Alpha Comae Berenices – An eclipse for a queen
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For discussing a surprising star of Coma Berenices, of historical importance ; one of the first stars, the main physical characteristics have been determined, there are nearly one hundred and fifty years and, having done a lot of ink, retains some interest, keeping a veil of mystery still, as observations to be conducted during the winter of 2014-2015 may help to lift – a chance every 26 years !
A thousand thank you to Christian Joye for his help and his masterful translation of the thought of Friedrich Struve and André Debackère for his suggestions and his careful reading.
Thank you to Matthew W. Muterspaugh (Tennessee State University) for clarifications about the eclipse to come and observations.
Reviews and comments welcome.
A mailing-list is available here : Alf-Com Eclipse (English / French).
Last minute news or, as we say now: Updates
Your observations, if you wish, will be published on this blog and sent to Matthew Muterspaugh as well as to the AAVSO. The AFOEV (Association Française des Observateurs d’Etoiles Variables), contacted about this, has not responded to our email.
Table / Content :
- The nights of Egypt – Mythology
- Diadem – A star in Coma Berenices
- The nights of Bath, and those of Dorpat – William Herschel and Friedrich Struve discovered the double stars
- Slowly nights – A Century of study of Alpha Comae Berenices system
- Algols nights – The eclipses of Alpha Comae Berenices
- Winter nights – Observation of the 2015 eclipse
- For a few more nights – In search for exoplanets
- Appendix – Friedrich Struve, Ueber Doppelsterne … full text
- For more information (historic)
The nights of Egypt
He has very long time, to the Hellenistic period in Egypt but a declining governed by the cult of Amun-Re, attentive to the heliacal risings of Sirius and dependent as ever on the Nile floods, the need to conquer was immeasurable ;dropoff window and ambition, glory, honor and revenge yet powerful engines.
Berenice of Cyrene was born in 267/266 BC; she was Princess of Cyrenaica in eastern Libya, a former province of Egypt, which had gained independence a few decades ago after a revolt. Daughter of King Governor Magas and APAME Queen of Macedonian origin – sometimes called Agas in some texts – the girl was promised, from a young age, son of Ptolemy II ruler of Egypt, pledge of friendship between the two kingdoms now in the process of reconciliation. The union would take place when the Prince was old to the throne of Egypt.
But this wedding was not celebrated. At least not until some detours. Because things are rarely as simple as they can be when fate is involved. And when some versatile expressed wishes too.
On the death of King Magas in 250 (given to 258 in some ancient chronologies), the mother of Berenice denounced the agreement possibly linked the fate of Cyrenaica to that of Egypt and preferred to offer his country and its daughter, aged fifteen years in marriage to Demetrius, a brother of the King of Macedonia, left more beneficial if it was because Macedonia was then combined with the immense Syria and dictated his law throughout the Middle East, the Aegean Sea to the Indus. Demetrius, who was older than ten years since the princess, and which he said he was very handsome, well done to his person, and very proud, as fair forsook the brisket to a more substantial piece, without removing great panache it must be said, and after a pure seat form only, the Queen Mother APAME who opposed a token resistance.
After a year of so distressing that cohabitation sterile, unable to bear the result of more affronts – after all the girl was Macedonian princess by her mother so she had to take – and Bernice had to slaughter the unseemly husband which quickly died by the sword one night in the bed of APAME, who tried hard to protect it to the end, but … the killers were too numerous and too well armed.
When Ptolemy II died three years later, Prince Ptolemaios spirited « living forever, Beloved of Ptah », the eldest son of the deceased, finally came to the throne of Egypt under the name of Ptolemy III Euergetes. In the process, he married Berenice of Cyrene free as before, overjoyed and all the joy of being able to honor its promise, finally.
The young queen, known as Berenice II of Egypt, was a popular, active and progressive sovereign who did not hear remain in the shadow of her husband, mixing politics and religion, as far as saving .dropoff window And it is reported that she sacrificed himself by participating in the Nemean Games to 245-241, as well as the Olympic Games later, but at an unspecified date, which is a challenge to say the least, a same time when access to stadiums, and participation in games, were forbidden to women. But this is questionable. Nevertheless, the couple lived happily as long as he could and had four son and two daughters.
