Estimate the brightness of variable stars

Master the Pogson Step and you’ll be able calculate with confidence.

Tools and materials required for variable star-watching. Credit: Paul Abel

We often think of the stars in the night sky as unchanging over the span of human lifetimes, but in fact a large proportion of them change over the course of weeks, days and even hours.

These are variable stars, exciting bodies that are essential in helping astronomers understand stellar evolution.

There are many reasons why stars vary. Some are red giants at the end of their lives that are expanding and contracting, causing them to slowly brighten and fade; these are known as pulsating variables – Mira in Cetus was one of the first to be identified.

In an eclipsing binary system, the variation is due to one star passing in front of (or behind) another.

Algol in Perseus is a splendid example and the change in magnitude is noticeable after just a few hours.

Tools & materials:

Star charts – You need to get these from the BAA or AAVSO as they will indicate suitable comparison stars. Your comparison stars can’t be variables too.

Tools – A selection of eyepieces, offering low to high power; you’ll need to use different comparison stars over time.

Materials – Red light torch, clipboard and paper for use at the telescope, sturdy notebook for your written-up notes.

Then there are eruptive variables, where the change in brightness is due to material from one star being transferred to the surface of another, often via a stream of hot gas that coalesces into an accretion disc.

It is believed temperature changes in the disc are responsible for the fluctuation in brightness. Such stars, SS Cygni being one example, can suddenly brighten from mag. +12.0 to mag. +8.0 in just a few hours.

There are many variable stars in the sky, and all require long-term study.

With professional telescope time at a premium, it is not surprising that the vast amount of variable star observations still come from amateur astronomers.

The main aim is to collect magnitude estimates of each star, which can be plotted and reveal long-term changes over time. The resulting chart is called a ‘light curve’.

The Variable Star Section of the British Astronomical Association and the American Association of Variable Star Observers are actively engaged in the long-term, systematic study of variables.

They provide the astrophysics community with much needed data and amateurs with great resources for reporting observations, including star charts and online forms.

You’ll also find some helpful beginner articles on these sites, as well as suggestions for variables you might want to start with.

Variable star observation doesn’t require any special equipment.

Observations can be made with the naked eye as well as with binoculars or a telescope, and moreover they can be made visually, without any photographic kit.

Making a magnitude estimate is usually done by comparing the brightness of the variable with two comparison stars, one slightly brighter and one slight fainter.

For accuracy, the Pogson Step Method uses increments of 0.1 (one-tenth of a magnitude) for magnitude estimates.

What follows is a real-life example of how it works.

Plotting magnitude estimates creates a ‘light curve’ that tracks a star’s variability over time
Plotting magnitude estimates creates a ‘light curve’ that tracks a star’s variability over time

Falling into step

On 31 August 2017 at 22:06 UT, we observed the star Chi Cygni and two comparison stars: Star A at mag. +6.4 and Star B at mag. +5.0.

Compared with A, we found Chi Cygni to be about six times brighter on the Pogson scale, so recorded it as ‘A+6’.

To work out the magnitude we subtract 0.6 from 6.4 (the magnitude of A), this gives an estimated magnitude of +5.8.

Comparing with star B, we found it to be about five times fainter, and so we recorded ‘B-5’.

To work out the magnitude we must now add 0.5 to the magnitude of B, this gives us +5.5.

We now take the average of these two values and this gives an estimated magnitude of +5.65, which can be rounded up to +5.7.

In some cases, you might find only one comparison star can be used, in which case you would just record one estimate.

Our step by step section shows us in action estimating SS Cygni as an example.

Unlike planetary work, you don’t need to worry about good seeing conditions when observing variable stars.

Don’t be afraid to experiment with different eyepieces, as you might find some comparison stars are some distance away from your variable.

What’s really important that you report your observations.

Use the online forms on the BAA and AAVSO websites to submit your magnitude estimates; you can then see your observations in the light curves for these stars, and your data can be used by professional scientists.

Variable star observing can be addictive, and it’s great to be making observations which really count.

We’re sure after a few months, you’ll soon find yourself wondering ‘what’s my star doing tonight?’

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Step 1

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Make sure you have all your star charts printed out beforehand.

You will need to make sure your eyes are dark adapted before you start observing, and this typically takes 20-30 minutes.

Use a red light torch to preserve your night vision.

Step 2

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Locate your variable star.

Use a star chart to make sure you have identified the comparison stars and the variable correctly – don’t be disheartened if this takes a while, especially if you’re not familiar with this part of the sky.

Step 3

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When you’ve selected your comparison stars and have identified the variable star, make the magnitude estimate by comparing their brightnesses.

Do this several times and average the result to take out any bias to ensure as accurate an estimate as possible.

Step 4

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Record your estimate along with date, time (UT) and telescope.

Record any conditions that affect your observing: for example, a bright Moon may influence your magnitude estimate.

Mist or haze can also make stars appear fainter than they are.

Step 5

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Once indoors, transfer all the information from Step 4 into a more permanent log book or a spreadsheet.

It’s useful to keep a log with records for each star, so all the observations are in one place.

If you keep it on a spreadsheet, keep your data backed up.

Step 6

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Report your observations to the BAA and AAVSO; you can upload each individually or in bulk.

By doing so you can provide valuable data and it is incredibly satisfying knowing you have made a real contribution to science.

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Paul Abel is an astronomer based at the University of Leicester