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Register a new userLithium depletion in solar-like stars: effect of overshooting based on realistic multi-dimensional simulations
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Isabelle Baraffe dr
Publication date
2017
fields
Physics
and research's language is
English
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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 $sim$ 50 Myr to $sim$ 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.
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Aims: We study the influence of rotation and disc lifetime on lithium depletion of pre-main sequence (PMS) solar-type stars. Methods: The impact of rotational mixing and of the hydrostatic effects of rotation on lithium abundances are investigated by computing non-rotating and rotating PMS models that include a comprehensive treatment of shellular rotation. The influence of the disc lifetime is then studied by comparing the lithium content of PMS rotating models experiencing different durations of the disc-locking phase between 3 and 9 Myr. Results: The surface lithium abundance at the end of the PMS is decreased when rotational effects are included. During the beginning of the lithium depletion phase, only hydrostatic effects of rotation are at work. This results in a decrease in the lithium depletion rate for rotating models compared to non-rotating ones. When the convective envelope recedes from the stellar centre, rotational mixing begins to play an important role due to differential rotation near the bottom of the convective envelope. This mixing results in a decrease in the surface lithium abundance with a limited contribution from hydrostatic effects of rotation, which favours lithium depletion during the second part of the PMS evolution. The impact of rotation on PMS lithium depletion is also found to be sensitive to the duration of the disc-locking phase. When the disc lifetime increases, the PMS lithium abundance of a solar-type star decreases owing to the higher efficiency of rotational mixing in the radiative zone. A relationship between the surface rotation and lithium abundance at the end of the PMS is then obtained: slow rotators on the zero-age main sequence are predicted to be more lithium-depleted than fast rotators due to the increase in the disc lifetime.
The periods of magnetic activity cycles in the Sun and solar-type stars do not exhibit a simple or even single trend with respect to rotation rate or luminosity. Dynamo models can be used to interpret this diversity, and can ultimately help us understand why some solar-like stars do not exhibit a magnetic cycle, whereas some do, and for the latter what physical mechanisms set their magnetic cycle period. Three-dimensional non-linear magnetohydrodynamical simulations present the advantage of having only a small number of tunable parameters, and produce in a dynamically self-consistent manner the flows and the dynamo magnetic fields pervading stellar interiors. We conducted a series of such simulations within the EULAG-MHD framework, varying the rotation rate and luminosity of the modeled solar-like convective envelopes. We find decadal magnetic cycles when the Rossby number near the base of the convection zone is moderate (typically between 0.25 and 1). Secondary, shorter cycles located at the top of the convective envelope close to the equator are also observed in our numerical experiments, when the local Rossby number is lower than 1. The deep-seated dynamo sustained in these numerical experiments is fundamentally non-linear, in that it is the feedback of the large-scale magnetic field on the large-scale differential rotation that sets the magnetic cycle period. The cycle period is found to decrease with the Rossby number, which offers an alternative theoretical explanation to the variety of activity cycles observed in solar-like stars.
To explore the physics of large-scale flows in solar-like stars, we perform 3D anelastic simulations of rotating convection for global models with stratification resembling the solar interior. The numerical method is based on an implicit large-eddy simulation approach designed to capture effects from non-resolved small scales. We obtain two regimes of differential rotation, with equatorial zonal flows accelerated either in the direction of rotation (solar-like) or in the opposite direction (anti-solar). While the models with the solar-like differential rotation tend to produce multiple cells of meridional circulation, the models with anti-solar differential rotation result in only one or two meridional cells. Our simulations indicate that the rotation and large-scale flow patterns critically depend on the ratio between buoyancy and Coriolis forces. By including a subadiabatic layer at the bottom of the domain, corresponding to the stratification of a radiative zone, we reproduce a layer of strong radial shear similar to the solar tachocline. Similarly, enhanced superadiabaticity at the top results in a near-surface shear layer located mainly at lower latitudes. The models reveal a latitudinal entropy gradient localized at the base of the convection zone and in the stable region, which however does not propagate across the convection zone. In consequence, baroclinicity effects remain small and the rotation iso-contours align in cylinders along the rotation axis. Our results confirm the alignment of large convective cells along the rotation axis in the deep convection zone, and suggest that such banana-cell pattern can be hidden beneath the supergranulation layer.
Accurate determination of stellar rotation periods is important for estimating stellar ages as well as for understanding stellar activity and evolution. While for about thirty thousand stars in the Kepler field rotation periods can be determined, there are over hundred thousand stars, especially with low photometric variability and irregular pattern of variations, for which rotational periods are unknown. Here, we investigate the effect of metallicity on the detectability of rotation periods. This is done by synthesising light curves of hypothetical stars, which are identical to our Sun, with the exception of the metallicity. These light curves are then used as an input to the period determination algorithms. We find that the success rate for recovering the rotation signal has a minimum close to the solar metallicity value. This can be explained by the compensation effect of facular and spot contributions. In addition, selecting solar-like stars with near-solar effective temperature, near solar photometric variability, and with metallicity between M/H = -0.35 and M/H = 0.35 from the Kepler sample, we analyse the fraction of stars for which rotational periods have been detected as a function of metallicity. In agreement with our theoretical estimate we found a local minimum for the detection fraction close to the solar metallicity. We further report rotation periods of 87~solar-like Kepler stars for the first time.
Based on radiation hydrodynamics modeling of stellar convection zones, a diffusion scheme has been devised describing the downward penetration of convective motions beyond the Schwarzschild boundary (overshoot) into the radiative interior. This scheme of exponential diffusive overshoot has already been successfully applied to AGB stars. Here we present an application to the Sun in order to determine the time scale and depth extent of this additional mixing, i.e. diffusive overshoot at the base of the convective envelope. We calculated the associated destruction of lithium during the evolution towards and on the main-sequence. We found that the slow-mixing processes induced by the diffusive overshoot may lead to a substantial depletion of lithium during the Suns main-sequence evolution.
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