There are quite a number of portraits of Berenice on coins, and there were a few marble busts and heads, as we can see in Alexandria, London, Rome and Cyrenaica in Benghazi, a city whose the name derives from the Greek Berenike directly.
« Today, the Graces are four in number: the three old was is added a fourth, newly formed and still wet scents, the blessed and radiant for all to see, Berenice, without which no Graces are not the Graces. »
So the poet Callimachus of Cyrene he sang the praises of his queen.
One day, while Ptolemy had gone to war somewhere in Syria to rescue his sister, Berenice another young widow of King Antiochus II Theos, that one in great danger of being passed by the weapons a rival faction – a very treacherous country Syria so that the hands of the Seleucids, allies of the Macedonians … – Berenice of Cyrene, overcome anxiety, cut a long lock of her hair which she placed in the temple ‘Arsinoe-Aphrodite in Alexandria, offering to the goddess, which she hoped to curry favor and effective protection for her husband for too long absent.
No doubt he would please the sacrifice in very high places, because the wick disappeared as soon as night had fallen, to the chagrin of the local clergy, circumspect. And willing – most importantly – do not end door overhang vis-à-vis the queen. Disappearance quite disconcerting that made more worried than reason still languishing in love, and settled in well menacing disposition towards the servants of the temple. It took all the subtlety of mind then, and persuasion of the royal astronomer Conon of Samos – but can we expect anything but the delicacy of mind on the part of an astronomer? – To bring in Berenice wiser provisions. To all this, there was a rational explanation not only the disappearance of noble loops boded no disaster, and protection of the husband was assured – that was certain – but the offering had so pleased the goddess that under his orders, Berenice’s hair had gone join heaven to appear in the sky, now and forever, as a fabulous stars haze … Amazement! And the astronomer Conon brandishing a feverish index, if somewhat worried again, and show the girl a nice little stunned newly emerged group of stars in the tail of Leo, which, through diplomacy, had agreed to separate from a tuft of hair: Coma Berenices flight was found!
« And so the Golden Crown of the daughter of Minos was not alone, for men to sit and shine in the sky among so many stars, and you should see me too, me, the beautiful loop Berenice, Cypris, while damp the waves of the sea, I climbed to the Immortals, Cypris placed me, new star among the former. « (1)
Berenice by Bernardo Strozzi
After more than twenty-five year reign as happy as eventful – politics and war leave rarely calm those who engage in it – Ptolemy III died a natural death in 222. Berenice did not long survive him: it was poisoned the following year by one of his son, Ptolemaios – yet – the future Ptolemy IV, by the way, also massacred the rest of the family – three brothers and an uncle – in a way that does can not be described here. This before marrying Arsinoe Philopator, one of his sisters.
« O tempora o mores ! ».
Thus, all twenty-five years and about the tiara Berenice he carries the heavens mourn the beautiful Macedonian princess, lost somewhere in the history of Egypt.
Bootes, the Hunting Dogs and Coma Berenices, by Sidney Hall (1788-1831),
in : Urania’s Mirror, or a view of the heavens, 1824.
Berenice’s Hair (Coma Berenices in Latin) is a constellation actually quite insignificant, stuck a little cavalier between the rear axle of the Lion and boots Philomenus Bouvier; the only constellation, with the ECU Sobieski, which owes its existence to a historical figure. Medium and devoid of bright stars size, the constellation is uncharacteristic and leaves only difficult to discern if one does not have a good sky; it still houses eight objects in Messier’s catalog, including a beautiful globular cluster (M53) and seven galaxies (M64, 85, 88, 91, 98, 99 and 100). The area corresponds more or less to the north galactic pole, a poor region in gaseous nebulae and stars but rich in galaxies of all sizes and distances. However, it is under a very transparent sky, see a small area riddled with faint stars, halfway between the constellation of the Hunting Dogs and Lion finer strands of Berenice, as designated by Conon the astronomer, a star cluster identified as such in 1935 and known as the Melotte 111 (80 stars located a little less than 300 al).
