Color-period Diagram Research Articles

Investigating 16 Open Clusters in the Kepler/K2–Gaia DR3 Field. I. Membership, Binary Systems, and Rotation

Using data from Gaia Data Release 3 and Kepler/K2, we present a catalog of 16 open clusters with ages ranging from 4–4000 Myr that 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 4381 stars identified as binary candidates and 49 stars identified as blue straggler stars. The fraction of binaries varies in each cluster, and the range is between 9% and 44%. We obtain the rotation periods of 5467 members, of which 4304 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 the 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 < < 2.5 mag.

Wide binaries demonstrate the consistency of rotational evolution between open cluster and field stars

Context. Gyrochronology enables the derivation of ages of late-type main sequence stars based on their rotation periods and a mass proxy, such as color. It has been explored in open clusters, but a connection to field stars has yet to be successfully established. Aims. We explore the rotation rates of wide binaries, representing enlightening intermediaries between clusters and field stars, and their overlap with those of open cluster stars. Methods. We investigated a recently created catalog of wide binaries, matched the cataloged binaries to observations by the Kepler mission (and its K2 extension), validated or re-derived their rotation periods, identified 283 systems where both stars are on the main sequence and have vetted rotation periods, and compared the systems with open cluster data. Results. We find that the vast majority of these wide binaries (236) line up directly along the curvilinear ribs defined by open clusters in color-period diagrams or along the equivalent interstitial gaps between successive open clusters. The parallelism in shape is remarkable. Twelve additional systems are clearly rotationally older. The deviant systems, a minority, are mostly demonstrably hierarchical. Furthermore, the position of the evolved component in the color-magnitude diagram for the additional wide binary systems that contain one is consistent with the main sequence component’s rotational age. Conclusions. We conclude that wide binaries, despite their diversity, follow the same spindown relationship as observed in open clusters, and we find that rotation-based age estimates yield the same ages for both components in a wide binary. This suggests that cluster and field stars spin down in the same way and that gyrochronology can be applied to field stars to determine their ages, provided that they are sufficiently distant from any companions to be considered effectively single. The results also suggest that the impact of metallicity variations on the spindown is likely not to be a major concern.

Rotation periods for cool stars in the open cluster Ruprecht 147 (NGC 6774)

Context. Gyrochronology allows the derivation of ages for cool main sequence stars based on their observed rotation periods and masses, or a suitable proxy thereof. It is increasingly well-explored for FGK stars, but requires further measurements for older ages and K – M-type stars. Aims. We study the 2.7 Gyr-old open cluster Ruprecht 147 to compare it with the previously-studied, but far more distant, NGC 6819 cluster, and especially to measure cooler stars than was previously possible there. Methods. We constructed an inclusive list of 102 cluster members from prior work, including Gaia DR2, and for which light curves were also obtained during Campaign 7 of the Kepler/K2 space mission. We placed them in the cluster color-magnitude diagram and checked the related information against appropriate isochrones. The light curves were then corrected for data systematics using Principal Component Analysis on all observed K2 C07 stars and subsequently subjected to periodicity analysis. Results. Periodic signals are found for 32 stars, 21 of which are considered to be both highly reliable and to represent single, or effectively single, Ru 147 stars. These stars cover the spectral types from late-F to mid-M stars, and they have periods ranging from 6 d – 33 d, allowing for a comparison of Ruprecht 147 to both other open clusters and to models of rotational spindown. The derived rotation periods connect reasonably to, overlap with, and extend to lower masses the known rotation period distribution of the 2.5 Gyr-old cluster NGC 6819. Conclusions. The data confirm that cool stars lie on a single surface in rotation period-mass-age space, and they simultaneously challenge its commonly assumed shape. The shape at the low mass region of the color-period diagram at the age of Ru 147 favors a recently-proposed model which requires a third mass-dependent timescale in addition to the two timescales required by a former model, suggesting that a third physical process is required to model rotating stars effectively.

ROTATION PERIODS FOR COOL STARS IN THE 4 Gyr OLD OPEN CLUSTER M67, THE SOLAR–STELLAR CONNECTION, AND THE APPLICABILITY OF GYROCHRONOLOGY TO AT LEAST SOLAR AGE

ABSTRACT We report rotation periods for 20 cool (FGK) main sequence member stars of the 4 Gyr-old open cluster M67 (=NGC 2682), obtained by analyzing data from Campaign 5 of the K2 mission with the Kepler Space Telescope. The rotation periods delineate a sequence in the color–period diagram (CPD) of increasing period with redder color. This sequence represents a cross-section at the cluster age of the surface P = P(t, M), suggested in prior work to extend to at least solar age. The current Sun is located marginally (approximately 1σ) above M67 in the CPD, as its relative age leads us to expect, and lies on the P = P(t, M) surface to within measurement precision. We therefore conclude that the solar rotation rate is normal as compared with cluster stars, a fact that strengthens the solar–stellar connection. The agreement between the M67 rotation period measurements and prior predictions further implies that rotation periods, especially when coupled with appropriate supporting work such as spectroscopy, can provide reliable ages via gyrochronology for other similar FGK dwarfs from the early main sequence to solar age and likely until the main sequence turnoff. The M67 rotators have a rotational age of 4.2 Gyr with a standard deviation of 0.7 Gyr, implying that similar field stars can be age-dated to precisions of ∼17%. The rotational age of the M67 cluster as a whole is therefore 4.2 Gyr, but with a lower (averaged) uncertainty of 0.2 Gyr.

