Why? Why do I do it?
Someone mentions a star they had a tough time splitting, so the first time the clouds part to unveil a clear sky, I grab a telescope, race outside, park it on my deck, and aim it into the land of the difficult and forbidding . . . . . . . . . . . . . . . . . . . . .
like a moth attracted to a porch light . . . . . . . . . .
like a dog unable to resist the urge to chase a cat . . . . . . . . . .
like a sports car junkie who can’t resist the lure of a straight stretch of road . . . . . . . . . .
only to find a police car sitting at the side of the road just as he breaks 100 mph.
But in the case of 17 Lyrae and 23 Aquilae, the specific “law” we have to obey is the 2.51 rule, and it works likes this:
When there is a full magnitude of difference between two stars, the fainter of the two radiates 2.51 times less light than it’s more brilliant companion. Not a big deal . . . . . . except that when there’s two full magnitudes of difference, the faintness factor is 2.51 squared (2.512, or 2.51 x 2.51). When there are three full magnitudes of difference, the faintness factor is 2.51 cubed, or 2.513, or 2.51 x 2.51 x 2.51. And the light radiated by the fainter star continues to decrease exponentially as the difference in magnitude increases arithmetically.
Unlike simple arithmetical increases, exponential increases tend to get out of hand quickly. And like the stern-jawed police officer intent on writing a ticket to the driver of the 100 mph sports car, exponents are unyielding. They only do one thing well: increase. So don’t plead for a break —- it won’t work. The Law is the Law is the Law (or the Law3). It’s exponential.
Now in the case of the two stars I was so enticingly enticed to torture myself with this time, 23 Aquilae is (supposedly) the easier of the two since there are only three full magnitudes of difference between the primary and secondary, meaning “B” is sixteen times fainter than “A.” But if you really want to defy the difficult, there’s a third star here that’s eight magnitudes dimmer than the primary — which translates to 1576 times fainter in the language of the exponential. I tried — but apparently it wasn’t available for viewing that night.
In the case of the other star, 17 Lyrae, the two main components co-exist with a difference of almost four magnitudes between them — meaning the secondary is about 40 times fainter than the primary. But I actually found that pair of stars to be much more cooperative than 23 Aquilae was.
Which raises that one word question again: WHY?
23 Aquilae (Σ 2492) (AB is H I 14) HIP: 94885 SAO: 124487
RA: 19h 18.5m Dec: + 01° 05′
Magnitudes AB: 5.28, 8.29 AC: 5.3, 13.5
Separation AB: 3.2″ AC: 10.10″
Position Angle AB: 3° (WDS 2007) AC: 70° (WDS 1999)
Distance: 381 Light Years
Spectral Classification: G9
I attacked this poor devil with all the gusto I could muster — and it couldn’t have cared less. My first approach was with a six inch Celestron f/8 refractor, but the skies battled me all the way. Seeing was jittering back and forth between a II and a I and the haze factor was at it’s murky best. It didn’t help that I made my first forensic approach about an hour after midnight, when Aquila had winged its way well past the meridian. In fact, there was so much murk I could swear I heard the Eagle gasping for fresh air.
A second attempt with my five inch f/15 D&G refractor bounced off the turbulent air as well, so I gave up the chase for a better night, which arrived about a week later.
I tried a flank attack this time with the Celestron six inch, sneaking up on my prey just as it strode confidently and unsuspectingly across the meridian. I could see by the seeing that I was going to win the struggle rather quickly, so I swapped oculars with a jocular grin on my face until I spied the secondary for the first time at the century mark (12mm Radian, 100x). Ah, nothing like the sweet taste of success! BUT —- what I was really starving for was a slice of black sky between the two stars. I had to reach deep into my eyepiece box to un-box a rarely used 6mm Radian, but after I had it parked in the diagonal, I leaned over and peered in the eyepiece . . . . . . . . . and was overcome with bicentennial bliss by all 200 of the x’s it served up —- as you can see here:
It was a view meant to be savored, and savor it I did. Until I started pondering that secondarial puzzle.
Now what we have here . . . . is a failure to communicate . . . . . . one essential detail —- distance.
