Transcript Neon Sedimentation in White Dwarfs

Convective Core Overshoot
Lars Bildsten (Lecturer) & Jared Brooks (TA)
Wikipedia says:
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 flights
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
Paxton et al ‘11
• Core
densities 1050 times
that of
water
• T=107 K
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
Why Should the Upward Cell Stop? ?
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
• 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 overstable 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!!
Pavlovski et al
Highly Accurate Work Enabled by
Photometry + Radial Velocities
Maxi-Lab
GO! ! !
Claret & Torres ‘16
Claret & Torres ‘16