The Observation of Variable Stars

Finding the Variable

Find variable stars is not a task as simple as it first appears. Often it is sometimes necessary to find just the field in which the variable lies, as the variable maybe invisible at the time. Usually it is best to have the variable chart and star field, together with lists of the comparison stars and their adopted magnitudes. Over time, this can be learned to be done from memory from the stars in the selected observing program. Most charts already have magnitudes specified on the chart, being true if the variable is bright. Magnitudes are found by the necessary photometric measures, generally available for the most suitable of the star near the variable star. Charts that do have magnitudes on them are expressed in whole numbers, minus the decimal point, as not to confuse the dot with the real stars.

Charts are readily obtained through a number of sources. Southern variables are obtained wholly from the Royal Astronomical Society of New Zealand (RASNZ) Variable Star Section.

All charts should be carefully examined, identifying the principle stars in the field. It is also worthy to compare the field of the chart with the apparent field of the telescope. It is best to know beforehand both the eyepieces magnification and field size of the eyepiece . Magnification an be determined using a dynamometer that give the exact focal length. This is preferable to the quoted focal lengths on older eyepieces as they can often be wrong. Field size can be determined by timing an equatorial star, aligned to move through the centre of the eyepiece.

For most telescopes used to observe variables, an equatorial mount with circles is preferable though not essential. Telescope drives could also be an advantage. If some experience has been gained, observers may only require an altazimuth mount. A reasonable finder on the telescope, and a decent pair of binoculars will be of great assistance.

With variable star observing the requirement of high magnification is rare, where medium to low magnifications will usually suffice. In some circumstances high magnification might make the apparent field darker. This can help to identify some stars particularly when they are a minimum brightness. Only experience will tell if it does make a difference in a particular telescope system.

One important requirement, is that the observer be familiar with the brightest stars and constellations. A decent star atlas is essential. Often new variables will not lie near a bright star. Those that do then require the observer to find the object quickly.

When searching for a new variable star, sometimes you cannot identify the field nor the star. A new attempt should be made afresh, perhaps after other searches with other more familiar variables. Once the variable has been found, it should be placed in the centre of the field. Observers should then double check to see if it is the variable sort, especially as fields are easy to misidentify. Next record the time and your estimate of the brightness. Take careful note from the chart of the magnitude range of the variables normal fluctuations. Checking least if it is in confines of possibility.

This field should be recognised and remembered for future reference. It is advisable, if possible, to again return to the field several times during the same night - ensuring future identification. First-timers are recommended to start with several bright variables then slowly begin to increase your repertoire. For the experience observers most of these comments may seem trivial, but it is worthy practice and learn for the novice. This is also true regardless of the type of deep-sky celestial body that is being observed.

Estimations of Brightness

Magnitudes of the comparison stars are usually given on the chart. These are used to compare brightness of the variable to the comparison stars. Usually, the use of two comparison stars is adequate. These stars are chosen to be typically one brighter and one fainter than the variable. Later more stars are used to check the initial first estimate if required.

Two methods are typically employed for variable stars. These are
the fractional method or the Pogson method.

The Fractional Method

The fractional method relies on estimating the brightness of the variable star between two comparison stars of known brightness. Here the brightness is expressed as a fractional difference. Differences should be between the comparison stars should not exceed more than about 0.5 magnitudes with the intervals expressed as fractions. I.e. 1/2, 1/4, 1/3, 1/5, 1/8 etc.

As an example, let the variable is the unknown V magnitude, the bright comparison star be X magnitude and the fainter comparison star be Y magnitude. If a variable was estimated to be 1/5th of the way between X and Y, then the record is made;

X (1) V (4) Y

The brightest star in this sequence is always written first,
this is followed by subsequent star in descending order.

Sometimes, the variable might be exactly the same brightness as the comparison star. This is recorded as X=Y. Further checks with other comparison stars should then be made, assessing that the brightness does agree with your estimate of equal brightness. It is always suitable to check against several comparison stars wherever possible, selecting those comparison stars that match also match the colour of the variable.

Occasionally the variable cannot be placed between any two stars in the field, or perhaps there is only one star of similar brightness. In this case, select two stars that are not as bright or faint as the variable, but make sure that each star is of either side of the variables brightness. If the star was fainter for example, the estimate is recorded as;

X (1) Y (4) V

This indicates that the variable is brighter than Y but fainter than X. In this example the magnitude of star Y is 4/5th fainter than the variable.

