# Binary Systems and Novae

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• 0:03 Binary Stars
• 1:45 Roche Lobes & Lagrange Points
• 4:57 White Dwarf & Novae
• 6:38 Lesson Summary

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Lesson Transcript
Instructor: Artem Cheprasov
This lesson will explain for you something known as the Algol paradox, what binary stars are, and how Roche lobes, the inner Lagrange point, novae, accretion disks, and novae are all involved in binary systems.

## Binary Stars

In a secluded town, there exists a barber. He is a man who shaves all and only the men in that town who don't shave themselves. This begs the question: who shaves the barber?

I love paradoxes like this. They make the mind scratch itself in wonder as to what happens and why, and paradoxes exist in just about every field in life, including astronomy. In astronomy there is a paradox called the Algol paradox, named after the binary star Algol. A binary star is a pair of stars that revolve around their common center of gravity.

We know that stars in a binary system are born at basically the same time. Binary stars are like fraternal twins because they don't always look exactly the same, but are born at the same time nonetheless. We also know that the more massive a star is, the shorter its lifespan and, therefore, the shorter its stay on the main sequence band on an H-R diagram. This is the band on the diagram that includes healthy adult stars, the ones not retiring or dying. Once a star decides to retire, it leaves the main sequence.

Now that you are aware of these little but important factoids, answer me this: why is it that in binary systems it is the lower mass stars that leave the main sequence before the higher mass stars? It's truly a paradoxical notion, one that will be explained in this lesson as we discuss the concepts of mass transfer and its relation to binary systems, novae, and white dwarfs.

## Roche Lobes and Lagrange Points

The answer to the Algol paradox, very briefly, is that binary stars may interact with one another in a way that results in mass transfer from one star to the other. When two stars are located close to one another, their gravitational fields and the rotation of the binary system results in something known as Roche lobes. A Roche lobe is a volume of space within a binary system that is gravitationally controlled by a star. Since there are two stars, there are two Roche lobes and, thus, an area of space each star controls.

Such lobes remind me of a dumbbell, and this notion will help you recall something else. On a dumbbell, if the weights were to be huge and very close together, it would be impossible to grasp. Thus, bigger weights and bigger Roche lobes must be far apart for comfort's sake, meaning the size of the Roche lobes will increase as the stars lie farther and farther apart from one another. On the other hand, the size of the Roche lobes will decrease if the stars are close together.

In between the two Roche lobes, right where they meet, is something known as the inner Lagrange point. Matter that leaves one star and reaches this point then makes its way to the other star. There are two ways matter can reach this inner Lagrange point. One is by a stellar wind blowing a star's gas away, and the other is by a star expanding so much that it actually fills its own Roche lobe. The way the latter point can occur is if the stars are close to one another and the lobes are, therefore, small to begin with.

Keeping all this in mind, it will now be easier to explain why the originally lower mass star in a binary system becomes a giant, while the originally more massive star remains on the main sequence. Again, this is exactly the opposite of what we would expect had these stars evolved separately and not in a binary system.

So, here's what happens. The originally higher mass star will at first begin to swell into a giant before the lower mass star, just as we would expect it to. There's no paradox at this point. But as it does so, it fills up its Roche lobe. This means it will transfer matter to the originally lower mass star. This means the higher mass star will lose mass and will become a lower mass star, while the originally lower mass star gains mass and becomes a giant.

This isn't very difficult to imagine. Just think of this thought experiment with me. Let's take two chemistry flasks and fill each with a bit of water and connect them with a tube. Each flask represents the Roche lobe. If one of the flasks were to magically begin filling up with more and more water, what would happen as it filled its Roche lobe? It would use the tube, the inner Lagrange point, as an overflow point in order to transfer mass, the water, to the other flask!

## White Dwarfs and Novae

This kind of process also helps explain something known as novae. A nova is the Latin term for 'new' and it is used to describe the sudden brightening of a star that makes it look like there is a new star in the sky, when in fact it's actually representative of a dying star, not a new one.

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