Convective Turnover Time Research Articles

Chromospheric activity among fast-rotating M dwarfs in the open cluster NGC 2516

We report radial velocities (RVs), projected equatorial velocities (v sin i) and CaII triplet (CaT) chromospheric activity indices for 237 late-K to mid-M candidate members of the young open cluster NGC 2516. These stars have rotation periods between 0.1 and 15 days. Intermediate resolution spectra were obtained using the Giraffe spectrograph at the Very Large Telescope. Membership was confirmed on the basis of RVs for 210 targets. We see a marked increase in the fraction of rapidly rotators as we move to cooler spectral types. About 20 per cent of M0-M1 stars have v sin i >15km/s, increasing to 90 per cent of M4 stars. Activity indices derived from the first two lines of the CaT (8498A and 8542A) show differing dependencies on rotation period and mass for stars lying above and below the fully convective boundary. Higher mass stars, of spectral type K3-M2.5, show chromospheric activity which increases with decreasing Rossby number (the ratio of period to convective turnover time), saturating for Rossby numbers <0.1. For cooler stars, which are probably fully convective and almost all of which have Rossby numbers <0.1, there is a clear decrease in chromospheric activity as (V-I)_0 increases, amounting to a fall of about a factor of 2-3 between spectral types M2.5 and M4. This decrease in activity levels at low Rossby numbers is not seen in X-ray observations of the coronae of cluster M-dwarfs or of active field M-dwarfs. There is no evidence for supersaturation of chromospheric activity for stars of any spectral type at Rossby numbers <0.01. We suggest that the fall in the limiting level of chromospheric emission beyond spectral type M3 in NGC~2516 is, like the simultaneous increase in rotation rates in field stars, associated with a change in the global magnetic topology as stars approach the fully convective boundary and not due to any decrease in dynamo-generated magnetic flux.

Theoretical values of convective turnover times and Rossby numbers for solar-like, pre-main sequence stars

Magnetic fields are at the heart of the observed stellar activity in late-type stars, and they are presumably generated by a dynamo mechanism at the interface layer between the radiative and the convective stellar regions. Since dynamo models are based on the interaction between differential rotation and convective motions, the introduction of rotation in the ATON 2.3 stellar code allows for explorations regarding a physically consistent treatment of magnetic effects in stellar structure and evolution, even though there are formidable mathematical and numerical challenges involved. As examples, we present theoretical estimates for both the local (tau_c) and global (tau_g) convective turnover times for rotating pre-main sequence solar-type stars, based on up-to-date input physics for stellar models. Our theoretical predictions are compared with the previous ones available in the literature. In addition, we investigate the dependence of the convective turnover time on convection regimes, the presence of rotation and atmospheric treatment. Those estimates, this quantities can be used to calculate the Rossby number, Ro, which is related to the magnetic activity strength in dynamo theories and, at least for main-sequence stars, shows an observational correlation with stellar activity. More important, they can also contribute for testing stellar models against observations. Our theoretical values of tau_c, tau_g and Ro qualitatively agree with those published by Kim & Demarque (1996). By increasing the convection efficiency, tau_g decreases for a given mass. FST models show still lower values. The presence of rotation shifts tau_g towards slightly higher values when compared with non-rotating models. The use of non-gray boundary conditions in the models yields values of tau_g smaller than in the gray approximation.

DISSIPATION EFFICIENCY IN TURBULENT CONVECTIVE ZONES IN LOW-MASS STARS

We extend the analysis of Penev et al. (2007) to calculate effective viscosities for the surface convective zones of three main sequence stars of 0.775Msun, 0.85Msun and the present day Sun. In addition we also pay careful attention to all normalization factors and assumptions in order to derive actual numerical prescriptions for the effective viscosity as a function of the period and direction of the external shear. Our results are applicable for periods that are too long to correspond to eddies that fall within the inertial subrange of Kolmogorov scaling, but no larger than the convective turnover time, when the assumptions of the calculation break down. We find linear scaling of effective viscosity with period and magnitudes at least three times larger than the Zahn (1966, 1989) prescription.

