Excitation of Gravity Waves by Fingering Convection, and the Formation of Compositional Staircases in Stellar Interiors

Abstract

Fingering convection (or thermohaline convection) is a weak yet important kind of mixing that occurs in stably-stratified stellar radiation zones in the presence of an inverse mean-molecular-weight gradient. Brown et al. (2013) recently proposed a new model for mixing by fingering convection, which contains no free parameter, and was found to fit the results of direct numerical simulations in almost all cases. Notably, however, they found that mixing was substantially enhanced above their predicted values in the few cases where large-scale gravity waves, followed by thermo-compositional layering, grew spontaneously from the fingering convection. This effect is well-known in the oceanographic context, and is attributed to the excitation of the so-called "collective instability". In this work, we build on the results of Brown et al. (2013) and of Traxler et al.(2011b) to determine the conditions under which the collective instability may be expected. We find that it is only relevant in stellar regions which have a relatively large Prandtl number (the ratio of the kinematic viscosity to the thermal diffusivity), O(10 −3 ) or larger. This implies that the collective instability cannot occur in main sequence stars, where the Prandtl number is always much smaller than this (except in the outer layers of surface convection zones where fingering is irrelevant anyway). It could in principle be excited in regions of high electron degeneracy, during He core flash, or in the interiors of white dwarfs. We discuss the implications of our findings for these objects, both from a theoretical and from an observational point of view.

Rotating double-diffusive convection in stably stratified planetary cores

“…Several theories have been proposed in the non-rotating case (Stern & Turner, 1969;Radko, 2013). For the moderate values of P r characterising planetary cores, their generation may rely on the mixing by nonlinear internal waves (Garaud et al, 2015). Yet, these mechanisms remain to be confirmed in the presence of rapid rotation.…”

“…Definition Earth (current) Stars L Lewis κ T /κ C 10 4 10 3 − 10 7 P r Prandtl ν/κ T 0.01 − 0.1 10 −6 Sc Schmidt ν/κ C 10 2 − 10 3 10 −3 − 10 1 Ek Ekman ν/(Ω s R 2 ) 10 −15 10 −18 Table 1: Dimensionless numbers characterising diffusive effects and typical values in the Earth's liquid core (Braginsky & Roberts, 1995;Labrosse, 2015) and stably stratified stellar envelopes (Garaud et al, 2015). Kinematic viscosity ν, thermal diffusivity κ T , compositional diffusivity κ C , planetary angular velocity Ω s and radius R.…”

A Reduced Model for Salt-Finger Convection in the Small Diffusivity Ratio Limit

“…Thus, neither mechanism for staircase formation is present. Having said this, Brown et al [10] and Garaud et al [48] recently discovered that staircases can form in three dimensions even when the flux increases monotonically with the density gradient, although their mechanism also relies on gravity wave generation. In summary, the possibility that the model (in two or three dimensions) captures staircase formation must be kept open, particularly at large Ra, since oceanic staircases are observed in regions with density ratios that are in fact quite small.…”

The C12(α,γ)O16deBoer1, Görres2, Wiescher3 et al. 2017Rev. Mod. Phys.20881431View full textAdd to dashboardCite

“…These later evolutionary phases are a rich site of fascinating challenges that include the interplay between nuclear burning (Couch et al, 2015;Farmer et al, 2016;Jones et al, 2017;Müller et al, 2016), convection (Meakin and Arnett, 2007;Viallet et al, 2013), rotation (Chatzopoulos et al, 2016;Heger et al, 2000;Rogers, 2015), radiation transport (Jiang et al, 2015(Jiang et al, , 2016, instabilities (Garaud et al, 2015;Wheeler et al, 2015), mixing (Maeder and Meynet, 2012;Martins et al, 2016), waves (Aerts and Rogers, 2015;Fuller et al, 2015;Rogers et al, 2013), eruptions (Humphreys and Davidson, 1994;Kashi et al, 2016;, and binary partners (Justham et al, 2014;Marchant et al, 2016;Pavlovskii et al, 2017). This bonanza of physical puzzles is closely linked with compact object formation by corecollapse supernovae (e.g., Eldridge and Tout, 2004;Özel et al, 2010;Perego et al, 2015;Sukhbold et al, 2016;Suwa et al, 2015;Timmes et al, 1996) and the diversity of observed massive star transients (e.g., Ofek et al, 2014;Smith et al, 2016;Van Dyk et al, 2000).…”