This work was created by Dr Jamie Love and Creative Commons Licence licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Multiple Star Systems

by Dr Jamie Love Creative Commons Licence 1997 - 2011

A few lessons back I mentioned binary stars and explained that they do not have any direct connection to star evolution. However, multiple star systems are common, complex and give rise to some interesting astronomical events that you will learn about today.

We tend to think of planets like the Earth orbiting a star like the Sun. The Sun is so much more massive than the Earth that it dominates the relationship - the Earth orbits the Sun. The Sun does not orbit the Earth. Even Jupiter, the most massive planet in our solar system, has little effect on the Sun. Jupiter's gravitational force tugs only slightly but the Sun clearly is in control of all the planets.
Multiple star systems are different. Stars are much more massive than planets so systems containing more than one star have more than one powerful gravitational pull working on them. Multiple star systems may have stars of different sizes (masses) but even the smallest stars have enough mass to "throw their weight around".

A binary star system, that is a system with two stars, is often seen as two stars dancing around an invisible center. Actually, that center has no hidden mass - instead it is the mid-point of the two stars' gravitational center. Watch a pair of figure skaters as they face each other, hold hands and spin together with their arms outstretched. The center of their spin is somewhere between them. Binary stars move the same way.
You will recall that the Earth-Moon system actually spins around a common center called the barycenter but that point is inside the Earth so it's easy to ignore (or forget) it. Some binary systems have a clearly dominating partner, like the Earth-Moon system, while others are made of pairs of similar mass. Regardless, two bodies will orbit their common barycenter - the center of mass of a system.

Tonight I'll show you some "classic" binary systems and, to keep the lesson flowing smoothly, I may say that one star orbits another but I hope you will understand I am just being too brief (lazy) to carry on about the barycenter. (But, it's there! ) Besides, often one star's mass dominates the other and we have a situation similar to the Earth-Moon barycenter. I'll also teach you the physics of some particularly interesting binaries because they have an important part to play in stellar evolution.

Let's start with the most famous pair of stars in our sky Mizar and Alcor! If you think back to your lessons in January you may recall that Mizar, the second star in the handle of the Big Dipper, has a companion star called Alcor. The Arabs called this naked eye double the "horse and rider". Mizar has a magnitude of 2.3 and Alcor's magnitude is 4.0. Because Mizar is the brighter of the pair it is called the primary star and is given the letter "A". Alcor is Mizar's dimmer partner so it is called a secondary and lettered "B".

Hey, you once told me that these two stars were an "optical double"! I'm confused!

So are astronomers! (And students of Astronomy. ) Here's the story.
If two stars are "linked together" by gravity - that is, if they orbit a common barycenter - they are called a binary pair and are truly a multiple star system. On the other hand, if the pair of stars do not share a barycenter, but simply appear to be side by side due to our line of sight, they are called "optical doubles".
So, is the Mizar/Alcor pair a binary pair or an optical double? That depends on whether they orbit each other or not. It takes a very long time to actually see stars move around each other and the farther apart they are the longer it will take for them to complete an orbit. (Kepler's laws apply to all orbits, not just planetary orbits, and his third law explains that the time taken to complete an orbit is proportional to the cube of its average distance between the two bodies.) Very careful measurements and very long, detailed observations are needed to determine if the Mizar/Alcor pair is a binary pair or an optical double.

The Hipparcos satellite is probably our best tool for measuring distances to this pair. Using precision measurements (and a technique called "parallax" which you will learn about in the November lessons) astronomers calculated that Mizar is 78.1 light-years away and Alcor is 81.1 light-years from us. That separation of three light-years is pretty large and astronomers agree that the gravitational attraction between Mizar and Alcor at those distances would be so weak that neighboring stars would pull them out of any barycenter they might try to share. That is, they are too far apart to have a stable orbit. Therefore, Mizar and Alcor are optical doubles - not binary stars.