Diadem is the main star of Coma Berenices. Its Latin name obviously refers to the crown of Queen Berenice; it is amusing to note also that the traditional Arabic name of the star, Al Dafirah means « the braid. » This is a fairly ordinary star on which the eyes do not stumble, except to look specifically – this is a good step to identify the cluster M53, located less than one degree away.
White, slightly yellow pulling Alpha Com – Com or Alf, either – shines at magnitude 4.32, slightly less than the star Beta of the constellation, whose brightness is equal to 4.23.
Diadem is No. 42 in the catalog of Flamsteed and 114378 in the Henry Draper. But the star has other alias again, the most emblematic of which are not without giving it even more mystery: Hipparcos, Gliese, 2MASS, Iras, AAVSO, STF, ADS and WDS, for instance – forty denominations grand total.
Membership of the star Gliese Catalogue puts us chip in his ear: the star is a close companion of the sun. Its parallax is somewhere between 60 and 65 s (+/- 19 percent) according to the authors, which adds to our interest in it.
The American Association of Variable Star Observers (AAVSO) is known by the following identifiers: 1305 + 18 and NSV6116 (New catalog of Suspected Variable). It is therefore a variable star, oddly enough characterized by a period of 9485.68 days and decked out with a more enigmatic « Mag. Range 4.32 – V «
But do not take the suspense any longer : they are the inscriptions of the star at the Washington Double Star Catalog (WDS), under the username + 1732AB 13100, and Aitken Double Star Catalog (ADS) under the name ADS 8804AB that motivate our interest this time. A new request to the International Variable Star Index (VSX) brings us the information that we needed to begin to see the truth: « Variability Types VSX – EA – β Persei deviation (Algol) Eclipsing systems ». This time, we are definitely fixed.
Alf Com is therefore both classified as a star and dual visual binary star eclipses. The devil!
The nights of Bath, and those of Dorpat
It is currently estimated that more than half of stellar systems located in a large portion of the galaxy around the Sun are actually double stars, or multiple systems with three or four stars or more. And so it is probably the same for the rest of the Milky Way, where the proportion is more difficult to verify. Among these double star whose components are physically linked to one another and will be called in a somewhat paradoxical « visual double stars, » some are pairs whose companions are quite widely separated in appearance as in reality, characterized by orbital periods may be counted in centuries, and whose appearance will change little or very little, if at all, during a human life, and others will be much tighter doubles, regular observation will highlight a small but real movement on the scale of a few years or less. The couple Mizar AB, for example, has an orbital period of at least several thousand years, while that of Sirius AB torque is 50 years.
This is Friedrich Georg Wilhelm von Struve (1793-1864) who first, discovered the duplicity of Alf Com in 1826. Newly graduated from the University of Dorpat in Russia – now Tartu, Estonia’s second city – the young Struve soon occupied most of his nights compiling as comprehensive catalog possible observable double stars from the northern hemisphere, up to 15 ° south declination reasonably accessible from the observatory; double stars for which there seems to be passionate since his very first work of 1813-1814, from that very formally, it was established astronomer at Observatoorium Dorpat, a new imperial institution.
Following a suggestion by Galileo hundred and fifty years ago, William Herschel (1738-1822, the discoverer of Uranus) was demonstrated in a long paper read at the meeting December 6, 1781 in front of the dignitaries of the Royal Society of London, the interest he had to measure double stars, and the method by which one could derive considerable distance stars.
Double stars, which we knew nothing, in truth, should be seen as a possible means, otherwise convenient access to the dimensions of the universe through the movement of their components, which could derive a measure of their hypothetical parallax, parallax which provided access indirectly then the masses of the stars measured by combining strong elegantly distance now known to the apparent brightness. Because we thought, essentially all the stars in the universe were identical, as were the faintest and most distant stars is called double did not show that in this aspect quite fortuitously two rating located on a line of sight, but in reality located at very different distances.
Herschel, William, On the parallax of the fixed stars, Philosophical Transactions of The Royal Society, vol 72, Londres, 1782.
And Herschel to tackle the task, and to seek, discover and observe as much as possible of double stars from the sky of Bath, England, where he had his observatory – preparatory work for future measures parallax.
