Mizar

My father was part-way through his apprenticeship as a bricklayer when the light escaped from its star and began its journey across space. He had left school in his early-teens, as was the norm for working class kids back then. War in Europe was brewing, and although he didn’t yet know it he’d soon be lying about his age so that he could sign up for the parachute regiment; his apprenticeship would be put on hold for the duration. Skip forward eighty three years to the present day; to be precise, to the tail-end of the day on which the Sun had set on 2020-21’s astronomical winter: the night before the Vernal/Spring Equinox. The sky was clear and there was only a slight breeze: almost perfect for a bit of star-gazing. Within the hour I could be found in my front garden looking back in time, in a manner of speaking, to those late 1930s. My target for the evening was Mizar in The Plough, a part of Ursa Major. Mizar is a binary star system which sits at about 83 light years (ly) from us – in other words, the light which fell into my telescope that evening left the stars’ surface 83 years ago. As it happens, the Mizar binary system is more intriguing than it appears at first sight: it has a few surprises up its metaphorical sleeve.

On the left is Ursa Major – the Great Bear. Technically, we ought to be calling it an asterism rather than a constellation since it has more to do with our innate human tendency to invent patterns where there are none than it does to an objectively fixed shape. Although some of the stars in Ursa Major are at roughly the same distance from us (in the region of 80-85 ly, light years – the distance light travels in eighty years) and have similar trajectories in space, others do not. Thus, in times past and in times yet to come what we might perceive as a bear would have appeared/will appear quite different. Mizar forms a particularly noticeable star within part of the large asterism of Ursa Major – it’s the kink in the prominent arm of what is commonly called The Plough (or Big Dipper, or Saucepan, or …). The images used above are taken from ‘Stellarium’, a free-to-download computer package allowing one to generate bespoke star maps.

My primary goal since beginning to dabble in astrophotography after my retirement has been to gain reasonable images of each of the planets in our solar system; to this I might add a long list of lunar features and a sunspot or two. I’ve made a start (see former posts here and here) but there’s so much more I want to do. Moreover, along the way I’d also like to capture images of a few more distant objects: galaxies, star clusters, nebulae. All this requires that I gain an understanding of what my telescope + astro-camera can achieve and the ways in which I might realise that potential. For instance, the telescope’s focal length and magnification, and the size of the CCD chip in the camera together limit the effective field of view (FoV) available to me and define the resolution achievable. Again, in the post immediately previous to this one I mentioned the need to align the telescope’s mount correctly using the Pole Star (Polaris) so that an object might be accurately tracked across the sky as the Earth rotates beneath. This is a task rendered difficult and uncomfortable, even painful, when one tries to manage it with creaking knees and an inflexible spine – finding a way to mitigate this remains on my ‘to do’ list. (I'm tempted to remark that the designers of the polarscopes on the market have really missed a trick here: building in a mirror or prism to allow the eyepiece to face outward or upward would solve this problem at a stroke.) I also expressed the hope that I could, with my smartphone attached to the telescope, use one of the many sky chart apps as a way of navigating to particular target objects. Thus it was on this particular evening that I decided to do some experiments in order to explore the issues. Given the aim, what follows almost necessary contains a technical element to it; hopefully not too much.

Although I currently see no way around the physical discomfort of the polar alignment process, I did at least achieve some success this time around – and the data to verify that statement. The results weren’t perfect, but I think I understand why. Objects initially centre-screen were therefore still drifting slowly off. Next time. However, by focusing on a star and generating images as a function of the exposure time, one can see when the image ceases to be circular and develops an elongation due to the inaccurate tracking. That is to say, we can ask how long an exposure is possible before there is blurring due to the star’s apparent motion across my laptop screen. Now, for all astrophotography it is necessary to collect a number of individual sub-exposures and then stack the best of them to generate a final image since this allows one to reduce the issues of atmospheric turbulence. For the purposes of this exercise I collected 500-1000 ‘subs’ and typically used the best 30% of them. The results are shown below.

These images show Mizar A and B (see below) with sub-exposures set to 51, 67, 130, 300 and 500 ms (milli-seconds) respectively left to right. The three shortest exposure times generated final images too faint to show up clearly in a blog post and I have therefore artificially altered the brightness. Only at 500 ms (i.e. ½ s) do we see evidence of distortion in both stars. Improved polar alignment will hopefully allow the extended exposure times of a few seconds required for more faint objects. However, even the results shown here are sufficient for the solar system targets I have in mind, and a great deal more besides. (I ought to note that the camera focus, a critical preliminary stage in the overall experiment, was achieved using a Bahtinov mask as discussed in earlier ‘stargazing’ posts.)

