Materials: Kippenhahn’s book Ch. 6 and 7, Cox & Giuli vol. 1 Ch. 14, Schwarzschild Ch. 7, Jermyn et al. 2022, Anders et al. 2022, Matteo Cantiello’s talk at KITP in 2017, review by Joyce & Tayar 2023.
In the previous lecture on energy transport we have dealt with the situation where energy diffusion (carried by photons, i.e., radiative energy transport, or carried by electrons, i.e., conductive energy transport) is sufficient to sustain the star and carry all the flux to maintain local energy conservation. However, this is not always the case! For example, we know this is not the case in the outer layers of the Sun, we can directly see that:
We can also see this is not the case in the envelopes of red supergiants, as for example Betelgeuse, VY Canis Majoris, etc. Less directly, we can also infer this to happen in the cores of massive stars: some stellar layers are not stably stratified and energy transport is not only diffusive.
In this lecture we will deal with convection, which allows for energy transport through macroscopic motion of matter resulting in a non-zero energy flux with a zero matter flux.
Convection involves turbulence (the “last” open problem of classical physics), and is because of this inherently multi-dimensional. Because of this, convection is usually one of the most approximate ingredients in stellar calculations, and often the root of many open problems.
Convection is a thermal instability (as we will see it kicks in if the temperature gradient is steeper than some threshold condition), although it results in local motion of gas/plasma: as we will see the velocities are very small compared to thermal velocities. Moreover, it is not unique to stars: the monsoon clouds in Tucson’s summer are also manifestation of convection in the Earth atmosphere!
Before discussing the details of the physics of convection by using oversimplified pictures dating back to Prandtl, have a look at the following animations of multi-dimensional simulations of convection, these are probably/hopefully closer to reality than many of the oversimplifications we will use later in this lecture.
N.B.: It is important to keep in mind that we adopt modeling simplifications to make the simulation of stars tractable, but these introduce systematic uncertainties which are active topic of research. Approximations are present also in the multidimensional simulations shown below, and therefore they should not be taken as the truth! However, these multi-dimensional simulations do not need to make the same assumptions we will discuss in this lecture, which makes them informative on how rough these approximations are.
What all these simulations of convection in different settings show is that the morphology of the convective flow is more complicated than what we will assume. You can imagine “thermal flux tubes” carried by the gas that transport energy in all these situations, but the way we describe them in spherically symmetric models of stars cannot (and does not attempt to) capture all the details we can see in the Sun and or a few nearby red supergiants, and we can simulate in restricted time and spatial domains.
Core convection in a massive star (Anders et al. 2022b)
This is a simulation of the temperature fluctuations (right) and vertical velocities (left) in “code units” using the code Dedalus.
Envelope convection in a red super-giant (Goldberg et al. 2022)
This is a 3D radiation-hydrodynamics simulation of large portions of the envelope of a red supergiant (not that different from Betelgeuse), computed with the ATHENA++ code.
Thermonuclear runaway during a Nova explosion (Casanova et al. 2018)
This is a 2D simulation of convection developing during a nova explosion using the FLASH code. The movie shows the (log10) mass fraction of $20\mathrm{Ne}$, and is taken from J. Jordi’s personal webpage (one of the co-authors).