An Observational Study of Tidal Synchronization in Solar-Type Binary Stars in the Open Clusters M35 and M34

We present rotation periods for the solar-type primary stars in 13 close (a~< 5 AU) single-lined spectroscopic binaries with known orbital periods (P) and eccentricities (e). All binaries are members of the open clusters M35 (150Myr) and M34 (250Myr). The binary orbital parameters and the rotation periods of the primary stars were determined from time-series spectroscopy and time-series photometry, respectively. Knowledge of the ages, orbital periods, and eccentricities of these binaries combined with the rotation periods and masses of their primary stars makes them particularly interesting systems for studying the rates of tidal circularization and synchronization. Our sample of 13 binaries includes six with orbital periods shortward of 13 days (a ~< 0.12 AU). The stars in these binaries orbit sufficiently close that their spins and orbits have evolved toward synchronization and circularization due to tidal interactions. We investigate the degree of tidal synchronization in each binary by comparing the angular rotation velocity of the primary stars to the angular velocity expected if the primary star was synchronized (e=0) or pseudo- synchronized (e>0) with the orbital motion. Of the six closest binaries two with circular orbits are not synchronized, one being subsynchronous and one being supersynchronous, and the primary stars in two binaries with eccentric orbits are rotating more slowly than pseudosynchronism. The remaining two binaries have reached the equilibrium state of both a circularized orbit and synchronized rotation. As a set, the six binaries present a challenging case study for tidal evolution theory, which in particular does not predict subsynchronous rotation in such close systems.Comment: 45 pages, 18 figures, 1 table, accepted for publication in Astrophysical Journa

The K2 M67 Study: Establishing the Limits of Stellar Rotation Period Measurements in M67 with K2 Campaign 5 Data

The open cluster M67 offers the unique opportunity to measure rotation periods for solar-age stars across a range of masses, potentially filling a critical gap in the understanding of angular momentum loss in older main sequence stars. The observation of M67 by NASA K2 Campaign 5 provided light curves with high enough precision to make this task possible, albeit challenging, as the pointing instability, 75d observation window, crowded field, and typically low-amplitude signals mean determining accurate rotation periods on the order of 25 - 30d is inherently difficult. Lingering, non-astrophysical signals with power at >25d found in a set of Campaign 5 A and F stars compounds the problem. To achieve a quantitative understanding of the best-case scenario limits for reliable period detection imposed by these inconveniences, we embarked on a comprehensive set of injection tests, injecting 120,000 sinusoidal signals with periods ranging from 5 to 35d and amplitudes from 0.05% to 3.0% into real Campaign 5 M67 light curves processed using two different pipelines. We attempted to recover the signals using a normalized version of the Lomb-Scargle periodogram and setting a detection threshold. We find that while the reliability of detected periods is high, the completeness (sensitivity) drops rapidly with increasing period and decreasing amplitude, maxing at 15% recovery rate for the solar case (i.e. 25d period, 0.1% amplitude). This study highlights the need for caution in determining M67 rotation periods from Campaign 5 data, but this can be extended to other clusters observed by K2 and, soon, TESS.Comment: 55 pages, 22 figures, published by Ap

A Gyrochronology and Microvariability Survey of the Milky Way's Older Stars Using Kepler's Two-Wheels Program

Even with the diminished precision possible with only two reaction wheels, the Kepler spacecraft can obtain mmag level, time-resolved photometry of tens of thousands of sources. The presence of such a rich, large data set could be transformative for stellar astronomy. In this white paper, we discuss how rotation periods for a large ensemble of single and binary main- sequence dwarfs can yield a quantitative understanding of the evolution of stellar spin-down over time. This will allow us to calibrate rotation-based ages beyond ~1 Gyr, which is the oldest benchmark that exists today apart from the Sun. Measurement of rotation periods of M dwarfs past the fully-convective boundary will enable extension of gyrochronology to the end of the stellar main-sequence, yielding precise ages ({\sigma} ~10%) for the vast majority of nearby stars. It will also help set constraints on the angular momentum evolution and magnetic field generation in these stars. Our Kepler-based study would be supported by a suite of ongoing and future ground-based observations. Finally, we briefly discuss two ancillary science cases, detection of long-period low-mass eclipsing binaries and microvariability in white dwarfs and hot subdwarf B stars that the Kepler Two-Wheels Program would facilitate.Comment: Kepler white pape

