arXiv subjects

Robert D. Mathieu

Publications and source records attributed to Robert D. Mathieu.

At least 37 records · Page 2Linked to original sources

arXiv2020

WIYN Open Cluster Study. LXXVII. Radial-Velocity Measurements and Spectroscopic Binary Orbits in the Open Cluster NGC 7789

We introduce the stellar sample of the WIYN Open Cluster Study radial-velocity survey for the rich open cluster NGC 7789 (1.6 Gyr, [Fe/H] = +0.02). This sample lies within an 18$'$ circular radius from the cluster center (10 pc in projection, or about 2 core radii), and includes giants, red-clump stars, blue stragglers, red stragglers, sub-subgiants, and main-sequence stars down to one mag below the turnoff. Our survey began in 2005 and comprises more than 9,000 radial-velocity measurements from the Hydra Multi-Object Spectrograph on the WIYN 3.5m telescope. We identify 564 likely cluster members and present the orbital solutions for 83 cluster binary stars with periods between 1.45$\,$d and 4200$\,$d. From the main-sequence binary solutions we fit a circularization period of 8.22$^{+3.51}_{-1.35}\,$d. We calculate an incompleteness-corrected main-sequence binary frequency of 31% $\pm$ 3% for binaries with periods less than 10$^{4}$ days, similar to other WOCS open clusters of all ages. We detect a blue straggler binary frequency of 31% $\pm$ 15%, consistent with the similarly aged cluster NGC 6819.

astro-ph.SR↗

arXiv2019

Accretion Kinematics in the T Tauri Binary TWA 3A: Evidence for Preferential Accretion onto the TWA 3A Primary

We present time-series, high-resolution optical spectroscopy of the eccentric T Tauri binary TWA 3A. Our analysis focuses on variability in the strength and structure of the accretion tracing emission lines H alpha and He I 5876A. We find emission line strengths to display the same orbital-phase dependent behavior found with time-series photometry, namely, bursts of accretion near periastron passages. Such bursts are in good agreement with numerical simulations of young eccentric binaries. During accretion bursts, the emission of He I 5876A consistently traces the velocity of the primary star. After removing a model for the system's chromospheric emission, we find the primary star typically emits ~70% of the He I accretion flux. We interpret this result as evidence for circumbinary accretion streams that preferentially feed the TWA 3A primary. This finding is in contrast to most numerical simulations, which predict the secondary should be the dominant accretor in a binary system. Our results may be consistent with a model in which the precession of an eccentric circumbinary disk gap alternates between preferentially supplying mass to the primary and secondary.

astro-ph.SR↗

arXiv2019

Constraining Mass Transfer Histories of Blue Straggler Stars with COS Spectroscopy of White Dwarf Companions

Recent studies show that the majority of blue straggler stars (BSSs) in old open clusters are formed through mass transfer from an evolved star onto a main-sequence companion, resulting in a BSS and white dwarf (WD) in a binary system. We present constraints on the mass transfer histories of two BSS-WD binaries in the open cluster NGC 188, using WD temperatures and surface gravities measured with HST COS far-ultraviolet spectroscopy. Adopting a Gaia-based cluster distance of $1847\pm107$ pc, we determine that one system, WOCS 4540, formed through Case C mass transfer resulting in a CO-core white dwarf with $T_{\text{eff}}=17000^{+140}_{-200}$ K and a $\log g=7.80^{+0.06}_{-0.06}$, corresponding to a mass of $0.53^{+0.03}_{-0.03}$ $M_{\odot}$ and a cooling age of $105^{+6}_{-5}$ Myr. The other system, WOCS 5379, formed through Case B mass transfer resulting in a He-core white dwarf with $T_{\text{eff}}=15500^{+170}_{-150}$ K and a $\log g=7.50^{+0.06}_{-0.05}$, corresponding to a mass of $0.42^{+0.02}_{-0.02}$ $M_{\odot}$ and an age of $250^{+20}_{-20}$ Myr. The WD parameters are consistent across four different cluster distance assumptions. We determine possible progenitor binary systems with a grid of accretion models using MESA, and investigate whether these systems would lead to stable or unstable mass transfer. WOCS 4540 likely resulted from stable mass transfer during periastron passage in an eccentric binary system, while WOCS 5379 challenges our current understanding of the expected outcomes for mass transfer from red giant branch stars. Both systems are examples of the value in using detailed analyses to fine-tune our physical understanding of binary evolutionary processes.