Large-scale magnetic topologies of early M dwarfs★

We present here additional results of a spectropolarimetric survey of a small sample of stars ranging from spectral type M0 to M8 aimed at investigating observationally how dynamo processes operate in stars on both sides of the full convection threshold (spectral type M4). The present paper focuses on early M stars (M0-M3), that is above the full convection threshold. Applying tomographic imaging techniques to time series of rotationally modulated circularly polarized profiles collected with the NARVAL spectropolarimeter, we determine the rotation period and reconstruct the large-scale magnetic topologies of six early M dwarfs. We find that early-M stars preferentially host large-scale fields with dominantly toroidal and non-axisymmetric poloidal configurations, along with significant differential rotation (and long-term variability); only the lowest-mass star of our subsample is found to host an almost fully poloidal, mainly axisymmetric large-scale field resembling those found in mid-M dwarfs. This abrupt change in the large-scale magnetic topologies of M dwarfs (occurring at spectral type M3) has no related signature on X-ray luminosities (measuring the total amount of magnetic flux); it thus suggests that underlying dynamo processes become more efficient at producing large-scale fields (despite producing the same flux) at spectral types later than M3. We suspect that this change relates to the rapid decrease in the radiative cores of low-mass stars and to the simultaneous sharp increase of the convective turnover times (with decreasing stellar mass) that models predict to occur at M3; it may also be (at least partly) responsible for the reduced magnetic braking reported for fully convective stars. Based on observations obtained at the Telescope Bernard Lyot (TBL), operated by the Institut National des Science de l'Univers of the Centre National de la Recherche Scientifique of France. E-mail: donati@ast.obs-mip.fr (J-FD); jmorin@ast.obs-mip.fr (JM); petit@ast.obs-mip.fr (PP); xavier.delfosse@obs.ujf-grenoble.fr (XD); thierry.forveille@obs.ujf-grenoble.fr (TF); auriere@ast.obs-mip.fr (MA); remi.cabanac@ast.obs-mip.fr (RC); dintrans@ast.obs-mip.fr (BD); rfares@ast.obs-mip.fr (RF); tgastine@ast.obs-mip.fr (TG); mmj@st-and.ac.uk (MMJ); lignieres@ast.obs-mip.fr (FL); fpaletou@ast.obs-mip.fr (FP); julio.ramirez@obspm.fr (JCRV); sylvie.theado@ast.obs-mip.fr (ST)

The evolution of ‘the moment of inertia’ of stars

AbstractObservations of the rotation periods of cool open cluster stars display a distinctive dichotomy when plotted against stellar mass/color. Other measures of stellar activity are also known to be dependent on stellar mass and structure, especially the onset and characteristics of convection zones. One proposal for understanding the observed rotation period dichotomy suggested dependencies on the moment of inertia of either the whole star or that of only the outer convection zone (Barnes 2003).The moment of inertia of stars with the mass between 0.1Msun and 3.0Msun have been calculated using a version of Yale Stellar evolution code (aka YREC). Each star has been evolved from stellar birthline to the onset of the core He burning. For easy comparison to observations, we have calculated the isochrones of these quantities as well as the convective turnover time, of interest to the activity community.

Modelling the differential rotation of F stars

AbstractWe model stellar differential rotation based on the mean‐field theory of fluid dynamics. DR is mainly driven by Reynolds stress, which is anisotropic and has a non‐diffusive component because the Coriolis force affects the convection pattern. Likewise, the convective heat transport is not strictly radial but slightly tilted towards the rotation axis, causing the polar caps to be slightly warmer than the equator. This drives a flow opposite to that caused by differential rotation and so allows the system to avoid the Taylor‐Proudman state. Our model reproduces the rotation pattern in the solar convection zone and allows predictions for other stars with outer convection zones. The surface shear turns out to depend mainly on the spectral type and only weakly on the rotation rate. We present results for stars of spectral type F which show signs of very strong differential rotation in some cases. Stars just below the mass limit for outer convection zones have shallow convection zones with short convective turnover times. We find solar‐type rotation and meridional flow patterns at much shorter rotation periods and horizontal shear much larger than on the solar surface, in agreement with recent observations. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Color, Rotation, Age, and Chromospheric Activity Correlations in Late‐Type Main‐Sequence Stars

A study of the rotation-activity-age relationships in a large sample of single late-type main-sequence stars is carried out, based on rotation period data from the literature, on our measurements of the Mg II k line chromospheric flux in IUE high-resolution spectra, and on Hipparcos parallaxes. The analysis of the rotation period data of open clusters and field stars indicates that the rotational period decreases linearly with increasing mass in stars of the same age and evolves as a power of age as t0.45. This information has enabled us to disentangle the role of age in the chromospheric activity-rotation relationship, as well as to analyze the behavior of the Mg II emission flux in terms of activity evolutionary paths and of activity isochrones. It is shown that the Mg II emission maintains a saturated level in very young stars until a certain age that depends on stellar mass, while at later stages it decays at a faster rate for more massive stars. We have also determined the convection turnover time from observational data and analyzed the relationship between the Mg II emission flux and the Rossby number. We reach the conclusion that there is no clear advantage in using the Rossby number instead of stellar age in describing the chromospheric Mg II losses, at least with the convective turnover time values currently in use.

