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My Optical De-PHI-ing Adventures, or How to Stretch a Star Apart: Phi [φ] Ursae Majoris (30 UMa)

How do you separate a pair of like magnitude stars with only 0.41 seconds of arc between them with a six inch f/10 refractor?  Well, you don’t.  But like a piece of salt water taffy, you can stretch and streeetch and streeeeetch them until they no longer resemble the original sharply defined object you were gazing at when you started.

First some mathematics, but I’ll keep it simple – we only need to divide a pair of numbers and we’re done.  The Dawes’ limit, a product of the fertile mind of the Reverend W. R. Dawes, states the limit of optical resolution for a given lens is a constant divided by the aperture of the lens.  If you’re measuring the lens in inches, that constant is 4.56; if you’re measuring the lens in millimeters, the constant is 115.8.

In the case of my six inch lens, divide 4.56 by six and you get .76”; or, since that six inches is equivalent to 152 millimeters, divide 115.8 by 152 and you come up with .76” again.  So – theoretically – my six inch lens should be able to resolve a pair of stars just .76 seconds of arc apart, provided the pair is of equal brightness.  It’s even quite possible to exceed the Dawes’ limit – the Reverend did it more than once, which I suspect led him to revise the limit a couple of times.  I haven’t breached the limit, but I did reach it a short time ago with a 60mm f/16.7 lens when I resolved Porrima.  At the time the two stars were separated by 1.95”, which compares quite well with the 1.93” Dawes’ limit for the lens.

So the goal here is not to de-Phi the Dawes’ limit, but to catch the Phi (φ) UMa pair in an elongated state.  Resolution may even be possible, given very good seeing conditions, sharp eyes, and a lens as optically perfect as possible – but don’t bet your Zeiss Orthos on it.

Let’s pin down Phi’s location first, and then get started.

Phi (φ) can be seen here in blue at the left center of this inverted image of the Great Bear, situated south of Upsilon (υ) and northeast of Theta (θ) Ursae Majoris.  (Stellarium screen image with labels added, click on the chart for a larger view).

Phi (φ) can be seen here in blue at the left center of this inverted image of the Great Bear, situated south of Upsilon (υ) and northeast of Theta (θ) Ursae Majoris. (Stellarium screen image with labels added, click on the chart for a larger view).

OΣ 208  (30 UMa, Phi [φ] UMa)            HIP: 48402   SAO: 27408
RA: 09h 52.1m   Dec: +54° 04’
Magnitudes: 5.28, 5.39
Separation:  0.41”
Position Angle: 300.7°  (WDS 2013 — see the Ephemerides of the 6th Orbit Catalog)
Distance: 437 Light Years
Spectral Classification: “A” & “B” are both A3

Considering what we’re attempting to do here, a good place to start is with the first night’s seeing quality.  One word will describe it: POOR.  Or if you want a pictorial point of reference, it was somewhere between a I and a II on this chart.  So even though I didn’t expect much, since the night was clear and the moon was obnoxiously full, I decided I might as well invest an hour in this project.

To start this stretcher-ous adventure at the top of the sky, I reached for a 6mm (253x) Astro-Tech High Grade Plössl, which yielded a round dot of hopping white light.  Then I put the 6mm in a 2.4x Dakin Barlow (608x), and that produced a smeared round dot of hopping white light immersed in an obnoxious glare.  Not having the good sense to know when to quit, I dropped a 4mm AT Plössl into the 2.4x Barlow (894x) and smeared the image a whole lot more, although the hopping white dot of light was still visible – sort of.  So I took the hint and dropped back to 608x, but this time I dug into my seldom used stash and pulled out a 2.5mm TMB Planetary since it has a wider field of view and longer eye relief.

The worst part of this whole exercise was an annoying high frequency hopping that was unaccountably insistent on leaping along an east-west axis.  I turned off the drive on my mount several times to see if there was a link between it and the hopping, but it didn’t make any difference – it was an east-west hop with no hope.

I was also having a problem at 608x (and higher) with the star flaring into a mushy comet if it strayed too far from the center of the field of view, which I suspect was caused by the pin-hole sized openings on both the top and bottom of the AT Plössls.  As long I kept the star centered with the hand controller (you need a darn good polar alignment at these magnifications), I could keep a reasonably sharp image.  The 2.5mm TMB has a similar pinhole opening at the bottom, but the lens at the top is much larger in diameter, providing more latitude with regard to keeping the image centered.  And its longer eye relief was more than welcomed by my no longer vibrant vision.

Regardless of how I tried to compensate for it, the hopping was still horrible.  But with patience – long periods of staring into the eyepiece while sitting rigidly still – I could occasionally capture what amounted to a visual snapshot of the image when the period between hops increased.  Those intervals were never long – maybe several tenths of a second – but with practice, I got better at grabbing that image and digesting it visually and mentally.

I persisted for about an hour, and during that time I had maybe a dozen glimpses of an elongated image along the 120-300 degree axis.  About half of that time, it very much resembled Porrima in a figure-8 configuration – a quivering and slightly smeared figure-8, but nevertheless clearly identifiable.

About an hour later I returned to Porrima to see if I could separate it with a 60mm f/15 Carton lensed refractor.   The seeing had turned to pure mush, so there wasn’t much hope – BUT – what I did see in it looked virtually identical to what I had seen in the six inch f/10 while I was looking at Phi (φ).

So – success of a sort – but certainly not very satisfying.