astro-ph.SR↗

arXiv2019

Blue Lurkers: Hidden Blue Stragglers on the M67 Main Sequence Identified from their Kepler/K2 Rotation Periods

At an age of 4 Gyr, typical solar-type stars in M67 have rotation rates of 20-30 days. Using K2 Campaign 5 and 16 light curves and the spectral archive of the WIYN Open Cluster Study, we identify eleven three-dimensional kinematic members of M67 with anomalously fast rotation periods of 2-8 days, implying ages of less than 1 Gyr. We hypothesize that these anomalously fast rotators have been spun up by mass transfer, mergers, or stellar collisions during dynamical encounters within the last Gyr, and thus represent lower-luminosity counterparts to the blue straggler stars. These 11 candidate post-interaction stellar systems have much in common with the blue stragglers including a high binary fraction (73%), a number of long-period, low-eccentricity binary systems, and in at least one case a UV excess consistent with the presence of a hot white dwarf companion. The identification of these 11 systems provides the first picture of the low-luminosity end of the blue straggler distribution, providing new constraints for detailed binary evolution models and cluster population studies. This result also clearly demonstrates the need to properly account for the impact of binaries on stellar evolution, as significant numbers of post-interaction binaries likely exist on cluster main sequences and in the field. These stars are not always easy to identify, but make up ~10% of the spectroscopic binary population among the solar-type stars in M67.

astro-ph.SR↗

arXiv2018

The K2 M67 Study: A Curiously Young Star in an Eclipsing Binary in an Old Open Cluster

We present an analysis of a slightly eccentric ($e=0.05$), partially eclipsing long-period ($P = 69.73$ d) main sequence binary system (WOCS 12009, Sanders 1247) in the benchmark old open cluster M67. Using Kepler K2 and ground-based photometry along with a large set of new and reanalyzed spectra, we derived highly precise masses ($1.111\pm0.015$ and $0.748\pm0.005 M_\odot$) and radii ($1.071\pm0.008\pm0.003$ and $0.713\pm0.019\pm0.026 R_\odot$, with statistical and systematic error estimates) for the stars. The radius of the secondary star is in agreement with theory. The primary, however, is approximately $15\%$ smaller than reasonable isochrones for the cluster predict. Our best explanation is that the primary star was produced from the merger of two stars, as this can also account for the non-detection of photospheric lithium and its higher temperature relative to other cluster main sequence stars at the same $V$ magnitude. To understand the dynamical characteristics (low measured rotational line broadening of the primary star and the low eccentricity of the current binary orbit), we believe that the most probable (but not the only) explanation is the tidal evolution of a close binary within a primordial triple system (possibly after a period of Kozai-Lidov oscillations), leading to merger approximately 1Gyr ago. This star appears to be a future blue straggler that is being revealed as the cluster ages and the most massive main sequence stars die out.

astro-ph.SR↗

arXiv2017

Pulsed Accretion in the T Tauri Binary TWA 3A

TWA 3A is the most recent addition to a small group of young binary systems that both actively accrete from a circumbinary disk and have spectroscopic orbital solutions. As such, it provides a unique opportunity to test binary accretion theory in a well-constrained setting. To examine TWA 3A's time-variable accretion behavior, we have conducted a two-year, optical photometric monitoring campaign, obtaining dense orbital phase coverage (~20 observations per orbit) for ~15 orbital periods. From U-band measurements we derive the time-dependent binary mass accretion rate, finding bursts of accretion near each periastron passage. On average, these enhanced accretion events evolve over orbital phases 0.85 to 1.05, reaching their peak at periastron. The specific accretion rate increases above the quiescent value by a factor of ~4 on average but the peak can be as high as an order of magnitude in a given orbit. The phase dependence and amplitude of TWA 3A accretion is in good agreement with numerical simulations of binary accretion with similar orbital parameters. In these simulations, periastron accretion bursts are fueled by periodic streams of material from the circumbinary disk that are driven by the binary orbit. We find that TWA 3A's average accretion behavior is remarkably similar to DQ Tau, another T Tauri binary with similar orbital parameters, but with significantly less variability from orbit to orbit. This is only the second clear case of orbital-phase-dependent accretion in a T Tauri binary.

