Stellar Evolution: Isochrones

In this post on stellar evolution, I’ll be discussing what are known as “isochrones”. In my last post we looked at evolutionary tracks on the H-R diagram for constant masses across time.

Isochrones are the opposite. They are plots of on the H-R diagram at constant time across all masses. Another way to think of this is to take thousands of stars, of varying masses, get them started at the same time, wait some millions of billions of years, come back, and see where they lie on the H-R diagram.

As I pointed out earlier (and common sense should tell you even if I didn’t), we can’t create stars in labs and we most certainly can’t just sit around for billions of years to see what happens. Instead, our chief tool is modeling. Astronomers will make a model, applying all applicable physical laws, such as the ideal gas laws, gravity, and the like. Models can then be fast-forwarded to any point in time, and then checked against observations and refined.

So let’s start by taking a look at a basic isochrone. The image to the right shows a typical H-R diagram with hot, blue stars to the left, and cool red stars to the right. Going diagonally from the upper left to the lower right, we can see a large section of the main sequence. Branching off from that are three trails which represent the distribution of stars after 10⁸, 10⁹, and 10¹⁰ years. What we learn from this is that, as this conglomeration of stars ages, stars will “peel off” the main sequence, starting with the massive stars in the upper left. The turn off will then work its way down the main sequence with the path it takes from there changing as it does.

That’s all well and good of course, but now how to test this aspect of the models? To apply some data to these, we need a large number of stars that all formed at very nearly the same time, but at a variety of different masses. Fortunately, nature provides a wonderful opportunity to find just such things: clusters.

Clusters form from a single cloud so the chemical composition is the same for all stars involved. The formation occurs relatively quickly in astronomical time scales, so now we have everything we need to be able to see if models can accurately reproduce the observed shape that nature creates.

So let’s take a look at a few and see how they do:

Here’s a set of isochrones for the globular cluster m92. The scale is different than the isochrone I presented and it actually covers a lot more area of the H-R diagram than mine. You’ll notice that the isochrones are only plotted for the part near the main sequence and one part later while there are data points that continue past the end of the theoretical tracks. The reason for this is that the tracks tend to merge as they approach that upper line which is known as the red giant branch (RGB). Thus, there’s no real point in plotting it over there.

What we can see is that this cluster fits the shape of these particular isochrones very nicely. It’s not perfect though. Many effects, such as unresolved binaries, slight differences in chemical composition, unusually fast rotations, and other things, contribute to the scatter. But overall, the data fits the isochrones pretty well.

47 Tucanae is another globular cluster (visible only from the southern hemisphere) which has a very nice fit with the theoretical models.

This sort of fitting is one of the goals of the research I participated in this summer. Our data wasn’t nearly as pretty though. Part of the reason is that we were studying an open cluster, which by definition has far fewer stars, but also because there was interference from an interstellar cloud which caused reddening and extinction.

But general shape matching isn’t the only thing that we should be able to predict based on isochrones. As with the evolutionary tracks, we should also see gaps where stars don’t spend much time. Again, we should, and do, observe the Hertzsprung Gap.

Another feature that we should observe and is one I’ve used, is known as the Red Giant Clump. This is a particular point near the RGB where stars slow down in their evolution for a time and tend to bottleneck. This happens at a fairly consistent color and luminosity, which gives it a feature astronomers can exploit to make corrections.

Are models perfect? Absolutely not. Models are still limited by what we’re able to realistically calculate. As computing power improves, we are able to take more and more into consideration, which should bring our models into better agreement with the data.

One example of this is that models are now beginning to consider a feature known as convective core overshoot. In this, convection that occurs in the interior of some stars, is able to provide the core with additional hydrogen, thus slightly changing the evolutionary features of the star.

So as with the evolutionary tracks I mentioned in my previous point, our main test of these theoretical models are to check where stars should and shouldn’t be, where they clump, and where they go, to observations of reality. If they match, we gain confidence in our models.

As you might expect, the general shape isn’t the only feature of models that we can test. In my future posts on stellar evolution, I’ll briefly discuss other properties of stars for which we can hold models accountable.