Convective Turnover Time Research Articles

A calibration of the Rossby number from asteroseismology

Stellar activity and rotation are tightly related in a dynamo process. Our understanding of this mechanism is mainly limited by our capability of inferring the properties of stellar turbulent convection. In particular, the convective turnover time is a key ingredient through the estimation of the stellar Rossby number, which is the ratio of the rotation period and the convective turnover time. In this work, we propose a new calibration of the (B − V) color index dependence of the convective turnover time, hence, of the stellar Rossby number. Our new calibration is based on the stellar structure properties inferred through the detailed modeling of solar-like pulsators using asteroseismic observables. We show the impact of this calibration via a stellar activity-Rossby number diagram by applying it to a sample of about 40 000 stars observed with Kepler and for which the values for the photometric activity proxy S​ph and surface rotation periods are available. Additionally, we provide a new calibration for the convective turnover time as function of the (GBP − GRP) color index for allowing applicability in the ESA Gaia photometric passbands.

Implementing a New Formulation in WRF-LES for Buoyant Plume Simulations: bPlume-WRF-LES Model

AbstractA new formulation—bPlume-WRF-LES model—was implemented within the Weather Research and Forecasting (WRF) Model to simulate the two-way coupling between the atmospheric boundary layer (ABL) and gas plume (denser and lighter) released into the atmosphere. The existing WRF large-eddy simulation (WRF-LES) modeling system was modified by coupling an additional transport equation for the plume gas mixture and by accounting for the buoyant production term in the turbulence kinetic energy equation. The focus of the work was to understand the effect of atmospheric forcings on plume rise, plume mixing, and plume dynamics during the early stages of plume development. For this purpose, the bPlume-WRF-LES model was used to simulate the release of buoyant plumes from a large area source into different atmospheric conditions with varying stratification and mean wind forcing values. Plumes released in a convective ABL background rise according to the 2/3 power law with time before reaching the boundary layer top and spreading laterally. The convective ABL eddy turnover time scale () dictates the rate at which plume mixes with the ambient air inside the convective boundary layer (CBL) and the plume dilution rate scales as . Both the stratification and wind forcing enhance the plume mixing from the early plume development stage, and dilute the plume much faster. An increase in the mean winds within the CBL contributes to uniform mixing and greater bent-over plume behavior at a shorter downwind distance from the source.

Photometric Variability as a Proxy for Magnetic Activity and Its Dependence on Metallicity

Abstract Understanding how the magnetic activity of low-mass stars depends on their fundamental parameters is an important goal of stellar astrophysics. Previous studies have shown that activity levels are largely determined by the stellar Rossby number, defined as the rotation period divided by the convective turnover time. However, we currently have little information on the role played by chemical composition. In this work, we investigate how metallicity affects magnetic activity, using photometric variability as an activity proxy. Similarly to other proxies, we demonstrate that the amplitude of photometric variability is well parameterized by the Rossby number, although in a more complex way. We also show that variability amplitude and metallicity are generally positively correlated. This trend can be understood in terms of the effect of metallicity on stellar structure, and hence the convective turnover time (or, equivalently, the Rossby number). Lastly, we demonstrate that the metallicity dependence of photometric variability results in a rotation-period detection bias, whereby the periods of metal-rich stars are more easily recovered for stars of a given mass.

A Knee Point in the Rotation–Activity Scaling of Late-type Stars with a Connection to Dynamo Transitions

Abstract The magnetic activity of late-type stars is correlated with their rotation rates. Up to a certain limit, stars with smaller Rossby numbers, defined as the rotation period divided by the convective turnover time, have higher activity. A more detailed look at this rotation–activity relation reveals that, rather than being a simple power-law relation, the activity scaling has a shallower slope for the low-Rossby stars than for the high-Rossby ones. We find that, for the chromospheric Ca II H&K activity, this scaling relation is well modeled by a broken two-piece power law. Furthermore, the knee point of the relation coincides with the axisymmetry to nonaxisymmetry transition seen in both the spot activity and surface magnetic field configuration of active stars. We interpret this knee point as a dynamo transition between dominating axi- and nonaxisymmetric dynamo regimes with a different dependence on rotation and discuss this hypothesis in the light of current numerical dynamo models.

