Stellar Rotation Rate Research Articles

The Minimum Mass of Rotating Main-sequence Stars and its Impact on the Nature of Extended Main-sequence Turnoffs in Intermediate-age Star Clusters in the Magellanic Clouds∗

Abstract Extended main-sequence turnoffs (eMSTOs) are a common feature in color–magnitude diagrams (CMDs) of young and intermediate-age star clusters in the Magellanic Clouds. The nature of eMSTOs is still debated. The most popular scenarios are extended star formation and ranges of stellar rotation rates. Here, we study implications of a kink feature in the main sequence (MS) of young star clusters in the Large Magellanic Cloud (LMC). This kink shows up very clearly in new Hubble Space Telescope observations of the 700 Myr old cluster NGC 1831 and is located below the region in the CMD where multiple or wide MSs, which are known to occur in young clusters and thought to be due to varying rotation rates, merge together into a single MS. The kink occurs at an initial stellar mass of 1.45 ± 0.02 M ⊙; we posit that it represents a lower limit to the mass below which the effects of rotation on the energy output of stars are rendered negligible at the metallicity of these clusters. Evaluating the positions of stars with this initial mass in CMDs of massive LMC star clusters with ages of ∼1.7 Gyr that feature wide eMSTOs, we find that such stars are located in a region where the eMSTO is already significantly wider than the MS below it. This strongly suggests that stellar rotation cannot fully explain the wide extent of eMSTOs in massive intermediate-age clusters in the Magellanic Clouds. A distribution of stellar ages still seems necessary to explain the eMSTO phenomenon.

Phase Transition Effects on the Dynamical Stability of Hybrid Neutron Stars

We study radial oscillations of hybrid non-rotating neutron stars composed by a quark matter core and hadronic external layers. At first, we physically deduce the junction conditions that should be imposed between two any phases in these systems when perturbations take place. Then we compute the oscillation spectrum focusing on the effects of slow and rapid phase transitions at the quark-hadron interface. We use a generic MIT bag model for quark matter and a relativistic mean field theory for hadronic matter. In the case of rapid transitions at the interface we find a general relativistic version of the reaction mode which has similar properties as its classical counterpart. We also show that the usual static stability condition $\partial M/\partial \rho_c\geq 0$, where $\rho_c$ is the central density of a star whose total mass is $M$, remains always true for rapid transitions but breaks down in general for slow transitions. In fact, for slow transitions we find that the frequency of the fundamental mode can be a real number (indicating stability) even for some branches of stellar models that verify $\partial M/\partial \rho_c \leq 0$. Thus, when secular instabilities are suppressed, as expected below some critical stellar rotation rate, it would be possible the existence of twin or even triplet stars with the same gravitational mass but different radii, with one of the counterparts having $\partial M/\partial \rho_c \leq 0$. We explore some astrophysical consequences of these results.

New Insights into the Formation of the Blue Main Sequence in NGC 1850

Abstract Recent discoveries of bimodal main sequences (MSs) associated with young clusters (with ages ≲1 Gyr) in the Magellanic Clouds have drawn a lot of attention. One of the prevailing formation scenarios attributes these split MSs to a bimodal distribution in stellar rotation rates, with most stars belonging to a rapidly rotating population. In this scenario, only a small fraction of stars populating a secondary blue sequence are slowly or non-rotating stars. Here, we focus on the blue MS in the young cluster NGC 1850. We compare the cumulative number fraction of the observed blue-MS stars to that of the high-mass-ratio binary systems at different radii. The cumulative distributions of both populations exhibit a clear anti-correlation, characterized by a highly significant Pearson coefficient of −0.97. Our observations are consistent with the possibility that blue-MS stars are low-mass-ratio binaries, and therefore their dynamical disruption is still ongoing. High-mass-ratio binaries, on the other hand, are more centrally concentrated.