astro-ph.SR↗

arXiv2017

On the Origin of Sub-subgiant Stars. III. Formation Frequencies

Sub-subgiants are a new class of stars that are optically redder than normal main-sequence stars and fainter than normal subgiant stars. Sub-subgiants, and the possibly related red stragglers (which fall to the red of the giant branch), occupy a region of the color-magnitude diagram that is predicted to be devoid of stars by standard stellar evolution theory. In previous papers we presented the observed demographics of these sources and defined possible theoretical formation channels through isolated binary evolution, the rapid stripping of a subgiant's envelope, and stellar collisions. Sub-subgiants offer key tests for single- and binary-star evolution and stellar collision models. In this paper, we synthesize these findings to discuss the formation frequencies through each of these channels. The empirical data, our analytic formation rate calculations, and analyses of sub-subgiants in a large grid of Monte Carlo globular cluster models suggest that the binary evolution channels may be the most prevalent, though all channels appear to be viable routes to sub-subgiant creation (especially in higher-mass globular clusters). Multiple formation channels may operate simultaneously to produce the observed sub-subgiant population. Finally, many of these formation pathways can produce stars in both the sub-subgiant and red straggler (and blue straggler) regions of the color-magnitude diagram, in some cases as different stages along the same evolutionary sequence.

astro-ph.SR↗

arXiv2017

On the Origin of Sub-subgiant Stars. I. Demographics

Sub-subgiants are stars observed to be redder than normal main-sequence stars and fainter than normal subgiant (and giant) stars in an optical color-magnitude diagram. The red straggler stars, which lie redward of the red giant branch, may be related and are often grouped together with the sub-subgiants in the literature. These stars defy our standard theory of single-star evolution, and are important tests for binary evolution and stellar collision models. In total, we identify 65 sub-subgiants and red stragglers in 16 open and globular star clusters from the literature; 50 of these, including 43 sub-subgiants, pass our strict membership selection criteria (though the remaining sources may also be cluster members). In addition to their unique location on the color-magnitude diagram, we find that at least 58% (25/43) of sub-subgiants in this sample are X-ray sources with typical 0.5-2.5 keV luminosities of order 10^30 - 10^31 erg/s. Their X-ray luminosities and optical-to-X-ray flux ratios are similar to those of RS CVn active binaries. At least 65% (28/43) of the sub-subgiants in our sample are variables, 21 of which are known to be radial-velocity binaries. Typical variability periods are <15 days. At least 33% (14/43) of the sub-subgiants are H-alpha emitters. These observational demographics provide strong evidence that binarity is important for sub-subgiant formation. Finally, we find that the number of sub-subgiants per unit mass increases toward lower-mass clusters, such that the open clusters in our sample have the highest specific frequencies of sub-subgiants.

astro-ph.SR↗

arXiv2017

On the Origin of Sub-Subgiant Stars II: Binary Mass Transfer, Envelope Stripping, and Magnetic Activity

Sub-subgiant stars (SSGs) lie to the red of the main-sequence and fainter than the red giant branch in cluster color-magnitude diagrams (CMDs), a region not easily populated by standard stellar evolution pathways. While there has been speculation on what mechanisms may create these unusual stars, no well-developed theory exists to explain their origins. Here we discuss three hypotheses of SSG formation: (1) mass transfer in a binary system, (2) stripping of a subgiant's envelope, perhaps during a dynamical encounter, and (3) reduced luminosity due to magnetic fields that lower convective efficiency and produce large star spots. Using the stellar evolution code MESA, we develop evolutionary tracks for each of these hypotheses, and compare the expected stellar and orbital properties of these models with six known SSGs in the two open clusters M67 and NGC 6791. All three of these mechanisms can create stars or binary systems in the SSG CMD domain. We also calculate the frequency with which each of these mechanisms may create SSG systems, and find that the magnetic field hypothesis is expected to create SSGs with the highest frequency in open clusters. Mass transfer and envelope stripping have lower expected formation frequencies, but may nevertheless create occasional SSGs in open clusters. They may also be important mechanisms to create SSGs in higher mass globular clusters.