3D simulations of oxygen shell burning with and without magnetic fields.

We present a first 3D magnetohydrodynamic (MHD) simulation of convective oxygen and neon shell burning in a non-rotating [Formula: see text] star shortly before core collapse to study the generation of magnetic fields in supernova progenitors. We also run a purely hydrodynamic control simulation to gauge the impact of the magnetic fields on the convective flow and on convective boundary mixing. After about 17 convective turnover times, the magnetic field is approaching saturation levels in the oxygen shell with an average field strength of [Formula: see text], and does not reach kinetic equipartition. The field remains dominated by small-to-medium scales, and the dipole field strength at the base of the oxygen shell is only [Formula: see text]. The angle-averaged diagonal components of the Maxwell stress tensor mirror those of the Reynolds stress tensor, but are about one order of magnitude smaller. The shear flow at the oxygen-neon shell interface creates relatively strong fields parallel to the convective boundary, which noticeably inhibit the turbulent entrainment of neon into the oxygen shell. The reduced ingestion of neon lowers the nuclear energy generation rate in the oxygen shell and thereby slightly slows down the convective flow. Aside from this indirect effect, we find that magnetic fields do not appreciably alter the flow inside the oxygen shell. We discuss the implications of our results for the subsequent core-collapse supernova and stress the need for longer simulations, resolution studies, and an investigation of non-ideal effects for a better understanding of magnetic fields in supernova progenitors.

Rotation-Activity Relation of Ca II and Mg I Infrared Emission Lines of Young Stars

To reveal detail of internal structure, relationship between chromospheric activity and Rossby number, N_R (= rotational period P / convective turnover time tau_c), has been extensively examined for main-sequence stars. The goal of our work is to apply same methods to pre-main-sequence (PMS) stars and identify appropriate model of tau_c for them. Yamashita et al. (2020) investigated relationship between N_R and strengths of Ca II infrared triplet (IRT; lambda 8498, 8542, 8662 A) emission lines of 60 PMS stars. Their equivalent widths are converted into emission line to stellar bolometric luminosity ratio (R'). The 54 PMS stars have N_R < 10^{-1.0} and show R' \sim 10^{-4.2} as large as maximum R' of zero-age main-sequence (ZAMS) stars. However, because all R' was saturated against N_R, it was not possible to estimate appropriate tau_c model for PMS stars. We noticed that Mg I emission lines at 8808 A is an optically thin chromospheric line, appropriate for determination of adequate tau_c for PMS stars. Using archive data of Anglo-Australian Telescope (AAT)/the University College London Echelle Spectrograph (UCLES), we investigated Mg I line of 52 ZAMS stars. After subtracting photospheric absorption component, Mg I line is detected as an emission line in 45 ZAMS stars, whose R' is between 10^{-5.9} and 10^{-4.1}. The Mg I line is not saturated yet in the saturated regime for Ca II emission lines, i.e. 10^{-1.6} < N_R < 10^{-0.8}. Therefore, adequate tau_c for PMS stars can be determined by measuring of their R' values.

Calibrating core overshooting parameters with two-dimensional hydrodynamical simulations

