Observing variable stars, using the naked eyes or binoculars, can be performed by secondary school pupils. A first approach without instrument, also accessible to primary school pupils, consist in ranking some bright stars of a constellation according to their visual brightness. It is possible, by this way, to stimulate active astronomical observation, to compare stars of different colours with the sensibility of human eye and to notice the effect of the colour absorption by the atmosphere.
More than 31000 variable stars are catalogued today. Most of these are pulsating or "eclipsing" stars. The observer estimates the brightness of the target star between two comparison stars using the Argelander or fractional method or some other method of his own, after a bit of experience. The main problem consist to express what the eyes see into a numerical expression reflecting the observation. Some sources of errors have to be rejected: the use of a too small or large instrument, comparison stars not well adapted, position of the observer, avoid suggestion when observing inside a group.
A simulation grouping session will show you that it is possible to perform accurate estimates on an artificial variable star. A reduction of the simulated observations will show which information can be extract from the light curve of a periodic variable star. These results are of some interest for the astronomical community.
- Stimulate an active observation
- become aware of the different sensibility of the human eyes
- become aware of the extinction due to atmospheric absorption
A simple drawing of a constellation with the brightest stars is presented to the observer (see fig. 1). The stars to rank are labelled using letters. A scale of the field of view serve as comparison with natural measures (a fist outstretched represents 10° in the sky).
After the observation, the corrected tables are presented (see fig. 2). The stars presented on the same line can be considered as of equal brightness for the human eye. The name, V magnitude and spectral type is presented for each star. The photoelectric V magnitude is slightly different from the v magnitude of the human eye, but can be compare crudely. The spectral type can be compared with the visual colour. The colour of a star (related to his superficial temperature) can be seen as pale blue, for the hottest, to orange or red for the coldest. A simple way to link spectral types and visual colours is as follows:
O-B-A: blue; A-F: white; F-G: yellow; G-K: orange; M-R-N-S: red
Stars of almost the same brightness can be classified in a different way by the observers due to the sensibility difference for each human eye. If the stars of a constellation were observed at a low altitude above horizon (less than 20°), the effect of atmospheric absorption could be detect. For example, a blue star of almost the same V brightness than a yellow or red one, will be perceived fainter for the same low altitude (See for example the stars E and G of Auriga).
Around 31000 stars are catalogued as variable, 15000 more are considered as suspect. These numbers are growing continuously. The main types are the following:
From a chart describing the position of the variable star, comparison stars are labelled by increasing brightness (A, B, C, ...). The observer has to perform an estimate using a pair of comparison star: one slightly brighter than the variable, the other slightly fainter. The comparison stars chosen must be: A-B or B-C or C-D or ... When the comparison stars are chosen, the observer has to express the brightness differences into a numerical expression. For example, compare the position of the point V between B and C on the graph below. How to express that position without using a ruler? Some estimates are proposed. Do you agree with them? What would have been your estimate?
Of course, it is easier to compare a position of a point on a line than to compare the brightness of two stars. In order to help the observer some methods are proposed, but when you will get some experience, you will probably use your own which could be a mixture of other methods.
finding the difference between A (the brightest comparison star) and v
| zero degree A (0) v or A = v | no difference between A and v even after careful examination. |
| one degree A (1) v | the two stars seem equal at first sight, but, after careful examination, existence of a very faint difference. |
| two degrees A (2) v | very faint difference at first sight, but, after careful examination, confirmation of that step. |
| three degrees A (3) v | faint difference at first sight. |
| four degrees A (4) v | clear difference at first sight. |
| five degrees A (5) v | big difference at first sight. |
finding the difference between B (the fainter comparison star) and v
You divide the brightness difference between the two comparison stars in ten steps. Then you "locate" the place of the variable inside that scale. If you have estimated B (2) v (8) C, that means that the luminosity difference between v and C is four times the one between B and v. If you disagree, correct your estimation: it could be B (3) v (7) C or B (1) v (9) C. Better?
After careful examination, you choose where is the smaller brightness difference between the variable star and the two comparison stars (C-v or v-D?). The choice done, you set a standard step for that difference (v (2) D). Then you compare that standard value with the other brightness difference (C-v): how many times does that standard difference is inside C-v? Twice? So you will get that estimate: C (4) v (2) D. A little more than twice? C (5) v (2) D looks better? Perhaps you would have prefer C (4.5) v (2) D?
The final estimate must be in the following form: A (x) v (y) B. Where A and B are, respectively, the brighter and the fainter comparison star, x and y are the number of steps of brightness difference between the variable and each comparison star. You must also record some more informations for each estimate such as the time (in U.T.)to the nearest minute, the name of the variable. Once at the beginning of the night, report the date, the name of the observer, the site, the instrument used, some remarks. A observing sheet could looks like this:
| Peter BLINDEST Liverpool (UK) B 50x10 | ||||||||||||
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Observing a too bright star with a big telescope will result in a lack of precision. The fainter variable star to be observed with any instrument must be around 0.5-1.0 magnitude brighter than the magnitude limit, depending of the site quality. Here below, you will find the lower and upper magnitude limits for some instruments.
| Binoculars 50x10 | 6.0 - 8.5 |
| Telescope 115 mm | 8.5 - 11.0 |
| Telescope 200 mm | 10.0 - 12.5 |
It is better to use the charts published by the variable stars observers associations: the comparison stars have been carefully selected to avoid some problems. However, if you decide to observe a lesser known variable, lacking chart references, you will need to choose your own comparison stars. Be careful to these points:
- The brightness difference between two consecutive comparison stars must be not too large and not to small. The better: A ¬ 0.4-0.5 mag. ® B.
- The comparison stars must be situated not too far from the target star and inside the field of view.
- The comparison stars must not be of too different colours.
- The variable and the comparison stars must be observed at the same orientation in spite of the field rotation of your telescope.
- When observing the same stars with several people, try to avoid suggestion, especially if the star exhibit rapid variations.
Several diodes mimics a real starfield, observed using binoculars, around the variable star RZ Cas. The variable itself is represented by a diode whose light can be modulated. The observers have to perform several estimates using one of the methods described. The observations are recorded on a sheet of paper using a red light to respect the eye adaptation to the darkness.
After the simulation, the participants describe their feelings about that experiment.
Example:
A = 6.8 B = 7.5
mV = 7,3
You can study for example RZ Cas !
When all the observations are reduced, prepare a graphic on a squared sheet of paper at a scale of 6 cm per hour (horizontally) and 1 cm per 0.1 magnitude (vertically). Remember that the maximum brightness, express by a smaller number in magnitude, must be placed at the top of the vertical axis.
Comparing all the graphs, will show you that everybody in the assistance has recorded the same phenomena during the simulation, with slight differences between the observers.