The Catalogue of Double Stars by William Herschel, published in 1782 in the Philosophical Transactions, with addenda from 1784 to 1821 was, therefore, in the early nineteenth century, the reference catalog on the matter, with some 800 entries (795-827 depending on version). What was even too little to the views of young Friedrich Wilhelm Struve, which therefore watched tirelessly in the continuity of Herschel, unsystematically even before 1820, and then rationally, mainly between 1824 and 1827, a period during which he inspected all the stars that were accessible from Estonia, more than 120,000 up to magnitude 8 – visually, it goes without saying – reviewing 400 stars per hour. 120000 stars including 3112 he discovered celestial couples, which he carefully considered, subsequently, the brightness of the components and their separation, and for which he also measured the tilt angle of the couple. The Observatory of Dorpat was at its peak and Struve who in the meantime had become the director, had to do this, since 1824, in addition to the excellent craftsmanship transit instrument signed Dollond and small achromat five feet that were installed since his arrival, the largest achromatic telescope in the world, a great spectacle precisely the aim of which, a french diameter of 9 inches to 13 feet focal length, was cut by Fraunhofer. A telescope that frequently gave higher magnifications to 1000 times and, above all, an equatorial mounted clockwork allowed such long comments, comfortable and detailed as necessary; a real innovation.
The Catalogus novus stellarum duplicium and multiplicium by Struve was published in 1827. The star under registration number is STF1728 Alpha Com.
The Washington Double Star Catalog, as amended in 2012, provides a corpus of 657 STF1728 measures accumulated between 1827 and 2011. The first entry is a determination by Friedrich Struve dating from the very end of October 1827 (1827.83) observation probably done the morning of 30 or 31 at a time of year when the star observed since Estonia is low enough on the western horizon after sunset (15 ° elevation a hour after the end of the day) and much higher in the early morning to the east (27 ° elevation one hour before the arrival of the Sun). The two components of the stars, measured micrometer, then have a separation of 0.57 arcsec only, more or less the theoretical resolution of the instrument had Struve (2). But this should not surprise us too much, because the man was an excellent observer, very capable in difficult situations likely to accumulate countless measures of all kinds, we have seen in any conditions, provided that the sky was clear, including in June, a time of year when the observatory of Dorpat knows little at night, the sun refused to even venture to 8 ° below the horizon at the time the summer solstice.
Curiously, the last determined by WDS STF1728 listed at the time this article was written, determination date 2011.488 gives a spacing of components almost equal to what it was a little less than two hundred years ago, that is: 0594 dropoff window. Immobility of the couple, then? Widely separated components from each other in reality and showing a tiny movement across the centuries? Uncertainty in the measurements? We can of course remove these assumptions, since we know that Diadem is in close vicinity of the sun. Chance, then?
Already in 1797, Herschel had the intuition that the parallax of stars probably was not, after all, the real greatness that should be sought in the measurement of double stars. This parallax too narrow to be confused with the instruments at his disposal, he had hoped, but it was not coming. So what? Some fixed stars, not least, showed variations in brightness; it was a fact now established (3). Why would not she showed other changes in addition? Incongruous movements, perhaps?
After re-observed number of double stars in its catalog after twenty or twenty-five years of infidelity for some, Herschel had concluded that there was movement at times, that this movement was not random and that, rather, it was in accordance with the laws of gravitation, as long as we would accept that the protagonists are actually related – major paradigm shift.
Herschel, William, Catalogue of 500 new nebulae, nebulous stars, planetary nebulae, and clusters of stars …, Philosophical Transactions, vol 92, Londres, 1802.
Herschel kept his word. In a new article which was read at the meeting in June 1803 the astronomer appointed five stars which he had calculated the orbits and the period of revolution, and a sixth for which he announced a possible future conjunction between the two components.
- Alpha Geminorum (Castor) period equal to 342 years and two months.
- Gamma Leonis, a period of about 1200 years.
- Epsilon Boötis, a period of at least 1,681 years.
- Zeta Herculis star for which a term conjunction is possible between the two components.
- Delta Serpentis, a period of about 375 years.
- Gamma Virginis, a period of about 708 years.
Herschel, William : Account of the changes that have happened, during the last twenty-five years, in the relative situation of double-stars ; with an investigation of the cause which they are owing, Philosophical Transactions, vol 93, Londres, 1830.