The extent of mixed regions around convective zones is one of the biggest uncertainties in stellar evolution. One-dimensional overshooting descriptions introduce a free parameter (fov) that is, in general, not well constrained from observations. Especially in small central convective regions, the value is highly uncertain due to its tight connection to the pressure scale height. Long-term multi-dimensional hydrodynamic simulations can be used to study the size of the overshooting region as well as the involved mixing processes. Here we show how one can calibrate an overshooting parameter by performing two-dimensional Maestro simulations of zero-age-main-sequence stars ranging from 1.3 to 3.5 M⊙. The simulations cover the convective cores of the stars and a large fraction of the surrounding radiative envelope. We follow the convective flow for at least 20 convective turnover times, while the longest simulation covers 430 turnover time scales. This allows us to study how the mixing as well as the convective boundary itself evolve with time, and how the resulting entrainment can be interpreted in terms of overshooting parameters. We find that increasing the overshooting parameter fov beyond a certain value in the initial model of our simulations changes the mixing behaviour completely. This result can be used to put limits on the overshooting parameter. We find 0.010 &lt; fov &lt; 0.017 to be in good agreement with our simulations of a 3.5 M⊙ mass star. We also identify a diffusive mixing component due to internal gravity waves that is active throughout the convectively stable layer, but it is most likely overestimated in our simulations. Furthermore, applying our calibration method to simulations of less massive stars suggests a need for a mass-dependent overshooting description where the mixing in terms of the pressure scale height is reduced for small convective cores.

Stochastic core spin-up in massive stars – implications of 3D simulations of oxygen shell burning

ABSTRACT It has been suggested based on analytic theory that even in non-rotating supernova progenitors stochastic spin-up by internal gravity waves (IGWs) during the late burning stages can impart enough angular momentum to the core to result in neutron star birth spin periods below $100\, \mathrm{ms}$, and a relatively firm upper limit of $500\, \mathrm{ms}$ for the spin period. We here investigate this process using a 3D simulation of oxygen shell burning in a 3 M⊙ He star. Our model indicates that stochastic spin-up by IGWs is less efficient than previously thought. We find that the stochastic angular momentum flux carried by waves excited at the shell boundary is significantly smaller for a given convective luminosity and turnover time than would be expected from simple dimensional analysis. This can be explained by noting that the waves launched by overshooting convective plumes contain modes of opposite angular wavenumber with similar amplitudes, so that the net angular momentum of excited wave packets almost cancels. We find that the wave-mediated angular momentum flux from the oxygen shell follows a random walk, but again dimensional analysis overestimates the random walk amplitudes since the correlation time is only a fraction of the convective turnover time. Extrapolating our findings over the entire lifetime of the last burning stages prior to collapse, we predict that the core angular momentum from stochastic spin-up would translate into long birth spin periods of several seconds for low-mass progenitors and no less than $100\, \mathrm{ms}$ even for high-mass progenitors.

Common dynamo scaling in slowly rotating young and evolved stars

One interpretation of the activity and magnetism of late-type stars is that these both intensify with decreasing Rossby number up to a saturation level, suggesting that stellar dynamos depend on both rotation and convective turbulence. Some studies have claimed, however, that rotation alone suffices to parametrise this scaling adequately. Here, we tackle the question of the relevance of turbulence to stellar dynamos by including evolved, post main sequence stars in the analysis of the rotation-activity relation. These stars rotate very slowly compared with main sequence stars, but exhibit similar activity levels. We show that the two evolutionary stages fall together in the rotation-activity diagram and form a single sequence in the unsaturated regime in relation only to Rossby numbers derived from stellar models, confirming earlier preliminary results that relied on a more simplistic parametrisation of the convective turnover time. This mirrors recent results of fully convective M dwarfs, which likewise fall on the same rotation-activity sequence as partially convective solar-type stars. Our results demonstrate that turbulence plays a crucial role in driving stellar dynamos and suggest that there is a common turbulence-related dynamo mechanism explaining the magnetic activity of all late-type stars.

Magnetic Inflation and Stellar Mass. V. Intensification and Saturation of M-dwarf Absorption Lines with Rossby Number

Abstract In young Sun-like stars and field M-dwarf stars, chromospheric and coronal magnetic activity indicators such as Hα, X-ray, and radio emission are known to saturate with low Rossby number (Ro ≲ 0.1), defined as the ratio of rotation period to convective turnover time. The mechanism for the saturation is unclear. In this paper, we use photospheric Ti i and Ca i absorption lines in the Y band to investigate magnetic field strength in M dwarfs for Rossby numbers between 0.01 and 1.0. The equivalent widths of the lines are magnetically enhanced by photospheric spots, a global field, or a combination of the two. The equivalent widths behave qualitatively similar to the chromospheric and coronal indicators: we see increasing equivalent widths (increasing absorption) with decreasing Ro and saturation of the equivalent widths for Ro ≲ 0.1. The majority of M dwarfs in this study are fully convective. The results add to mounting evidence that the magnetic saturation mechanism occurs at or beneath the stellar photosphere.