However, as anyone who has ever worked with real scientific data will tell you, the data are rarely that neat and tidy. Experimental errors and mechanical limits to precision mean that the two distances quoted above for these two stars could be off a little bit. It is within the limits of statistics and Hipparcos' precision that Mizar may be a little bit farther from us than 78.1 light-years and Alcor might be a little bit closer than 81.1 light-years. It is possible that these two stars are separated by only 0.7 light-years! That is not too far away to form stable orbits. (In August I will tell you about objects orbiting our Sun at those kinds of distances - in a place called the Oort Cloud.) Sadly, at those kinds of distances it would take millions of years to complete one orbit (remember Kepler's third law) so we have to wait a long time to see that motion. Statistics, experimental errors and precision are very important concepts in science but to fully understand them requires a level of mathematics that I am not willing to teach in this course. (It would scare off many students!) That said, if you are thinking about a career in science you can expect to take several math courses that will allow you to appreciate the "details of error".

One last thing before I leave this subject. Due to these errors and math, it is possible that the calculated distances are so far off that Mizar might actually be farther away than Alcor! That is unlikely but possible. Scientists say, "it is within experimental error but of low confidence", meaning "it's possible but I doubt it"! As a compromise, and for fun, if these two stars are the same distance from us (say they are both 79 light-years from us) they would have a separation of only 0.27 light-years. That is very close and would make a stable orbit with a period of about 750,000 years.

So, which measurements do you believe?

I suspect that Mizar and Alcor are nothing more than an optical double but I want to believe that they are a binary pair - because I think that would be cool! Also, it helps with this lesson to imagine they are a binary pair because I think it will help you to better mulit-star systems. Therefore, throughout this lesson, I will assume that Mizar and Alcor are binary stars, not an optical pair. You should make it a point to have a good look at them some night soon. You don't need binoculars to see the pair but it helps.

Astronomers immediately note two things about any binaries or optical doubles they find - how far apart they are from each other and their orientation to each other. Because we are talking about observational astronomy, these distances and orientations are measured in degree or fractions of a degree (not kilometers).
Astronomers use angles to describe the separation between binary stars. You know one degree (1o) has 60 arc minutes (60') which is the same as 3600 arc seconds (3600''). I taught you this in the section on eclipses.

Let's use the Mizar/Alcor pair to illustrate this.

Mizar and Alcor are 11.8' apart - that's "eleven point eight minutes of arc", or about 1/5 of a degree. This is enough of a separation to be seen by the naked eye. Remember, this tiny fraction of a degree is the separation we see from our position far from the pair. In fact, these two stars are very far apart!

Another important bit of information about a binary star system is the direction of the secondary star from the primary star with respect to Polaris. This is called the position angle (or PA) of a binary star. Specifically, you imagine a line drawn from the secondary star (B) to the primary (A) and then on to Polaris. (We'll call Polaris "P".) This angle, "BAP" is the position angle of the binary stars.

If you draw a line from Alcor (B) to Mizar (A) and Polaris (P) it will make an angle of 71o. That means the PA of the Mizar/Alcor pair is 71o or, to put in another way, Alcor is 71 degrees (eastward) from Mizar with respect to Polaris. In fact, we could make more precise measurements and include minutes and seconds of arc, but I think you get the idea.

A secondary that is exactly due east of its primary will have a PA of 90o. If the secondary is on the same line as the line drawn to Polaris then the pair has a PA of 0o and if the secondary is on the opposite side the pair have a PA of 180o. And so it goes.

But those values (separation and PA) must change as they move around their barycenter. Right?

Very right, but it takes a long time to notice that change - at least with this pair (Mizar/Alcor).

The motion of binary stars is a very important idea that all astronomers, including amateurs, should understand.
As these two stars orbit each other they will very gradually shift their positions and, here on Earth, we will see them move around each other (if we could live for millions of years! ).

If their orbit is perpendicular to our perspective, we will see them perform a circular "dance". Their separation will be constant (if the orbital plane is perpendicular to our view) but their position angle will change.