Two nights later I was back with the six inch f/10 once again under slightly better seeing conditions, about midway between a II and a III.  The erratic hop was still present, but instead of hopping on an east-west axis, it varied randomly – sort of a hip, a hop, and a spinning jump that never landed in the same place twice.  But there were times when the hopping settled down almost long enough to call it staying put, so it was a definite improvement.

I started with the 2.5mm TMB (608x), which gave me a more distinct image than I had seen during the previous session.  At times, I had clear glimpses of a slightly compressed figure eight cursed with a frequent and frantic hop.  I decided to drop back to the 3.2mm TMB (475x), which resulted in a clearer image (much of the blurring and scatter around the image was gone), but the less frantic image had now become a much smaller image, making it harder to detect the dueling dots.  But again, with intense staring, coupled with sitting rigid as a rock, I was able to see an obvious elongation during the relatively calm tenths of a second when the hopping paused for breath.

I was suddenly struck with an incurable itch to experiment, so I slipped the 3.2mm TMB into a 2.4x Dakin Barlow (1140x) and found myself staring at a sphere of smeared light nested in a larger sphere of smeared light, all of it plagued by the ever-present high frequency hopping, with rumors of two stars buried in there somewhere.

So I returned to the bare naked 3.2mm TMB (475x) and contented myself with grabbing quick glimpses of that poor elongated and tortured figure eight.  I sat there for another hour trying to coax a clearer view from the sky gods, but they ignored me.

The following night I found unexpected clear skies over my head, along with seeing that had improved to a solid III.  When I first put Phi (φ) under the TMB’s 3.2mm 475x lens, I noticed immediately the hopping frequency was down to about 25% of what it had been during the previous session.  And in sheer de-PHI-ance of expectation, I could even see a diffraction ring surrounding the shimmering figure eight outline of the two stars!  I had to concentrate very hard because the hopping was still a distraction, but the visible diffraction rings made coaxing a precise focus from the image a much easier chore.  In fact, I caught so many delectable, almost sharp, snapshots of the outline of two distinct touching globes that I couldn’t resist reaching for the 2.5mm TMB (608x) in hopes of cracking the pair apart.

That move doubled the hopping frequency, so I quadrupled my concentration — the momentarily distinct images I had seen at 475x were a mere hope now.  I waged a visual battle to grab Phi’s frantic photons long enough to re-arrange them into a distinct image, but all I could extract was mainly the blurred, smeared, and elongated blob I had seen on the previous two nights.  It was clear the possibility of seeing a black streak between the two stars was hopeless, but occasionally I was so close I could taste it.

Shown below is a graphic of the images I saw during the three nights just described:

Star images courtesy of Sky Safari -- click for a larger view.

Star images courtesy of Sky Safari — click for a larger view.

The magnifications shown at the bottom right of the chart don’t necessarily match the elongated images from left to right — and that’s because of the poor seeing.  The elongated image at the right corresponds to what I saw at 608x on the second night, as well as what I could see at 475x on the third night when the seeing was significantly better.  What I saw at 1140x is impossible to reproduce — fortunately.

There’s a chapter written by Christopher Taylor (pp. 97-136) in Bob Argyle’s Observing and Measuring Visual Double Stars which describes the observational art of sub-arcsecond vision, and it includes this statement:

“The real image is the disk [Airy disk] and the fundamental point about that is that it is often still there even on second-rate nights when the outer envelope of the seeing blur may reach several times the Dawes’ limit.  Though then quite invisible to an observer not specifically trained to work at the diffraction limit, the Airy disk will time and again reveal itself to a trained eye as an intense nucleus buried in the heart of that seeing blur.”  (First edition, 2004, p. 120)

Now there are several pages prior to the quote above which deal with training the eye to see that kind of detail, so there’s more involved than just running out and staring at a highly magnified hopping star for an hour.  I don’t want to mislead anyone into thinking it only takes an hour of practice to penetrate the blur.  In the same way that averted vision improves with effort, or star colors become more obvious after many nights of experience, you have to work hard at this.  I’ve literally spent hours riveted to intimately embracing stars, all of which finally paid a substantial dividend on the paired stars of Phi (φ).

At any rate, what I found during these three sessions was the two dots of light buried in the seeing blur were clearly present when I concentrated very hard on the center of the image.  But it only happened when the frequency of the hopping gyrations slowed enough that I could grab quick, fleeting glimpses.  I’m determined to hold out for a night when I can see a more distinct and more stable image, something similar to a night of average seeing at about 300x or so.  A class I or II night will come along eventually, hopefully this year.

 Until then, clear and calm skies!  😎


2 Responses

  1. Hi John, I read throught your star stretching post with interest as just
    before I was reading the Bedford Catalogue double stars in Leo, one
    caught my eye Struve 1504 a pair of 7 mag. stars split by 1.2” and
    I was wondering if I had any chance of splitting them with my 80mm
    scope after reading your post I think I will give it a go and see what


    • Hi Pat,

      Theoretically you should be able to do it, but what the Dawes’ limit doesn’t take into account is progressively fainter magnitudes. I suspect it will be tough on that pair — I looked up the magnitudes, and the WDS puts them at 7.92 and 8.05. By the time you factor in the increased magnification, there won’t be a lot of light left to work with for that 80mm lens. On the other hand, if any lens is capable of it, the Zeiss should certainly be the one.

      I’ll be interested to hear how you do on it!


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