Can amateurs still contribute usefully to the development of astronomical science ? Until the beginning of the XXth century, this question did not apply and many amateurs had built or possessed instruments which were as powerful as the ones used by professionals : noteworthy examples are William Herschel who was a musician before he became a famous astronomer or Pons, the janitor of the Marseilles Observatory, who, seeing his employers examine the sky night after night, decided he would do the same and discovered 34 new comets ! In the middle of the XIXth century, the world's largest telescope belonged to Lord Rosse, an English nobleman, and it was superseded in 1918 only when the Mount Wilson 100-inch telescope was commissioned.

Nowadays, modern techniques have so much improved that it seems difficult for amateurs to contribute to the progress of astronomy. There remain however a few fields in which their contribution can still be very helpful, notably in the study of variable stars. In an 1880 report of the Advisory Committee on Provincial Astronomical Observatories addressed to the Ministry of Education, Mr. Loewy, its reporter, wrote :

" Through the analysis of the characteristics and the length of the period of such wonderful variations of brightness, very probable conclusions can be reached as to the physical constitution of these celestial bodies, their rotation period, their distance from the Earth, the stage of their stellar evolution and many other questions of the same order. "

Since this report was published, the interest of astronomers for variable stars has kept on growing. The number of catalogued variable stars is now well over 40,000. This number is so high and the characteristics of these stars so varied that it is impossible for professional astronomers to monitor and study all of them. As early as 1916, Michel Luizet (1866-1918), France's most famous variable star observer, wrote :

" Since every year new variable stars are added to the already quite long list of stars recognized as variable, the number of observers, and therefore, the number of observations is obviously insufficient. And yet, no other astronomical work is easier to tackle than the study of these stars! Many variable stars can indeed be observed with the unaided eye ; [...] with a small refractor or a good pair of binoculars, the field of study widens. So simple an equipment completed by a celestial atlas is obviously available to most amateur astronomers. With this equipment and some willingness, method and regularity, an observer can certainly do an excellent and useful work in this branch of astronomy.

It is by using simple methods of visual photometry that American, German, British, Russian, Japanese and also French observers have made our knowledge on variable stars progress. Even the best known variable as Mira Ceti or SS Cygni (every eruption of which has been followed since 1896) must be permanently monitored because their light curve often shows an anomalous behaviour or unexpected accidents that are always related to a modification of their spectrum. Thus, a team of radio-astronomers at Nan‡ay has used the observations of some mira-type stars made by AFOEV observers to prove the existence of a correlation with a time-lag between optical and radio variations. Many novae have been discovered by amateurs, sometimes before they had reached their maximum brightness ; immediately informed, professional astronomers have thus been able to observe them by spectrography and the spectra thus obtained have allowed the nature of these objects to be better known. Moreover, orbital telescope time allotment is limited and the contribution of amateurs has become essential to "locate" the star on its light curve at the very moment when the professional astronomer has the telescope at his disposal.

The beginner in the observation of variable stars, often equipped with a small instrument and whose leisure time may not allow him to collect a dense dataset of observations may ask himself whether a few random observations made during in the course of a week-end off or through a clearing in the cloud cover are of any value at all. Andr, Danjon wrote :

" In astronomy, every observation has its own value. A well-made observation will one day or another find its use and an observation that failed leaves an irreparable gap "

The scientific interest of the observation of variable stars is therefore not negligible and it would be a pity if the observations of an amateur were kept locked in a drawer. However, publishing his own observations and putting them at the specialists' disposal is obviously very difficult for an amateur. This problem finds its solution in the regrouping of amateurs in an association that publish the observations of its members and make them available to professionals. An isolated observation, apparently of no use, becomes one of the links of a chain forged by the whole group. Today, the observations collected by the AFOEV are computer-processed and stored in digital form at the "Centre de Données Astronomique" (Center for Astronomical Data) of the Strasbourg Observatory where they can be freely used by the professional astronomers of the whole world (and they don't refrain from using this possibility).

Team work entails some discipline. Although the programme of the association is by no means irremediably frozen and new variable stars are added to the initial list, it is necessary to set some limits. The AFOEV programme includes mostly long-period variables (mirae and semi-regulars). The amplitude of variation of most of these stars is large enough for individual errors to have a lesser relative importance. Thus, it is in the interest of the beginner who makes his own programme to select stars that are well followed by other observers ; he will thus have the possibility of comparing his observations with those of his fellow observers and thus evaluate the acccuracy of his estimates. Cataclysmic variables are also well observed at the AFOEV : however, these stars are rather faint and reserved to trained observers.

