Challenging visual binaries: the case of γ2 Andromedae
2020 June 3
The stars in their revolutions
Among the huge number of visually observable double stars in the sky, there are a significant number of true physical binaries whose orbital revolutions can actually be followed in amateur instruments over an interval of a few years. These range in orbital period from δ (delta) Equulei AB (Otto Struve pair OΣ 535), with a period of 5.7 years (a fairly tough amateur challenge, but accessible at its widest to a 12-inch telescope on fine nights); through fairly easy cases like the 60-year ξ (xi) Ursae Majoris, and finally to longer-period systems with fast passages at periastron (the point on the orbit at which separation is smallest) which just happen to fall in our own epoch. Of the latter, the most famous instance is γ (gamma) Virginis, which swept through the dramatic periastron on its 169-year orbit in spring 2005.
Rapid motion is defined as that obvious to the eye over a year or two without the need for precise measurement. In any of these systems, this generally only occurs when the apparent separation is around an arcsecond (arcsec, ″) or less. They therefore provide interesting observational challenges for the more ambitious and determined telescopist – with the drama of dynamic motion, combined with a non-trivial test of the observer’s skill and instrument.1 One of the most glamorous of these, but also one of the toughest around a large part of its orbit, is γ2 Andromedae (OΣ 38).
The γ Andromedae system
Although much admired as one of the great showpieces of the sky for some 200 years,2,3,4 surprisingly it appears that Almach was first noticed to be double only in 1778, by Christian Mayer of Mannheim – the first astronomer to make double stars a specific subject of observation.5 This seems especially curious given that the principal occupation of practical astronomers of the 17th and 18th centuries, back at least to the time of Flamsteed, was the intent telescopic staring at stars in pursuit of accurate positions, at magnifications that should have been quite sufficient to split this conspicuous 10arcsec pair. A close examination of the earlier observing logs of Greenwich, Paris or Berlin might perhaps reveal something interesting.
This wide, obvious pairing consists ostensibly of a type K3 II bright red giant, accompanied by a type B9 or A main-sequence star, at a distance of about 260 light-years.6 At that range, an angular separation of 10arcsec equates to a distance between the two stars of at least 800au and possibly a great deal more, so obvious orbital motion is not to be expected even if they are gravitationally bound to each other. In fact, there has been no detectable relative motion of γ1 and γ2, convincingly greater than the likely errors of observation, ‘since records began’ (that is, none since the first accurate measurements in 1830). The relevant measures of apparent separation ρ (in arcseconds), and orientation on the sky, i.e. position angle θ (in degrees), are:
(ρ, θ)= (10.33″, 62.4°) at 1830.02 (Struve I, mean of six nights);7
(10.55″, 62.3°) at 1830.75 (Bessel, six nights);7
(9.58″, 62.6) at 1991.25 (Hipparcos).8
It is not at all obvious, therefore, that this double star is actually a binary. However, this is one of those seemingly paradoxical cases, where absence of visible relative motion of two stars actually proves them to be physically connected. Both components of Almach have substantial proper motions, and those two motions against the background of more distant stars are virtually the same in both speed and direction.9 γ1& γ2 are members of a ‘common proper motion’ or ‘CPM’ system, physically partnered and travelling through the galaxy in company. Despite the repeated close scrutiny of Almach in the best instruments of the day, it was not noticed that γ2 is itself a close double until Struve II (see note 7) brought the powers of the new Pulkovo 15-inch – then the largest refractor in the world – to bear on this double star in the autumn of 1842.10 The new pair was then at 0.48arcsec separation and in that respect at least, it is typical of the Pulkova or ‘OΣ’ doubles, which are on the whole a much closer and tougher set of targets for the observer than the Dorpat or ‘Σ’ pairs (see note 7).
The pay-off from that, of course, is that they are much more likely to be in visibly rapid orbital motion, adding the further fascination of dynamic change to their appeal as challenging tests of instrument and observer. It is this, together with its membership of the beautiful Almach triple system, which makes γ2 such an enticing target.11
The orbit of γ2
The γ2 system has completed nearly three full revolutions since discovery, during which time a large number of very careful (ρ, θ) measures have been taken, so it is no surprise that the orbit has now been determined to a fair approximation.12 The binary revolves with a period of 60-odd years around a highly elongated ellipse which is tilted very nearly ‘broadside on’at about 20° to our line of sight.13 In that respect, this system is roughly comparable to binaries like γ Virginis, but it lies at some 10 times the distance of that pair so its orbit appears only about a tenth of the angular size. This is a fundamental difference both for would-be observers and for the orbit-computer, since the increased distance reduces the apparent major axis of the orbit from the generous ~6arcsec of γ Virginis (a very easy object for virtually any telescope around the greater part of its revolution) to about 0.6arcsec. We are therefore confronted with a serious challenge to telescopic resolving power, and errors of measurement are increased tenfold relative to the size of the value measured.
That last point is vital, as those errors are already significant even for the orbital analysis of much wider and easier pairs, and it follows that accurate orbit computation of γ2 and other such ‘subarcseconders’ remains a decidedly non-trivial challenge. This is a very far cry from solar system astrometry,14 where orbits of new comets, asteroids etc. encircle the entire sky and those self-same errors of measurement are now small enough, relatively, to pin the orbit down to quite high precision from a mere three observations spread over a few weeks.
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