arXiv subjects

R. Hirschi

Publications and source records attributed to R. Hirschi.

At least 19 recordsLinked to original sources

arXiv2026

3D simulations of a complete convective silicon shell burning phase

We present 3D hydrodynamic simulations of a complete silicon shell burning phase until fuel exhaustion at the end of the evolution of a 14$M_\odot$ core-collapse supernova progenitor, using a reduced 25-isotope nuclear network. We investigate how realistic turbulent convection affects this burning phase, which has a more complicated set of nuclear reactions than previous burning phases. We find broad similarities between the 3D simulation and the 1D \textsc{MESA} model. However, due to more realistic feedback from the very stiff convective boundaries in the hydrodynamic simulations, the 3D simulation experiences lower convective boundary mixing (CMB) compared to 1D, and hence entrains less fresh fuel into the silicon shell. This leads to the silicon shell in the 3D model burning for roughly 800\,s shorter. We find that the nuclear burning timescales for the dominant reactions are faster than the mixing timescale, making this entire process a convective-reactive event. The angular-averaged energy generation profile shows a double-peaked structure, where the region between the positive peaks are close to zero, or are negative. We find that throughout the base of this silicon shell, many $(\alpha, p)$ and their inverse reactions are important. The forward and reverse rates are very similar, so slight fluctuations in the temperature cause regions to be either exoergic or endoergic, leading to a complicated energy generation evolution. This study presents an exploration using a single reduced nuclear network, however, due to the sensitivity of this burning phase future studies should investigate the impact of more complete nuclear networks.

astro-ph.SR↗

arXiv2026

Fast-spinning massive black holes from slowly rotating low-metallicity stars: Implications for GW231123

The origin of massive black holes in the early universe remains uncertain and still unexplored. Pop III stars are among the first stellar sources capable of producing such remnants, but their evolution is very sensitive to rotation. We explore how slow initial rotation influences the evolution and black hole formation of very massive Pop III stars, and assess their potential to become massive, fast-spinning black holes consistent with GW events such as GW231123. We compute a grid of non-rotating and slowly rotating Pop III stellar models with initial masses of 80, 85, and 90 $M_\odot$ using the GENEC code. Our models include rotationally induced mixing and angular-momentum transport by magnetic torques. We analyse the CO core masses and their volume-averaged adiabatic index to assess stability against electron-positron pair creation. From the angular-momentum profiles at the end of He burning, we estimate the resulting black hole masses and dimensionless spins under the assumption of direct collapse. Our non-rotating and slowly rotating 80 and 85 $M_\odot$ models develop carbon-oxygen core masses between 31 and 36 $M_\odot$ and have an adiabatic index that remains above 4/3. Our models thus predict that Pop III stars can keep most of their mass and collapse directly to form black holes of 80 to 85 $M_\odot$ with dimensionless spins up to $a_{\rm BH} \lesssim 0.7$. Initially slowly rotating, massive Pop III stars can form very massive, rapidly spinning black holes just below the pair-instability regime. This supports interpreting the lower boundary of the PISN mass gap as a smooth, structure-dependent transition and identifies single-star Pop III evolution as a possible channel for massive fast-spinning black holes observed by gravitational-wave detectors, subject to the uncertain efficiency of internal angular-momentum transport and mass-loss prescriptions.

astro-ph.SR↗

arXiv2026

Phlegethon: a fully compressible magnetohydrodynamic code for simulations in stellar astrophysics

