Fun Facts About Albireo

A few months ago I decided I wanted to find out once and for all whether the wide components of Albireo (Beta Cygni) were a physical pair. Albireo is my favorite double, as it is for many people, with its bright orange and blue colors. After showing it to my wife through a telescope while we were on vacation, I realized I didn't actually know very much about it. Anyway, I figured with Hipparcos data this would be straightforward. Since it was first measured in 1822, the pair of stars has barely budged in relative position. Some amateur books I've seen claim it is a physical pair, despite the lack of an orbit. The A component is itself a spectroscopic and speckle pair, but since you can't split this inner pair visually, I wasn't too interested in it, at least at first.

The two wide components have the same parallax to within Hipparcos' errors of measurement: 8.46 and 8.67 mas, +/-0.5 mas, corresponding to a distance of about 115 pc. An angular separation of 34.5 arcsec corresponds to a linear separation of about 4000 AU in the plane of the sky. Of course, we have no information on the separation in the radial direction, and can't rule out the possibility that the components are up to several parsecs apart. Suppose we assume that the geometry is not too bizarre, and the semimajor axis of the orbit is of order 10,000 AU. Then if the total mass of the system is ~10 solar masses (the system has two late-B main sequence stars plus a K giant), the back-of-the-envelope estimate for the period would be several hundred thousand years. That's a very long time and the orbital motion should not be apparent in any data available. That is consistent with what I've read about the system.

But wait! When I looked at the Hipparcos proper motions for the two main components, which I expected to be the same within their errors, I got a surprise.

The two main components, A and B, are HIP 95947 and 95951, respectively. The proper motions are small but significantly different (see table below). This didn't seem right so I decided to compare the Hipparcos data for this system with that in the WDS. The measurement parameters are very different, of course. I took the Hipparcos main catalog data for the two stars, used the NOVAS routines to compute apparent positions at 10-year intervals, and differenced the positions to produce computed B-A separations and position angles as a function of time. These I compared with the WDS observational data supplied by Brian Mason — see Fig. 1. In the figure, the nominal Hipparcos computed positions are the green solid lines, and the 3-sigma lines (based on the listed mean error in the Hipparcos proper motions) are the blue dashed lines. The WDS observations are the red crosses. As you can see, the position angles aren't bad but the separations are way out to lunch. The Hipparcos catalog data postdicts a significant evolution in separation that just isn't visible in the data. Something's wrong.

At this point I obviously needed to look at what Hipparcos did with the A component, the spectroscopic/speckle pair (K3II + B9V). The K giant dominates in terms of brightness and color, and is what the visual observer sees. But Hipparcos was able to get individual measurements on the two components, which are separated by about 0.4 arcsec (~50 AU in the plane of the sky). The fainter star is referred to as the C component in the Hipparcos catalog. The 20 years of speckle data in the WDS for this inner pair shows a very small change in separation but a significant evolution in position angle, and one is tempted to guess an orbital period of maybe 100-200 years.

The proper motion of the A component was what I used for the B-A computed lines in Fig. 1, because that's what's in the main Hipparcos catalog. But the double star annex has a proper motion for the C component, and the motion of C seems to be almost directly opposite that of A:

Note that the errors for C are much larger than for the other two stars. I took the Hipparcos data for A and C and played the same game as for the wide pair. The result is Fig. 2. The C-A observations aren't too far from the computed lines over the short period for which observations are available. (We expect some divergence, because the computed motions are linear while this pair is obviously orbiting.)

Going back to the wide components, B orbits the A-C pair. So what I should have used for the Fig. 1 computations was the proper motion of B and the proper motion of the center of mass of A and C. Of course, we don't know what the relative masses of A and C are, but the simplest assumption is equal masses. (One might argue that A must have originally been more massive than C because it evolved to giant stage earlier. But giants shed mass. So who knows?) Assuming equal masses, I simply averaged the A and C proper motions, obtaining -1.03 +/- 1.2 mas/yr in RA and +0.43 +/- 1.5 mas/yr in Dec for the proper motion of the alleged center of mass. Note that, within the mean errors, this is the same proper motion as for the B component. That is what we should expect.

Using this proper motion of the center of mass in place of that for just the A component, I recomputed Fig. 1, obtaining Fig. 3 (which is still labelled B-A). This fixed the problem in separation, although the position angles are now off a bit. Perhaps tweaking the mass ratio in the center of mass arithmetic might make everything right, but it's more likely that the small remaining discrepancies are just the effect of the poor proper motion data for C.

I don't know whether Albireo is officially a Hipparcos problem star, but if not, it should be. The problem of the orbital motions of long-period binaries contaminating "snapshot" proper motion measurements is of course well known. Albireo is an interesting case simply because there is so much data available for it, we can figure out pretty well what's going on. Even though this little exercise is probably not very scientifically useful in the grand scheme of things, I had some fun with it and satisfied my original curiosity about the system.