How to observe variable stars

Not all stars shine with constant brightness. Here we show you how to chart their variations.
Written by Gary Poyner.
Image Credit: 
Gary Poyner

To repeat a well-worn phrase: “The observation of variable stars is the one aspect of amateur astronomy where the amateur, armed with a simple pair of binoculars or small telescope, can make a useful scientific contribution”. That statement is as true today as it was long before the age of CCD technology. Professional astronomers simply do not have the time to spend monitoring the nightly variations of variable stars, but they are extremely interested in their behaviour. Amateur observers can provide data for professionals to use in their research. But regardless of whether you want to do ‘real’ science or not, observing these fascinating and enigmatic objects can be very rewarding in itself. And with the aid of a pair of binoculars or a telescope, there are enough interesting objects to keep active amateurs busy for years.
There are many different types of variable star that can be observed from even a light-polluted urban location. Mira (omicron (ο) Ceti) and semi-regular type pulsating stars vary over months or just a few weeks. Symbiotic stars, whose variations tend to be slow and irregular, can suddenly erupt by several magnitudes in a few days. Then there are R Coronae stars, whose magnitude may not vary by more than half a magnitude for many months, then suddenly fade by eight or nine magnitudes in less than a week – completely unpredictably – only to rise to maximum brightness again over several weeks. Even more spectacular are the cataclysmic variables, whose brightness can rise by more than five magnitudes in a single night, fade after a day and then repeat themselves in a period of a couple of weeks to many years.

Tools and materials

Torch - A dim red torch is essential for reading a star chart and logging observations in your notebook once you have made them. LED torches are best, but red cellophane on a white light works too.
Watch - Recording the time of a variable star observation accurately is very important, especially for those stars that vary over short time periods. All times should be recorded in UT (GMT) and to the nearest minute.
Notebook - Several items should be recorded in your notebook: the date and time of the observation; the star observed; the estimate, either Fractional or Pogson Step; and the class of observation, either:
1: very confident, 
2: average confidence – maybe due to moonlight or cloud, or 
3: low confidence, but still worth recording. Note localised weather conditions, or problems with light pollution. Finally, the instrument used should also be recorded.
Variable star chart - Use an official chart to locate and observe the variable. The comparison stars listed on the chart have very accurately measured magnitudes, and are carefully selected to have a suitable colour, ie. they don’t include red stars. The right ascension and declination of the star will also be recorded on the chart, and in some cases basic information about the star’s type and magnitude range will also be included.

Beware of bias

The nature of the star is an important factor to take into consideration when you attempt to put together an observing programme. The slow variation of Mira stars, for example, need not be observed more than three times a month – perfect if you can only manage the odd night here and there to observe. Eruptive and cataclysmic stars, however, need to be monitored on a nightly basis, which takes a little more dedication. Bias is a major problem to both inexperienced and experienced observers alike, and it’s important not to over-observe a variable. A star that varies over a period of 400 days will change in brightness very slowly indeed, so any change in its magnitude is not likely to be noticed on consecutive nights. However, the memory of the observation made a night earlier will still be fresh in your mind and will be difficult to ignore. Plan your observing sessions around the period of the stars you are observing.

Limiting magnitudes for various optical instruments

Aperture          Instrument                   Limiting mag.

10x50               Binoculars                             +9.5

15cm                Reflector                              +13.0

22cm                Reflector                              +14.5

25cm                Reflector                              +15.0

35cm                Schmidt-Cassegrain             +16.7

40cm                Reflector                              +16.8

45cm                Reflector                              +16.7

Choosing the correct star to observe with your chosen instrument is another important consideration. A 6-inch (15cm) reflector will not show you a ‘dwarf nova’ in outburst if its magnitude range is +15.0 to +18.0. Likewise, a 
12-inch (30cm) reflector is really too large an instrument for the RV Tauri-type star R Scuti, which varies between magnitude +4.2 and +8.6. Choose your stars carefully and build your programme around the magnitude limits of your telescope or binoculars.

The table above gives limiting magnitudes for a variety of instruments used in light-polluted skies near Birmingham. This should only be used as a very rough guide, as experience and quality of optics/eyepieces both play a major role on the limiting magnitude.
To inexperienced observers, the prospect of measuring the magnitude of a star to a few tenths of a magnitude may seem daunting, but providing a few procedures are followed accurately, it is straightforward. The first thing that is required is an accurate variable-star chart. Magnitudes taken from commercial planetarium software can sometimes lead to inconsistent results when the data is analysed and compared with official charts.
To make the observation, compare the brightness of the variable to two or more of the comparison stars on the chart – one fainter and one brighter. Two methods are in common use, the Fractional and the Pogson Step method, the former being more suited to beginners. The Pogson Step is recommended for those who have some experience in this type of observing, as it requires the eye to recognise differences of one tenth of a magnitude. The fractional method simply requires the brightness of the variable to be expressed as a fraction of the difference between two comparison-star magnitudes.
There are several hurdles to overcome before a confident observation can be made. Correctly identifying the variable itself is the most common problem faced by the newcomer. The Purkinje Effect – the shift of the eye’s peak sensitivity towards the blue end of the spectrum at low light levels and its consequences on red stars – is another. However, the satisfaction of developing a light curve over weeks or months more than makes up for all the preparation that has gone on before.
In our star-hopping guide to observing T Cephei we take a look at how to observe the Mira-type star T Cephei. It has a range of magnitude from +5.2 to +11.3 over a period of 388 days, it’s circumpolar from the UK and is due at maximum brightness during early November 2005.

Step 1  - Start off with a wide field chart to locate T Cephei – perfect for binocular users and finder scopes. Star hop down from beta (β) Cephei to the two field stars marked 67 and 71 on the chart. AAVSO charts (see website) have the magnitudes next to the comparison stars with the decimal point omitted. Don’t look for the variable at this stage, just the field stars.

Step 2 - Once you have the 67 and 71 stars in view, change chart to a 3º field and look carefully for the variable star. If you are using a small telescope and the variable appears very bright, change to binoculars or stop down the aperture. If you are using binoculars and the variable still isn’t visible, note the faintest star you can see. This is still important information to record.
Step 3 - Once you have identified the variable, find two suitable comparison stars – one brighter and one fainter. The difference between these two stars should be no more than magnitude 0.5 – any greater than this and the accuracy of the reduced magnitude will be affected. Bring the variable and comparison stars to the centre of the field of view in turn and make an estimate.
Step 4 - Let’s say you decide the variable is slightly fainter than the 101 star, and brighter than the 105 star. Divide the difference between the two stars (in this case magnitude 0.4) into a fraction, and place the variable’s brightness in it. The fraction you choose is thirds, and you see that T Cephei is one third fainter than 101 and therefore two thirds brighter than 105. You write 101(1) v (2)105 (‘v’ being the variable). This is your estimate.
Step 5 - Once indoors you can work out the reduced magnitude. The difference is magnitude 0.4. Divide this by the fraction you have chosen (thirds) and you get 0.13. Since the variable is fainter than the 10.1 star, you must then add 0.13 to 10.1, resulting in 10.23 or 10.2. This is the reduced magnitude. You can also multiply 0.13 by two and subtract from 10.5 to achieve the same result.
Step 6 - Spreadsheets are marvellous tools for logging observations. All of the information you note down in your observing log can be recorded alongside the final reduced magnitude. The great advantage of the spreadsheet, however, is that it can be configured to produce a light curve from your observations. This can be then be sent by email to any one of the major observing groups if necessary.

This How to originally appeared in the November 2005 issue of BBC Sky at Night Magazine.

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