We present PHLEGETHON, a fully compressible, Eulerian magnetohydrodynamic (MHD) code designed for multidimensional simulations in stellar astrophysics. The code uses a time-explicit, second-order, finite-volume method optimized to model a wide range of dynamical processes in stars, from very low-Mach-number turbulent convection in the cores of massive stars to supersonic flows in subsurface convection zones. PHLEGETHON employs low-dissipation Riemann solvers and a well-balanced method to accurately capture slow flows arising from strongly stratified media. The induction equation is solved using a staggered constrained-transport method to ensure divergence-free evolution of the magnetic field. The MHD equations are coupled to arbitrary nuclear reaction networks solved in a time-implicit approach, together with super-time-stepping for efficient treatment of thermal diffusion. Equations of state appropriate for stellar plasmas are available, accounting for partial ionization, electron degeneracy, and electron-positron pair production. The code is implemented in a compact and user-friendly manner, and it scales to tens of thousands of CPU cores using MPI-based domain decomposition. We perform several verification tests to demonstrate the accuracy and versatility of the code, and present simulations of magnetoconvection in a core-collapse supernova progenitor star. The rich variety of physical effects and numerical methods implemented in PHLEGETHON enables the code to model diverse multidimensional processes that play a crucial role in stellar-interior dynamics, such as reactive convection, convective boundary mixing, internal-wave excitation, and magnetic-field amplification mechanisms. Within a single framework, these phenomena can be investigated across a wide range of stellar evolutionary stages, from main-sequence stars to supernova progenitors. PHLEGETHON is publicly accessible online.

astro-ph.SR↗

arXiv2025

The fate of rotating massive stars across cosmic times

The initial mass and metallicity of stars both have a strong impact on their fate. Stellar axial rotation also has a strong impact on the structure and evolution of massive stars. In this study, we exploit the large grid of GENEC models, covering initial masses from 9 to 500 $M_{\odot}$ and metallicities ranging from $Z=10^{-5}$ (nearly zero) to 0.02 (supersolar), to determine the impact of rotation on their fate across cosmic times. Using the carbon-oxygen core mass and envelope composition as indicators of their fate, we predict stellar remnants, supernova engines, and spectroscopic supernova types for both rotating and non-rotating stars. We derive rates of the different supernova and remnant types considering two initial mass functions to help solve puzzles such as the absence of observed pair-instability supernovae. We find that rotation significantly alters the remnant type and supernova engine, with rotating stars favouring black hole formation at lower initial masses than their non-rotating counterparts. Additionally, we confirm the expected strong metallicity dependence of the fates with a maximum black hole mass predicted to be below 50 $M_{\odot}$ at SMC or higher metallicities. A pair-instability mass gap is predicted between about 90 and 150 $M_{\odot}$, with the most massive black holes below the gap found at the lowest metallicities. Considering the fate of massive single stars has far-reaching consequences across many different fields within astrophysics, and understanding the impact of rotation and metallicity will improve our understanding of how massive stars end their lives, and their impact on the universe.

astro-ph.SR↗

arXiv2024

3D simulations of convective shell Neon-burning in a massive star

The treatment of convection remains a major weakness in the modelling of stellar evolution with one-dimensional (1D) codes. The ever increasing computing power makes now possible to simulate in 3D part of a star for a fraction of its life, allowing us to study the full complexity of convective zones with hydrodynamics codes. Here, we performed state-of-the-art hydrodynamics simulations of turbulence in a neon-burning convective zone, during the late stage of the life of a massive star. We produced a set of simulations varying the resolution of the computing domain (from 1283 to 10243 cells) and the efficiency of the nuclear reactions (by boosting the energy generation rate from nominal to a factor of 1000). We analysed our results by the mean of Fourier transform of the velocity field, and mean-field decomposition of the various transport equations. Our results are in line with previous studies, showing that the behaviour of the bulk of the convective zone is already well captured at a relatively low resolution (2563), while the details of the convective boundaries require higher resolutions. The different boosting factors used show how various quantities (velocity, buoyancy, abundances, abundance variances) depend on the energy generation rate. We found that for low boosting factors, convective zones are well mixed, validating the approach usually used in 1D stellar evolution codes. However, when nuclear burning and turbulent transport occur on the same timescale, a more sophisticated treatment would be needed. This is typically the case when shell mergers occur.

astro-ph.SR↗

arXiv2023

The nuclear reaction network WinNet

We present the state-of-the-art single-zone nuclear reaction network WinNet that is capable of calculating the nucleosynthetic yields of a large variety of astrophysical environments and conditions. This ranges from the calculation of the primordial nucleosynthesis, where only a few nuclei are considered, to the ejecta of neutron star mergers with several thousands of involved nuclei. Here we describe the underlying physics and implementation details of the reaction network. We additionally present the numerical implementation of two different integration methods, the implicit Euler method and Gears method along with their advantages and disadvantages. We furthermore describe basic example cases of thermodynamic conditions that we provide together with the network and demonstrate the reliability of the code by using simple test cases. With this publication, WinNet is publicly available and open source at GitHub and Zenodo.