A color-period diagram for the open cluster M 48 (NGC 2548), and its rotational age

Rotation periods are increasingly being used to derive ages for cool single field stars. Such ages are based on an empirical understanding of how cool stars spin down, acquired by constructing color-period diagrams (CPDs) for a series of open clusters. Our main aims here are to construct a CPD for M 48, to compare this with other clusters of similar age to check for consistency, and to derive a rotational age for M 48 using gyrochronology. We monitored M 48 photometrically for over 2 months with AIP's STELLA I 1.2 m telescope and the WiFSIP 4K imager in Tenerife. Light curves with 3 mmag precision for bright (V~14 mag) stars were produced and then analysed to provide rotation periods. A cluster CPD has then been constructed. We report 62 rotation periods for cool stars in M 48. The CPD displays a clear slow/I-sequence of rotating stars, similar to those seen in the 625 Myr-old Hyades and 590 Myr-old Praesepe clusters, and below both, confirming that M 48 is younger. A similar comparison with the 250 Myr-old M 34 cluster shows that M 48 is older and does not possess any fast/C-sequence G or early K stars like those in M 34, although relatively fast rotators do seem to be present among the late-K and M stars. A more detailed comparison of the CPD with rotational evolution models shows that the cluster stars have a mean age of 450 Myr, and its (rotating) stars can be individually dated to +-117 Myr (26%). Much of this uncertainty stems from intrinsic astrophysical spread in initial periods, and almost all stars are consistent with a single age of 450 Myr. The gyro-age of M 48 as a whole is 450+-50 Myr, in agreement with the previously determined isochrone age of 400+-100 Myr.

Overview of semi-sinusoidal stellar variability with the CoRoT satellite

To date, the CoRoT space mission has produced more than 124,471 light curves. Classifying these curves in terms of unambiguous variability behavior is mandatory for obtaining an unbiased statistical view on their controlling root-causes. The present study provides an overview of semi-sinusoidal light curves observed by the CoRoT exo-field CCDs. We selected a sample of 4,206 light curves presenting well-defined semi-sinusoidal signatures. The variability periods were computed based on Lomb-Scargle periodograms, harmonic fits, and visual inspection. Color-period diagrams for the present sample show the trend of an increase of the variability periods as long as the stars evolve. This evolutionary behavior is also noticed when comparing the period distribution in the Galactic center and anti-center directions. These aspects indicate a compatibility with stellar rotation, although more information is needed to confirm their root-causes. Considering this possibility, we identified a subset of three Sun-like candidates by their photometric period. Finally, the variability period versus color diagram behavior was found to be highly dependent on the reddening correction.

THE COLOR-PERIOD DIAGRAM AND STELLAR ROTATIONAL EVOLUTION—NEW ROTATION PERIOD MEASUREMENTS IN THE OPEN CLUSTER M34

We present results from a 5-month photometric survey for stellar rotation periods combined with a 4-year radial-velocity survey for membership and binarity in the 220Myr open cluster M34. We report surface rotation periods for 120 stars, 83 of which are late-type cluster members. A comparison to previous work serves to illustrate the importance of high cadence long baseline photometric observations and membership information. The new M34 periods are less biased against slow rotation and cleaned for non-members. The rotation periods of the cluster members span more than an order of magnitude from 0.5 day up to 11.5 days, and trace two distinct rotational sequences - fast (C) and moderate-to-slow (I) - in the color-period diagram. The sequences represent two different states in the rotational evolution of the late-type cluster members. We use the color-period diagrams for M34 and for younger and older clusters to estimate the timescale for the transition from the C to the I sequence and find ~<150Myr, ~150-300Myr, and ~300-600Myr for G, early-mid K, and late K dwarfs, respectively. The small number of stars in the gap between C and I suggest a quick transition. We estimate a lower limit on the maximum spin-down rate (dP/dt) during this transition to be ~0.06 days/Myr and ~0.08 days/Myr for early and late K dwarfs, respectively. We compare the I sequence rotation periods in M34 and the Hyades for G and K dwarfs and find that K dwarfs spin down slower than the Skumanich rate. We determine a gyrochronology age of 240Myr for M34. We measure the effect of cluster age uncertainties on the gyrochronology age for M34 and find the resulting error to be consistent with the error estimate for the technique. We use the M34 I sequence to redetermine the coefficients in the expression for rotational dependence on color used in gyrochronology (abridged).