The stellar rotation–activity relation for a sample of SuperWASP and ASAS-SN field stars

AbstractIt is well established that late-type main-sequence (MS) stars display a relationship between X-ray activity and the Rossby number,Ro, the ratio of rotation period to the convective turnover time. This manifests itself as a saturated regime (where X-ray activity is constant) and an unsaturated regime (where X-ray activity anti-correlates with Rossby number). However, this relationship breaks down for the fastest rotators. We cross-correlated SuperWASP visually classified photometric light curves and All-Sky Automated Survey for Supernovae automatically classified photometric light curves with XMM-Newton X-ray observations to identify 3 178 stars displaying a photometrically defined rotational modulation in their light curve and corresponding X-ray observations. We fitted a power-law to characterise the rotation–activity relation of 900 MS stars. We identified that automatically classified rotationally modulated light curves are not as reliable as visually classified light curves for this work. We found a power-law index in the unsaturated regime of G- to M-type stars of$\beta=-1.84\,\pm\,0.18$for the SuperWASP catalogue, in line with the canonical value of$\beta=-2$. We find evidence of supersaturation in the fastest rotating K-type stars, with a power-law index of$\beta_{s}=1.42\pm0.26$.

Low-mass X-ray binaries: the effects of the magnetic braking prescription

We present a population study of low- and intermediate-mass X-ray binaries (LMXBs) with neutron star accretors, performed using the detailed 1D stellar evolution code MESA. We identify all plausible Roche-lobe overflowing binaries at the start of mass transfer, and compare our theoretical mass transfer tracks to the population of well-studied Milky Way LMXBs. The mass transferring evolution depends on the accepted magnetic braking (MB) law for angular momentum loss. The most common MB prescription ("Skumanich MB") originated from observations of the time-dependence of rotational braking of Sun-type stars, where the angular momentum loss rate depends on the donor mass $M_d$, donor radius $R_d$, and rotation rate $\Omega$, $\dot{J} \propto M_d R_d^{\gamma} \Omega^3$. The functional form of the Skumanich MB can be also obtained theoretically assuming a radial magnetic field, isotropic isothermal winds, and boosting of the magnetic field by rotation. Here we show that this simple form of the Skumanich MB law gives mass transfer rates an order of magnitude too weak to explain most observed persistent LMXBs. This failure suggests that the standard Skumanich MB law should not be employed to interpret Galactic, or extragalactic, LMXB populations, with either detailed stellar codes or rapid binary population synthesis codes. We investigate modifications for the MB law, and find that including a scaling of the magnetic field strength with the convective turnover time, and a scaling of MB with the wind mass loss rate, can reproduce persistent LMXBs, and does a better job at reproducing transient LMXBs.

Revisiting the connection between magnetic activity, rotation period, and convective turnover time for main-sequence stars

The connection between stellar rotation, stellar activity, and convective turnover time is revisited with a focus on the sole contribution of magnetic activity to the Ca II H&amp;K emission, the so-called excess flux, and its dimensionless indicator R+HK in relation to other stellar parameters and activity indicators. Our study is based on a sample of 169 main-sequence stars with directly measured Mount Wilson S-indices and rotation periods. The R+HK values are derived from the respective S-indices and related to the rotation periods in various B–V-colour intervals. First, we show that stars with vanishing magnetic activity, i.e. stars whose excess flux index R+HK approaches zero, have a well-defined, colour-dependent rotation period distribution; we also show that this rotation period distribution applies to large samples of cool stars for which rotation periods have recently become available. Second, we use empirical arguments to equate this rotation period distribution with the global convective turnover time, which is an approach that allows us to obtain clear relations between the magnetic activity related excess flux index R+HK, rotation periods, and Rossby numbers. Third, we show that the activity versus Rossby number relations are very similar in the different activity indicators. As a consequence of our study, we emphasize that our Rossby number based on the global convective turnover time approaches but does not exceed unity even for entirely inactive stars. Furthermore, the rotation-activity relations might be universal for different activity indicators once the proper scalings are used.

