# Can you have binary stars with the same radius but different masses?

## Main Question or Discussion Point

The title speaks for itself. I'm just curious and I couldn't find anything on it. Particularly, what if they are a close binary (period less than 50 days)?

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cepheid
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The title speaks for itself. I'm just curious and I couldn't find anything on it. Particularly, what if they are a close binary (period less than 50 days)?
I think there are a few problems with this. For a main sequence star, mass determines most of the other properties, including radius. For more information, see here:

http://en.wikipedia.org/wiki/Main_sequence

Well, supposedly chemical composition affects things as well. But if the stars are in a binary system, then they are probably coeval, which is fancy astronomer talk for, "they formed at the same time." They also probably formed from the same cloud of material too, so presumably their chemical compositions are similar. So, if they have very different masses, then they are going to have very different radii, when both of them are in the main sequence phase of their lifetimes. Okay, well, what if one star is a low mass and therefore small radius star, and the other one is high mass and much larger? Isn't it conceivable that once the small star evolves off the main sequence and becomes a red giant, that it can enlarge to attain a radius comparable to its much larger companion? The stars will then have similar radii but still very different masses. Answer: NO. The problem with this is as follows: more massive stars have much much shorter main sequence lifetimes than lower mass stars. So in the binary system in this scenario I've proposed above, it is actually the larger of the two companions that will evolve off the main sequence first, becoming a red giant (and a very big one at that).

But if the stars are in a binary system, then they are probably coeval, which is fancy astronomer talk for, "they formed at the same time."
This is probably the most common origin for binary stars, but sometimes stars do capture each other or even collide. So OP's senario, while rare, probably does exist somewhere in our galaxy.

Interesting, thank you for the replies. I am most interested in close binaries, in which case a captured case would I think be extremely rare.

Even a solitary star, in the course of after main sequence evolution, will undergo repeated expansions and contractions. And in the end, become much smaller than any main sequence star.

In case of a close binary, the evolution after main sequence is very different because a star which expands overflows into the other.

And the star receiving the overflow changes both its mass and radius.

Now, if both stars are filling their Roche lobes then the radii of Roche lobe are different for different masses. However, if they do not, they can have same radius for different masses.

Simply put, if they are identically constituted by virtue of physical properties, then they are similar to one another as directly proportional to the relation of the radii. On the other hand, if the stars of the binary system are, although uniform, different in composition, then they are, in all probability, of distinct masses. A helium balloon is obviously going to be considerably lighter than a mound of bricks around the same dimensions. However, as accordingly noted by several people already, as the stars are coeval*, the stars likely have similar compositions in addition to eual radii and therefore should have about the same mass in collective consideration.

*Matter + manner of conglomerative accretion + time = recipe for star formation. In this case, the variables are all the same, so it seems that most partners, if not all binary systems, should, in theory, have virtually the same mass per unit^3. In example, the should have the same total mass given equal radii.

Cheers, newcomer from Earth.

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