Gyrochronology and its usage for main sequence cool star ages

The construction of all age indicators consists of certain basic steps which lead to the identification of the properties desirable for stellar age indicators. Prior age indicators for main sequence field stars possess only some of these properties. The measured rotation periods of cool stars are particularly useful in this respect because they have well-defined dependencies that allow stellar ages to be determined with ~20% errors. This method, called gyrochronology, is explained informally in this talk, shown to have the desired properties, compared to prior methods, and used to derive ages for samples of main sequence field stars.Comment: 10 pages, 6 figures, presented at IAU258, Ages of Star

A connection between the morphology of the X-ray emission and rotation for solar-type stars in open clusters

It is suggested that the three-segmented morphology of the soft X-ray emission from cluster and field stars may be understood in terms of the recent classification of rotating stars into three kinds: those lying on the convective sequence, on the interface sequence, or in the gap between them.Comment: 7 pages, 1 (color) figure, accepted by ApJ Letter

Evidence of New Magnetic Transitions in Late-Type Dwarfs from Gaia DR2

The second Gaia data release contains the identification of 147 535 low-mass ($\le 1.4 M_{\odot}$) rotational modulation variable candidates on (or close to) the main sequence, together with their rotation period and modulation amplitude. The richness, the period and amplitude range, and the photometric precision of this sample make it possible to unveil, for the first time, signatures of different surface inhomogeneity regimes in the amplitude-period density diagram. The modulation amplitude distribution shows a clear bimodality, with an evident gap at periods $P \le 2$ d. The low amplitude branch, in turn, shows a period bimodality with a main clustering at periods $P \approx$ 5 - 10 d and a secondary clustering of ultra-fast rotators at $P \le 0.5$ d. The amplitude-period multimodality is correlated with the position in the period-absolute magnitude (or period-color) diagram, with the low- and high-amplitude stars occupying different preferential locations. Here we argue that such a multimodality represents a further evidence of the existence of different regimes of surface inhomogeneities in young and middle-age low-mass stars and we lay out possible scenarios for their evolution, which manifestly include rapid transitions from one regime to another. In particular, the data indicate that stars spinning up close to break-up velocity undergo a very rapid change in their surface inhomogeneities configuration, which is revealed here for the first time. The multimodality can be exploited to identify field stars of age $\sim$ 100 -- 600 Myr belonging to the slow-rotator low-amplitude sequence, for which age can be estimated from the rotation period via gyrochronology relationships.Comment: 15 pages, 6 figures, Accepted by Ap

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

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. We study the nearby, 3 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. 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. [...] Periodic signals are found for 32 stars, 21 of which are considered to be both highly reliable and to represent single, or effectively single, Ru147 stars. These stars cover the spectral types from late-F to mid-M stars, and they have periods ranging from 6d-32d, allowing for a comparison of Ruprecht 147 to both of the 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. 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 Ru147 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.Comment: 40 pages (17 pages + Appendix), 51 figures, Accepted for publication in A&

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

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. 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. 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. 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. 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.Comment: 23 pages, 19 figures, published in A&A 675, A180 (2023

Stellar rotation, binarity, and lithium in the open cluster IC4756

An important aspect in the evolutionary scenario of cool stars is their rotation and the rotationally induced magnetic activity and interior mixing. Stars in open clusters are particularly useful tracers for these aspects because of their known ages. We aim to characterize the open cluster IC4756 and measure stellar rotation periods and surface differential rotation for a sample of its member stars. Thirty-seven cluster stars were observed continuously with the CoRoT satellite for 78 days in 2010. Follow-up high-resolution spectroscopy of the CoRoT targets and deep Str\"omgren $uvby\beta$ and H$\alpha$ photometry of the entire cluster were obtained with our robotic STELLA facility and its echelle spectrograph and wide-field imager, respectively. We determined high-precision photometric periods for 27 of the 37 CoRoT targets and found values between 0.155 and 11.4 days. Twenty of these are rotation periods. Twelve targets are spectroscopic binaries of which 11 were previously unknown; orbits are given for six of them. Six targets were found that show evidence of differential rotation with $\Delta\Omega/\Omega$ in the range 0.04-0.15. Five stars are non-radially pulsating stars with fundamental periods of below 1d, two stars are semi-contact binaries, and one target is a micro-flaring star that also shows rotational modulation. Nine stars in total were not considered members because of much redder color(s) and deviant radial velocities with respect to the cluster mean. H$\alpha$ photometry indicates that the cluster ensemble does not contain magnetically over-active stars. The cluster average metallicity is -0.08$\pm$0.06 (rms) and its logarithmic lithium abundance for 12 G-dwarf stars is 2.39$\pm$0.17 (rms). [...]Comment: A&A, in pres

Angular Momentum Loss from Cool Stars: An Empirical Expression and Connection to Stellar Activity

We show here that the rotation period data in open clusters allow the empirical determination of an expression for the rate of loss of angular momentum from cool stars on the main sequence. One significant component of the expression, the dependence on rotation rate, persists from prior work; others do not. The expression has a bifurcation, as before, that corresponds to an observed bifurcation in the rotation periods of coeval open cluster stars. The dual dependencies of this loss rate on stellar mass are captured by two functions, $f(B-V)$ and $T(B-V)$, that can be determined from the rotation period observations. Equivalent masses and other [UBVRIJHK] colors are provided in Table 1. Dimensional considerations, and a comparison with appropriate calculated quantities suggest interpretations for $f$ and $T$, both of which appear to be related closely (but differently) to the calculated convective turnover timescale, $\tau_c$, in cool stars. This identification enables us to write down symmetrical expressions for the angular momentum loss rate and the deceleration of cool stars, and also to revive the convective turnover timescale as a vital connection between stellar rotation and stellar activity physics.Comment: 20 pages, 9 color figures; this version includes corrections listed in the associated journal erratu