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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 MNRAS

We perform two-dimensional numerical simulations of core convection for zero-age-main-sequence stars covering a mass range from 3 $M_\odot$ to 20 $M_\odot$. The simulations are performed with the fully compressible time-implicit code MUSIC. We study the efficiency of overshooting, which describes the ballistic process of convective flows crossing a convective boundary, as a function of stellar mass and luminosity. We also study the impact of artificially increasing the stellar luminosity for 3 $M_\odot$ models. The simulations cover hundreds to thousands of convective turnover timescales. Applying the framework of extreme plume events previously developed for convective envelopes, we derive overshooting lengths as a function of stellar masses. We find that the overshooting distance ($d_{\rm ov}$) scales with the stellar luminosity ($L$) and the convective core radius ($r_{\rm conv}$). We derive a scaling law $d_{\rm ov} \propto L^{1/3} r_{\rm conv}^{1/2}$ which is implemented in a 1D stellar evolution code and the resulting stellar models are compared to observations. The scaling predicts values for the overshooting distance that significantly increase with stellar mass, in qualitative agreement with observations. Quantitatively, however, the predicted values are underestimated for masses $\gtrsim 10 M_\odot$. Our 2D simulations show the formation of a nearly-adiabatic layer just above the Schwarzschild boundary of the convective core, as exhibited in recent 3D simulations of convection. The most luminous models show a growth in size with time of the nearly-adiabatic layer. This growth seems to slow down as the upper edge of the nearly-adiabatic layer gets closer to the maximum overshooting length and as the simulation time exceeds the typical thermal diffusive timescale in the overshooting layer., Comment: 13 pages, accepted for publication in MNRAS

Stellar convection is a non-local process responsible for the transport of heat and chemical species. It can lead to enhanced mixing through convective overshooting and excitation of internal gravity waves (IGWs) at convective boundaries. The relationship between these processes is still not well understood and requires global hydrodynamic simulations to capture the important large-scale dynamics. The steep stratification in stellar interiors suggests that the radial extent of such simulations can affect the convection dynamics, the IGWs in the stably stratified radiative zone, and the depth of the overshooting layer. We investigate these effects using two-dimensional global simulations performed with the fully compressible stellar hydrodynamics code MUSIC. We compare eight different radial truncations of the same solar-like stellar model evolved over approximately 400 convective turnover times. We find that the location of the inner boundary has an insignificant effect on the convection dynamics, the convective overshooting and the travelling IGWs. We relate this to the background conditions at the lower convective boundary which are unaffected by the truncation, as long as a significantly deep radiative layer is included in the simulation domain. However, we find that extending the outer boundary by only a few percent of the stellar radius significantly increases the velocity and temperature perturbations in the convection zone, the overshooting depth, the power and the spectral slope of the IGWs. The effect is related to the background conditions at the outer boundary, which are determined in essence by the hydrostatic stratification and the given luminosity., Comment: Accepted in MNRAS 2022 April 29

Artificially increasing the luminosity and the thermal diffusivity of a model is a common tactic adopted in hydrodynamical simulations of stellar convection. In this work, we analyse the impact of these artificial modifications on the physical properties of stellar interiors and specifically on internal gravity waves. We perform two-dimensional simulations of solar-like stars with the MUSIC code. We compare three models with different luminosity enhancement factors to a reference model. The results confirm that properties of the waves are impacted by the artificial enhancement of the luminosity and thermal diffusivity. We find that an increase in the stellar luminosity yields a decrease in the bulk convective turnover timescale and an increase in the characteristic frequency of excitation of the internal waves. We also show that a higher energy input in a model, corresponding to a larger luminosity, results in higher energy in high frequency waves. Across our tests with the luminosity and thermal diffusivity enhanced together by up to a factor of 104, our results are consistent with theoretical predictions of radiative damping. Increasing the luminosity also has an impact on the amplitude of oscillatory motions across the convective boundary. One must use caution when interpreting studies of internal gravity waves based on hydrodynamical simulations with artificially enhanced luminosity., Comment: 16 pages, 13 figures; accepted for publication in A&A

Our ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and convective boundaries. However, the codes used to compute such simulations are usually tested on extremely simple problems and the reliability and reproducibility of their predictions for turbulent flows is unclear. We define a test problem involving turbulent convection in a plane-parallel box, which leads to mass entrainment from, and internal-wave generation in, a stably stratified layer. We compare the outputs from the codes FLASH, MUSIC, PPMSTAR, PROMPI, and SLH, which have been widely employed to study hydrodynamic problems in stellar interiors. The convection is dominated by the largest scales that fit into the simulation box. All time-averaged profiles of velocity components, fluctuation amplitudes, and fluxes of enthalpy and kinetic energy are within $\lesssim 3\sigma$ of the mean of all simulations on a given grid ($128^3$ and $256^3$ grid cells), where $\sigma$ describes the statistical variation due to the flow's time dependence. They also agree well with a $512^3$ reference run. The $128^3$ and $256^3$ simulations agree within $9\%$ and $4\%$, respectively, on the total mass entrained into the convective layer. The entrainment rate appears to be set by the amount of energy that can be converted to work in our setup and details of the small-scale flows in the boundary layer seem to be largely irrelevant. Our results lend credence to hydrodynamic simulations of flows in stellar interiors. We provide in electronic form all outputs of our simulations as well as all information needed to reproduce or extend our study., Comment: 20 pages, 19 figures, new Fig. B.2, new clarifications, electronic materials updated, accepted for publication in A&A

