Double-star diagrams

The Pup is straining at his leash.

In connection with the stars’ luminosity and the dominance of Sirius over all others, John Goss asked: “Has anyone caught a glimpse of Sirius B recently?”

Sirius is a double star, and, as he remarked and as is well known, the difference in brightness between the two stars of the pair is so great that the glare of the primary (Sirius A) makes its companion very difficult to see.

Since Sirius is known as the Dog Star (it’s the chief star of constellation Canis Major, the Greater Dog, and also it was supposed to bring the Dog Days of summer), its diminutive companion is inevitably dubbed the Pup. The Pup is a white dwarf: its mass, almost equal to that of the Sun, collapsed long ago into a volume about as small as the Earth’s. Its orbit around the primary star takes 50 years, and is eccentric (elliptical) enough that the two can appear separated by as little as 2.6 seconds of arc (3600ths of a degree) or as much as 11.

So how far apart are they now?

This gives me a pretext to revive my double-star plotting program. I haven’t used it for a long time, so like all the computer systems knocked out by Microsoft’s bombshell of about this time last year (I say no more) it has had to be rebuilt with several hours of work, and in the process slightly improved. Here is the Pup moving in its orbit around the great Dog:

You can see that in 2015 the pair is approaching its most open state. Sirius B is a little more than 10 seconds northeast-by-east from A.

Though Sirius is a star of winter evenings, it is still – as we showed a couple of days ago – about 20 degrees above the post-sunset horizon. So you might be able to give it one last try with your telescope, before waiting for it to reappear in late autumn’s eastern sky.

Sirius B’s magnitude of 8.5 means that it is slightly dimmer than Neptune, or about as bright as Saturn’s satellite Titan, and would be fairly easily found in many amateurs’ telescopes, but for its closeness to the 10,000-times brighter star.

In the diagram, the symbols for the stars are sized for their magnitude. Stars of course don’t really look like circles to us, being vastly too far away: they look like points with light bristling out of them, and the light-spikes of Sirius A will bristle out well beyond the orbit of Sirius B, maybe three or more times as far!

The scale in centimeters is for printing on paper and is meaningless on your monitor.

The orbit we see the companion star trace is not the true ellipse, because it is moving in a plane that is not face-on to our viewpoint. It’s not always certain which way a companion star’s orbit is tilted toward us, but in this case Sirius B is thought to be now in the nearer part.  This is the half shaded gray. The straight line is the axis of the true orbit – from the companion’s nearest-in point (periastron) to its farthest-out (apastron).

Here is what the true orbit would look like if it were perpendicular to us (the gray area now merely serving as a reminder of the tilt we have pushed it out of):

And even this isn’t the true orbit, in this sense: it’s not really that Sirius B revolves around a stationary Sirius A. Rather, they both revolve around their common center of mass (barycenter), which would be nearer to A than to B because A is about 2.4 times more massive than B. Sometime I’ll extend my program so as to be able to draw this motion of both parts of a double around their barycenter.

Being one of the nearest stars to us, Sirius has a relatively rapid “proper motion” across the sky – it changes its position, relative to the background, by more than a second a year. So what is really shown by precisely measured observations is Sirius A moving southward on the map while B accompanies it, sometimes ahead, sometimes to the west, and so on – both tracing wavy courses, A smoother, B more wavy.

Indeed this was what led to the discovery of the companion star. Friedrich Bessel in 1844 suspected that the slightly wobbly motion of Sirius meant that it was being pulled by an unseen companion; and that companion was first detected by Alvan Graham Clark (son of the American telescope-maker Alvan Clark) in 1862.

I’ve only seen the Pup Star once, and that was when I visited Charles Gale in the northern outskirts of Atlanta. He was at that time editor of the Astronomical League’s Reflector  magazine, and had encouraged me to produce my second Astronomical Calendar.  He got Sirius in his telescope and coached me until I realized that yes, I could just discern that other little prick of light nestling deep among the dazzling rays. IThe white dwarf was then about as far from the primary star as it is now.)  This was an example of how skill is more important than sharpness of eyesight (he wore glasses).

He explained to me that he was keen on double-star observing because of its advantage for amateur astronomers who have to live under suburban light-pollution: you’re trying to “split” two points, not pick out dim extended shapes against the glow of the background.  To please him I then devised my first page of double-star diagrams for the Astronomical Calendar. Back then, it was made on paper, with orbit pictures pasted onto graph paper of various calibrations to show the scales, but it was the forerunner of my double-star-plotting program.

Well, Sirius isn’t the best for showing off the program, because both the stars are white. Here’s Alpha Centauri, with its colors: primary star of spectral type G (like the Sun), secondary K (cooler and redder).

A pair more equal, more contrasting in color, tilted more steeply to us, and at times (though not now) much farther apart than the Sirian pair.