This involved a new way of designing the star as an object possibly different from the Sun, with features that would soon detail.
A Dorpat in two decades at most, the indefatigable Struve accumulated so many observations and measurements of double stars that he was soon able to surpass the master, and establish irrefutable conclusions from the computation almost complete explanation to pure and hard, as to the true nature of the « double star phenomenon, » which he will draw up a fairly advanced portrait in 1837, in a pamphlet of sixty pages published in St. Petersburg: Ueber Doppelsterne nach den auf der Sternwarte mit Dorpater Frauenhofers grossem Fernrohre von 1824 bis 1837 Angestellten Micrometermessungen.
« It is remarkable that the suns can rotate around other suns so quickly, with a period of the same order as the planet Uranus takes to browse its orbit around the sun. We must conclude that either these suns are closer Uranus our sun, or that the total mass of the two stars, because of their speed is significantly greater than the mass of our sun. Comments should be discussed further and will lead to an obvious conclusion. Regarding the orbits of double stars, it seems that of ξ of the Big Dipper, as measured by Mädler, is the most reliable. If we knew the parallax of these 2 stars and consequently their distance from Earth, we could calculate the elements of the orbit and in particular flattening. For the moment, we are reduced to estimate, according to the latest information, one of the stars is about 2 million AU us. ξ of the Big Dipper is a star of 4th magnitude to which it is estimated the distance to 7 ½ million AU. Under these assumptions, and with a lot of arbitrariness, we can infer the relationship between mass and magnitude of these stars, and from their apparent magnitudes, describe these double stars as follows:
ξ of the Big Dipper is a double star whose two stars have masses equal to 117 times and 42 times that of the Sun, and therefore equal to 159 times that of our sun together. If we take these two bodies the same density as the sun, their diameters are respectively 4 and 3 ½ 9/10 times that of the sun. Their orbit is elliptical with a 60 ½ years. On this path, the average distance is 83 2/5 AU, almost 4 ½ times the distance Uranus-Sun. The minimum distance of 50 AU and the maximum distance of 117 AU. The inclination of their plane of movement is 37 ° 45 ‘relative to the ecliptic. Their apparent diameters, given the distance, are for 2 star: 1/400 « and 1/565″. By observing these two stars in our best telescope with a resolution of ½ », and in view of the atmospheric dispersion of light in the instrument and the eye, it must be discernible. « (4) (5)
The descriptive astronomy was born.
But back to Alf Com. In the final paragraphs of his brief, Struve notes:
« I have here two remarkable cases. ζ Hercules: in 6 years the companion star has completely disappeared and reappeared on the other side. The star 42 of Coma Berenices was twofold from 1827 to 1829 and is now larger than a single star sentence. In 1833, even with a magnification of 1,000 times, I saw a simple round shape without distortion. But in 1835, the star has increased again; and she appeared twice, well separated in 1836. It is likely that the companion star has not yet reached its end position, but will return to its former position in 8 years. It is difficult to estimate accurately because the light comes from stars that are too little spaced from one another, and it is also possible that there is a brightness change. « (5)
Thus, the behavior of the star ζ Hercules, had he revealed as predicted by Herschel many years ago (6); and the star 42 Comae Berenices showed the same propensity to be displayed in conjunction every 12 or 13 years, or every 24 or 25 years, it was not possible to serve it.
Nocturne, slow …
Following our story, as an ostinato-Larghetto, is in the soft, routine stirring patiently repeated observations, observatories observatories, repeated determinations of the orbit of Alf Com repeated determinations throughout decades and successive refinements of the orbital parameters of the star, with small touches.
Astronomy double stars had moved to Dorpat Pulkovo, Russia, just south of St. Petersburg, where Otto Struve – the son of Friedrich – observed stellar couples with the latest in home Merz & Mahler Munich, a real monster of optical and mechanical precision: an equatorial refractor 15 inches in diameter (38 cm), new bigger telescope in the world.
Struve, Otto, Observations and orbit of the double star Σ 1728 = 42 Comae Berenices, Montly notices of the Royal astronomical Society, 1875.