Spectroscopic and physical parameters of Galactic O-type stars

Context.Massive stars play a key role in the evolution of galaxies and our Universe.Aims.Our goal is to compare observed and predicted properties of single Galactic O stars to identify and constrain uncertain physical parameters and processes in stellar evolution and atmosphere models.Methods.We used a sample of 53 objects of all luminosity classes and with spectral types from O3 to O9.7. For 30 of these, we determined the main photospheric and wind parameters, including projected rotational rates accounting for macroturbulence, and He and N surface abundances, using optical spectroscopy and applying the model atmosphere code FASTWIND. For the remaining objects, similar data from the literature, based on analyses by means of the CMFGEN code, were used instead. The properties of our sample were then compared to published predictions based on two grids of single massive star evolution models that include rotationally induced mixing.Results.Any of the considered model grids face problem in simultaneously reproducing the stellar masses, equatorial gravities, surface abundances, and rotation rates of our sample stars. The spectroscopic masses derived for objects below ~30M⊙tend to be smaller than the evolutionary ones, no matter which of the two grids have been used as a reference. While this result may indicate the need to improve the model atmosphere calculations (e.g. regarding the treatment of turbulent pressure), our analysis shows that the established mass problem cannot be fully explained in terms of inaccurate parameters obtained by quantitative spectroscopy or inadequate model values ofVroton the zero age main sequence. Within each luminosity class, we find a close correlation of N surface abundance and luminosity, and a stronger N enrichment in more massive and evolved O stars. Additionally, we also find a correlation of the surface nitrogen and helium abundances. The large number of nitrogen-enriched stars above ~30M⊙argues for rotationally induced mixing as the most likely explanation. However, none of the considered models can match the observed trends correctly, especially in the high mass regime.Conclusions.We confirm mass discrepancy for objects in the low mass O-star regime. We conclude that the rotationally induced mixing of helium to the stellar surface is too strong in some of the models. We also suggest that present inadequacies of the models to represent the N enrichment in more massive stars with relatively slow rotation might be related (among other issues) to problematic efficiencies of rotational mixing. We are left with a picture in which invoking binarity and magnetic fields is required to achieve a more complete agreement of the observed surface properties of a population of massive main-sequence stars with corresponding evolutionary models.

An HST/STIS Optical Transmission Spectrum of Warm Neptune GJ 436b

Abstract GJ 436b is a prime target for understanding warm Neptune exoplanet atmospheres and a target for multiple James Webb Space Telescope (JWST) Guaranteed Time Observation programs. Here, we report the first space-based optical transmission spectrum of the planet using two Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) transit observations from 0.53 to 1.03 μm. We find no evidence for alkali absorption features, nor evidence of a scattering slope longward of 0.53 μm. The spectrum is indicative of moderate to high metallicity (∼100–1000× solar), while moderate-metallicity scenarios (∼100× solar) require aerosol opacity. The optical spectrum also rules out some highly scattering haze models. We find an increase in transit depth around 0.8 μm in the transmission spectra of three different sub-Jovian exoplanets (GJ 436b, HAT-P-26b, and GJ 1214b). While most of the data come from STIS, data from three other instruments may indicate this is not an instrumental effect. Only the transit spectrum of GJ 1214b is well fit by a model with stellar plages on the photosphere of the host star. Our photometric monitoring of the host star reveals a stellar rotation rate of 44.1 days and an activity cycle of 7.4 years. Intriguingly, GJ 436 does not become redder as it gets dimmer, which is expected if star spots were dominating the variability. These insights into the nature of the GJ 436 system help refine our expectations for future observations in the era of JWST, whose higher precision and broader wavelength coverage will shed light on the composition and structure of GJ 436b’s atmosphere.

Theory and evidence of global Rossby waves in upper main-sequence stars: r-mode oscillations in many Kepler stars

Asteroseismic inference from pressure modes (p modes) and buoyancy, or gravity, modes (g modes) is ubiquitous for stars across the Hertzsprung--Russell diagram. Until now, however, discussion of r modes (global Rossby waves) has been rare. Here we derive the expected frequency ranges of r modes in the observational frame by considering the visibility of these modes. We find that the frequencies of r modes of azimuthal order $m$ appear as groups at slightly lower frequency than $m$ times the rotation frequency. Comparing the visibility curves for r modes with Fourier amplitude spectra of Kepler light curves of upper main-sequence B, A and F stars, we find that r modes are present in many $\gamma$ Dor stars (as first discovered by Van Reeth et al. 2016), spotted stars, and so-called Heartbeat stars, which are highly eccentric binary stars. We also find a signature of r modes in a frequently bursting Be star observed by Kepler. In the amplitude spectra of moderately to rapidly rotating $\gamma$ Dor stars, r-mode frequency groups appear at lower frequency than prograde g-mode frequency groups, while in the amplitude spectra of spotted early A to B stars, groups of symmetric (with respect to the equator) r-mode frequencies appear just below the frequency of a structured peak that we suggest represents an approximate stellar rotation rate. In many Heartbeat stars, a group of frequencies can be fitted with symmetric $m=1$ r modes, which can be used to obtain rotation frequencies of these stars.