We perform 2D, fully compressible, time-implicit simulations of convection in a solar-like model with the MUSIC code. Our main motivation is to explore the impact of a common tactic adopted in numerical simulations of convection that use realistic stellar conditions. This tactic is to artificially increase the luminosity and to modify the thermal diffusivity of the reference stellar model. This work focuses on the impact of these modifications on convective penetration (or overshooting) at the base of the convective envelope of a solar-like model. We explore a range of enhancement factors for the energy input and confirm the increase in the characteristic overshooting depth with the increase in the energy input. Our results highlight the importance of the impact of penetrative downflows on the thermal background below the convective boundary. This is a result of compression and shear which induce local heating and thermal mixing. The artificial increase in the energy flux intensifies the heating process by increasing the velocities in the convective zone and at the convective boundary, revealing a subtle connection between the local heating of the thermal background and the plume dynamics. This heating also increases the efficiency of heat transport by radiation which may counterbalance further heating and helps to establish a steady state. The modification of the thermal background by penetrative plumes impacts the width of the overshooting layer. Our results suggest that an artificial modification of the radiative diffusivity in the overshooting layer, rather than only accelerating the thermal relaxation, could also alter the dynamics of the penetrating plumes and thus the width of the overshooting layer. Results from simulations with an artificial modification of the energy flux and of the thermal diffusivity should be regarded with caution if used to determine an overshooting width., Comment: 13 pages, 14 figures; accepted for publication in A&A

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 figures

Context. The large quantity of high-quality asteroseismic data that obtained from space-based photometric missions and the accuracy of the resulting frequencies motivate a careful consideration of the accuracy of computed oscillation frequencies of stellar models, when applied as diagnostics of the model properties. Aims. Based on models of red-giant stars that have been independently calculated using different stellar evolution codes, we investigate the extent to which the differences in the model calculation affect the model oscillation frequencies. Methods. For each of the models, which cover four different masses and different evolution stages on the red-giant branch, we computed full sets of low-degree oscillation frequencies using a single pulsation code and, from these frequencies, typical asteroseismic diagnostics. In addition, we carried out preliminary analyses to relate differences in the oscillation properties to the corresponding model differences. Results. In general, the differences in asteroseismic properties between the different models greatly exceed the observational precision of these properties, in particular for the nonradial modes whose mixed acoustic and gravity-wave character makes them sensitive to the structure of the deep stellar interior. In some cases, identifying these differences led to improvements in the final models presented here and in Paper I; here we illustrate particular examples of this. Conclusions. Further improvements in stellar modelling are required in order fully to utilise the observational accuracy to probe intrinsic limitations in the modelling. However, our analysis of the frequency differences and their relation to stellar internal properties provides a striking illustration of the potential of the mixed modes of red-giant stars for the diagnostics of stellar interiors., Comment: Astronomy and Astrophysics, in the press. Paper resubmitted to arXiv to correct author list in metadata

(Abridged). We introduce the Aarhus Red Giants Challenge, a series of detailed comparisons between widely used stellar evolution and oscillation codes aiming at establishing the minimum level of uncertainties in properties of red giants arising solely from numerical implementations. Using 9 state-of-the-art stellar evolution codes, we defined a set of input physics and physical constants for our calculations and calibrated the convective efficiency to a specific point on the main sequence. We produced evolutionary tracks and stellar structure models at fixed radius along the red-giant branch for masses of 1.0 M$_\odot$, 1.5 M$_\odot$, 2.0 M$_\odot$, and 2.5 M$_\odot$, and compared the predicted stellar properties. Once models have been calibrated on the main sequence we find a residual spread in the predicted effective temperatures across all codes of ~20 K at solar radius and ~30-40 K in the RGB regardless of the considered stellar mass. The predicted ages show variations of 2-5% (increasing with stellar mass) which we track down to differences in the numerical implementation of energy generation. The luminosity of the RGB-bump shows a spread of about 10% for the considered codes, which translates into magnitude differences of ~0.1 mag in the optical V-band. We also compare the predicted [C/N] abundance ratio and found a spread of 0.1 dex or more for all considered masses. Our comparisons show that differences at the level of a few percent still remain in evolutionary calculations of red giants branch stars despite the use of the same input physics. These are mostly due to differences in the energy generation routines and interpolation across opacities, and call for further investigations on these matters in the context of using properties of red giants as benchmarks for astrophysical studies., Comment: accepted for publication in Astronomy and Astrophysics