As I’ve already made quite clear, the 2.51 legal code is unforgiving. But distance can make a difference — or not. In this case – not . . . . . . . . . . because the secondary is much too close to the primary for us to catch any kind of a break. Now if it was at the distance of the “C” component — 10.10 seconds of arc — our night life would have taken a turn toward the less strenuous and culminated in the more successful.
There’s a definite inter-play between differences of magnitude and distance, a give and a take that can make or break your attempt to pry two stars apart. I’m not about to attempt a definitive answer as to what aperture will crack the code under different combinations of distance and magnitude difference, but there’s a chart on page five of Haas’s book which will give you a rough idea of what to expect. In fact, in a recent article in Sky and Telescope (September 2012, pages 68 to 71), Sissy Haas has proposed a project to collect observations for a sample of stars which suffer from distance and magnitude difference difficulties ——- and not surprisingly, 23 Aquilae is on it.
So the ultimate question before the jury is: how low can you go? Referring to aperture, of course.
Obviously there are a lot of variables involved — seeing, transparency, sky glow, optical quality (telescope and eyepiece), observational ability — and probably some others, less obvious and more subtle. One way to un-perplex this puzzle is to rate the difficulty in terms of splitting two stars of the same magnitude — and in this case, I would say splitting 23 Aquilae is roughly equivalent to splitting a pair of sixth or seventh magnitude stars of the same magnitude which are in the neighborhood of 1.4 arc seconds apart.
But that’s not definitive — so don’t try to take it to the bank.
Meanwhile —– how about if we wander north now and take a look at 17 Lyrae, which is about thirty degrees of declination north of 23 Aquilae, and see what terrible tortures distance and magnitude differences can dangle in front of our telescope this time.
17 Lyrae (Σ 2461) (AB is H II 68) HIP: 93917 SAO: 67835
RA: 19h 07.4m Dec: +32° 30′
***** Magnitudes Separation Position Angle WDS
AB: 5.26, 9.10 3.7″ 290° 2001
Distance: 132 Light Years
Spectral Classification: F0
Now as you can quickly see, we’re dealing here with a secondary that is almost a full magnitude fainter than that of 23 Aquilae. I said above it’s 40 times fainter, but it’s actually somewhere in the neighborhood of 35 or 36 times fainter. But it’s farther away from the primary, too — by five tenths of a second of arc (.5″) — which doesn’t sound like much, but that puts it 16% further away than 23 Aquilae’s secondary.
So let’s compare and contrast the two secondaries now for magnitude and distance. One is 16 times fainter than its primary (23 Aquilae), the other is 36 times fainter than its primary (17 Lyrae). The brighter of the two, 23 Aql-B, is at a distance of 3.2″; the fainter of the two, 17 Lyr-B, is at a distance of 3.7″, or 16% further away from the primary.
Which leads to a new question: Is that additional distance enough to offset the difference in faintness? (Fortunately in this comparison, the primaries are virtually the same magnitude — 5.26 and 5.28 — so we don’t have a glowing complication there to complicate things).
What I found was 17 Lyrae is a very cooperative star at five and six inches of aperture, unlike its like-illuminated relative thirty degrees to the south. But there are two mitigating factors here: first, 17 Lyrae has the advantage of being located thirty degrees closer to the zenith than 23 Aquilae (which means less atmospheric muck to peer through) —– and second, the seeing was marginally better because of the increased distance from the horizon.
At a minimum, I would say the differences in distance and magnitude tend to offset each other in this comparison. If I was to risk creeping out on the end of a limb, I would say those two factors combine to make 17 Lyrae marginally easier to split. All I can say for sure is the first time I looked at it with a six inch refractor (which was the Celestron f/8), 17 Lyr-B was beaming back at me proudly. If I didn’t know better, I would even swear it winked.
Here’s what it looked like in my six inch f/10 at 203x:
But what are those two stars located at equal distances to the east and west of the AB pair? And what about all those stars to the north?