The images shown above give us a first insight into the complexity of the Mizar binary system. Now, the binary star that one is supposed to be able to see with the naked eye, but which in practice requires good eyesight and the absence of light polluted skies – or the use of a pair of binoculars – comprises Mizar and the fainter star Alcor. They are at a distance of approximately one lightyear (1 ly) from each other and are therefore only weakly bound together gravitationally; they therefore take several hundred thousand years to orbit each other. It turns out that Mizar and Alcor are themselves both binary stars, and whilst the dwarf star associated with Alcor is too small/dim to be seen directly, the Mizar binary – Mizar A and Mizar B – can be resolved even with my amateur setup. These two stars, one much brighter that the other, orbit each other every 5000 years or so at a very close distance – only about ten times the distance from the Sun to Pluto. It takes about 5½ hours for the Sun’s light to reach Pluto, meaning that the Mizar A⸱⸱⸱B distance is only about 55 lh (light hours; the Earth orbits the Sun at a distance of approximately 8½ light minutes). The stars are all relatively young at about 370 million years; by comparison, the Sun is approximately twelve times as old at 4½ billion years.

The above is an inverted image of the view I captured. (I inverted it simply because it’s easier to see ‘black’ stars against a pale background; the superimposed circles should also help.) Mizar A and B are on the right and Alcor – the principal component to the binary system visible with binoculars – is on the left. The figures shown below will hopefully be easier to follow as I’ve added labels. The image is the result of stacking the best 40% of 1000 individual 75 ms frames, so 30 s in total. I probably ought to have collected more data, but the evening’s experiment was about testing my stargazing equipment rather than achieving polished pictures.

We’re not finished with the complexity of this system yet: both Mizar A and Mizar B have been discovered to be binary stars in their own right (Aa and Ab, Ba and Bb should you have a desire to label them). These pairs have orbital periods as short as three weeks or so. As with Alcor’s partner star, they are not visible using anything other than the most sophisticated equipment. However, it’s still an interesting star system to have examined: not a simple binary pair at all but rather a multi-star system – a sextuplet if you will. I was delighted to have seen three stars within the system although being able to add something of their ‘backstory’ enhances the fun. There are several good descriptions of the system available online, e.g. here, here and here .

We need to cover a few preliminaries before I can tell you what the results reveal. Specifically, we need to understand the measurement scale used to describe the apparent separation of two objects in the sky. From one horizon across the arc of the sky to the opposite horizon is 180º (i.e. half a circle), but a degree is too large a unit for many purposes, so we may divide it into sixty arc minutes (arcmin, sometimes simply ′). The Moon and the Sun both appear to be about 30 arcmin across for example, ½º. Even an arcmin is too large on occasion so we may divide that again into sixty arc seconds (arcsec or ′′). Having got that under our belt, the diagram below shows the results obtained.

The Mizar⸱⸱⸱Alcor separation as seen from the Earth is about 11.8 arcmin. This separation gives me the chance to measure experimentally my telescope+camera’s field-of-view. On this basis I estimate my equipment’s field-of-view – the amount of the sky displayed on my laptop screen – to be 16 x 9 arcmin. This is small; it’s no wonder I have to make mosaics in order to create an image of the Moon. The Mizar A and B pair offered one more useful measurement. When viewed from the Earth they appear separated by 14.4 arcsec; this suggests that I can hope to resolve objects separated by only 4-5 arcsec. I’m quite happy with that.

Dad would have enjoyed reading this post, not because he was into astronomy as such, but nevertheless ...  Only later in my life, when I had watched my children begin to shape their lives, did I more fully realise how important his support had been as I moved inexorably towards a life so different to his own. This included helping me to buy my very first telescope, which I still have. It therefore seems entirely natural to think of him as I reflect on my evening with Mizar.

P.s. I also tried my idea of using a smartphone app as a way of locating specific targets. It was evident that the apps – I tried two very popular ones – are not sensitive enough to make inroads to this problem. I may give it one more try, we shall see. The more likely next step is to try to set and properly calibrate the Right Ascension and Declination circles on the telescope's mount.
By the way, a convenient way to measure larger separations in the sky is to use your fingers when held out at arm’s length. For instance, the tip of your little finger marks out 1º; more details on these universal measuring hacks are all over the internet, e.g. here.

P.p.s. Dr. DirkFroebrich, a professional astronomer and former colleague who I’ve mentioned before (e.g. here) kindly responded to an image I posted on Twitter by sharing his own image of the very system I based my experiment on. He’d apparently used the system for a very similar experiment when setting up the Beacon Observatory, of which he is Director.

The equipment and software I used.

The telescope:  Skywatcher 150PL Newtonian reflector (i.e. a 150 mm primary mirror) on an EQ3/2 tripod mount with motor-driven RA/Dec movement,

The astrocamera:  Altair Astro GPCAM-290C, connected to a laptop via USB2.

Capture software:  SharpCap

Stacking software: AutoStakkert2