astro-ph.IM↗

arXiv2023

Very Massive Star Models: I. Impact of Rotation and Metallicity and Comparisons with Observations

In addition to being spectacular objects, Very Massive Stars (VMS) are suspected to have a tremendous impact on their environment and on the whole cosmic evolution. The nucleosynthesis both during their advanced stages and their final explosion may contribute greatly to the overall enrichment of the Universe. Their resulting supernovae are candidates for the most superluminous events and their extreme conditions also lead to very important radiative and mechanical feedback effects, from local to cosmic scale. We explore the impact of rotation and metallicity on the evolution of very massive stars across cosmic times. With the recent implementation of an equation of state in the GENEC stellar evolution code, appropriate for describing the conditions in the central regions of very massive stars in the advanced phases, we present new results on VMS evolution from Population III to solar metallicity. Low metallicity VMS models are highly sensitive to rotation, while the evolution of higher metallicity models is dominated by mass loss effects. The mass loss affects strongly their surface velocity evolution, breaking quickly at high metallicity while reaching the critical velocity for low metallicity models. The comparison to observed VMS in the LMC shows that the mass loss prescriptions used for these models are compatible with observed mass loss rates. In our framework for modelling rotation, our models of VMS need a high initial velocity to reproduce the observed surface velocities. The surface enrichment of these VMS is difficult to explain with only one initial composition, and could suggest multiple populations in the R136 cluster. At a metallicity typical of R136, only our non- or slowly rotating VMS models may produce Pair Instability supernovae. The most massive black holes that can be formed are less massive than about 60 M$_\odot$.

astro-ph.SR↗

arXiv2023

3D stellar evolution: hydrodynamic simulations of a complete burning phase in a massive star

Our knowledge of stellar evolution is driven by one-dimensional (1D) simulations. 1D models, however, are severely limited by uncertainties on the exact behaviour of many multi-dimensional phenomena occurring inside stars, affecting their structure and evolution. Recent advances in computing resources have allowed small sections of a star to be reproduced with multi-D hydrodynamic models, with an unprecedented degree of detail and realism. In this work, we present a set of 3D simulations of a convective neon-burning shell in a 20 M$_\odot$ star run for the first time continuously from its early development through to complete fuel exhaustion, using unaltered input conditions from a 321D-guided 1D stellar model. These simulations help answer some open questions in stellar physics. In particular, they show that convective regions do not grow indefinitely due to entrainment of fresh material, but fuel consumption prevails over entrainment, so when fuel is exhausted convection also starts decaying. Our results show convergence between the multi-D simulations and the new 321D-guided 1D model, concerning the amount of convective boundary mixing to include in stellar models. The size of the convective zones in a star strongly affects its structure and evolution, thus revising their modelling in 1D will have important implications for the life and fate of stars. This will thus affect theoretical predictions related to nucleosynthesis, supernova explosions and compact remnants.

astro-ph.SR↗

arXiv2022

Spin-down and reduced mass loss in early-type stars with large-scale magnetic fields

Magnetism can greatly impact the evolution of stars. In some stars with OBA spectral types there is direct evidence via the Zeeman effect for stable, large-scale magnetospheres, which lead to the spin-down of the stellar surface and reduced mass loss. So far, a comprehensive grid of stellar structure and evolution models accounting for these effects was lacking. For this reason, we computed and studied models with two magnetic braking and two chemical mixing schemes in three metallicity environments with the MESA software instrument. We find notable differences between the subgrids, which affects the model predictions and thus the detailed characterisation of stars. We are able to quantify the impact of magnetic fields in terms of preventing quasi-chemically homogeneous evolution and producing slowly-rotating, nitrogen-enriched ("Group 2") stars. Our model grid is fully open access and open source.

astro-ph.SR↗

arXiv2022

The effects of surface fossil magnetic fields on massive star evolution: IV. Grids of models at Solar, LMC, and SMC metallicities

