### How far apart are stars in a binary system?

• I'm wondering how far apart from one another the stars are in binary systems.
What is the distribution of the separation between binary stars? Are most of the binary stars very far apart like Sirius (8.2 to 31.5 AU)? Are there many stars in orbits even wider? Are there more pairs with grazing orbits?

Is there a database similar to exoplanets.org where I could see the distance between the pair of stars for all the binary systems we know of?

Proxima centauri is currently 13kAU away from the binary it's orbitting - that's about 0.2 light years. Whether that counts as a binary star for your purposes (technically, it's a binary of Proxima Centauri and Alpha Centauri A+B)... In any case, on such a scale, it's obvious that 5.5 AU is _not_ a far separation, as those things go :)

I guess I misread Wikipedia. Fixed it in the question

2 years ago

Distances ($$a$$) between binary stars vary wildly, from the order of the radius of the stars, to more than a light-year! The plot below (from here) shows a compilation of several surveys, with the color indicating the method by which they've been detected.

Separations are roughly normally distributed in $$\log a$$, peaking at a typical separation of tens of AU. The corresponding periods have median values of a few hundred years (e.g. Raghavan et al. 2010; Duquennoy & Mayor 1991).

As commented by Oddthinking, if stars are too close we are no longer able to resolve them visually (green bars). But we can still detect them spectroscopically (yellow bars): If we observe the blended spectral lines of two stars, we see the lines shift back and forth as the two stars orbit each other and their light is Doppler shifted.

On the other hand, if stars are too far from each other, their orbital periods of several thousand years makes it impractical to observe them orbit each other (we have only observed double stars for some 200 years); instead they're detected because they simply follow the same path through space — i.e. they have a common proper motion (blue bars).

As commented by PM2Ring, the fact that the two $$x$$ axes suggest a 1:1 correspondence between orbital radius and period seems odd — by Kepler's law, this also depends on mass. My random guess is that, because low-mass stars (which are most abundant) are poorly constrained (difficult to observe) and high-mass stars are rare, then most observed binaries are of the order of a Solar mass. If they're not too far from each other in mass, then there is an approximate correspondence.

Now i wanna see the radiative patterns of those \$10^{-1}\$ day pairs!

[Hi, an ignoramus here from HNQ, hoping this is appropriate] I am guessing it is harder to distinguish binary stars that are very close to each other as binary stars. Would that lead to bias in this chart because of sampling problems at the lower end?

@Oddthinking I'm not so sure about that... as they get closer together, the doppler signature gets more and more pronounced. That's why the observations down there are mostly listed as "spectroscopic".

@Oddthinking those kind of observational biases are generally a big problem in astronomy. And as Hobbs pointed out it is even not always clear in which direction they work.

@Oddthinking Good question! There _is_ a limit to how close stars can be and still be visually separated. In the plot, those stars comprise the green (and orange) bars. But stars that are very close are not detected visually, but rather _spectroscopically_ (yellow… well… curry bars I guess), i.e. by looking at the blended spectrum of the two stars. Then, over time, one can see the spectral lines shift back and forth, as the stars move perpendicularly to and along our line of sight.

The linked site says *"Superimposed on these results is the distribution of orbital radii calculated from Hipparcos or spectroscopic parallaxes in the Washington Double Star Catalog."* But I don't understand how that works. How can you equate a given radius to a given period when all of those systems have different masses? (I didn't read the full article, just the info near the chart).

@PM2Ring This is somewhat outside my comfort zone, but for spectroscopic parallaxes the masses _are_ known, since we know their spectral type.

Ok. But how can all the binaries with (for example) a log period from 3.5 to 4.5 have a log radius from 1 to 1.74, which is what the tallest bar in that graph seems to be saying?

@PM2Ring Ah sorry, now I see what you mean. Yes, those axes are somewhat misleading, because as you suspect, there _isn't_ a 1:1 correspondence between radius and period — it depends on mass (Kepler's law). My guess is that because low-mass stars (which are most abundant) are poorly constrained (difficult to observe) and high-mass stars are rare, then _most_ observed binaries are of the order of a Solar mass. If they're not too far from each other in mass, then there is an approximate correspondence. This is just my guess though.

@Joe Thanks for catching that error. I'll edit :)