Lithium depletion in solar-like stars: effect of overshooting based on realistic multi-dimensional simulations

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.Comment: 7 pages, 3 figures, Accepted for publication in ApJ Letter

Eigenvectors, Circulation and Linear Instabilities for Planetary Science in 3 Dimensions (ECLIPS3D)

This is the final version. Available on open access from EDP Sciences via the DOI in this recordContext. The study of linear waves and instabilities is necessary to understand the physical evolution of an atmosphere, and can provide physical interpretation of the complex flows found in simulations performed using Global Circulation Models (GCM). In particular, the acceleration of superrotating flow at the equator of hot Jupiters has mostly been studied under several simplifying assumptions, the relaxing of which may impact final results. Aims. We develop and benchmark a publicly available algorithm to identify the eigenmodes of an atmosphere around any initial steady state. We also solve for linear steady states. Methods. We linearise the hydrodynamical equations of a planetary atmosphere in a steady state with arbitrary velocities and thermal profile. We then discretise the linearised equations on an appropriate staggered grid, and solve for eigenvectors and linear steady solutions with the use of a parallel library for linear algebra: ScaLAPACK. We also implement a posteriori calculation of an energy equation in order to obtain more information on the underlying physics of the mode. Results. Our code is benchmarked against classical wave and instability test cases in multiple geometries. The steady linear circulation calculations also reproduce expected results for the atmosphere of hot Jupiters. We finally show the robustness of our energy equation, and its power to obtain physical insight into the modes. Conclusions. We have developed and benchmarked a code for the study of linear processes in planetary atmospheres, with an arbitrary steady state. The calculation of an a posteriori energy equation provides both increased robustness and physical meaning to the obtained eigenmodes. This code can be applied to various problems, and notably to further study the initial spin up of superrotation of GCM simulations of hot Jupiter.European Union Horizon 2020Leverhulme TrustScience and Technology Facilities Council (STFC

Models of thermal conduction and non-local transport of relevance to space physics with insights from laser–plasma theory

Models of solar and space plasmas require an accurate model for thermal transport. The simplest such model is to assume that the fluid approach is valid and that local transport models can be used. These local transport coefficients are derived under the assumption that the electron mean-free path is “small” compared to the temperature scale length. When this approximation breaks down, non-local transport models or thermal flux limiters must be used to maintain a physically realistic model. This article will review the background theory of how small is “small” for the mean-free path and what options there are for including non-local transport within the fluid framework. Much of this recent work has been motivated by laser–plasma theory, where mean-free paths can be large and the Spitzer–Harm approach is never used

Comparison of two- and three-dimensional compressible convection in a pre-main sequence star

Extending our recent studies of two-dimensional stellar convection to 3D, we compare three-dimensional hydrodynamic simulations to identically set-up two-dimensional simulations, for a realistic pre-main sequence star. We compare statistical quantities related to convective flows including: average velocity, vorticity, local enstrophy, and penetration depth beneath a convection zone. These statistics are produced during stationary, steady-state compressible convection in the star's convection zone. Our simulations with the MUSIC code confirm the common result that two-dimensional simulations of stellar convection have a higher magnitude of velocity on average than three-dimensional simulations. Boundary conditions and the extent of the spherical shell can affect the magnitude and variability of convective velocities. The difference between 2D and 3D velocities is dependent on these background points; in our simulations this can have an effect as large as the difference resulting from the dimensionality of the simulation. Nevertheless, radial velocities near the convective boundary are comparable in our 2D and 3D simulations. The average local enstrophy of the flow is lower for two-dimensional simulations than for three-dimensional simulations, indicating a different shape and structuring of 3D stellar convection. We perform a statistical analysis of the depth of convective penetration below the convection zone, using the model proposed in our recent study (Pratt et al. 2017). Here we analyze the convective penetration in three dimensional simulations, and compare the results to identically set-up 2D simulations. In 3D the penetration depth is as large as the penetration depth calculated from 2D simulations.Comment: 13 pages, 8 figure

Extreme value statistics for two-dimensional convective penetration in a pre-Main Sequence star