(Note: The expression of X (4) Y (1) V would indicate the magnitude of the star Y is 1/5th fainter than the variable.)

If the estimate is from a brighter star, it is expressed as;
V (1) X (4) Y

This example indicates that the variable is brighter by 1/5th the amount that X is brighter than Y.

Calculating the Magnitude by the Fractional Method

Suppose the estimate was really 1/5th the light between X and Y. Then the difference also becomes 4/5th the interval between Y and X. The total of these two in difference, then remains exactly 1.00, which it must always be.

Two examples of the results can be calculated as follows;

Example 1 and 2
X (1) V (4) Y
X = 6.45Y = 7.77
Y-X = 1.32
1/5 = 0.26
4/5 = 1.06
Mag of V = 6.71

X (2) V (3) Y
X = 6.45 Y = 6.77
Y-X = 0.32
1/3 = 0.11
2/3 = 0.21
Mag of V = 6.66

The result in the first example is added to X because the variable is fainter than X. This gives the result; 6.45+0.26 = 6.71. Similarly, the same result is obtained from Y, hence, 7.77-1.06 = 6.71.

Suppose, as in Example 3, is one of the occasions where we have to estimate 'V' from fainter X and fainter Y. Example 4 shows if the reverse of this is true, with the 'V' star brighter than either X or Y. These can both be shown;

Example 3 and 4
X (2) Y (3) V
X = 6.45 Y = 6.77
Y-X = 0.32
V = 0.32 x 3/2
V = 0.48
V = 6.77 + 0.48
Mag of 'V' = 7.25

V (2) X (3) Y
X = 6.45 Y = 6.77
Y-X = 0.32
V = 0.32 x 2/3
V = 0.21
V = 6.77- 0.21
Mag. of V = 6.24

The Pogson Step Method

This method estimates brightness in 0.1 magnitude divisions using as many comparison stars as possible. Typically, we select one star being brighter and one being fainter than the variable. This has the advantage in detecting variability using either the comparison star or any incorrectly stated magnitude. It also means that one comparison star may have to be used especially if no other suitable star is available.

The key to this methodology is that the eye must be trained to make estimates to tenths of a magnitude. To learn this method, one has to first be able to recognise in a telescopic magnitude differences of 1/10th. 2/10th, 3/10ths, etc. Estimates between star with a difference of 0.5 magnitudes are deemed too inaccurate for visual estimates. Sometimes this circumstance cannot be avoided, but this seldom happens unless the magnitude range of the variable is high. It advised only to be used by those who have observational experience with variables.

In time when more experience is gained it is best to forget the comparison magnitudes entirely and do the measurements totally unbiased. Naturally, the magnitude can be calculated later by looking-up its brightness in the charts.

Many of the advanced and experienced observers have be so well trained that they can estimate as low as 0.05 magnitudes. More amazingly, some can find each variable on their observing list within thirty to sixty seconds!

Calculating the Magnitude by the Pogson Method

Suppose the variable is the same estimate as Example 1 in the fractional method. The magnitudes are X = 6.45 and Y = 6.77, and the deduced variables magnitude is 6.51. If other observations of comparison stars were made, in tenth of a magnitude, of Z and W, both with the individual magnitudes of Z = 6.31 and W = 6.63. then the estimates for the variable.

Example 5, becomes;
Z - 0.2 mag. = 6.51W + 0.2 mag. = 6.43
Mean of Estimate = 6.47

These results state that Z was estimated by the observer to be 0.2 magnitudes brighter than the variable star while the W star was observed to be 0.2 magnitudes fainter. (Note: The signs are the reverse of the direction of the magnitude.) In the final reduction of the data, as seen in Example 5, the deduced magnitude is the mean or average value of all the observed estimates. If we also used values from the fractional method in Example 1, This would give a mean brightness calculated by;

Example 6
X (2) V (3)
Y = 6.51C - 0.2,
D + 0.2 = 6.43
Sum of Values = 12.98
Mean = 6.49

The deduced magnitude is therefore 6.49, rounded to 6.5.

There are also different ways in which the results can be calculated. Some use so-called weighted means that are applied especially to those that use the Fractional Method. If such estimates are obtained using the Fractional Method they should be recorded with the observations something in the 'Remarks' column.

Also applying to both methods is that if the variable cannot be seen in the your telescope, this also should be recorded. Your variable is simple expressed fainter than the lowest observed comparison star, as xx.x. Such recording at least set a maximum brightness that the variable could be seen.


Last Update : 13th November 2012

Southern Astronomical Delights © (2012)

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