On the other hand, if their orbit is along a plane which is edge-on from our perspective, the two stars will appear to approach each other, appear to collide (but they don't really) and then move past each other. In that case their position angle changes abruptly (as they "switch sides") but their separation changes smoothly.
When they appear to collide one star actually passes in front of the other and may affect the total light output. This is called an eclipsing binary. We'll come back to eclipsing binaries shortly.

Off hand, I don't know how Mizar and Alcor will change over the millions of years. They move too slowly for mere mortals to notice. I suspect that their orbit is neither perfectly perpendicular nor planer to our view so I suspect that BOTH their PA and separation will change over the millions of years it takes for them to complete an orbit. It's a fair guess that most pairs of stars will gradually change their separation angle and position angle as they slowly orbit each other. [Opps! I mean as they slowly orbit their barycenter! ]

Yeah, but if they don't share a barycenter, they have nothing to do with real binaries.

Well Mizar and Alcor may not be a real binary pair but it is going to far to say they have nothing to do with multistar systems. It turns out that Mizar really IS a multistar - regardless of Alcor! In 1650 Giovanni Battista Riccioloi, the Jesuit astronomer of Bologna, used a crude telescope to see that Mizar has a small companion. It is much closer to Mizar than Alcor and it is truly linked to Mizar. Riccioloi's observation was the first discovery of a binary pair!

A small telescope reveals that Mizar's unnamed companion, which we call "C" because it is the third member of this system to be discovered, is only 14.4" from Mizar. That's 14.4 arc seconds - far below the ability of your eyes to resolve the two points of light. Actually, these two stars, A and C, are separated by 60 billion kilometers and take about 10,000 years to complete an orbit. This is a much smaller distance and much shorter orbital period than the Mizar/Alcor (A/B) pair. [Kepler's third law tells us why the orbital periods are shorter for objects with smaller orbits.]
The angle of separation (14.4") is far too small to be seen with the naked eye or even binoculars. But a good telescope shows that Mizar's companion (C) is found at PA (position angle) 152o. That places it roughly southeast of Mizar.

Don't just read that! Picture it in your mind's eye. You learn more by imagining how it would look. (I can't draw everything! )
Try to imagine how these three stars are situated with respect to each other and with respect to Polaris. Better yet, back up and get the information you need (from above) and draw it. Include the angles and also draw the separations to scale (roughly). You'll learn a lot that way. (Like that you need a big piece of paper to include Alcor in the image if you draw it to scale.)

You might think that this small unnamed companion of Mizar would be pretty dim but you'd be wrong. Mizar's near neighbor is about as bright as Alcor but their separation is so small that we see only a single point of light. Indeed, the "magnitude" for the star we think of as Mizar is really the light of Mizar(A) plus its close neighbor(C), added together.

Careful measurements of Mizar's light (using a technique involving spectroscopy) show that it has ANOTHER companion! It is very close to Mizar - only 0.007 of a second of arc. That is the angle made by a penny at a distance of about 500 kilometers! This star, which we can call "D" because it is the fourth member of this system to be discovered, takes only 20 days to orbit Mizar (which is really "A" in this system - just to remind you).

Confused? It gets worse. Or better, depending on how you like it!

The star we have named "C" has a companion orbiting it, which we can call "E". "E" takes about half a year to orbit "C" (which takes thousands of years to orbit "A").

As you can see, the dot of light in our sky that we call Mizar is actually a quartet of stars or a binary-binary! With Alcor, this would be a quintuple system!

