Gyrochronology

In case there was any confusion, we live in a dynamic universe. Stars are born. They die. Galaxies collide. Things happen.

In trying to put together a comprehensive picture of how this all happens, one of the things we need to know as astronomers, is in what order things happen. How has our universe evolved?

Knowing how to tell just how old objects in the universe are is a serious challenge. There's some tricks out there, like looking at the main sequence turn off for clusters, but for isolated stars, it's much more challenging. Stars that are still on the main sequence pretty much all look the same for a given mass. Although they cook up heavy elements in their cores, most of it will never reach the surface and even if it did, there would be no way to be certain that those heavy elements weren't present when the star formed.

For isolated stars, one of our best hopes is to look at how fast the star is spinning. As stars age, they radiate away energy in various manners, burning off the angular momentum with which they're born. So if stars of similar masses all started off with the same rotational speed, and spun down at the same rate, the amount by which they'd slowed down would tell us the age.

Sadly, nature's rarely so simple.

Dating stars from their spin can be done (known as gyrochronology) but it's a tricky business.

A paper in last month's ApJ discusses the problems and some of the solutions.

The idea is to calibrate the method by looking at the rotation period for stars for which we know the age. As I pointed out before, clusters offer this potential. Then, by plotting the period vs the age, we would hopefully be able to make some sort of relation.

This paper built on previous work which looked at clusters like the Pleiades, M34, NGC3532 and the Hyades. In specific, the authors added M35 to the list of clusters for which the periods were plotted.

As I hinted at before, things aren't quite so simple, mainly because there's other variables to consider. One of the ones you might expect is that the mass plays a factor. This study concentrated on “late” type stars; stars that are on the low end of the mass scale (G, K, and M spectral classes).

Another issue is that, even for a single cluster, there's apparently not just one sequence that stars for a given age, but two! Here's what I mean:From this picture, you can see that there's a line going diagonally from the lower left to the upper right, and one along the bottom. Incase you're unfamiliar with the terminology, the B-V (bottom axis) is the color. Bluer (hotter and more massive stars) are to the left. Cooler (less massive and redder) stars are to the right.

What this means, is that for stars of a given mass, you can have have two possible periods! Blah. Very blah.

The first question that should be asked from here is, "Why are there two sequences in the first place?"

The notion is that there's two different processes that are controlling how the star is spinning down at work. To understand one of them, let's consider a very simplistic model of stars:

Stars form as giant clouds of gas collapse. Since angular momentum is conserved the forming star spins up, faster towards the center (what will become the core). Once the star is formed, the core will be rotating faster than the surface. Since stars aren't solid, that means there's not a good way for the outer layers to steal the angular momenum from the core and for the rotational period of the core and the outside to even out. As such, the observed period of the star will be longer. The authors call this the "C sequence" for "convective". In this one, the core and shell are decoupled.

Quite often, however, this won't be the case. Stars will quite often have strong magnetic fields that act like anchors, and they drag the surface layers of the star along. This will speed up the outer layers and defines the second, faster sequence (the bottom one) which the authors call the "I sequence" for "interface".

Well, that's all well and good, but it still doesn't tell us anything about the age. At least, not until you start looking at the ratio of stars on each sequence vs cluster age. When that's plotted up, young clusters tend to have more stars that are on the C sequence with slow rotators. As you get to old clusters, more and more stars are on the I sequence (short periods). Obviously, stars will tend to switch from one to the other as the clusters age. The idea here is that the friction between the layers of the star will help create a dynamo and set up a magnetic field which will switch stars from the C to the I.

Regardless of what the processes are that govern the switch, the main thing is that it happens. And it works out that there's a fairly well defined way it changes from one to the other. The ratio of the number of stars on each sequence is directly correlated with the age!

So how well does it work? Using the data from M35 to help calibrate the method and then applying it to M35 gave the authors an age of 134 million years with about a 3% uncertainty. This isn't quite the 150 million year age given from the main sequence turn off, but it's still not a bad approximation.

Meanwhile, there's still a few niggling bits to clear up. The big one is what's with the stars that aren't in either sequence? There's a lot of stars that fall somewhere in between. The authors predict that these stars are likely close binaries that have slowed without the benefit of magnetic fields, but rather, through tidal locking. At least one of the dozen or so stars caught in between is known to be a binary star with a period of 10.33 days. This orbital period is strikingly similar to the 10.13 rotational period which lends support to this prediction. Additionally, 3 of the other stars in the gap are photometric binaries (in otherwords, their brightness changes in a manner consistent with what's expected for a binary system).

So overall, this method looks like it works pretty well. Undoubtedly, more clusters will be added and the relation further refined. Obviously, isolated stars can't take advantage of this method either, since it requires a ratio of many coevolutionary stars. But that's a challenge that will have to be met in another paper.

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Meibom, S., Mathieu, R., & Stassun, K. (2009). STELLAR ROTATION IN M35: MASS-PERIOD RELATIONS, SPIN-DOWN RATES, AND GYROCHRONOLOGY The Astrophysical Journal, 695 (1), 679-694 DOI: 10.1088/0004-637X/695/1/679