Theoretical estimates of the convective turnover time for low-mass, rotating pre-main sequence stars

AbstractThe Rossby number Ro is an important quantity related to the well-known magnetic activity-rotation correlation for main sequence, solar-type stars. For such stars, Ro can be obtained by a semi-empirical relationship between the convective turnover time τc and the B-V colour index, but an equivalent activity-rotation correlation seems not to exist for pre-main sequence stars. In this work we report theoretical estimates of τc for low-mass, rotating pre-main sequence stars under either the Full Spectrum of Turbulence (FST) or the classical Mixing Length Theory (MLT) convection models. The results for the MLT models show that the lower the convection efficiency the higher τc, while the FST models give τc lower than those for the MLT. The presence of a parametric magnetic field lowers the convection efficiency, resulting in smaller τc values.

Evolutionary status of UV Piscium and its comparison with other short period RS CVn binaries

From the derived elements of UV Piscium, the evolutionary status of both of its components are compared with the Schaller et al. models and also with other main sequence systems having spectral types of late F to K range. From these models the ages of the components of UV Psc are determined. The Rossby number, which is a measure of chromospheric activity, has been derived from the convective turnover time scales and also from the age estimates.

Simulations of magneto-convection in the solar photosphere

We have developed a 3D magnetohydrodynamics simulation code for applications in the solar convection zone and photosphere. The code includes a non-local and non-grey radiative transfer module and takes into account the effects of partial ionization. Its parallel design is based on domain decomposition, which makes it suited for use on parallel computers with distributed memory architecture. We give a description of the equations and numerical methods and present the results of the simulation of a solar plage region. Starting with a uniform vertical field of 200 G, the processes of flux expulsion and convective field amplification lead to a dichotomy of strong, mainly vertical fields embedded in the granular downflow network and weak, randomly oriented fields filling the hot granular upflows. The strong fields form a magnetic network with thin, sheet- like structures extending along downflow lanes and micropores with diameters of up to 1000 km which form occasionally at vertices where several downflow lanes merge. At the visible surface around optical depth unity, the strong field concentrations are in pressure balance with their weakly magnetized surroundings and reach field strengths of up to 2 kG, strongly exceeding the values corresponding to equipartition with the kinetic energy density of the convective motions. As a result of the channelling of radiation, small flux concentrations stand out as bright features, while the larger micropores appear dark in brightness maps owing to the suppression of the convective energy transport. The overall shape of the magnetic network changes slowly on a timescale much larger than the convective turnover time, while the magnetic flux is constantly redistributed within the network leading to continuous formation and dissolution of flux concentrations.

The stellar activity-rotation relationship revisited: Dependence of saturated and non-saturated X-ray emission regimes on stellar mass for late-type dwarfs

We present the results of a new study on the relationship between coronal X-ray emission and stellar rotation in late-type main-sequence stars. We have selected a sample of 259 dwarfs in the range 0.5–2.0, including 110 field stars and 149 members of the Pleiades, Hyades, α Persei, IC 2602 and IC 2391 open clusters. All the stars have been observed with ROSAT, and most of them have photometrically-measured rotation periods available. Our results confirm that two emission regimes exist, one in which the rotation period is a good predictor of the total X-ray luminosity, and the other in which a constant saturated X-ray to bolometric luminosity ratio is attained; we present a quantitative estimate of the critical rotation periods below which stars of different masses (or spectral types) enter the saturated regime. In this work we have also empirically derived a characteristic time scale, , which we have used to investigate the relationship between the X-ray emission level and an X-ray-based Rossby number : we show that our empirical time scale resembles the theoretical convective turnover time for , but it also has the same functional dependence on as in the color range . Our results imply that – for non-saturated coronae – the Lx – Prot relation is equivalent to the vs. Re relation.