By the way, at one time it was thought that Alcor had a companion but it turns out that those early astronomers were wrong. (Phew!) Alcor is all alone - unless, of course, we include it as a distant relative of Mizar's quartet.
And the idea of "relatives" is not too far off the mark. Astronomers often study the characteristics to stars to decide if they are "related" - in terms of their history, chemistry or origins. Careful analysis shows that all four of Mizar's stars rotate very slowly causing the underlying shells to not mix very much. That causes their atmospheres to show strange chemical abundancies due to the slow and gentle separation of the elements. For example, star A has an atmosphere with high levels of silicon and strontium. Star C's atmosphere is low in calcium and aluminum but rich in silicon and rare elements like samarium and cerium. Maybe tidal friction caused these stars to slow their spinning and now causes them to display these wonderful, differentiated atmospheres. Alcor (star B) on the other hand, spins very fast (a hundred times faster than the Sun) and its atmosphere is so unstable it actually pulses a little bit. Alcor shows no sign of the chemical separations seen with the Mizar quartet. Clearly, if Alcor is related to Mizar it is through a distant relationship. Alcor is too far away to be affected by the tidal friction of the Mizar stars. Does that mean it is not orbiting Mizar at all? Or does it mean it is just not orbiting close enough? Did Alcor and the Mizar stars experience different origins (times of formation and composition)? The list of questions goes on and on.

Many stars are actually multiple star systems locked together by their gravitational attraction and orbiting each other (I mean, their barycenters) in very complex ways. Astronomers love multistar systems because they are complicated and allow us to address complicated questions about star formation and evolution.

Most stars are multiple systems. Our own star, the Sun, is a bit unusual in that it's all alone.

How do these multiple star systems come about?

We used to think that stars "captured" passing stars in order to form multiple systems but now we don't think that happens often, if at all. (It has to do with some complex physics involving the interaction of moving masses.) Instead, we believe that the members of a multiple system simply formed from the same nebular materials in the same region and became gravitationally linked as they evolved. That means all the stars in a multi-star system are about the same age, having formed from the same nebula.

However, just because stars in a multiple star system grew from the same nebula does not mean that they will all be the same kind of stars. Recall that stars are different because of their masses.

Are there many binary stars with different partners?

Yes! The most famous binary is Algol and this is really a poorly matched pair.
Unfortunately, this is a bad time of the year to find Algol because it is a fairly northern constellation and at sunset it's near or below the horizon for most people. On the other hand, if you stay up late (or wait about a month or two) you can get a decent view.

Here's the northeast horizon around midnight on July 1st as seen from a latitude of 37o.
(Remember, this is a view towards the north so it is upside-down from the view you may be used to because I usually orient my images to face south.)

If you are at a lower latitude, say in Dallas at 33o, then this image will be slightly lower on the horizon and you may have to stay up later to see Algol.
If you are farther north, say Chicago at 42o, this image will appear higher in the sky and you will see Capella and TAURUS sneaking above the horizon too.

Polaris is an obvious place to start in order to get your bearings. Notice I have labeled Kocab. You will recall that Kocab is the second brightest star in the Little Dipper. (It's in the top of the "bowl".) If you extend a line from Kocab to Polaris and then beyond Polaris you pass by a familiar constellation. CASSIOPEIA is easily identified by its W-shape. If you continue slightly pass CASSIOPEIA and slightly away from it you find a group of stars that are our topic for tonight.

The constellation directly below CASSIOPEIA, rising from the eastern horizon, is PERSEUS, a hero from Greek mythology.
One of PERSEUS' legs extends to the horizon (in this view) but if you waited a few hours for TAURUS to rise you would see that PERSEUS' right leg forms a gentle arc towards the Pleiades.

The brightest star in PERSEUS is Mirphak.
That star is 620 light-years away.
Mirphak is an F-type star with a luminosity 6000 times greater than the Sun.

But Algol (Beta Persei) is the star we want to focus on tonight. It's the bright star in PERSEUS' other (left) leg.

Use your "page up" and "page down" buttons to quickly change from this view, showing these lines, to the view above where only CASSIOPEIA is outlined. Use this to get your bearings and to understand how to find PERSEUS, Mirphak and Algol.

What's special about Algol?

Algol is an eclipsing binary.

Algol A, the primary partner, is a white star and it's about 100 times as luminous as the Sun. This is NOT a white dwarf, just a white star. It's far too big and bright to be a dwarf! Recall that a white dwarf is about the size of the Earth. Well, Algol A is much bigger, about three times as big as the Sun!

