Science Sunday: Drop That Stellar Beat – The Kappa Mechanism

One of the most fascinating things to me in our Universe is the fact that stars, these ridiculously massive, hot, bright objects that provide the necessary energy for existence as we know it, are not at all static objects. We see our own Sun in the sky, and we really only see one small bright yellow disc. Look a little closer (never look directly at the Sun!), and you see its surface changing every 11 years. Sunspots grow and disappear, prominences arc wildly over its surface, flares spew out light, energy, and a cornucopia of charged particles into space, etc. And ours is just a run-of-the-mill Main Sequence star! What I want to talk about here is something that exhibits the dynamic side of evolved versions of stars like ours: stellar pulsation.

Now, while stars upon close examination are indeed dynamic objects, they do have a tendency to at least maintain their size. As has been discussed before, all stars produce nuclear energy in their cores. This energy heats up the gas in the star, and provides the necessary gas pressure needed to hold the star up against the collapse of all its considerable mass. The more massive the star, the more energy needed to hold it up against the collapse of its fatness. If the star were to contract a small bit, the increased gravitational pressure would cause the core to produce more energy, thereby increasing the gas pressure, restoring it to its equilibrium state. This maintenance of shape by the interplay between gravitational collapse and gas pressure is called hydrostatic equilibrium. Be thankful for it. We’d never have had a chance to exist without it!

So, what does hydrostatic equilibrium have to do with stellar pulsation (and in particular, the kappa mechanism)? Well, all types of stellar pulsations occur when this equilibrium state is thrown out of whack. For massive thermal pulses, like those that occur in the stars that I study for my thesis, the star’s balanced state is disrupted by periodic changes in the type of fusion occurring in its core. However, I’ll save that little discussion for another post (if you really want the technical nitty gritty though, check out this 1983 review paper by Icko Iben and Alvio Renzini on AGB star evolution). For the shorter-term pulsations that I want to focus on here, the balance is ruined by changes in the type and properties of gas in the star.

I want to take a brief little detour here and talk a little bit about opacity. Opacity, denoted by the greek letter “kappa”, tells you how difficult it is for light to penetrate a substance. Something with a low opacity will let light pass through easily (like a window, dry air, or the vacuum of space). Opaque substances block most or all light from passing through (like a lamp shade, or a wall). When an opaque thing interacts with light, it’ll either scatter that light away, or absorb it.

Right, so that’s opacity. In stars, the opacity of the gas in the star typically decreases as temperature and density of the gas increases. This means that as you move inward from the surface toward the stellar core, the gas becomes less and less opaque to light (as temperature and density increase as you get close to the core). This also means that if the star contracts a little bit (increasing the temperature and density of the interior), the opacity of its atmosphere decreases and allows radiation to escape more easily, reaching the gas in that star’s atmosphere and restoring that equilibrium state. However, in stars that are unstable to opacity-driven pulsations, there exists a layer of gas (typically partially-ionized hydrogen or helium) in the stellar atmosphere whose opacity increases as temperature and density increase. Thus, if the star were to contract a little, that layer would become more opaque, and radiation would have an increasingly difficult time permeating the atmosphere.

Now here’s the kicker. If the star contracts, the gas in that opaque layer heats up. When the gas heats up, it becomes ionized and that ionized form is more opaque than the non-ionized form. The radiation is going into fully ionizing the gas in that layer and heating up the gas below it, though not creating gas pressure IN that opaque layer to counteract gravity. So, the star continues to shrink until the buildup of radiative pressure below that opaque layer is just too much and the gas has reached maximum opacity. Then, just like a piston with heated gas beneath it, the cumulative radiative pressure forces the star’s atmosphere outward!

The gas beneath that piston then cools, allowing the it to come back down to its rest state. Same thing happens in a star—the buildup of radiative pressure gets released, the gas becomes cooler, less ionized, and less opaque, and so the star can contract again. And thus we have the lub-dub of evolved stars. Radiative pressure builds beneath the opaque layer until it’s just too much and expands outward. The cooled gas (and thus lower gas pressure) allows the star’s atmosphere to contract and build its opacity back up. Then pump back out, and “relax” in.


And I think that is damn cool.For some stars (Cepheid variables), this pulsation cycle can range between 1 to 100 days. For other stars (RR Lyrae), this pulsation can happen in under a day. These pulsations can change a star’s radius by some ridiculous values (25% for some Cepheids!), and their brightnesses can just about double (RR Lyrae and Cepheids)! We know that the duration of the pulsation is linked to the average brightness of the star itself (called the period-luminosity relationship for variable stars. Thank Henrietta Swan Leavitt for that one). As such, we can use stars that show these variations to calculate distances and map things out in 3D space! Just from that beat, that little stellar instability, we can learn about the layout of our local Universe.


The magic of Google