3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension

Context: Long-term variability in solar cycles represents a challenging constraint for theoretical models. Mean-field Babcock-Leighton dynamos that consider non-instantaneous rising flux tubes have been shown to exhibit long-term variability in their magnetic cycle. However a relation that parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of stellar parameters is still missing. Aims: We aim to find a general parameterization of the rise-time of magnetic flux tubes for solar-like stars. Methods: By considering the influence of magnetic tension on the rise of non-axisymmetric flux tubes, we predict the existence of a control parameter referred as $\Gamma_{\alpha_1}^{\alpha_2}$. This parameter is a measure of the balance between rotational effects and magnetic effects (buoyancy and tension) acting on the magnetic flux tube. We carry out two series of numerical experiments (one for axisymmetric rise and one for non-axisymmetric rise) and demonstrate that $\Gamma_{\alpha_1}^{\alpha_2}$ indeed controls the rise-time of magnetic flux tubes. Results: We find that the rise-time follows a power law of $\Gamma_{\alpha_1}^{\alpha_2}$ with an exponent that depends on the azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In the case of non-axisymmetric rise, the tension force modifies the force balance acting on the magnetic flux tube. We identified the three independent parameters required to predict the rise-time of magnetic flux tubes, that is, the stellar rotation rate, the magnetic flux density of the flux tube, and its azimuthal wavenumber. We combined these into one single relation that is valid for any solar-like star. We suggest using this generalized relation to constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo models.

The vertical structure of the boundary layer around compact objects

Context. Mass transfer due to Roche lobe overflow leads to the formation of an accretion disk around a weakly magnetized white dwarf (WD) in cataclysmic variables. At the inner edge of the disk, the gas comes upon the surface of the WD and has to get rid of its excess kinetic energy in order to settle down on the more slowly rotating outer stellar layers. This region is known as the boundary layer (BL). Aims. In this work we investigate the vertical structure of the BL, which is still poorly understood. We shall provide details of the basic structure of the two-dimensional (2D) BL and how it depends on parameters such as stellar mass and rotation rate, as well as the mass-accretion rate. We further investigate the destination of the disk material and compare our results with previous one-dimensional (1D) simulations. Methods. We solve the 2D equations of radiation hydrodynamics in a spherical geometry using a parallel grid-based code that employs a Riemann solver. The radiation energy is considered in the two-temperature approach with a radiative flux given by the flux-limited diffusion approximation. Results. The BL around a non-rotating WD is characterized by a steep drop in angular velocity over a width of only 1% of the stellar radius, a heavy depletion of mass, and a high temperature (500 000 K) as a consequence of the strong shear. Variations in Om_star, M_star, and M_dot influence the extent of the changes of the variables in the BL but not the general structure. Depending on Om_star, the disk material travels up to the poles or is halted at a certain latitude. The extent of mixing with the stellar material also depends on Om_star. We find that the 1D approximation matches the 2D data well, apart from an underestimated temperature.

Extended Main-sequence Turn-offs in Intermediate-age Star Clusters: Stellar Rotation Diminishes, but Does Not Eliminate, Age Spreads