During his probation period, the beginner will observe the same stars as often as possible so as to get more and more familiar with their field. Then he will progressively make his observations less frequent - long-period variables should be observed once every 8 or 10 days, which will allow him to increase rapidly the volume of his programme.

The AFOEV programme includes practically no Algol-type variables and no cepheids as the observation of this type of stars requires an availability which is not compatible with the various obligations, mostly professional, of an amateur. As a matter of fact, for this type of variable, an isolated observation is of practically no value and only complete series of observations covering a whole night or at least a great part of the night will give an observer the opportunity to monitor the eclipse of an Algol-type binary or the maximum brightness of an RR-Lyrae variable.

First of all, the unaided eye allows studying several bright variables but, notwithstanding the fact that the method offers limited possibilities, it entails several risks of errors, mostly because the comparison stars are not necessarily in the vicinity of the variable. A pair of binoculars is the best instrument to get trained in the study of variable stars as its wide field facilitates the identification of the asterisms around the variable, thus allowing an accurate localization of the star. But in this case also, one has to be extremely careful if the comparison stars are too distant from the variable. Whenever the choice is possible, a reflector is preferable to a refractor. A refractor's drawback is its long focus with, as a consequence, a limited field compared with a reflector whose extra advantage is, diameter for diameter, a cheaper price and the possiblity of making it by oneself.

If for the larger instruments, an equatorial mounting fitted with accurate setting circles or, nowadays, computer-driven makes pointing at a faint variable easier, an altazimuth mounting will be easier to manage. The instrument must however be fitted with a good finder with which one can find the variable by hopping from star to star.

Star charts can be supplied at cost price to AFOEV members. The original tracings were drawn by Antoine Brun, the founder of AFOEV. As they became tarnished and brittle with time, they were redrawn and several new charts were added. These photocopied 13x18cm (5"x7") charts are used to locate the variable and include the sequence of comparison stars with their identification letter and their magnitude given to one decimal place. The comparison stars are indentified by letters (a, b, c, d,...) and their visual magnitude is given as an integer, for instance 114 for visual magnitude 11,4 as a decimal point may be mistaken for a star. Indices, for instance c1 , mean that the star was added to the sequence between c and d.

These charts give all the necessary information on the star designation, its position for equinoxes 1900, 1950 and 2000, the value of its annual precession in right ascension and declination, its type of variability, its mean brightness at maximum and minimum, its period and its spectrum.

For a given variable, the number of available charts depends on its brightness at minimum light. Usually, there are four overlapping charts A, B, C,and D.

• Chart A (scale 1cm [0.4"] to 1ø) covers a 12øx12ø field and includes all stars down to magnitude 7,5. It is used to locate the variable in its constellation with the unaided eye and for some bright variable stars to estimate their brightness when they are near their maximum. They have been drawn after Antoine Brun's "Atlas photométrique des constellations" (Photometric Atlas of Constellations).
• Chart B, usually drawn after the Bonner Durchmusterung, covers a 2øx2ø field down to magnitude 10,5 approximately.
• Chart C (field covered : 40'x40') shows stars down to magnitude 13.
• Chart D covers a 20'x20' field, sometimes 10'x10' only or even less, and shows the faintest stars necessary for the observation of the variable.
  

When they join the association, the observers are provided with an updated catalogue of the available charts.

For a beginner, searching for the variable and identifying it is the most delicate and most tedious part of the job, though as an amateur astronomer he will certainly be familiar with locating celestial objects. It is highly advisable to begin with "conveniently-situated" variables i.e. stars situated in the vicinity of easily identifiable fairly bright stars. This search is the only serious difficulty that a beginner may experience, and with some practice and training, both easily obtained, even "difficult" stars will be quickly found and when one year later the celestial round brings a given constellation back, he will be surprised and delighted to find almost at first glance a star which he had observed a year before.

If the instrument is on an equatorial mounting, the variable and its field will be easily found either with the help of setting circles or of a computerized object locator. In the case of an altazimuth mounting, it will be necessary first to identify the region of the variable with the help of chart A. Then, using the finder and starting from a known bright star, the observer will go star-hopping to the brightest star in chart B. Then with a low-magnification ocular giving the widest field and making use of star alignments or remarkable patterns of his own choice, the observer will finally come to the variable's field. This is done step by step, using if necessary the chart showing the faintest stars and more and more powerful oculars. Once the field has been clearly identified, the observer checks whether the variable is visible and if so, proceeds to an estimate of its brightness.