This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this record.We examine a penetration layer formed between a central radiative zone and a large convection zone in the deep interior of a young low-mass star. Using the Multidimensional Stellar Implicit Code (MUSIC) to simulate two-dimensional compressible stellar convection in a spherical geometry over long times, we produce statistics that characterize the extent and impact of convective penetration in this layer. We apply extreme value theory to the maximal extent of convective penetration at any time. We compare statistical results from simulations which treat non-local convection, throughout a large portion of the stellar radius, with simulations designed to treat local convection in a small region surrounding the penetration layer. For each of these situations, we compare simulations of different resolution, which have different velocity magnitudes. We also compare statistical results between simulations that radiate energy at a constant rate to those that allow energy to radiate from the stellar surface according to the local surface temperature. Based on the frequency and depth of penetrating convective structures, we observe two distinct layers that form between the convection zone and the stable radiative zone. We show that the probability density function of the maximal depth of convective penetration at any time corresponds closely in space with the radial position where internal waves are excited. We find that the maximal penetration depth can be modeled by a Weibull distribution with a small shape parameter. Using these results, and building on established scalings for diffusion enhanced by large-scale convective motions, we propose a new form for the diffusion coefficient that may be used for one-dimensional stellar evolution calculations in the large P\'eclet number regime. These results should contribute to the 321D link.The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework (FP7/2007-2013)/ERC grant agreement no. 32047

Multi-dimensional structure of accreting young stars

This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this recordThis work is the first attempt to describe the multi-dimensional structure of accreting young stars based on fully compressible time implicit multi-dimensional hydrodynamics simulations. One major motivation is to analyse the validity of accretion treatment used in previous 1D stellar evolution studies. We analyse the effect of accretion on the structure of a realistic stellar model of the young Sun. Our work is inspired by the numerical work of Kley \& Lin (1996, ApJ, 461, 933) devoted to the structure of the boundary layer in accretion disks. We analyse the redistribution of accreted material with a range of values of specific entropy relative to the bulk specific entropy of the material in the accreting object's convective envelope. A primary goal is to understand whether and how accreted energy deposited onto a stellar surface is redistributed in the interior. This study focusses on the high accretion rates characteristic of FU Ori systems. We find that the highest entropy cases produce a distinctive behaviour in the mass redistribution, rms velocities, and enthalpy flux in the convective envelope. This change in behaviour is characterised by the formation of a hot layer on the surface of the accreting object, which tends to suppress convection in the envelope. We analyse the long-term effect of such a hot buffer zone on the structure and evolution of the accreting object with 1D stellar evolution calculations. We study the relevance of the assumption of redistribution of accreted energy into the stellar interior used in the literature. One conclusion is that, for a given amount of accreted energy transferred to the accreting object, a treatment assuming accretion energy redistribution throughout the stellar interior could significantly overestimate the effects on the stellar structure, in particular, on the resulting expansion.Part of this work was funded by the Royal Society Wolfson Merit award WM090065, the French Programme National de Physique Stellaire (PNPS) and Programme National Hautes Energies (PNHE), and by the ´ European Research Council through grants ERC-AdG No. 320478-TOFU and ERC-AdG No. 341157-COCO2CASA. This work used the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility (www.dirac.ac.uk ). This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the National EInfrastructure. This work also used the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and the University of Exeter

Two-dimensional simulations of internal gravity waves in a 5 M⊙M_{\odot} Zero-Age-Main-Sequence model

Main-sequence intermediate-mass stars present a radiative envelope that supports internal gravity waves (IGWs). Excited at the boundary with the convective core, IGWs propagate towards the stellar surface and are suspected to impact physical processes such as rotation and chemical mixing. Using the fully compressible time-implicit code MUSIC, we study IGWs in two-dimensional simulations of a zero-age-main-sequence 5 solar mass star model up to 91\% of the stellar radius with different luminosity and radiative diffusivity enhancements. Our results show that low frequency waves excited by core convection are strongly impacted by radiative effects as they propagate. This impact depends on the radial profile of radiative diffusivity which increases by almost 5 orders of magnitude between the centre of the star and the top of the simulation domain. In the upper layers of the simulation domain, we observe an increase of the temperature. Our study suggests that this is due to heat added in these layers by IGWs damped by radiative diffusion. We show that non-linear effects linked to large amplitude IGWs may be relevant just above the convective core. Both these effects are intensified by the artificial enhancement of the luminosity and radiative diffusivity, with enhancement factors up to $10^4$ times the realistic values. Our results also highlight that direct comparison between numerical simulations with enhanced luminosity and observations must be made with caution. Finally, our work suggests that thermal effects linked to the damping of IGWs could have a non-negligible impact on stellar structure.Comment: 15 pages, 10 figures, accepted for publication in MNRA