Abstract Extended main-sequence turn-off (eMSTO) regions are a common feature in color–magnitude diagrams of young- and intermediate-age star clusters in the Magellanic Clouds. The nature of eMSTOs remains debated in the literature. The currently most popular scenarios are extended star formation activity and ranges of stellar rotation rates. Here we study details of differences in main-sequence turn-off (MSTO) morphology expected from spreads in age versus spreads in rotation rates, using Monte Carlo simulations with the Geneva syclist isochrone models that include the effects of stellar rotation. We confirm a recent finding of Niederhofer et al. that a distribution of stellar rotation velocities yields an MSTO extent that is proportional to the cluster age, as observed. However, we find that stellar rotation yields MSTO crosscut widths that are generally smaller than observed ones at a given age. We compare the simulations with high-quality Hubble Space Telescope data of NGC 1987 and NGC 2249, which are the two only relatively massive star clusters with an age of ∼1 Gyr for which such data is available. We find that the distribution of stars across the eMSTOs of these clusters cannot be explained solely by a distribution of stellar rotation velocities, unless the orientations of rapidly rotating stars are heavily biased toward an equator-on configuration. Under the assumption of random viewing angles, stellar rotation can account for ∼60% and ∼40% of the observed FWHM widths of the eMSTOs of NGC 1987 and NGC 2249, respectively. In contrast, a combination of distributions of stellar rotation velocities and stellar ages fits the observed eMSTO morphologies very well.

Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

Abstract We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ∼50 Myr to ∼4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.

Evidence for photometric activity cycles in 3203 Kepler stars

In recent years it has been claimed that the length of stellar activity cycles is determined by the stellar rotation rate. It is observed that the cycle period increases with rotation period along the so-called active and inactive sequences. In this picture the Sun occupies a solitary position in between the two sequences. Our goal is to measure cyclic variations of the stellar light curve amplitude and the rotation period using four years of Kepler data. Periodic changes of the light curve amplitude or the stellar rotation period are associated with an underlying activity cycle. Using the McQuillan et al. 2014 sample we compute the rotation period and the variability amplitude for each Kepler quarter and search for periodic variations of both time series. To test for periodicity in each stellar time series we consider Lomb-Scargle periodograms and use a selection based on a False Alarm Probability (FAP). We detect amplitude periodicities in 3203 stars between 0.5-6 years covering rotation periods between 1-40 days. Given our sample size of 23,601 stars and our selection criteria that the FAP is less than 5%, this number is almost three times higher than that expected from pure noise. We do not detect periodicities in the rotation period beyond those expected from noise. Our measurements reveal that the cycle period shows a weak dependence on rotation rate, slightly increasing for longer rotation period. We further show that the shape of the variability deviates from a pure sine curve, consistent with observations of the solar cycle. Our measurements do not support the existence of distinct sequences in the P_rot-P_cyc plane, although there is some evidence for the inactive sequence for rotation periods between 5-25 days. Unfortunately, the total observing time is too short to draw sound conclusions on activity cycles with similar length as the solar cycle.

Are pulsars spun up or down by SASI spiral modes?

Pulsars may either be spun up or down by hydrodynamic instabilities during the supernova explosion of massive stars. Besides rapidly-rotating cases related to bipolar explosions, stellar rotation may affect the explosion of massive stars in the more common situations where the centrifugal force is minor. Using 2D simulations of a simplified setup in cylindrical geometry, we examine the impact of rotation on the Standing Accretion Shock Instability (SASI) and the corotation instability, also known as low-T/|W|. The influence of rotation on the saturation amplitude of these instabilities depends on the specific angular momentum in the accretion flow and the ratio of the shock to the neutron star radii. The spiral mode of SASI becomes more vigorous with faster rotation only if this ratio is large enough. A corotation instability develops at large rotation rates and impacts the dynamics more dramatically, leading to a strong one-armed spiral wave. Non-axisymmetric instabilities are able to redistribute angular momentum radially and affect the pulsar spin at birth. A systematic study of the relationship between the core rotation period of the progenitor and the initial pulsar spin is performed. Stellar rotation rates for which pulsars are spun up or down by SASI are estimated. Rapidly spinning progenitors are modestly spun down by spiral modes, less than $\sim 30\%$, when a corotation instability develops. Given the observational constraints on pulsar spin periods at birth, this suggests that rapid rotation might not play a significant hydrodynamic role in most core-collapse supernovae.