Characterizing stellar convection in multiple dimensions is a topic at the forefront of stellar astrophysics. Numerical simulations are an essential tool for this task. We present an extension of the existing numerical tool-kit A-MaZe that enables such simulations of stratified flows in a gravitational field. The finite-volume based, cell-centered, and time-explicit hydrodynamics solver of A-MaZe was extended such that the scheme is now well-balanced in both momentum and energy. The algorithm maintains an initially static balance between gravity and pressure to machine precision. Quasi-stationary convection in slab-geometry preserves gas energy (internal plus kinetic) on average despite strong local up- and down-drafts. By contrast, a more standard numerical scheme is demonstrated to result in substantial gains of energy within a short time on purely numerical grounds. The test is further used to point out the role of dimensionality, viscosity, and Rayleigh number for compressible convection. Applications to a young sun in 2D and 3D, covering a part of the inner radiative zone as well as the outer convective zone, demonstrate that the scheme meets its initial design goal. Comparison with results obtained for a physically identical setup with a time-implicit code show qualitative agreement., Comment: 12 pages, 8 figures, accepted 30/08/2019 for publication by Astronomy & Astrophysics

Several recent spectroscopic investigations have presented conflicting results on the existence of Na-rich asymptotic giant branch (AGB) stars in the Galactic globular cluster M4 (NGC6121). The studies disagree on whether or not Na-rich red giant branch (RGB) stars evolve to the AGB. For a sample of previously published HER- MES/AAT AGB and RGB stellar spectra we present a re-analysis of O, Na, and Fe abundances, and a new analysis of Mg and Al abundances; we also present CN band strengths for this sample, derived from low-resolution AAOmega spectra. Following a detailed literature comparison, we find that the AGB samples of all studies consistently show lower abundances of Na and Al, and are weaker in CN, than RGB stars in the cluster. This is similar to recent observations of AGB stars in NGC 6752 and M 62. In an attempt to explain this result, we present new theoretical stellar evolutionary models for M 4; however, these predict that all stars, including Na-rich RGB stars, evolve onto the AGB. We test the robustness of our abundance results using a variety of atmospheric models and spectroscopic methods; however, we do not find evidence that systematic modelling uncertainties can explain the apparent lack of Na- rich AGB stars in M4. We conclude that an unexplained, but robust, discordance between observations and theory remains for the AGB stars in M 4., Comment: 25 pages, 21 figures, 15 tables, accepted for publication in MNRAS

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 Letters

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., Comment: 18 pages, 12 figures, accepted to Astronomy and Astrophysics Journal

We 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., Comment: 11 pages, 11 figures, accepted for publication in A&A

Context: We study the impact of two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from a one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star. Methods: We perform hydrodynamic implicit large-eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over hundreds of convective turnover times, permitting the collection of well-converged statistics. Results: We evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional stellar evolution calculations, so that our results are focused toward the 321D link. The inclusion in the spherical shell of the boundary between the radiative and convection zones decreases the amplitude of convective velocities in the convection zone. The inclusion of near-surface layers in the spherical shell can increase the amplitude of convective velocities, although the radial structure of the velocity profile established by deep convection is unchanged. The impact from including the near-surface layers depends on the speed and structure of small-scale convection in the near-surface layers. Larger convective velocities in the convection zone result in a commensurate increase in the overshooting layer width and decrease in the convective turnover time. These results provide support for non-local aspects of convection., Comment: 14 pages, 9 figures, abbreviated abstract, accepted for publication in Astronomy & Astrophysics, reproduced with permission, c ESO

This 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., Comment: 11 pages, 11 figures, accepted for publication in A&A

Stellar models provide a vital basis for many aspects of astronomy and astrophysics. Recent advances in observational astronomy -- through asteroseismology, precision photometry, high-resolution spectroscopy, and large-scale surveys -- are placing stellar models under greater quantitative scrutiny than ever. The model limitations are being exposed and the next generation of stellar models is needed as soon as possible. The current uncertainties in the models propagate to the later phases of stellar evolution, hindering our understanding of stellar populations and chemical evolution. Here we give a brief overview of the evolution, importance, and substantial uncertainties of core helium burning stars in particular and then briefly discuss a range of methods, both theoretical and observational, that we are using to advance the modelling., Comment: To appear in Astronomische Nachrichten, special issue "Reconstruction the Milky Way's History: Spectroscopic surveys, Asteroseismology and Chemo-dynamical models", Guest Editors C. Chiappini, J. Montalb\'an, and M. Steffen, AN 2016 (in press)