THE KEPLER CLUSTER STUDY: STELLAR ROTATION IN NGC 6811

We present rotation periods for 71 single dwarf members of the open cluster NGC6811 determined using photometry from NASA's Kepler Mission. The results are the first from The Kepler Cluster Study which combine Kepler's photometry with ground-based spectroscopy for cluster membership and binarity. The rotation periods delineate a tight sequence in the NGC6811 color-period diagram from ~1 day at mid-F to ~11 days at early-K spectral type. This result extends to ~1 Gyr similar prior results in the ~600 Myr Hyades and Praesepe clusters, suggesting that rotation periods for cool dwarf stars delineate a well-defined surface in the 3-dimensional space of color (mass), rotation, and age. It implies that reliable ages can be derived for field dwarf stars with measured colors and rotation periods, and it promises to enable further understanding of various aspects of stellar rotation and activity for cool stars.

A SIMPLE NONLINEAR MODEL FOR THE ROTATION OF MAIN-SEQUENCE COOL STARS. I. INTRODUCTION, IMPLICATIONS FOR GYROCHRONOLOGY, AND COLOR-PERIOD DIAGRAMS

We here introduce a simple nonlinear model to describe the rotational evolution of cool stars on the main sequence. It is formulated only in terms of the Rossby number (Ro = P/τ), its inverse, and two dimensionless constants which we specify using solar and open-cluster data. The model has two limiting cases of stellar rotation, previously called C and I, that correspond to two observed sequences of fast and slowly rotating stars in young open clusters. The model describes the evolution of stars from C-type, with particular mass and age dependencies, to I-type, with different mass and age dependencies, through the rotational gap, g, separating them. The proposed model explains various aspects of stellar rotation, and provides an exact expression for the age of a rotating cool star in terms of P and τ, thereby generalizing gyrochronology. Using it, we calculate the time interval required for stars to reach the rotational gap—a monotonically increasing, mildly nonlinear function of τ. Beginning with the range of initial periods indicated by observations, we show that the (mass-dependent) dispersion in rotation period initially increases, and then decreases rapidly with the passage of time. The initial dispersion in period contributes up to 128 Myr to the gyro-age errors of solar-mass field stars. Finally, we transform to color–period space, calculate appropriate isochrones, and show that this model explains some detailed features in the observed color–period diagrams of open clusters, including the positions and shapes of the sequences, and the observed density of stars across these diagrams.

A nonlinear model for rotating cool stars

AbstractA simple nonlinear model is introduced here to describe the rotational evolution of main sequence cool (FGKM) stars. It is formulated only in terms of the ratio of a star's rotation period, P, to its convective turnover timescale, τ, and two dimensionless constants which are specified using solar- and open cluster data. The model explains the origin of the two sequences, C/fast and I/slow, of rotating stars observed in open cluster color-period diagrams, and describes their evolution from C-type to I-type through the rotational gap, g, separating them. It explains why intermediate-mass open cluster stars have the longest periods, while higher- and lower-mass cool stars have shorter periods. It provides an exact expression for the age of a rotating cool star in terms of P and τ, thereby generalizing gyrochronology. The possible range of initial periods is shown to contribute upto 128 Myr to the gyro age errors of solar mass field stars. A transformation to color-period space shows how this model explains some detailed features in the color-period diagrams of open clusters, including the shapes and widths of the sequences, and the observed number density of stars across these diagrams.

STELLAR ROTATION IN M35: MASS-PERIOD RELATIONS, SPIN-DOWN RATES, AND GYROCHRONOLOGY

We present the results of a 5 month photometric time-series survey for stellar rotation over a 40'x40' field on the 150 Myr open cluster M35. We report rotation periods for 441 stars and determine their cluster membership and binarity based on a decade-long radial-velocity survey, proper-motion measurements, and multi-band photometric observations. We find that 310 of the stars with measured rotation periods are late-type members of M35. Their distribution of rotation periods span more than two orders of magnitude from ~0.1-15 days, not constrained by the sampling frequency and the time-span of the survey. With an age between the zero-age main-sequence and the Hyades, and with ~6 times more rotation periods than measured in the Pleiades, M35 permit detailed studies of early rotational evolution of late-type stars. Nearly 80% of the 310 rotators lie on two distinct sequences in the color-period plane, defining clear relations between stellar rotation period and color (mass). The M35 color-period diagram enables us to determine timescales for the transition between the two rotational states for G and K dwarfs, respectively. These timescales are inversely related to the mass of the convective envelope, and offer constraints on the rates of internal and external angular momentum transport and of the evolution of stellar dynamos. A comparison to the Hyades, confirm the Skumanich (1972) spindown-dependence for G dwarfs on one rotational state, but suggest that K dwarfs spin down more slowly. The locations of the rotational sequences in the M35 color-period diagram support the use of rotational isochrones to determine ages for coeval stellar populations. We use such gyrochronology to determine "gyro-ages" for M35. We use the M35 data to evaluate new color dependencies for the rotational isochrones.