Orbital diagram of Alf Com, as described by Otto Struve, Monthly notices of the Royal Astronomical Society in 1875.
The components of the pair forming Alf Com was so tight in 1895 as the American astronomer Thomas Jefferson Jackson See could not see the star in a form oblong hardly eye of the Clark telescope 26 inches from Leander McCormick Observatory in Virginia, with a magnification of 1300x. Using his observations and any that had preceded it drifted orbital period was equal to 25,556 years.
(See TJJ, On the orbit of 42 Comae Berenicis, Monthly notices of the RAS, 1896 sup.)
The determinations of the orbit of Alpha Comae Berenices then successive regularly, every time a bit more accurate.
Bibliography or « selected pieces » from a century of astronomical papers published in any language about Alpha Com and available online – without counting the innumerable steps publications.
- Doberck W. 1908
- Aitken Robert Grant 1918
- Laves Kurt. 1927
- Crawford R. T. 1928
- Haffner H 1948
- Pavel F. 1949
- Lippincott Sarah 1961
- Hartkopf W. & al 1989
- Hoffleit Dorrit 1996
- Bartkevicius & al 2001
- Pavlovic & al 2005
- Zasche & al 2009
- Hartkopf & al 2010
Basically, the question implicitly raised by Friedrich Struve in 1837, it was whether or not Alf Com occurred at intervals, real eclipses that could be observed, and not mere appulses (or reconciliation) which probably would have resulted in this nineteenth century infancy scientific progress, to connect two still very distinct phenomena: the visual double stars and eclipsing binary, with Algol (Beta Persei) became the archetype and thus to make a big step in the description of the star as an object rather than physical as mere abstraction. But this, Struve probably was not aware, even though the idea had been issued by John Goodricke, an extremely young English amateur astronomer who had a tragic fate, this from 1782, while Herschel was still regarded as the stars were double in appearance. The brightness variations of the star Algol were known since the middle of the seventeenth century, but it is Goodricke who demonstrated their periodic and attributed them an explanation quite plausible, unverifiable at the time: c ‘is an invisible companion of Algol, which regularly before passing the main star, producing eclipses. In fact, the couple is so tight that it is impossible to observe as such to the eye; only its eclipses, which are held every 2 days and 21 hours betray. Eclipses which are highlighted by tracking over time the changes in brightness of the star. Modern catalogs contain thousands of eclipsing binaries, the orbital period is from a few tens of minutes to several hundred days.
The Eclipsing Binary Simulator, a fun tool to become familiar with the phenomenon of « eclipsing binary »
Whether Alf Com produces eclipses !
Sarah Lee Lippincott in 1961 showed that eclipses Alf Com were undeniably possible: maximum of two hours duration, essential monitoring over several days, the date of the combination can not be determined with precision.
And then … nothing ! The literature reports no observation or even any attempt to observe the phenomenon priori.
The last opportunity dated to highlight eclipses Alf Com was calculated for 1989. Using data from many observations speckle interferometry (speckle interferometry) conducted over a dozen years, especially with the 4 telescope meter Kitt Peak (accuracy: Possible separation components around 0025 « and even 0001 » on the brightest stars), William Harold McAlister and Hartkopf of Georgia State University in Atlanta predicted a total or partial occlusion of a star by the other for February 15, 1989, with an uncertainty of plus or minus two weeks of the date, characterized by a general decrease in brightness torque between 0.1 and 0.8 magnitude over a period of 1.3 days. While stressing that the absence of eclipse was also possible because the orbital inclination of the couple was measured at 90,063 ° +/- 0.04 ° (circular CBAT 4678 of 22 November 1988). The two researchers also notaient the orbit calculated by them was somewhat different orbits previously calculated from micrometric observations. The Sky and Telescope magazine launched the alert in its February 1989 issue (Vigil for a single stellar eclipse): « Imagine two ping-pong balls separated by 200 feet (60 meters) orbiting around each other all 26 years. You have a good scale model of the visual binary star Alpha Comae Berenices, a pair of dwarf type F6, slightly larger and hotter than the Sun … « . And then …
And nothing more. It seems that the star has not been sufficiently followed in 1989, a conclusion can be drawn in one direction or another.