The stellar rotation–activity relationship in fully convective M dwarfs

The coronal activity-rotation relationship is considered to be a proxy for the underlying stellar dynamo responsible for magnetic activity in solar and late-type stars. While this has been studied in considerable detail for partly-convective stars that are believed to operate an interface dynamo, it is poorly unconstrained in fully-convective stars that lack the necessary shear layer between radiative core and the convective envelope. We present new X-ray observations of 19 slowly-rotating fully-convective stars with rotation periods from the MEarth Project. We use these to calculate X-ray luminosities (or upper limits for undetected sources) and combine these with existing measurements from \citet{wrig16b}. We confirm the existence of fully-convective stars in the X-ray unsaturated regime and find that these objects follow the same rotation-activity relationship seen for partly-convective stars. We measure the power-law slope of the relationship between Rossby number (the ratio of the rotation period to the convective turnover time) and the fractional X-ray luminosity for X-ray unsaturated fully-convective stars for the first time, and find it to be consistent with that found for partly-convective stars. We discuss this implications of this result for our understanding of stellar magnetic dynamos in fully- and partly-convective stars. Finally, we also use this data to improve empirical estimates of the convective turnover time for fully-convective stars.

Enhanced Stellar Activity for Slow Antisolar Differential Rotation?

Abstract High-precision photometry of solar-like members of the open cluster M67 with Kepler/K2 data has recently revealed enhanced activity for stars with a large Rossby number, which is the ratio of rotation period to the convective turnover time. Contrary to the well established behavior for shorter rotation periods and smaller Rossby numbers, the chromospheric activity of the more slowly rotating stars of M67 was found to increase with increasing Rossby number. Such behavior has never been reported before, although it was theoretically predicted to emerge as a consequence of antisolar differential rotation (DR) for stars with Rossby numbers larger than that of the Sun, because in those models the absolute value of the DR was found to exceed that for solar-like DR. Using gyrochronological relations and an approximate age of 4 Gyr for the members of M67, we compare with computed rotation rates using just the B − V color. The resulting rotation–activity relation is found to be compatible with that obtained by employing the measured rotation rate. This provides additional support for the unconventional enhancement of activity at comparatively low rotation rates and the possible presence of antisolar differential rotation.

On the Origin of the Double-cell Meridional Circulation in the Solar Convection Zone

Abstract Recent advances in helioseismology, numerical simulations and mean-field theory of solar differential rotation have shown that the meridional circulation pattern may consist of two or more cells in each hemisphere of the convection zone. According to the mean-field theory the double-cell circulation pattern can result from the sign inversion of a nondiffusive part of the radial angular momentum transport (the so-called Λ-effect) in the lower part of the solar convection zone. Here, we show that this phenomenon can result from the radial inhomogeneity of the Coriolis number, which depends on the convective turnover time. We demonstrate that if this effect is taken into account then the solar-like differential rotation and the double-cell meridional circulation are both reproduced by the mean-field model. The model is consistent with the distribution of turbulent velocity correlations determined from observations by tracing motions of sunspots and large-scale magnetic fields, indicating that these tracers are rooted just below the shear layer.

Sensitivities of Summertime Mesoscale Circulations in the Coastal Carolinas to Modifications of the Kain-Fritsch Cumulus Parameterization.

