Convective Core Overshoot Lars Bildsten (Lecturer) & Jared Brooks (TA) Convective overshoot is a phenomenon of convection carrying material beyond an unstable region of the atmosphere into a stratified, stable region. Overshoot is caused by the momentum of the convecting material, which carries the material beyond the unstable region.... This overshoot is responsible for most of the turbulence experienced in the cruise phase of commercial air flightsconvectionunstableatmospherestratifiedmomentumturbulence Wikipedia says:

Overshooting Top

From the Space Station

“Overshoot” during Convection Convection occurs in the cores of main sequence stars more massive than the sun due to the highly concentrated CNO burning. This fully mixes the core, which evolves over time, depleting the H and making a pure He core at the end of the Main Sequence. The extent of the Convective core, as we will show, depends on a number of physical properties of the star, and how one accounts for the potentially uncertain physics of ‘overshoot’.

Why does it matter in stars? Sets the Main sequence lifetime! Determines the fully mixed Helium core mass for the next phase of evolution. Sets how much of the star experienced prolonged convection, potentially relevant to core magnetism (ask Jim or Matteo!) Fun physics problem...

Setting the Stage: Core Properties Core densities times that of water T=10 7 K Paxton et al ‘11

Simple Understanding of Extent of the Convective Core Heat transport is via radiative transfer, so the flux and hydrostatic balance equations are: If we combine these, we obtain a simple equation true at any location in a star

Onset of Convection Convection occurs when an adiabatically displaced fluid element continue to accelerate... Or in terms of ideal gas, when the background T gradient exceeds For CNO burning, nearly all the stellar luminosity is present at the core, allowing for a calc (where I assume same opacity for Eddington as in the core)

So, What’s the Condition? The product, is nearly a pure number for stars of constant opacity that can be modeled as Eddington Standard Models, so => centrally condensed burning will trigger convection, and the specific location depends on both how centrally concentrated burning is and the stellar structure details. Eventually, heat can be carried out via radiative transfer..

What Happens when Convecting? Convection in the core only needs to go fast enough to get the heat out. When very sub-sonic, the convective speed needed to carry the flux is determined via This allows us to estimate the velocity and find, roughly, that for a large part of the star, we get About one part in 1000

Not Too Bad!

Convection speeds do change, but all are sub-sonic! 750 miles per hour is the speed of sound, and some storms get up to 100 MPH

These and other works motivate a phenomenological approach of simply extending the convective zone boundary beyond the normally determined region by some fixed fraction of the local scale height => Fixed Step Overshoot Why Should the Upward Cell Stop? ?

Clearly evident in the HR diagram, as the He cores are larger and the stars live longer on the Main Sequence. Is a testable hypothesis from studies of open clusters, especially those where ages are independently known from lithium depletion of low mass pre-main sequence stars

But, Abundances Change!!! The burning of the H into Helium in the core means that it, on average, gets heavier than the outer envelope. Such a mean molecular weight change then modifies the condition for convection to that referred to as the Ledoux criterion. It is more stringent, in the sense that the temperature gradient needs to be even steeper to overcome the mean molecular weight barrier... Let’s see how that changes things!

Uncertain Physics Problem, for Sure Not only is the implementation within any code a challenge, but so is the physics. Keep in mind that the convective instability, when it initially goes, is on a fast timescale, comparable to the dynamic timescale. Another option is for the oscillation to be over- stable due to buoyant oscillations that, over time, allow for heat transfer that mitigates the thermal term. Stars on the main sequence live many thermal times!

Double Lined Eclipsing Binaries Inclination constrained Eclipses provide radius information Both radial velocities give the mass ratio..... Basically, gold mines for overshoot calibration, as both stars MUST have the same age!!

Highly Accurate Work Enabled by Photometry + Radial Velocities Pavlovski et al

Maxi-Lab

GO! ! !

Claret & Torres ‘16