Half an orbit later, or in the course of 2000, took place another conjunction between the two Alf Com components, but this time, no date was given for the occurrence of any eclipse, and n ‘there was no supervision. But we will return.
The next « window » observation is given for the month of January 2015. The orbit this time is determined by Matthew Muterspaugh (Tennessee State University), William Hartkopf (US Naval Observatory), and colleagues: The phase differential astrometry data archive. II. Updated binary star orbits and a long period eclipsing binary, The astronomical journal, december 2010.
To characterize the orbit of Alf Com, visual data were taken into account, over a very long period, as well as comments by speckle interferometry, high-flying astrometric observations (accuracy of about 35 for μas the positioning of the stars on tight couples) and spectroscopic observations (radial velocity determinations, with some doubts, it seems, in the case of Alf Com); all combined for better accuracy on the subject than anything that has ever been published. The combination would have on 24 January 2015, nearly three or four days (« Within about a week to »), it would take 1.5 days, and the tightest approach would be to 0.32 mas. Putting things in the worst case (1 σ error on the estimated distance of the star and the inclination of the orbital plane – reasonable error), add Muterspaugh and Hartkopf, there would still eclipse, but this one would be a little less deep as no separation would be equal, at best, 0.38 mas; other errors on the orbital parameters would only shift the date of the phenomenon. Finally, the authors point out that this is the very geometry of the couple that prevents the occurrence of eclipses with a delay of half an orbital period (as in the conjunction of 2000); namely, with an inclination of the orbital plane of Alf Com equal to 90,054 ° and an eccentricity to 0.4957, new calculated values, the couple’s separation is not less than 0.9 mas then, and under these conditions, the stellar disks not even tangent.
Considering an apparent diameter roughly equivalent to 0.7 mas for both stars, the eclipse of January 2015 would have a magnitude of about 0.50 or so, the more favorable, and brightness decline could reach 20 % .dropoff window It would still be equal to 15% in less favorable conditions, which is still accessible to the amateur observation in a very large extent.
But before going further, briefly summarize what we know about the components of Alpha Comae Berenices.
Alf Com AB is a very homogeneous system, with A and B components almost similar brightness, of 4.98 magnitude for the component A, and 5.18 for component B (VSX / Hipparcos). These are main sequence stars of spectral class F5 / F5 (some sources give F6 B). The overall mass of the system is commonly estimated at between 2.4 and 2.8 solar masses, with the A and B 1.43 1.37 solar mass (Muterspaugh Hartkopf and estimate the total at 2.45 solar mass). The surface temperature of these stars is given for equal to 6600 degrees and individual luminosities of the two components worth 2.7 and 2.0 times that of the Sun (case F5 / F6). Their actual diameter is about 1.25 solar diameter. The semi-major axis of the orbit is estimated at 12.5 AU. The orbital period determined by Muterspaugh and Hartkopf is 9485.68 days (25.97 years).
For the record, the WDS mentions the existence of a companion in Alf C Com. This is a 11.45 magnitude star located at 87.20 « Alf Com AB, angle 346 °, for the year 2001. The WDS cites only 13 records position between 1851 and 2001 for this star. Besides the name STF1728AB, C was assigned, it is pointed at the UCAC4 catalog under the number 538-054275; its position is: J2000 AR: 13h09m57.750s DE: + 17 ° 33’11.46 « . But we will only mention its existence because its membership in Alf Com system is controversial. For the record, we will give proper motions of STF1728AB and STF1728C mas / year in RA / Dec or -433.13 / 141.24 and -11.8 / -1.0, from which everyone will be able to form an opinion. Parallax companion C and its spectral class is not known.
The golden age of the french science of the binary stars
Up : André Danjon with a 49 cm refracto, Observatoire de Strabourg, micromètre interférentiel à demi onde, 1935-1938.
Middle : Paul Baize with the 38 cm equatorial, Observatoire de Paris, 1951-1953.
Bottom : Paul Couteau with the great 74 cm refractor, Observatoire de Nice, 1972-1973.
An eclipse every 26 years in the hair of Berenice, for the recollection of a queen, then. But for what benefit?