Magnetic fields can drastically change predictions of evolutionary models of massive stars via mass-loss quenching, magnetic braking, and efficient angular momentum transport, which we aim to quantify in this work. We use the MESA software instrument to compute an extensive main-sequence grid of stellar structure and evolution models, as well as isochrones, accounting for the effects attributed to a surface fossil magnetic field. The grid is densely populated in initial mass (3-60 M$_\odot$), surface equatorial magnetic field strength (0-50 kG), and metallicity (representative of the Solar neighbourhood and the Magellanic Clouds). We use two magnetic braking and two chemical mixing schemes and compare the model predictions for slowly-rotating, nitrogen-enriched ("Group 2") stars with observations in the Large Magellanic Cloud. We quantify a range of initial field strengths that allow for producing Group 2 stars and find that typical values (up to a few kG) lead to solutions. Between the subgrids, we find notable departures in surface abundances and evolutionary paths. In our magnetic models, chemical mixing is always less efficient compared to non-magnetic models due to the rapid spin-down. We identify that quasi-chemically homogeneous main sequence evolution by efficient mixing could be prevented by fossil magnetic fields. We recommend comparing this grid of evolutionary models with spectropolarimetric and spectroscopic observations with the goals of i) revisiting the derived stellar parameters of known magnetic stars, and ii) observationally constraining the uncertain magnetic braking and chemical mixing schemes.

astro-ph.SR↗

arXiv2022

Realistic 3D hydrodynamics simulations find significant turbulent entrainment in massive stars

Our understanding of stellar structure and evolution coming from one-dimensional (1D) stellar models is limited by uncertainties related to multi-dimensional processes taking place in stellar interiors. 1D models, however, can now be tested and improved with the help of detailed three-dimensional (3D) hydrodynamics models, which can reproduce complex multi-dimensional processes over short timescales, thanks to the recent advances in computing resources. Among these processes, turbulent entrainment leading to mixing across convective boundaries is one of the least understood and most impactful. Here we present the results from a set of hydrodynamics simulations of the neon-burning shell in a massive star, and interpret them in the framework of the turbulent entrainment law from geophysics. Our simulations differ from previous studies in their unprecedented degree of realism in reproducing the stellar environment. Importantly, the strong entrainment found in the simulations highlights the major flaws of the current implementation of convective boundary mixing in 1D stellar models. This study therefore calls for major revisions of how convective boundaries are modelled in 1D, and in particular the implementation of entrainment in these models. This will have important implications for supernova theory, nucleosynthesis, neutron stars and black holes physics.

astro-ph.SR↗

arXiv2022

The impact of $^{17}$O$+α$ reaction rate uncertainties on the s-process in rotating massive stars

Massive stars are crucial to galactic chemical evolution for elements heavier than iron. Their contribution at early times in the evolution of the Universe, however, is unclear due to poorly constrained nuclear reaction rates. The competing $^{17}$O($α,γ$)$^{21}$Ne and $^{17}$O($α,n$)$^{20}$Ne reactions strongly impact weak s-process yields from rotating massive stars at low metallicities. Abundant $^{16}$O absorbs neutrons, removing flux from the s-process, and producing $^{17}$O. The $^{17}$O($α,n$)$^{20}$Ne reaction releases neutrons, allowing continued s-process nucleosynthesis, if the $^{17}$O($α,γ$)$^{21}$Ne reaction is sufficiently weak. While published rates are available, they are based on limited indirect experimental data for the relevant temperatures and, more importantly, no uncertainties are provided. The available nuclear physics has been evaluated, and combined with data from a new study of astrophysically relevant $^{21}$Ne states using the $^{20}$Ne($d,p$)$^{21}$Ne reaction. Constraints are placed on the ratio of the ($α,n$)/($α,γ$) reaction rates with uncertainties on the rates provided for the first time. The new rates favour the ($α,n$) reaction and suggest that the weak s-process in rotating low-metallicity stars is likely to continue up to barium and, within the computed uncertainties, even to lead.

nucl-ex↗

arXiv2022

Very massive star winds as sources of the short-lived radioactive isotope $^{26}$Al