On Differential Rotation and Overshooting in Solar-like Stars

Abstract We seek to characterize how the change of global rotation rate influences the overall dynamics and large-scale flows arising in the convective envelopes of stars covering stellar spectral types from early G to late K. We do so through numerical simulations with the ASH code, where we consider stellar convective envelopes coupled to a radiative interior with various global properties. As solar-like stars spin down over the course of their main sequence evolution, such a change must have a direct impact on their dynamics and rotation state. We indeed find that three main states of rotation may exist for a given star: anti-solar-like (fast poles, slow equator), solar-like (fast equator, slow poles), or a cylindrical rotation profile. Under increasingly strict rotational constraints, the last profile can further evolve into a Jupiter-like profile, with alternating prograde and retrograde zonal jets. We have further assessed how far the convection and meridional flows overshoot into the radiative zone and investigated the morphology of the established tachocline. Using simple mixing length arguments, we are able to construct a scaling of the fluid Rossby number , which we calibrate based on our 3D ASH simulations. We can use this scaling to map the behavior of differential rotation versus the global parameters of stellar mass and rotation rate. Finally, we isolate a region on this map (R of ≳ 1.5–2) where we posit that stars with an anti-solar differential rotation may exist in order to encourage observers to hunt for such targets.

Incidence of stellar rotation on the explosion mechanism of massive stars

AbstractHydrodynamical instabilities may either spin-up or down the pulsar formed in the collapse of a rotating massive star. Using numerical simulations of an idealized setup, we investigate the impact of progenitor rotation on the shock dynamics. The amplitude of the spiral mode of the Standing Accretion Shock Instability (SASI) increases with rotation only if the shock to the neutron star radii ratio is large enough. At large rotation rates, a corotation instability, also known as low-T/W, develops and leads to a more vigorous spiral mode. We estimate the range of stellar rotation rates for which pulsars are spun up or down by SASI. In the presence of a corotation instability, the spin-down efficiency is less than 30%. Given observational data, these results suggest that rapid progenitor rotation might not play a significant hydrodynamical role in the majority of core-collapse supernovae.

Dissecting the Extended Main Sequence Turn-off of the Young Star Cluster NGC 1850

We use the Wide Field Camera 3 onboard the Hubble Space Telescope to obtain deep, high-resolution photometry of the young (~ 100 Myr) star cluster NGC1850 in the Large Magellanic Cloud. We analyze the cluster colour-magnitude diagram (CMD) and find that it hosts an extended main sequence turn-off (MSTO) and a double MS. We demonstrate that these features cannot be due to photometric errors, field star contamination, or differential reddening. From a comparison with theoretical models and Monte Carlo simulations, we show that a coeval stellar population featuring a distribution of stellar rotation rates can reproduce the MS split quite well. However, it cannot reproduce the observed MSTO region, which is significantly wider than the simulated ones. Exploiting narrow-band Halpha imaging, we find that the MSTO hosts a population of Halpha-emitting stars which are interpreted as rapidly rotating Be-type stars. We explore the possibility that the discrepancy between the observed MSTO morphology and that of the simulated simple stellar population (SSP) is caused by the fraction of these objects that are highly reddened, but we rule out this hypothesis. We demonstrate that the global CMD morphology is well-reproduced by a combination of SSPs that cover an age range of ~ 35 Myr as well as a wide variety of rotation rates. We derive the cluster mass and escape velocity and use dynamical evolution models to predict their evolution starting at an age of 10 Myr. We discuss these results and their implications in the context of the extended MSTO phenomenon.

EVIDENCE FOR CLUSTER TO CLUSTER VARIATIONS IN LOW-MASS STELLAR ROTATIONAL EVOLUTION

ABSTRACT The concordance model for angular momentum evolution postulates that star-forming regions and clusters are an evolutionary sequence that can be modeled with assumptions about protostar–disk coupling, angular momentum loss from magnetized winds that saturates in a mass-dependent fashion at high rotation rates, and core-envelope decoupling for solar analogs. We test this approach by combining established data with the large h Per data set from the MONITOR project and new low-mass Pleiades data. We confirm prior results that young low-mass stars can be used to test star–disk coupling and angular momentum loss independent of the treatment of internal angular momentum transport. For slow rotators, we confirm the need for star–disk interactions to evolve the ONC to older systems, using h Per (age 13 Myr) as our natural post-disk case. There is no evidence for extremely long-lived disks as an alternative to core-envelope decoupling. However, our wind models cannot evolve rapid rotators from h Per to older systems consistently, and we find that this result is robust with respect to the choice of angular momentum loss prescription. We outline two possible solutions: either there is cosmic variance in the distribution of stellar rotation rates in different clusters or there are substantially enhanced torques in low-mass rapid rotators. We favor the former explanation and discuss observational tests that could be used to distinguish them. If the distribution of initial conditions depends on environment, models that test parameters by assuming a universal underlying distribution of initial conditions will need to be re-evaluated.