Aha! Now we’ve stumbled across the seldom seen stellar truth about 17 Lyrae! If you reach up and pull back the old WDS curtain, you’ll find this:
17 Lyrae (Σ 2461) (AB is H II 68) (Ca, Cb is KUI 90) HIP: 93917 SAO: 67835
RA: 19h 07.4m Dec: +32° 30′
***** Magnitudes Separation Position Angle WDS
AB: 5.26, 9.10 3.7″ 290° 2001
AC: 5.26, 10.80 245.0″ 55° 1983
AD: 5.26, 8.99 137.3″ 292° 2009
AE: 5.26, 10.90 141.5″ 119° 2002
AF: 5.26, 10.59 166.9″ 352° 2009
AI: 5.26, 11.40 48.0″ 50° 2008
CE: 10.80, 10.90 219.8″ 200° 1983
CG: 10.80, 12.90 124.2″ 138° 1933
CH: 10.80, 12.97 151.1″ 20° 1998
CR: 10.80, 14.20 59.9″ 52° 1910
EG: 10.90, 12.89 115.6″ 60° 1998
Ca, Cb: 10.80, 11.40 .20″ 93° 2002
Distance: 132 Light Years
Spectral Classifications A: F0 Ca: M3 Cb :M5 D:A2
Status: AC is optical; Ca, Cb are gravitationally linked.
Now I haven’t tried to dissect a multiple star with this many components since I gave Eta (η) Cassiopeiae a shot last year. But I couldn’t resist this one. And I got all but a few of them, too. Let’s look at the sketch above, but this time we’ll put it side by side with the labeled version:
Now the Ca, Cb pair was obviously out of reach. And I didn’t have the skies for prying the 14.2 magnitude “R” component loose, but considering it hasn’t been measured since 1910, it may not even be where it was then. That leaves the 11.4 magnitude “I” component, located 48.0″ northeast of the primary, where it shines at 6.14 magnitudes less than the primary — which in exponential language, is about 260 times fainter than the primary. And I didn’t see it all. No matter how many times I looked, and no matter how many times I tried, it absolutely refused to come out from behind the overshadowing primarial glow — yet it was within twelve arc seconds of being a full minute of arc away from the primary!
So here’s another factor to consider. It’s one thing to deal with a six magnitude difference when the stars are, for example, magnitudes of 2.0 and 8.0. It’s another when the stars involved have magnitudes of 5.26 and 11.40. Eleventh magnitude stars are always significantly harder to see anyway, so whatever scheme or classification scheme you might come up with for the brighter magnitudes will begin to fail when the obnoxiously fainter magnitudes come into play.
Of course you can always attack with more aperture. But more aperture results in more glow from the brighter stars, too. As I said, there are a LOT of factors involved in trying to establish a definitive rule or classification scheme for splitting stars with large differences of magnitude.
On the other hand —– and there’s always an other hand (especially if you’re ambidextrous):
After I had written all of the above, I found myself with a night of category III and IV seeing — actually, it wasn’t a night, because it only lasted about an hour. But in that single hour, I was able to take a critical look at 23 Aquilae with a Tele Vue 102mm f/8.8 refractor. And very much to my surprise, I was able to a get a very clean split at 106x (a 20mm Astro-Tech Plössl lodged in a 2.4x Barlow, which converted it to an 8.3mm eyepiece). But even more surprising, I could actually see that beady little diminutive secondary in the 20mm Plössl (44x) without the leg up provided by the Barlow. It wasn’t a clean split by any means, but I was thrilled right out of my particle pickin’ gourd that I saw it at all!
Now that’s about the same level of difficulty a pair of sixth or seventh magnitude stars spaced 1.4″ apart would give me, so that makes me even more confident about my earlier comparison.
And how did I do on 17 Lyrae that night? Not well at all. By the time I got to it, the seeing had spun itself into a whirling vortex and slipped right down the old stellar drain with a silent scream, leaving the primary suffering from such a dreadful attack of unfocused yellow star bloat there wasn’t the first glimmer of a hope for catching sight of the secondary.
So –– it just goes to show, you just never know.
Clear Skies! 😎
P.S. — Meant to include this, but it slipped right out of my star-cluttered mind — Thanks to Javier for mentioning 23 Aquilae, and thanks to Pat for directing me to 17 Lyrae. Both suggestions came at about the same time, which couldn’t have worked out better!
(WDS data updated 4/14/2013)