The $^{26}$Al short-lived radioactive nuclide is the source of the observed galactic diffuse $γ$-ray emission at 1.8 MeV. While different sources of $^{26}$Al have been explored, such as AGB stars, massive stars winds, and supernovae, the contribution of very massive stars has never been studied. We study the stellar wind contribution of very massive stars, i.e stars with initial masses between 150 and 300 M$_\odot$, to the enrichment in $^{26}$Al of the galactic interstellar medium. We discuss the production of $^{26}$Al by studying rotating and non-rotating very massive stellar models with initial masses between 150 and 300 M$_\odot$ for metallicities Z=0.006, 0.014, and 0.020. We confront this result to a simple Milky Way model taking into account both the metallicity and the star formation rate gradients. We obtain that very massive stars in the Z=0.006-0.020 metallicity range might be very significant contributors to the $^{26}$Al enrichment of the interstellar medium. Typically, the contribution of the winds of massive stars to the total quantity of $^{26}$Al in the Galaxy increases by 150\% when very massive stars are considered. Very massive stars, despite their rarity, might be important contributors to $^{26}$Al and overall very important actors for nucleosynthesis in the Galaxy.

astro-ph.SR↗

arXiv2022

The p-process in exploding rotating massive stars

The p-process nucleosynthesis can explain proton-rich isotopes that are heavier than iron, which are observed in the Solar System, but discrepancies still persist and important questions concerning the astrophysical site(s) of the p-process remain unanswered. We investigate how the p-process operates in exploding rotating massive stars that have experienced an enhanced s-process nucleosynthesis during their life through rotational mixing. We computed 25 $M_{\odot}$ stellar models at a metallicity of $Z=10^{-3}$ with different initial rotation velocities and rates for the uncertain $^{17}$O($α$,$γ$)$^{21}$Ne reaction. The nucleosynthesis calculation, followed with a network of 737 isotopes, was coupled to stellar evolution, and the p-process nucleosynthesis was calculated in post-processing during both the final evolutionary stages and spherical explosions of various energies. In our models, the p-nuclides are mainly synthesized during the explosion, but not much during the ultimate hydrostatic burning stages. The p-process yields mostly depend on the initial number of trans-iron seeds, which in turn depend on the initial rotation. We found that the impact of rotation on the p-process is comparable to the impact of rotation on the s-process. From no to fast rotation, the s-process yields of nuclides with mass number $A<140$ increase by $3-4$ dex, and so do the p-process yields. Fast rotation with a lower $^{17}$O($α,γ$) rate significantly produces s- and p-nuclides with $A\geq140$. Our results suggest that the contribution of core-collapse supernovae from massive stars to the solar (and Galactic) p-nuclei has been underestimated in the past, and more specifically, that the contribution from massive stars with sub-solar metallicities may even dominate. A more detailed study including stellar models with a wide range of masses and metallicities remains to be performed.

astro-ph.SR↗

arXiv2022

Dynamics in a stellar convective layer and at its boundary: Comparison of five 3D hydrodynamics codes

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 $\lesssim 3σ$ of the mean of all simulations on a given grid ($128^3$ and $256^3$ grid cells), where $σ$ 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.