Benchmarking the Multi-dimensional Stellar Implicit Code MUSIC

11 pages, 11 figures, accepted for publication in A&AWe present the results of a numerical benchmark study for the MUlti-dimensional Stellar Implicit Code (MUSIC) based on widely applicable two- and three-dimensional compressible hydrodynamics problems relevant to stellar interiors. MUSIC is an implicit large eddy simulation code that uses implicit time integration, implemented as a Jacobian-free Newton Krylov method. A physics based preconditioning technique which can be adjusted to target varying physics is used to improve the performance of the solver. The problems used for this benchmark study include the Rayleigh-Taylor and Kelvin-Helmholtz instabilities, and the decay of the Taylor-Green vortex. Additionally we show a test of hydrostatic equilibrium, in a stellar environment which is dominated by radiative effects. In this setting the flexibility of the preconditioning technique is demonstrated. This work aims to bridge the gap between the hydrodynamic test problems typically used during development of numerical methods and the complex flows of stellar interiors. A series of multi-dimensional tests are performed and analysed. Each of these test cases is analysed with a simple, scalar diagnostic, with the aim of enabling direct code comparisons. As the tests performed do not have analytic solutions we verify MUSIC by comparing to established codes including ATHENA and the PENCIL code. MUSIC is able to both reproduce behaviour from established and widely-used codes as well as results expected from theoretical predictions. This benchmarking study concludes a series of papers describing the development of the MUSIC code and provides confidence in the future applications.This project has received funding from the European Unions Seventh Framework Programme for research, technological development and demonstration under grant agreement no 320478. The calculations for this paper were performed on the DiRAC Complexity machine, jointly funded by STFC and the Large Facilities Capital Fund of BIS, and the University of Exeter Super- computer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and the University of Exeter. We are very thankful to Colin McNally for providing his results for the Kelvin-Helmholtz test

The acceleration of superrotation in simulated hot Jupiter atmospheres

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordContext. Atmospheric superrotating flows at the equator are a nearly ubiquitous result when conducting simulations of hot Jupiters. One theory explaining how this zonally-coherent flow reaches equilibrium has already been developed in the literature. This understanding, however, relies on the existence of either an initial superrotating flow or a sheared flow, coupled with a slow evolution that permits a linear steady state to be reached. Aims. A consistent physical understanding of superrotation is needed for arbitrary drag and radiative timescales, along with the relevance of taking linear steady states into account, needs to be assessed. Methods. We obtained an analytical expression for the structure, frequency, and decay rate of propagating waves in hot Jupiter atmospheres around a state at rest in the 2D shallow-water β–plane limit. We solved this expression numerically and confirmed the robustness of our results with a 3D linear wave algorithm. We then compared it with 3D simulations of hot Jupiter atmospheres and studied the nonlinear momentum fluxes. Results. We show that under strong day-night heating, the dynamics do not transit through a linear steady state when starting from an initial atmosphere in solid body rotation. We further demonstrate that non–linear effects favor the initial spin-up of superrotation and that acceleration due to the vertical component of the eddy–momentum flux is critical to the initial development of superrotation . Conclusions. We describe the initial phases of the acceleration of superrotation, including the consideration of differing radiative and drag timescales, and we conclude that eddy-momentum-driven superrotating equatorial jets are robust, physical phenomena in simulations of hot Jupiter atmospheres.Leverhulme TrustScience and Technology Facilities Counci

Unveiling the magnetic nature of chromospheric vortices

Context. Vortex structures in the Sun’s chromosphere are believed to channel energy between different layers of the solar atmosphere. Aims. We investigate the nature and dynamics of two small-scale quiet-Sun rotating structures in the chromosphere. Methods. We analysed two chromospheric structures that show clear rotational patterns in spectropolarimetric observations taken with the Interferometric Bidimensional Spectrometer at the Ca II 8542 Å line. Results. We present the detection of spectropolarimetric signals that manifest the magnetic nature of rotating structures in the chromosphere. Our observations show two long-lived structures of plasma that each rotate clockwise inside a 10 arcsec2 quiet-Sun region. Their circular polarisation signals are five to ten times above the noise level. Line-of-sight Doppler velocity and horizontal velocity maps from the observations reveal clear plasma flows at and around the two structures. A magnetohydrodynamics simulation shows these two structures are plausibly magnetically connected. Wave analysis suggests that the observed rotational vortex pattern could be due to a combination of slow actual rotation and a faster azimuthal phase speed pattern of a magnetoacoustic mode. Conclusions. Our results imply that the vortex structures observed in the Sun’s chromosphere are magnetic in nature and that they can be connected locally through the chromospher