During this search, observers should avoid going to the extreme limit of tiredness. If the search proves to be too difficult, it is preferable to temporarily give up, have a rest and try again at the next observing session.

Except when using a photometer, a visual observer does not "measure" the brightness of the star. The observation consists in estimating its brightness by comparing it with nearby non-variable stars whose brightness has been measured with a photometer or more recently by photoelectric photometry or by CCD's.

Once the variable has been located and the comparison stars identified, the observer looks for the star which appears to be just a little brighter than the variable and the star which seems to him just a little fainter. Let "c" be the star slightly brighter than the variable (designated as "v") and "d" the star which appears slightly fainter. Estimating the brightness of the variable consists in determining by how many steps (hereinafter, "degrees") "c" differs in brightness from the variable on the one hand, and "v" from "d" on the other hand, the brighter star always coming first. The idea of "degree" was invented by Herschel and refined around the midddle of the XIXth century by Argelander, the author of the famous Bonn catalogue (BD). He defined them thus :

• " If at first sight, the stars appear to be equally bright and I recognize after a close examination and repeated passages from "c" to "v" and from "v" to "c" that, except at rare moments, "v" is brighter than "c", I shall say that "c" is 1 "degree" brighter than "v" and I shall write c 1 v

• If, although they seem to shine equally bright at first sight, star "c" appears, on closer examination, to be without hesitation brighter than "v", I estimate the difference to be 2 "degrees" and I write
  c 2 v

• A difference that is obvious at first sight is equivalent to 3 "degrees" and is written
  c 3 v

• An even more obvious difference between the two stars represents 4 "degrees" and is noted
  c 4 v

• Finally if a real disproportion exists between the two stars, this difference is equivalent to 5 "degrees"
  c 5 v "

Having compared the variable "v" with the brighter star "c", the same method is applied to the comparison between "v" and "d", the fainter star, so as to obtain finally an expression such as, for instance :

The estimated magnitude of the variable is then derived by applying the formulae :

where x and y are the number of "degrees" between "c" and "v" and "v" and "d" respectively. The operation finally amounts to a mere rule of three. Let us assume values 79 and 85 (i.e. magnitudes 7.9 and 8.5) for stars "c" and "d" respectively. 3+2 = 5 "degrees" are equal to a difference of 8.5 - 7.9 = 0.6 magnitudes. In our example, the value of the "degree" is 0.6/5 = 0.12 magnitudes whence the concluded magnitude for "v":

The result of this arithmetical operation must be rounded to the nearest tenth of magnitude, that is 8.3 in our example. Writing 8.26 entails a risk for the beginner to believe that visual estimates enable him to reach an accuracy of one hundedth of magnitude. Such an accuracy is obtained by photoelectric or CCD photometry at the cost of complicated and difficult procedures.

To get even more certain and check the first estimate, it is advisable, if the sequence allows it , to compare "v" with more than two stars, for instance : assuming c = 79, d = 85 and e = 88,

When it is impossible to observe the slightest difference between the two stars and after going several times from the variable to the comparison star and conversely, it seems that each star appears alternatingly brighter, they are said to be of equal brightness and the observer will write :

Another method of visual estimate is Pogson's fractional method, derived from Argelander's method. The magnitude difference between the comparison stars whose brightness frame the variable's brightness is divided into ten "degrees". In our example, the estimate would be something like this :

Lastly, Pickering's method consists in dividing arbitrarily the difference in magnitude between the two comparison stars into as many "degrees" as there are tenths of magnitude, a "degree" being therefore equal to 0.1 magnitudes. Taking the example above, the magnitude difference between "c" and "d" is 0.6 i.e. 6 "degrees". If for instance, the brightness of "v" appears to be halfway between the two comparison stars but slightly closer to the faintest star, the observer will write

The observation is written down in a notebook or even a mere sheet of paper. All the observations will be written down in chronological order. The observer should mention the date on top of the page or of the series of observations and for each observation : the variable's designation, the time of observation (hour and minute ; the latter is important in the case of a cataclysmic variable) and the detail of the comparison. A dim light, either an under-powered bulb or a bulb screened by a red transparent paper will be used to examine the charts and make note of the results which will be arranged like this :

The estimates written down in the copy-book or on the sheet of paper will then be copied in an observation logbook containing the following indications :

