Stars

I have what I think is a stupid question, but I cannot find any publication that addresses it. Historically, I have always been interested in planets and DSO's. Recently, I have developed an interest in double stars. I have been actively seeking them out for observation. Now I am wondering why there are so many double stars. Why can't triple stars or quadruple stars, etc. exist? am I not looking in the right place? What laws of physics apply that keep multiple stars from attracting and orbiting eachother relative to double stars? :S

Hey Rick, there are many examples of multiple star systems in the sky. Alpha Centauri is the closest one to us and it has 3 stars in it.

Hello:
You ask a very good question: why are there so many double stars. In fact, that's the subject for my doctoral thesis! About 60% of nearby stars are binaries. Some are visual binaries, whereas others were discovered spectroscopically. This means that solitary stars, like the Sun, and somewhat unusual. But we do not know the reason why so many stars are binaries. Clearly, if we want to understand star formation, we need to understand binary star formation. Several groups (myself included) are currently pursuing the answer to this question. To do this, we make observations to measure the fraction of stars are binaries, using samples of stars of different ages. This has already been done for main sequence stars, and for T Tauri stars (these are stars that are just about done forming). My research is on Class I protostars. These are stars that are at the point in thier birth where they are putting on the most weight, and are thought to be around 100,000 to a million years old. Our hypothesis is that stars do not form in isolation, and that stars tend to form in binary, or higher order multiple groups. These multiple groups (tripples, quadruples, etc) are initially gravitationally unstable, and in a short period of time the lower mass star(s) will tend to get gravitationally ejected, leaveing the most massive pair as a tight binary. In this model, the Sun would have been the ejected star. So, by observing a sample of very young stars, we want to catch them while the binary fraction is still high. In a few months, I'll be able to announce the result of our research.
As mentioned by others, tripple and higher order systems do exist, but they tend to be hard to observe visually. All stable tripple and higher order systems must be heirarchical. This means that for a tripple star, for example, the separation of two of the stars must be much less than the separation from that pair to the third star. In this way, the third star does not gravitationally perturb the central binary (at least not that much), and the third star orbits far enough out that it feels the gravity of the two stars as if it were just one. So, it is typically the case that in a tripple or higher order system, one or more of the binaries is too close to visually resolve, and can be discovered spectroscopically. This is the case for Castor, which appears as a nice double star but actually has several more members. Epsilon Lyrae is one of the few quadruple systems that can be visually resolved.

Cheers
Mike Connelley

Rick Olson said:

I have what I think is a stupid question, but I cannot find any publication that addresses it. Historically, I have always been interested in planets and DSO's. Recently, I have developed an interest in double stars. I have been actively seeking them out for observation. Now I am wondering why there are so many double stars. Why can't triple stars or quadruple stars, etc. exist? am I not looking in the right place? What laws of physics apply that keep multiple stars from attracting and orbiting eachother relative to double stars? :S

As Michael Connelley point out, non-hierarchical multiples don't seem to exist. I think it's pretty unlikely that they don't form, so the question is really, why aren't they stable?

Here's one stab at a reason. Consider the triples that are hierarchical. There are a couple of kinds (not necessarily mutually exclusive). One is where the AB separation is much less than the AC separation, so that we can take AB first as a pair, and then treat that pair as a single entity in the (AB)C pair.

The other kind is where A is much larger than both B and C, so that even if they are comparable distances, B and C don't affect one another and we can treat the AB pair independently of the AC pair. It wouldn't be much different from the Sun and any two of the planets.

In both cases, the bodies can be taken two at a time, which Newton long ago showed results in the elliptical orbits that Kepler characterized in his three laws. In the first case, A and B orbit each other in a pair of ellipses, and the center of mass of A and B orbits with C in another pair of ellipses. In the second case, B and C both orbit A in two distinct ellipses.

You may have heard of the so-called three-body problem, which remains unsolved more than 300 years after Newton's Principia Mathematica. What this means is that we don't know the full set of equilibrium orbits that three mutually attracting bodies can take, although we do know some of them, corresponding to cases where the stars *cannot* be taken one at a time. When I say "orbits," incidentally, these orbits may be very odd-looking indeed, with loops and swirls, not at all like the staid ellipses we are used to when considering only two mutually attracting bodies.

My guess is that these weird orbits are an indication that these three-body solutions, although in equilibrium, are not really stable. They probably exhibit some kind of positive feedback, so that once the stars begin deviating from their orbits, there is no mechanism that brings them "back on track," so to speak; rather, they tend to deviate even further, at an ever increasing pace, until one of the stars is ejected and the system can now be treated as a stable binary.

We might imagine, for instance, that as a deviation from equilibrium begins, two of the stars get closer to each other at closest approach than they had before. Each time, the close approach accelerates them more than at previous approach, which in turn brings the next close approach even closer, until finally, they approach so closely that the speed of the smaller one exceeds the escape velocity of the larger one, ejecting the smaller one clean out of the system.

This would be an example of positive feedback in operation. It may be that there is no three-body solution that exhibits negative feedback, which would serve to bring the orbits back on track if they began deviating, but I don't know if that's been proven.

It's a very interesting question!

Brian Tung

Hello;
Why are there so many binary stars? The answer is that (practically) all stars form in binary and multiple systems. Recent research (such as mine) has shown that the fraction of stars with a companion increases for very young stars. Single stars like the Sun may have been ejeced from a tripple star system early in its history. There are a large number of tripple, quadruple, and higher order multiple stars. If I recall correctly, there are 6 stars in the Castor system. Systems with more components become systematically more rare, i.e. there are fewer tripples than binaries, fewer quadruples than tripples, etc. All systems are bound by gravity. There aren't that many tripple systems that can be resolved with an amateur scope since one component is often a spectroscopic binary (i.e. the binary companion cannot be seen, but we can observe the doppler shift of its primary star). The formation of close binaries may require the presence of a wider companion star. Easily resolved tripple systems are rare for two other reasons. 1) To be easily resolved they'll need to be far apart, which means they'd be easily stripped off in the cluster where they formed, so such systems are unlikely to survive and 2) The system will be unstable unless two of the stars are much closer than the distance from that pair to the third star. Thus, the closer pair will be hard to split. I have resolved such a star, gamma Andromidae, which is a ~10" binary and the B component is a 0.4" binary itself.

Cheers
Mike Connelley