Using planetary transits to estimate magnetic cycles lengths in Kepler stars

AbstractObservations of various solar-type stars along decades showed that they could have magnetic cycles, just like our Sun. These observations yield a relation between the rotation period Prot and the cycle length Pcycle of these stars. Two distinct branches for the cycling stars were identified: active and inactive, classified according to stellar activity level and rotation rate. In this work, we determined the magnetic activity cycle for 6 active stars observed by the Kepler telescope. The method adopted here estimates the activity from the excess in the residuals of the transit light curves. This excess is obtained by subtracting a spotless model transit from the light curve, and then integrating over all the residuals during the transit. The presence of long term periodicity is estimated from the analysis of a Lomb-Scargle periodogram of the complete time series. Finally, we investigate the rotation-cycle period relation for the stars analysed here.

Characterizing the feedback of magnetic field on the differential rotation of solar-like stars

The aim of this article is to study how the differential rotation of solar-like stars is influenced by rotation rate and mass in presence of magnetic fields generated by a convective dynamo. We use the ASH code to model the convective dynamo of solar-like stars at various rotation rates and masses, hence different effective Rossby numbers. We obtained models with either prograde (solar-like) or retrograde (anti-solar-like) differential rotation. The trends of differential rotation versus stellar rotation rate obtained for simulations including the effect of the magnetic field are weaker compared with hydro simulations (ΔΩ∝(Ω/Ω⊙)0.44 in the MHD case and ΔΩ∝(Ω/Ω⊙)0.89 in the hydro case), hence showing a better agreement with the observations. Analysis of angular momentum transport revealed that the simulations with retrograde and prograde differential rotation have opposite distribution of the viscous, turbulent Reynolds stresses and meridional circulation contributions. The thermal wind balance is achieved in the prograde cases. However, in retrograde cases Reynolds stresses are dominant for high latitudes and near the top of the convective layer. Baroclinic effects are stronger for faster rotating models.

Dynamo saturation in rapidly rotating solar-type stars

The magnetic activity of solar-type stars generally increases with stellar rotation rate. The increase, however, saturates for fast rotation. The Babcock-Leighton mechanism of stellar dynamos saturates as well when the mean tilt angle of active regions approaches ninety degrees. Saturation of magnetic activity may be a consequence of this property of the Babcock-Leighton mechanism. Stellar dynamo models with a tilt angle proportional to the rotation rate are constructed to probe this idea. Two versions of the model - treating the tilt angles globally and using Joy's law for its latitude dependence - are considered. Both models show a saturation of dynamo-generated magnetic flux at high rotation rates. The model with latitude-dependent tilt angles also shows a change in dynamo regime in the saturation region. The new regime combines a cyclic dynamo at low latitudes with an (almost) steady polar dynamo.

Are the gyro-ages of field stars underestimated?

By using the current photometric rotational data on eight galactic open clusters, we show that the evolutionary stellar model (isochrone) ages of these clusters are tightly correlated with the period shifts applied to the (B-V)_0 - P_rot ridges that optimally align these ridges to the one defined by Praesepe and the Hyades. On the other hand, when the traditional Skumanich-type multiplicative transformation is used, the ridges become far less aligned due to the age-dependent slope change introduced by the period multiplication. Therefore, we employ our simple additive gyro-age calibration on various datasets of Galactic field stars to test its applicability. We show that, in the overall sense, the gyro-ages are systematically greater than the isochrone ages. The difference could exceed several giga years, depending on the stellar parameters. Although the age overlap between the open clusters used in the calibration and the field star samples is only partial, the systematic difference indicates the limitation of the currently available gyro-age methods and suggests that the rotation of field stars slows down with a considerably lower speed than we would expect from the simple extrapolation of the stellar rotation rates in open clusters.