Numerical simulations of surface convection in a late M-dwarf

Based on detailed 2D and 3D numerical radiation-hydrodynamics (RHD) simulations of time-dependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of a prototypical late-type M-dwarf (Teff~2800K log(g)=5.0, solar chemical composition). The RHD models predict stellar granulation qualitatively similar to the familiar solar pattern. Quantitatively, the granular cells show a convective turn-over time scale of ~100s, and a horizontal scale of 80km; the relative intensity contrast of the granular pattern amounts to 1.1%, and root-mean-square vertical velocities reach 240m/s at maximum. Deviations from radiative equilibrium in the higher, formally convectively stable atmospheric layers are found to be insignificant allowing a reliable modeling of the atmosphere with 1D standard model atmospheres. A mixing-length parameter of alpha=2.1 provides the best representation of the average thermal structure of the RHD model atmosphere while alternative values are found when fitting the asymptotic entropy encountered in deeper layers of the stellar envelope alpha=1.5, or when matching the vertical velocity field alpha=3.5. The close correspondence between RHD and standard model atmospheres implies that presently existing discrepancies between observed and predicted stellar colors in the M-dwarf regime cannot be traced back to an inadequate treatment of convection in the 1D standard models. The RHD models predict a modest extension of the convectively mixed region beyond the formal Schwarzschild stability boundary which provides hints for the distribution of dust grains in cooler (brown dwarf) atmospheres.

Small-scale magnetic fields on late-type M-dwarfs

We performed kinematic studies of the evolution of small-scale magnetic fields in the surface layers of M-dwarfs. We solved the induction equation for a prescribed velocity field, magnetic Reynolds number ReM, and boundary conditions in a Cartesian box, representing a volume comprising the optically thin stellar atmosphere and the uppermost part of the optically thick convective envelope. The velocity field is spatially and temporally variable, and stems from detailed radiationhydrodynamics simulations of convective flows in a proto-typical late-type M-dwarf (Teff = 2800 K, log g = 5.0, solar chemical composition, spectral type ≈M6). We find dynamo action for ReM ≥ 400. Growth time scales of the magnetic field are comparable to the convective turn-over time scale (≈150 sec). The convective velocity field concentrates the magnetic field in sheets and tubular structures in the inter-granular downflows. Scaling from solar conditions suggests that field strengths as high as 20 kG might be reached locally. Perhaps surprisingly, ReM is of order unity in the surface layers of cooler M-dwarfs, rendering the dynamo inoperative. In all studied cases we find a rather low spatial filling factor of the magnetic field.

Subphotospheric convection and magnetic activity dependence on metallicity and age: Models and tests

We present an extensive study on the dependence of the convective turnover time (conv) on the stellar metallicity and age for main-sequence stars of masses 0.6{1.6 M. To this aim we have used and compared predictions by stellar models based on the classical Mixing Length Theory and models incorporating a Full Spectrum of Turbulence treatment of subphotospheric convection. We show that the metallicity eect is relevant for dG stars but negligible for dK stars, while stellar age is important when computing the turnover times for red dwarfs younger than logt 8:5 yr. A scatter by up to a factor 3 could be spuriously introduced in the activity vs. Rossby number relationships if such eects are neglected. We have tested our model predictions on the metallicity eect by comparison with the observed median X-ray luminosities for dG and dK stars in the open clusters NGC 2516, the Pleiades, and Blanco 1, having similar age but likely dierent metal contents. We show that our model predictions, taking into account also the dependence of the coronal plasma emissivity on the metal abundance, are in agreement with the observations in all cases except for the dK stars in the metal-rich cluster Blanco 1, where our assumption of a rotation period distribution similar to those of the other cluster need to be conrmed by future observations.

Winds from Luminous Late‐Type Stars. I. The Effects of Nonlinear Alfven Waves

We present the results of magnetohydrodynamic (MHD) modeling of winds from luminous late-type stars using a 2.5-dimensional, nonlinear MHD computer code. We assume that the wind is generated within an initially hydrostatic atmosphere and is driven by torsional Alfven waves generated at the stellar surface. Two cases of topology are considered: case I has longitudinally uniform density distribution and isotropic radial magnetic field over the stellar surface, and case II has an isotropic, radial magnetic field with a transverse density gradient, which we refer to as an atmospheric We use the same set of boundary conditions for both models.The calculations are designed to model a cool luminous star, for which we assume an initial hydrostatic pressure scale height of 0.072 R*, an Alfven wave speed of 92 km s-1 at the surface, and a wave period of 76 days, which roughly corresponds with the convective turnover time. For case I the calculations produce a wind with terminal velocity of ~22 km s-1 and a mass loss rate comparable to the expected value of 10-6 M☉ yr-1. For case II we predict a two-component wind: a fast (25 km s-1) and relatively dense wind outside of the hole and a slow (15 km s-1), rarefied wind inside of the hole.