Evolved Eclipsing Binaries and the Age of the Open Cluster NGC 752

We present analyses of improved photometric and spectroscopic observations for two detached eclipsing binaries at the turnoff of the open cluster NGC 752: the 1.01 day binary DS And and the 15.53 d BD $+$37 410. For DS And, we find $M_1 = 1.692\pm0.004\pm0.010 M_\odot$, $R_1 = 2.185\pm0.004\pm0.008 R_\odot$, $M_2 = 1.184\pm0.001\pm0.003 M_\odot$, and $R_2 = 1.200\pm0.003\pm0.005 R_\odot$. We either confirm or newly identify unusual characteristics of both stars in the binary: the primary star is found to be slightly hotter than the main sequence turn off and there is a more substantial discrepancy in its luminosity compared to models (model luminosities are too large by about 40%), while the secondary star is oversized and cooler compared to other main sequence stars in the same cluster. The evidence points to non-standard evolution for both stars, but most plausible paths cannot explain the low luminosity of the primary star. BD $+$37 410 only has one eclipse per cycle, but extensive spectroscopic observations and the TESS light curve constrain the stellar masses well: $M_1 = 1.717\pm0.011 M_\odot$ and $M_2 = 1.175\pm0.005 M_\odot$. The radius of the main sequence primary star near $2.9R_\odot$ definitively requires large convective core overshooting ($> 0.2$ pressure scale heights) in models for its mass, and multiple lines of evidence point toward an age of $1.61\pm0.03\pm0.05$ Gyr (statistical and systematic uncertainties). Because NGC 752 is currently undergoing the transition from non-degenerate to degenerate He ignition of its red clump stars, BD $+$37 410 A directly constrains the star mass where this transition occurs.Comment: 34 pages, 23 figures, accepted for Astronomical Journa

A Robust Measure of Tidal Circularization in Coeval Binary Populations: The solar-type spectroscopic Binary Population in The Open Cluster M35

We present a new homogeneous sample of 32 spectroscopic binary orbits in the young (~ 150 Myr) main-sequence open cluster M35. The distribution of orbital eccentricity vs. orbital period (e-log(P)) displays a distinct transition from eccentric to circular orbits at an orbital period of ~ 10 days. The transition is due to tidal circularization of the closest binaries. The population of binary orbits in M35 provide a significantly improved constraint on the rate of tidal circularization at an age of 150 Myr. We propose a new and more robust diagnostic of the degree of tidal circularization in a binary population based on a functional fit to the e-log(P) distribution. We call this new measure the tidal circularization period. The tidal circularization period of a binary population represents the orbital period at which a binary orbit with the most frequent initial orbital eccentricity circularizes (defined as e = 0.01) at the age of the population. We determine the tidal circularizationperiod for M35 as well as for 7 additional binary populations spanning ages from the pre main-sequence (~ 3 Myr) to late main-sequence (~ 10 Gyr), and use Monte Carlo error analysis to determine the uncertainties on the derived circularization periods. We conclude that current theories of tidal circularization cannot account for the distribution of tidal circularization periods with population age.Comment: 37 pages, 9 figures, to be published in The Astrophysical Journal, February 200

A Transiting Hot Jupiter Orbiting a Metal-Rich Star

We announce the discovery of Kepler-6b, a transiting hot Jupiter orbiting a star with unusually high metallicity, [Fe/H] = +0.34 +/- 0.04. The planet's mass is about 2/3 that of Jupiter, Mp = 0.67 Mj, and the radius is thirty percent larger than that of Jupiter, Rp = 1.32 Rj, resulting in a density of 0.35 g/cc, a fairly typical value for such a planet. The orbital period is P = 3.235 days. The host star is both more massive than the Sun, Mstar = 1.21 Msun, and larger than the Sun, Rstar = 1.39 Rsun.Comment: 12 pages, 2 figures, submitted to the Astrophysical Journal Letter