The secondary component (B) is a large, red(ish) giant that is only three times as luminous as the Sun.
Notice that the secondary is larger but less luminous than the primary. We assign the names, "primary" and "secondary", based upon the order in which they are discovered and that has to do with luminosity, not mass. Also notice that because stars in multiple systems are fairly close to each other (relatively speaking) any difference in their relative magnitudes will be the same difference as their absolute magnitudes because the stars are the same distance from Earth (roughly).

These two stars are separated by only 10.5 million kilometers - far too close to be seen as two distinct points of light. For the sake of comparison, Mercury is about 60 million kilometers from the Sun.
The secondary (B) takes 2 days, 20 hours, 48 minutes and 56 seconds to complete an orbit around the primary (A) and the path of its orbit makes a plane that is almost edge-on to our view.

Because the secondary is larger but dimmer than the primary, the secondary eclipses the primary. This causes the overall magnitude of "Algol" (the two stars together) to dip abruptly as the secondary blocks off the brighter, smaller primary star.
The alignment isn't perfect so this is only a partial eclipse - only 74% of the primary is hidden - but that is enough to cause the overall magnitude of Algol to drop from 2.1 to 3.4.
Algol's maximal eclipse lasts about 20 minutes but the entire event, from the beginning of the eclipse to the end of the eclipse, takes over nine hours.
Then it repeats itself like clockwork every 2 days, 20 hours, 48 minutes and 56 seconds.

There is a slight drop in magnitude when the secondary moves behind the primary but it's only a small amount.

From our knowledge of stellar evolution we can make some assumptions about the Algol system.
We can assume that they are the same age because we assume they formed from the same nebula - at the same time. The star that has grown into the secondary was the more massive so it aged quicker and left the Main Sequence, becoming a red giant, before its partner.

I'd like to draw your attention to two important things.
First, I have drawn this all wrong! Remember these two stars orbit their barycenter. Besides, the red giant is the more massive of the pair, so it would be better to say that the primary (the bright Algol A) is orbiting the secondary (the dimmer Algol B). At least that would be closer to the truth! On the other hand, it's common for astronomers to think about it as I have diagrammed it because we tend to focus our attention on the brighter star. It's "natural" to make that mistake.
The other important thing to understand is that Algol B is a giant and, like all giants, it has a "fluffy" surface. In other words, the materials at the giant's surface are not held very tightly. (Recall I mentioned this long ago when I told you about the structure of red giants.)

Yeah. So what?!

So, this particular giant is very close to its white partner - closer than Mercury is to the Sun! Indeed, this secondary is so close to its primary that the primary is pulling materials from the surface of the giant and onto its own surface.

That might seem wrong but think about it. Algol's secondary is more massive than its primary but the fuzzy nature of the red giant's surface means it is easy for its smaller, denser companion to steal some materials.

This process is called mass transfer and it's an important part of the lives of many binaries.
The primary will continue to capture materials from its companion and increase in mass. As its mass increases it will age faster and eventually leave the Main Sequence. The final outcome of the pair will depend upon the amount of mass transferred and whether or not mass will then be "retransferred" back to the secondary, once the secondary has aged into a red giant.

This can get very complicated, but it's this complexity that fascinates astronomers so they make a special point to study mass transfer in binaries in order to better understand these events. As the materials move from one star's surface to another it is heated by friction and whipped around by magnetic fields. This causes the material to emit radio waves that radioastronomers can detect and measure in order to get an idea of how the mass transfer is proceeding.
The Algol system is a wonderful source of informative radio waves because of the mass transfer going on. Indeed, if Algol's white star (Algol A) was a white dwarf (which it is not) we might expect this mass transfer to produce a nova someday.

Huh? What?

Ah, I thought that would get your attention. Allow me to explain this important process in our next lesson. I'll also show how to find some more multiple star systems and teach you a few more stars and constellations.




This work was created by Dr Jamie Love and Creative Commons Licence licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.