Tethered balloon measurements of biogenic VOCs in the atmospheric boundary layer

Biogenic volatile organic compounds (BVOCs) were measured on tethered balloon platforms in 11 deployments between 1985 and 1996. A series of balloon sampling packages have been used to describe boundary layer dynamics, BVOC distribution, chemical transformations of BVOCs, and to estimate BVOC emission rates from terrestrial vegetation. Measurements indicated a slow decrease of concentration for BVOCs with altitude in the mixed layer when sampling times were greater than average convective turnover time; surface layer concentrations were more variable because of proximity to various emission sources in the smaller surface layer footprint. Mixed layer concentrations of isoprene remained fairly constant in the middle of the day, in contrast to canopy-level isoprene concentrations, which continued to increase until early evening. Daytime emissions, which increase with temperature and light, appear to be balanced by changes in entrainment and oxidation. Daytime measurements of methacrolein and methyl vinyl ketone, reaction products of the atmospheric oxidation of isoprene, showed fairly constant ratio to each other with altitude throughout the mixed layer. BVOC emission flux estimates using balloon measurements and from the extrapolation of leaf level emissions to the landscape scale were in good agreement.

Relating stellar cycle periods to dynamo calculations

Stellar magnetic activity in slowly rotating stars is often cyclic, with the period of the magnetic cycle depending critically on the rotation rate and the convective turnover time of the star. Here we show that the interpretation of this law from dynamo models is not a simple task. It is demonstrated that the period is (unsurprisingly) sensitive to the precise type of non-linearity employed. Moreover the calculation of the wave-speed of plane-wave solutions does not (as was previously supposed) give an indication of the magnetic period in a more realistic dynamo model, as the changes in length-scale of solutions are not easily captured by this approach. Progress can be made, however, by considering a realistic two-dimensional model, in which the radial length-scale of waves is included. We show that it is possible in this case to derive a more robust relation between cycle period and dynamo number. For all the non-linearities considered in the most realistic model, the magnetic cycle period is a decreasing function of IDI (the amplitude of the dynamo number). However, discriminating between different non-linearities is difficult in this case and care must therefore be taken before advancing explanations for the magnetic periods of stars.

The Theoretical Calculation of the Rossby Number and the ``Nonlocal'' Convective Overturn Time for Pre-Main-Sequence and Early Post-Main-Sequence Stars

This paper provides estimates of convective turnover timescales for Sun-like stars in the pre-main-sequence and early post-main-sequence phases of evolution, based on up-to-date physical input for the stellar models. In this first study, all models have solar abundances, which is typical of the stars in the Galactic disk, where most of the available data have been collected. A new feature of these models is the inclusion of rotation in the evolutionary sequences, thus making it possible to derive theoretically the Rossby number for each star along its evolutionary track, based on its calculated rotation rate and its local convective turnover time near the base of the convection zone. Global turnover times are also calculated for the complete convection zone. This information should make possible a new class of observational tests of stellar theory that were previously impossible with semiempirical models, particularly in the study of stellar activity and in research related to angular momentum transfer in stellar interiors during the course of stellar evolution.

Lyapunov exponents for solar surface convection

We have carried out detailed 2D numerical radiation hydrodynamics calculations, specifically designed to model time-dependent, compressible convection in the surface layers of the Sun. These simulations, which take into account a realistic equation of state and use an elaborate scheme to describe multi-dimensional, non-local, frequency-dependent radiative transfer, allow a direct comparison with observed photometric and spectroscopic properties of solar granulation. Their purpose is to enhance our understanding of the dynamics and thermal structure of convective stellar atmospheres, and to investigate the generation of acoustic energy by turbulent convection. Here, we briefly present some of the main properties of our solar convection models. In particular, we demonstrate the chaotic behaviour of solar surface convection, estimating the magnitude of the two largest Lyapunov exponents, λ 1 and λ 2, by analysing the time evolution of three simulations with slightly different initial conditions. We find that both λ 1 and λ 2 are positive and of similar magnitude, as expected for a chaotic system of high dimension. The corresponding characteristic time scale λ 1 −1 of approximately 320 s is comparable to the convective turnover time.

A STUDY OF VARIABILITY IN A SAMPLE OF G AND K GIANTS

ABSTRACT Eight years of Ca II surface activity records from Mount Wilson Observatory measured for 12 bright G-K III stars have been analyzed in order to detect periodic variations attributable to rotation. We also present photometric V-band data for these stars from the Fairborn 0.25m Automatic Photometric Telescope (APT) that yielded a photometric period in one case and rms deviations from apparently constant brightness levels for the remaining 11 stars. The Ca II data yielded rotation periods for 10 out of 12 giant stars. We demonstrate that the photometric variability and non-variability of these stars can be predicted from their Rossby numbers calculated from our observed rotation periods and convective turnover times scaled up from the main sequence.