astro-ph.SR↗

arXiv2016

Accretion and Magnetic Reconnection in the Classical T Tauri Binary DQ Tau

Binary star-formation theory predicts that close binaries (a<100 AU) will experience periodic pulsed accretion events as streams of material form at the inner edge of a circumbinary disk, cross a dynamically cleared gap, and feed circumstellar disks or accrete directly onto the stars. The archetype for the pulsed-accretion theory is the eccentric, short-period, classical T Tauri binary DQ Tau. Low-cadence (~daily) broadband photometry has shown brightening events near most periastron passages, just as numerical simulations would predict for an eccentric binary. Magnetic reconnection events (flares) during the collision of stellar magnetospheres near periastron could, however, produce the same periodic, broadband behavior when observed at a one-day cadence. To reveal the dominate physical mechanism seen in DQ Tau's low-cadence observations, we have obtained continuous, moderate-cadence, multi-band photometry over 10 orbital periods, supplemented with 27 nights of minute-cadence photometry centered on 4 separate periastron passages. While both accretion and stellar flares are present, the dominant timescale and morphology of brightening events are characteristic of accretion. On average, the mass accretion rate increases by a factor of 5 near periastron, in good agreement with recent models. Large variability is observed in the morphology and amplitude of accretion events from orbit-to-orbit. We argue this is due to the absence of stable circumstellar disks around each star, compounded by inhomogeneities at the inner edge of the circumbinary disk and within the accretion streams themselves. Quasi-periodic apastron accretion events are also observed, which are not predicted by binary accretion theory.

astro-ph.SR↗

arXiv2016

WIYN Open Cluster Study. LXXI. Spectroscopic Membership and Orbits of NGC 6791 Sub-Subgiants

In an optical color-magnitude diagram sub-subgiants (SSGs) lie red of the main sequence and fainter than the base of the red giant branch in a region not easily populated by standard stellar-evolution pathways. In this paper, we present multi-epoch radial velocities for five SSG candidates in the old and metal-rich open cluster NGC 6791 (8 Gyr, [Fe/H] = +0.30). From these data we are able to make three-dimensional kinematic membership determinations and confirm four SSG candidates to be likely cluster members. We also identify three member SSGs as short-period binary systems and present their orbital solutions. These are the first SSGs with known three-dimensional kinematic membership, binary status, and orbital parameters since the two SSGs in M67 studied by Mathieu et al. 2003. We also remark on the other properties of these stars including photometric variability, H$α$ emission, and X-ray luminosity. The membership confirmation of these SSGs in NGC 6791 strengthens the case that SSGs are a new class of nonstandard stellar evolution products, and that a physical mechanism must be found that explains the evolutionary paths of these stars.

astro-ph.SR↗

arXiv2016

Determining the Age of the Kepler Open Cluster NGC 6819 With a New Triple System and Other Eclipsing Binary Stars

As part of our study of the old (~2.5 Gyr) open cluster NGC 6819 in the Kepler field, we present photometric (Kepler and ground-based BVRcIc) and spectroscopic observations of the detached eclipsing binary WOCS 24009 (Auner 665; KIC 5023948) with a short orbital period of 3.6 days. WOCS 24009 is a triple-lined system, and we verify that the brightest star is physically orbiting the eclipsing binary using radial velocities and eclipse timing variations. The eclipsing binary components have masses M_B =1.090+/-0.010 Msun and M_C =1.075+/-0.013 Msun, and radii R_B =1.095+/-0.007 Rsun and R_C =1.057+/-0.008 Rsun. The bright non-eclipsing star resides at the cluster turnoff, and ultimately its mass will directly constrain the turnoff mass: our preliminary determination is M_A =1.251+/-0.057 Msun. A careful examination of the light curves indicates that the fainter star in the eclipsing binary undergoes a very brief period of total eclipse, which enables us to precisely decompose the light of the three stars and place them in the color-magnitude diagram. We also present improved analysis of two previously discussed detached eclipsing stars in NGC 6819 (WOCS 40007 and WOCS 23009) en route to a combined determination of the cluster's distance modulus (m-M)_V=12.38+/-0.04. Because this paper significantly increases the number of measured stars in the cluster, we can better constrain the age of the color-magnitude diagram to be 2.21+/-0.10+/-0.20 Gyr. Additionally, using all measured eclipsing binary star masses and radii, we constrain the age to 2.38+/-0.05+/-0.22 Gyr. The quoted uncertainties are estimates of measurement and systematic uncertainties (due to model physics differences and metal content), respectively.

astro-ph.SR↗

arXiv2015

WIYN Open Cluster Study XXXII: Stellar Radial Velocities in the Old Open Cluster NGC 188