• date, time (UT), date and time transformed into Julian day and decimal fraction of day (tables are published by AFOEV to that effect)
• name and designation of the variable
• detail of the comparison
• concluded magnitude as deduced from the comparison
• quality of the comparison
• quality of the sky (1 : good, 2 : fairly good, 3 : poor)
• instrument used and magnification
• addditional remarks

For instance :

Special report forms can be obtained from Emile Schweitzer, 16 rue de Plobsheim F-67100 Strasbourg, the recorder of the AFOEV database. The observations, however, may be sent on any medium provided that some conditions be respected. They are meant to facilitate the editor's task and include the mention of the observer's name and first name, the month and year, the total number of observations in the month, the instruments used and the main site of observation. The stars should be sorted by increasing right ascensions and the observations relative to each star in chronogical order.

The reports are to be sent monthly to the bulletin's editor, as far as possible during the first days of the following month. The observations are more and more frequently sent by e-mail.

The errors inherent in the methods of observations are impossible to avoid as these methods are subjective. Errors can be accidental (misidentification of the variable, for example) or systematic (arising either from the instrument used or from the observer). The main causes are :

• errors caused by the "Ceraski phenomenon" (named after a couple of Russian astronomers who lived at the beginning of the XIXth century). This error is also known as the "position angle error" and can be defined thus : when two stars of equal brightness are aligned so that the the line-of-stars is perpendicular to the line-of-eyes, an observer may systematically see the "upper" star brighter than the "lower" one. Similarly, when the stars are aligned so that the line-of-stars is parallel to the line-of-eyes, one of the stars may appear brighter than the other. This equation is strictly personal to the observer ; it remains constant on the whole and always works in the same direction. For example, a given observer will always see the right-hand star 0.3 magnitudes brighter than the left-hand star while another observer will judge it to be 0.2 magnitudes fainter. To eliminate this cause of error, "panoramic" vision of the field, i.e. centering the variable to compare it with nearby stars, should be avoided. On the contrary, each star should be successively centered in the field of the instrument and the observer should tilt his head on one side then to the other
  

• errors caused by the "Purkinje effect" (after the name of a Czech physiologist), sometimes called the "Galissot effect". Even though an observer apparently does not perceive any difference in colours between the stars he compares, his retina may be more sensitive to some wavelengths. For that reason, red stars - this is the case of the numerous long period variables included in our programmes - seem to become brighter as the observer's eye lingers over them. To eliminate this cause of error, the observer should only give quick glances at them. It is also possible to use a light green filter which appreciably reduces the difference in colours. An excellent solution is to slightly "spread" the star images by using extra- or intra-focal vision, which has the further advantage of facilitating the estimates while reducing the redness of the star.
  

• fatigue due to an uncomfortable position at the ocular - especially with Cassegrainian telescopes ; it strongly influences the estimates and will entail errors. It is recommended to settle down comfortably at the telescope and manage a few breaks in the observing session for rest and relaxation.
  

• looking into ephemerides before observing or remembering previous observations entails a risk of "error by suggestion", a risk to which all observers and particularly beginners are liable. The association does indeed make available to its members a table predicting the dates of maximum and minimum light of long period variables but this is only with the aim of helping the observer in the preparation of his observing session : as a matter of fact, it is useless to observe avariable of magnitude 14 at minimum light with a 3-inch refractor or a 4-inch reflector. Refraining from looking into ephemerides or recent observations, increasing the number of stars on one's personal programme and observing each of them at intervals several days apart are excellent remedies to combat this cause of error. However, cataclysmic variables must on the contrary be observed on each observing session.
  

The photographic observation of variable stars is less and less practiced although it has the advantage of offering an indisputable and impersonal evidence. To be comparable with visual observations, photographic observations must however respect particular spectral characteristics as regards the type of film. Commercial photographic films should therefore be used with a filter.

The photoelectric observation of variable stars requires a fairly elaborate equipment whose assembly requires a solid knowledge of electronics if a reasonable cost is looked for. Moreover, it can be implemented with fairly large aperture telescopes only. On the other hand, it can reach an acccuracy of a few hundredths of magnitude and the observation of a variable in different spectral bands is possible. It is mainly directed at the study of low amplitude variables. CCD imagers are more and more easily available to amateurs and allow observing faint variables.

AFOEV is a registered association whose statutes were adopted in 1927 and modified twice in 1973 and in 1986. Its headquarters are at the Strasbourg Observatory.

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