astro-ph.SR↗

arXiv2021

UVES analysis of red giants in the bulge globular cluster NGC 6522

NGC 6522 is a moderately metal-poor bulge globular cluster ([Fe/H]$\sim$$-$1.0), and it is a well-studied representative among a number of moderately metal-poor blue horizontal branch clusters located in the bulge. The NGC 6522 abundance pattern can give hints on the earliest chemical enrichment in the central Galaxy. The aim of this study is to derive abundances of the light elements C and N; alpha elements O, Mg, Si, Ca, and Ti; odd-Z elements Na and Al; neutron-capture elements Y, Zr, Ba, La, and Nd; and the r-process element Eu. We verify if there are first- and second-generation stars: we find clear evidence of Na-Al, Na-N, and Mg-Al correlations, while we cannot identify the Na-O anti-correlation from our data. High-resolution spectra of six red giants in the bulge globular cluster NGC 6522 were obtained at the 8m VLT UT2-Kueyen telescope in FLAMES+UVES configuration. In light of Gaia data, it turned out that two of them are non-members, but these were also analysed. Spectroscopic parameters were derived through the excitation and ionisation equilibrium of FeI and FeII lines from UVES spectra. The abundances were obtained with spectrum synthesis. The present analysis combined with previous UVES results gives a mean radial velocity of vrhel = -15.62+-7.7 km.s-1 and a metallicity of [Fe/H] = -1.05+-0.20 for NGC 6522. Mean abundances of alpha elements for the present four member stars are enhanced with [O/Fe]=+0.38, [Mg/Fe]=+0.28, [Si/Fe]=+0.19, and [Ca/Fe]=+0.13, together with the iron-peak element [Ti/Fe]=+0.13, and the r-process element [Eu/Fe]=+0.40.The neutron-capture elements Y, Zr, Ba, and La show enhancements in the +0.08 < [Y/Fe] < +0.90, 0.11 < [Zr/Fe] < +0.50, 0.00 < [Ba/Fe] < +0.63, 0.00 < [La/Fe] < +0.45, and -0.10 < [Nd/Fe] < +0.70 ranges. We also discuss the spread in heavy-element abundances.

astro-ph.GA↗

arXiv2021

Multidimensional low-Mach number time-implicit hydrodynamic simulations of convective helium shell burning in a massive star

Context. Multidimensional hydrodynamic simulations of convection in stellar interiors are numerically challenging, especially for flows at low Mach numbers. Methods. We explore the benefits of using a low-Mach hydrodynamic flux solver and demonstrate its usability for simulations in the astrophysical context. The time-implicit Seven-League Hydro (SLH) code was used to perform multidimensional simulations of convective helium shell burning based on a 25 M$_\odot$ star model. The results obtained with the low-Mach AUSM$^{+}$-up solver were compared to results when using its non low-Mach variant AUSM$_\mathrm{B}^{+}$-up. We applied well-balancing of the gravitational source term to maintain the initial hydrostatic background stratification. The computational grids have resolutions ranging from $180 \times 90^2$ to $810 \times 540^2$ cells and the nuclear energy release was boosted by factors of $3 \times 10^3$, $1 \times 10^4$, and $3 \times 10^4$ to study the dependence of the results on these parameters. Results. The boosted energy input results in convection at Mach numbers in the range of $10^{-2}$ to $10^{-3}$. Standard mixing-length theory (MLT) predicts convective velocities of about $1.6 \times 10^{-4}$ if no boosting is applied. Simulations with AUSM$^{+}$-up show a Kolmogorov-like inertial range in the kinetic energy spectrum that extends further toward smaller scales compared with its non low-Mach variant. The kinetic energy dissipation of the AUSM$^{+}$-up solver already converges at a lower resolution compared to AUSM$^{+}_{\mathrm{B}}$ -up. The extracted entrainment rates at the boundaries of the convection zone are well represented by the bulk Richardson entrainment law and the corresponding fitting parameters are in agreement with published results for carbon shell burning.

astro-ph.SR↗

arXiv2021

Convective core entrainment in 1D main sequence stellar models

3D hydrodynamics models of deep stellar convection exhibit turbulent entrainment at the convective-radiative boundary which follows the entrainment law, varying with boundary penetrability. We implement the entrainment law in the 1D Geneva stellar evolution code. We then calculate models between 1.5 and 60 M$_{\odot}$ at solar metallicity ($Z=0.014$) and compare them to previous generations of models and observations on the main sequence. The boundary penetrability, quantified by the bulk Richardson number, $Ri_{\mathrm{B}}$, varies with mass and to a smaller extent with time. The variation of $Ri_{\mathrm{B}}$ with mass is due to the mass dependence of typical convective velocities in the core and hence the luminosity of the star. The chemical gradient above the convective core dominates the variation of $Ri_{\mathrm{B}}$ with time. An entrainment law method can therefore explain the apparent mass dependence of convective boundary mixing through $Ri_{\mathrm{B}}$. New models including entrainment can better reproduce the mass dependence of the main sequence width using entrainment law parameters $A \sim 2 \times 10^{-4}$ and $n=1$. We compare these empirically constrained values to the results of 3D hydrodynamics simulations and discuss implications.

astro-ph.SR↗