(Abridged) We present the results of our ongoing radial-velocity (RV) survey of the old (7 Gyr) open cluster NGC 188. Our WIYN 3.5m data set spans a time baseline of 11 years, a magnitude range of 12<=V<=16.5 (1.18-0.94 MSun), and a 1 deg. diameter region on the sky. With the addition of a Dominion Astrophysical Observatory (DAO) data set we extend our bright limit to V = 10.8 and, for some stars, extend our time baseline to 35 years. Our magnitude limits include solar-mass main-sequence stars, subgiants, giants, and blue stragglers (BSs), and our spatial coverage extends radially to 17 pc (~13 core radii). For the WIYN data we find a measurement precision of 0.4 km/s for narrow-lined stars. We have measured RVs for 1046 stars in the direction of NGC 188, finding 473 to be likely cluster members. We detect 124 velocity-variable cluster members, all of which are likely to be dynamically hard-binary stars. Using our single member stars, we find an average cluster RV of -42.36 +/- 0.04 km/s. We use our precise RV and proper-motion membership data to greatly reduce field-star contamination in our cleaned color-magnitude diagram, from which we identify six stars of note that lie far from a standard single-star isochrone. We find the binaries to be centrally concentrated, providing evidence for the presence of mass segregation in NGC 188. We observe the BSs to populate a bimodal spatial distribution that is not centrally concentrated, suggesting that we may be observing two populations of BSs in NGC 188, including a centrally concentrated distribution as well as a halo population. Finally, we find NGC 188 to have a global RV dispersion of 0.64 +/- 0.04 km/s. When corrected for unresolved binaries, the NGC 188 RV dispersion has a nearly isothermal radial distribution. We use this mean-corrected velocity dispersion to derive a virial mass of 2300 +/- 460 MSun.

astro-ph.SR↗

arXiv2015

WIYN Open Cluster Study. XXXVI. Spectroscopic Binary Orbits in NGC 188

We present 98 spectroscopic binary orbits resulting from our ongoing radial-velocity survey of the old (7 Gyr) open cluster NGC 188. All but 13 are high-probability cluster members based on both radial-velocity and proper-motion membership analyses. Fifteen of these member binaries are double lined. Our stellar sample spans a magnitude range of 10.8 <=V<= 16.5 (1.14-0.92 Msun) and extends spatially to 17 pc (~13 core radii). All of our binary orbits have periods ranging from a few days to on the order of 10^3 days, and thus are hard binaries that dynamically power the cluster. For each binary, we present the orbital solutions and place constraints on the component masses. Additionally, we discuss a few binaries of note from our sample, identifying a likely blue straggler-blue straggler binary system (7782), a double-lined binary with a secondary star which is under-luminous for its mass (5080), two potential eclipsing binaries (4705 and 5762), and two binaries which are likely members of a quadruple system (5015a and 5015b).

astro-ph.SR↗

arXiv2015

Implications for the Formation of Blue Straggler Stars from HST Ultraviolet Observations of NGC 188

We present results of a Hubble Space Telescope far-ultraviolet (FUV) survey searching for white dwarf (WD) companions to blue straggler stars (BSSs) in open cluster NGC 188. The majority of NGC 188 BSSs (15 of 21) are single-lined binaries with properties suggestive of mass-transfer formation via Roche lobe overflow, specifically through an asymptotic giant branch star transferring mass to a main sequence secondary, yielding a BSS binary with a WD companion. In NGC 188, a BSS formed by this mechanism within the past 400 Myr will have a WD companion hot and luminous enough to be directly detected as a FUV photometric excess with HST. Comparing expected BSS FUV emission to observed photometry reveals four BSSs with WD companions above 12,000 K (younger than 250 Myr) and three WD companions with temperatures between 11,000-12,000 K. These BSS+WD binaries all formed through recent mass transfer. The location of the young BSSs in an optical color-magnitude diagram (CMD) indicates that distance from the zero-age main sequence does not necessarily correlate with BSS age. There is no clear CMD separation between mass transfer-formed BSSs and those likely formed through other mechanisms, such as collisions. The seven detected WD companions place a lower limit on the mass-transfer formation frequency of 33%. We consider other possible formation mechanisms by comparing properties of the BSS population to theoretical predictions. We conclude that 14 BSS binaries likely formed from mass transfer, resulting in an inferred mass-transfer formation frequency of approximately 67%.

