroseismic age of 6.2 +/- 1.4 (stat) +/- 0.6 (sys) Gyr for the primary places $\alpha$ Men B within a small population of M dwarfs with precisely measured ages. We combined multiple ground-based spectroscopy surveys to reveal an activity cycle of 13.1 +/- 1.1 years, a period similar to that observed in the Sun. We used different gyrochronology models with the asteroseismic age to estimate a rotation period of ~30 days for the primary. Alpha Men A is now the closest (d=10pc) solar analog with a precise asteroseismic age from space-based photometry, making it a prime target for next-generation direct imaging missions searching for true Earth analogs., Comment: Accepted to The Astrophysical Journal; 15 pages, 10 figures

Our understanding of the properties and demographics of exoplanets critically relies on our ability to determine fundamental properties of their host stars. The advent of Gaia and large spectroscopic surveys has now made it in principle possible to infer properties of individual stars, including most exoplanet hosts, to very high precision. However, we show that in practice, such analyses are limited both by uncertainties in the fundamental scale, and by uncertainties in our models of stellar evolution, even for stars similar to the Sun. For example, we show that current uncertainties on measured interferometric angular diameters and bolometric fluxes set a systematic uncertainty floor of $\sim$2% in temperature, $\sim$2% in luminosity, and $\sim$4% in radius. Comparisons between widely available model grids suggest uncertainties of order $\sim$5% in mass and $\sim$20% in age for main sequence and subgiant stars. While the radius uncertainties are roughly constant over this range of stars, the model dependent uncertainties are a complex function of luminosity, temperature, and metallicity. We provide open-source software for approximating these uncertainties for individual targets, and discuss strategies for reducing these uncertainties in the future., Comment: Submitted, 11 pages, 6 figures. Google colab notebook available at https://colab.research.google.com/drive/1tmOHsat2g2-fYU8Y2UJIdV6VWCI9RjTf?usp=sharing

We report the discovery of TOI-561, a multi-planet system in the galactic thick disk that contains a rocky, ultra-short period planet (USP). This bright ($V=10.2$) star hosts three small transiting planets identified in photometry from the NASA TESS mission: TOI-561 b (TOI-561.02, P=0.44 days, $R_b = 1.45\pm0.11\,R_\oplus$), c (TOI-561.01, P=10.8 days, $R_c=2.90\pm0.13\,R_\oplus$), and d (TOI-561.03, P=16.3 days, $R_d=2.32\pm0.16\,R_\oplus$). The star is chemically ([Fe/H]$=-0.41\pm0.05$, [$\alpha$/H]$=+0.23\pm0.05$) and kinematically consistent with the galactic thick disk population, making TOI-561 one of the oldest ($10\pm3\,$Gyr) and most metal-poor planetary systems discovered yet. We dynamically confirm planets b and c with radial velocities from the W. M. Keck Observatory High Resolution Echelle Spectrometer. Planet b has a mass and density of $3.2\pm0.8\,M_\oplus$ and $5.5^{+2.0}_{-1.6}\,$g$\,$cm$^{-3}$, consistent with a rocky composition. Its lower-than-average density is consistent with an iron-poor composition, although an Earth-like iron-to-silicates ratio is not ruled out. Planet c is $7.0\pm2.3\,M_\oplus$ and $1.6\pm0.6\,$g$\,$cm$^{-3}$, consistent with an interior rocky core overlaid with a low-mass volatile envelope. Several attributes of the photometry for planet d (which we did not detect dynamically) complicate the analysis, but we vet the planet with high-contrast imaging, ground-based photometric follow-up and radial velocities. TOI-561 b is the first rocky world around a galactic thick-disk star confirmed with radial velocities and one of the best rocky planets for thermal emission studies., Comment: Accepted at The Astronomical Journal; 25 pages, 10 figures

We use models of stellar angular momentum evolution to determine ages for $\sim500$ stars in the APOGEE-\textit{Kepler} Cool Dwarfs sample. We focus on lower main-sequence stars, where other age-dating tools become ineffective. Our age distributions are compared to those derived from asteroseismic and giant samples and solar analogs. We are able to recover gyrochronological ages for old, lower-main-sequence stars, a remarkable improvement over prior work in hotter stars. Under our model assumptions, our ages have a median relative uncertainty of $14\%$, comparable to the age precision inferred for more massive stars using traditional methods. We investigate trends of galactic $\alpha$-enhancement with age, finding evidence of a detection threshold between the age of the oldest $\alpha$-poor stars and that of the bulk $\alpha$-rich population. We argue that gyrochronology is an effective tool reaching ages of 10--12 Gyr in K- and early M-dwarfs. Finally, we present the first effort to quantify the impact of detailed abundance patterns on rotational evolution. We estimate a $\sim15\%$ bias in age for cool, $\alpha$-enhanced (+ 0.4 dex) stars when standard solar-abundance-pattern rotational models are used for age inference, rather than models that appropriately account for $\alpha$-enrichment., Comment: 22 pages, 11 figures, 3 tables. Submitted to AAS Journals. Electronic version of Table 3 is available as ancillary file (sidebar on the right). For a brief video explaining this paper, see https://youtu.be/z5qQLUZzFDc. The code developed to interact with, interpolate, and sample the stellar models is publicly available at https://github.com/zclaytor/kiauhoku/