Convective core entrainment in 1D main-sequence stellar models

Abstract

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⊙ 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, RiB, varies with mass and to a smaller extent with time. The variation of RiB 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 RiB with time. An entrainment law method can therefore explain the apparent mass dependence of convective boundary mixing through RiB. New models including entrainment can better reproduce the mass dependence of the main sequence width using entrainment law parameters A ∼ 2 × 10−4 and n = 1. We compare these empirically constrained values to the results of 3D hydrodynamics simulations and discuss implications.

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

“…This is an important aspect if the results of entrainment studies from hydrodynamic simulations are to be used in 1D calculations. Recently, the Bulk-Richardson entrainment scaling was applied to stellar evolution calculations (Staritsin 2013;Scott et al 2021). Scott et al (2021) show that it naturally leads to a mass-dependent efficiency of CBM, which is suggested by observations.…”

“…Recently, the Bulk-Richardson entrainment scaling was applied to stellar evolution calculations (Staritsin 2013;Scott et al 2021). Scott et al (2021) show that it naturally leads to a mass-dependent efficiency of CBM, which is suggested by observations. However, their study indicates that values of n < 1 result in a too efficient mixing and that the values for A that are commonly found in hydrodynamic simulations are too large.…”

“…Instead, it is best to use theoretical prescriptions like the entrainment law. Recently, 1D stellar evolution models using the entrainment law on the main-sequence have been computed by Scott et al (2021) and better reproduce the mass dependence of the main-sequence width. New 1D models during other phases of stellar evolution will be needed to assess the ability of the entrainment law to represent convective boundary mixing in 1D models throughout stellar evolution.…”

Massive Star Modeling and Nucleosynthesis

“…This reduction of the core size in turn reduces the luminosity increase of the model during the main sequence. Recently, Scott et al (2021) presented a grid of models, with mass ranging between 1.5 and 60 M ⊙ , computed with the entrainment law and compared them to similar models computed with a penetrative overshoot. They find that the entrainment CBM scheme leads to a natural increase of the mixed region with mass, improving agreement with the observational constraints derived by Castro et al (2014).…”

“…In contrast with Staritsin (2013), they obtain an entrained mass that increases with time. This difference is due to the difference in the implementation: Staritsin (2013) scales the instantaneous entrained distance with the Richardson number (d ent = V ent t), while Scott et al (2021), following Cristini et al (2019), scale the mass entrainment rate (Ṁ ent ) with Ri B , building a cumulative entrainment. Note that while the cumulative implementation reproduces the trend seen in the hydro simulation, it is not clear how the secular evolution differs from the evolution on a dynamical timescale probed by 3D modeling.…”