What About Binary Systems?


In the constellation of Perseus, there is a star named Algol that exists in a binary system. The binary consists of two stars: a massive main-sequence star and a less massive giant.

According to what we’ve explored so far…that doesn’t make any sense.

More massive stars evolve faster than less massive ones. They expand into giants before less massive stars do. In any one binary system out there, we should observe a more massive giant and a less massive main-sequence star, not the other way around.

But the Algol system is not alone in this peculiarity. Over half the stars in the universe are binaries, and in a number of those, the more massive star is still on the main sequence.

Why?

This peculiarity is known as the Algol paradox, and in order to understand it, we need to look at a special feature of binary systems: the Roche lobes.

These Roche lobes are defined by the gravitational fields of the two stars, combined with the rotation of the binary system.

The mechanics are fairly simple. Any matter inside either of the Roche lobes is controlled by the gravitational force of the star within that lobe. Unsurprisingly, we call the surface of the Roche lobes the Roche surface. Last but not least, the size of the Roche lobes depends on the mass of the stars and the distance between the stars.

So, if we have stars that are far apart, the Roche lobes will also be large. In this case, they won’t matter as much for stellar evolution. Everything will proceed as normal, as it does for most binary stars.

However…if the stars are close together, the Roche lobes will be small. And if that’s the case, when a star expands to become a giant, it can completely fill its Roche lobe.

The result? Anything that leaves the giant star’s Roche lobe, the star loses. But it doesn’t just disappear into space. The Langrangian point, also known as the inner Lagrange point or L1, acts like a spout in a tank that’s connected to another tank. Mass flows from one star to the other.

So what are the implications of all this?

Well, we start with two main-sequence stars that formed at the same time out of the same giant molecular cloud. Star A is more massive than Star B, so it evolves more quickly and expands into a giant first.

When it does, it fills its Roche lobe, and material starts flowing over the inner Lagrange point to fall onto Star B. Now, Star A is a giant and Star B is on the main sequence, but Star A has lost some of its mass to Star B, so Star B is actually the more massive one—and the younger one.

So, if stars can transfer their mass like this…could they theoretically transfer all their mass?

The answer is yes.

We see the evidence of this in the form of rapidly-rotating giants. Most giant stars rotate slowly for the same reason ice skaters spread their arms if they want to slow down: they are very big stars. But some giants rotate much more quickly than they should, and the working hypothesis is that they are merged stars.

Essentially, what happens is both stars in a binary system expand to fill their Roche lobes. Their mass spills out into space because it can’t fall on one or the other—gravity isn’t strong enough beyond the Roche surface.

Model calculations indicate that, if the stars are close enough together and expand quickly enough, they can actually merge into such a single, rapidly rotating star.

The coolest bit is that these stars may still have separate cores that orbit rapidly around one another, eventually settling down due to friction and merging together.

Something else special happens when matter from a main-sequence star falls onto a white dwarf companion.

In this scenario, there’s a catch to the inflating material actually reaching its destination star, and it comes in the form of the law of conservation of angular momentum.

Basically, any matter flowing from one star to another can’t actually fall directly onto the star. It’s like pulling out the stopper in a bathtub. Does the water immediately just fall down the drain, or does it swirl down in a whirlpool?

The same thing happens with stars that have white dwarf companions. The result is an accretion disk, which is essentially a whirlpool of material around the star.

(If you call it a star. White dwarfs are not really stars—they are more accurately described as compact objects, something we’ll cover in more depth soon enough.)

The mass falling into a whirlpool around this white dwarf came from a giant star’s atmosphere. That means it’s mostly hydrogen. It’s ready nuclear fuel that the formerly main-sequence giant was never able to use, due to the lack of convection throughout its interior.

Right now, we’ve still got this hydrogen swirling around in the white dwarf’s accretion disk. But friction will eventually slow the accretion disk and let that hydrogen fall onto the surface of the white dwarf.

The result?

A white dwarf is an Earth-sized ball of degenerate matter—matter that is intensely hot, but squeezed so tightly together that it can’t regulate its own temperature. Alone, outside of a binary system, there’s nothing to heat it up anymore and it’ll just gradually cool off over billions of years.

But adding mass to the star changes the equation. The white dwarf’s intense gravity compresses the new hydrogen matter until it becomes degenerate as well…but this new hydrogen layer keeps growing hotter as more falls onto the star.

At this point, something similar to the helium flash in medium-mass stars happens.

Essentially, we’ve got a buildup of degenerate hydrogen on the surface of the white dwarf. There’s no mechanism to keep its temperature stable, so it keeps growing hotter. Eventually, the temperature is driven up so high that hydrogen fusion kicks in. But then, something unexpected happens.

The proton-proton chain—a hydrogen fusion reaction—drives the temperature up so high that the CNO cycle, a nuclear fusion reaction generally only seen in massive, hot, main-sequence stars kicks in.

But there’s still no mechanism to keep the temperature stable. Within seconds, it’s driven up so high that…

Kaboom!

In more sciency words—a nova explosion.

This is the explosion of the white dwarf’s surface layers as they expand and are blasted off the object. And it can keep happening, again and again, every time more hydrogen mass from the white dwarf’s companion accumulates. The process can take anywhere from a few years to thousands of years.

Anyway, there’s mass transfer in binary systems for you—and with that, we have covered the entire lifespans of low- and medium-mass stars! Next up, we’ll follow the story of how massive stars meet their end. And yes, there will be more explosions.

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