Two mesoscale circulations, the Sandhills circulation and the sea breeze, influence the initiation of deep convection over the Sandhills and the coast in the Carolinas during the summer months. The interaction of these two circulations causes additional convection in this coastal region. Accurate representation of mesoscale convection is difficult as numerical models have problems with the prediction of the timing, amount, and location of precipitation. To address this issue, the authors have incorporated modifications to the Kain-Fritsch (KF) convective parameterization scheme and evaluated these mesoscale interactions using a high-resolution numerical model. The modifications include changes to the subgrid-scale cloud formulation, the convective turnover time scale, and the formulation of the updraft entrainment rates. The use of a grid-scaling adjustment parameter modulates the impact of the KF scheme as a function of the horizontal grid spacing used in a simulation. Results indicate that the impact of this modified cumulus parameterization scheme is more effective on domains with coarser grid sizes. Other results include a decrease in surface and near-surface temperatures in areas of deep convection (due to the inclusion of the effects of subgrid-scale clouds on the radiation), improvement in the timing of convection, and an increase in the strength of deep convection.

Updates in the NCEP GFS Cumulus Convection Schemes with Scale and Aerosol Awareness

Abstract The current operational NCEP Global Forecast System (GFS) cumulus convection schemes are updated with a scale-aware parameterization where the cloud mass flux decreases with increasing grid resolution. The ratio of advective time to convective turnover time is also taken into account for the scale-aware parameterization. In addition, the present deep cumulus convection closure using the quasi-equilibrium assumption is no longer used for grid sizes smaller than a threshold value. For the shallow cumulus convection scheme, the cloud-base mass flux is modified to be given by a function of mean updraft velocity. A simple aerosol-aware parameterization where rain conversion in the convective updraft is modified by aerosol number concentration is also included in the update. Along with the scale- and aerosol-aware parameterizations, more changes are made to the schemes. The cloud-base mass-flux computation in the deep convection scheme is modified to use convective turnover time as the convective adjustment time scale. The rain conversion rate is modified to decrease with decreasing air temperature above the freezing level. Convective inhibition in the subcloud layer is used as an additional trigger condition. Convective cloudiness is enhanced by considering suspended cloud condensate in the updraft. The lateral entrainment in the deep convection scheme is also enhanced to more strongly suppress convection in a drier environment. The updated NCEP GFS cumulus convection schemes display significant improvements especially in the summertime continental U.S. precipitation forecasts.

Rossby numbers of fully convective and partially convective stars

AbstractIn this work, we investigate the stellar magnetic activity in the theoretical point of view, through the use of stellar structure and evolution models. We present theoretical values of convective turnover times and Rossby numbers for low-mass stars, calculated with the ATON stellar structure and evolution code. We concentrate our analysis on fully convective and partially convective stars motivated by recent observations of X-ray emission of slowly rotating fully convective stars, which suggest that the presence of a tachocline is not a central key for magnetic fields generation. We investigate the behavior of the convective turnover time evolution, as well as its radial profile inside the star. A discussion about the location where the convective turnover time is calculated in the stellar interior is also addressed. Our theoretical results are compared to observational data from low-mass stars.

CONVECTIVE PROPERTIES OF ROTATING TWO-DIMENSIONAL CORE-COLLAPSE SUPERNOVA PROGENITORS

ABSTRACT We explore the effects of rotation on convective carbon, oxygen, and silicon shell burning during the late stages of evolution in a 20 M ⊙ star. Using the Modules for Experiments in Stellar Astrophysics we construct one-dimensional (1D) stellar models both with no rotation and with an initial rigid rotation of 50% of critical. At different points during the evolution, we map the 1D models into 2D and follow the multidimensional evolution using the FLASH compressible hydrodynamics code for many convective turnover times until a quasi-steady state is reached. We characterize the strength and scale of convective motions via decomposition of the momentum density into vector spherical harmonics. We find that rotation influences the total power in solenoidal modes, with a slightly larger impact for carbon and oxygen shell burning than for silicon shell burning. Including rotation in 1D stellar evolution models alters the structure of the star in a manner that has a significant impact on the character of multidimensional convection. Adding modest amounts of rotation to a stellar model that ignores rotation during the evolutionary stage, however, has little impact on the character of the resulting convection. Since the spatial scale and strength of convection present at the point of core collapse directly influence the supernova mechanism, our results suggest that rotation could play an important role in setting the stage for massive stellar explosions.