VARIABLE STARS : Part 5
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
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 eyepiece’s
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
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
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
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
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 variable’s 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-timer’s 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
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
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 variable’s 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
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 variable’s magnitude is 6.51.
If other observations of comparison stars were made, in tenth of a
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
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
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
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