astro-ph.SR↗

arXiv2015

Barium Surface Abundances of Blue Stragglers in the Open Cluster NGC 6819

We present the barium surface abundance of 12 blue stragglers (BSs) and 18 main-sequence (MS) stars in the intermediate-age open cluster NGC 6819 (2.5 Gyr) based on spectra obtained from the Hydra Multi-object Spectrograph on the WIYN 3.5 m telescope. For the MS stars we find [Fe/H] = $+$0.05 $\pm$ 0.04 and [Ba/Fe] = $-$0.01 $\pm$ 0.10. The majority of the BS stars are consistent with these values. We identify five BSs with significant barium enhancement. These stars most likely formed through mass transfer from an asymptotic giant branch star that polluted the surface of the BS with the nucleosynthesis products generated during thermal pulsations. This conclusion aligns with the results from the substantial work done on the BSs in old open cluster NGC 188 that identifies mass transfer as the dominant mechanism for BS formation in that open cluster. However, four of the BSs with enhanced barium show no radial-velocity evidence for a companion. The one star that is in a binary is a double-lined system, meaning the companion is not a white dwarf and not the remnant of a prior AGB star. In this paper we attempt to develop a consistent scenario to explain the origin of these five BSs.

astro-ph.SR↗

arXiv2015

Stellar Radial Velocities in the Old Open Cluster M67 (NGC 2682) I. Memberships, Binaries, and Kinematics

(Abridged) We present results from 13776 radial-velocity (RV) measurements of 1278 candidate members of the old (4 Gyr) open cluster M67 (NGC 2682). The measurements are the results of a long-term survey that includes data from seven telescopes with observations for some stars spanning over 40 years. For narrow-lined stars, RVs are measured with precisions ranging from about 0.1 to 0.8 km/s. The combined stellar sample reaches from the brightest giants in the cluster down to about 4 magnitudes below the main-sequence turnoff (V = 16.5), covering a mass range of about 1.34 MSun to 0.76 MSun. Spatially, the sample extends to a radius of 30 arcmin (7.4 pc in projection at a distant of 850 pc or 6-7 core radii). We find M67 to have a mean RV of +33.64 km/s (with an internal precision of +/- 0.03 km/s). For stars with >=3 measurements, we derive RV membership probabilities and identify RV variables, finding 562 cluster members, 142 of which show significant RV variability. We use these cluster members to construct a color-magnitude diagram and identify a rich sample of stars that lie far from the standard single star isochrone, including the well-known blue stragglers, sub-subgiants and yellow giants. These exotic stars have a binary frequency of (at least) 80%, more than three times that detected for stars in the remainder of the sample. We confirm that the cluster is mass segregated, finding the binaries to be more centrally concentrated than the single stars in our sample at the 99.8% confidence level. The blue stragglers are centrally concentrated as compared to the solar-type main-sequence single stars in the cluster at the 99.7% confidence level. Accounting for both measurement precision and undetected binaries, we derive a RV dispersion in M67 of 0.59 +0.07 -0.06 km/s, which yields a virial mass for the cluster of 2100 +610 -550 MSun. WIYN Open Cluster Study. LXVII.

astro-ph.SR↗

arXiv2015

A spin-down clock for cool stars from observations of a 2.5-billion-year-old cluster

The ages of the most common stars - low-mass (cool) stars like the Sun, and smaller - are difficult to derive because traditional dating methods use stellar properties that either change little as the stars age or are hard to measure. The rotation rates of all cool stars decrease substantially with time as the stars steadily lose their angular momenta. If properly calibrated, rotation therefore can act as a reliable determinant of their ages based on the method of gyrochronology. To calibrate gyrochronology, the relationship between rotation period and age must be determined for cool stars of different masses, which is best accomplished with rotation period measurements for stars in clusters with well-known ages. Hitherto, such measurements have been possible only in clusters with ages of less than about one billion years, and gyrochronology ages for older stars have been inferred from model predictions. Here we report rotation period measurements for 30 cool stars in the 2.5-billion-year-old cluster NGC 6819. The periods reveal a well-defined relationship between rotation period and stellar mass at the cluster age, suggesting that ages with a precision of order 10 per cent can be derived for large numbers of cool Galactic field stars.

astro-ph.SR↗