Alf Com is an absolutely unique, as far as we know. This is the only visual double star that is likely to produce eclipses. If the 2015 combination is not properly followed, it was not until the year 2041 for a new opportunity for a final response to the nagging question of « invisible eclipse » or not there are-t it, and if so, when? But it is here that a first somewhat superficial reading grid. A key, a formidable constraint for theorists, who can put their comments in perspective and refine their orbital calculations to better speculate Alf Com. What is at stake in the end, the respective masses and diameters of its components and other fundamental data, essential details to understand the physical phenomena at work in the stars and get in return a better calibration of the solar neighborhood and the more distant universe.
The most pragmatic approach is to consider that the estimate of Muterspaugh and Hartkopf is good, that the combination will be in the predetermined time range, and if there is eclipse the brightness down will be close to 0.5 0.8 magnitude, making its detection available to any observer, even with very little and / or moderately familiar with the brightness of variable stars estimation methods. The visual observation practicable, going easier. In this case, care should be taken to observe at least once or twice a clear night (do not forget that it is winter and there will perhaps not many nights off during the period it will therefore be necessary to make some effort not to repeat the failure of 1989 …), to the naked eye or with a small pair of binoculars, from 20 to 30 January 2015. Although identify the area and familiar with the brilliance Alf Com normal early in January if we have the opportunity, would be a good idea. The goal here is not to make a precise measurement of the brightness down – yet – but just to identify the occurrence of the eclipse – which can both last only a few hours – and give an alarm immediately to the canvas on up to the forum and mailing lists astronomical across the country and especially abroad (do not hesitate, given the rarity of the phenomenon, to relay information, including in broken English to list a priori not affected, even to make « off-topic », although it will always find at the other end of the keyboard, an observer can pursue ongoing observations). Postpone the time of observation to the minute should be sufficient.
If desired, it is quite possible to attempt a visual estimate in glory; This is not very difficult first approach. The detection limit is generally accepted to 0.1 magnitude variation for a seasoned observer. The French Association of Variable Star Observers (AFOEV) offers a comprehensive protocol that can be found here:
A more obvious, if we have the opportunity, would take at least a few photographs of the area of sky showing Alf Com, observed every night, even if it does not detect brightness down to the eye priori. A target of 50 to 100 mm on a simple tripod, if we do not have better, will do nicely as installation time should not exceed a few seconds, so as not to saturate the stars (Alf Com very bright). Care should be taken to properly fit the double at the center of the image and to have comparison stars in a fairly wide field. Proceed by short « bursts, » with a trigger, possibly bracketant and repeating shots every ten minutes, for example. Arrange to have offset images / flat / dark (for more information about the calibration of images), would be even better, although it is primarily here to objectify a burst down, not to make measurements at a millimagnitude closely. The images can be taken with any digital camera capable of working in RAW raw mode; the best thing to do prior tests. IRIS software (freeware: http://www.astrosurf.com/buil/iris/iris.htm; many tutorials), after a short period of grip, makes it easy to deal with its camera images to make measurements very precise brightness after converting to TIF format. The software also allows to estimate if the time of poses that are applied are correct; used for this, the test images, the « cut » function: all stellar image with a tray in top curve is saturated and unusable for a measurement of gloss.
Iris : the « cutting » tool – Alf Com 5 sec exposure FS102 f6 – The star appears saturated despite the very short exposure of 5 seconds. Defocused images with this setup seems imperative. Increasing the exposure time will result in better accuracy.
Monitoring the eclipses of the star Algol, in December or January could be an excellent training in the visual estimation or shooting. The star varies between magnitudes 2.1 and 3.4 back in about 12 hours. We find moments of minima provided on the Olivier Ravet page. A little app (link on the author page) assesses at any time the status of the binary and estimate the brightness in advance or afterwards. The software also allows to determine the moments secondary minima, which are not deeper than magnitude 0.1, and also last twelve hours, and whose follow-up will train the precision photometry.
[Note : for a better precision on the timing of the minimas go to the VSX page, « Ephemeris »]
Alf Com of images captured during the winter 2014-2015 will potentially valuable, even if they seem to show nothing; although archive these images in RAW format, or FIT, and destroy any. Take care to note also observed for each range, including in case of negative report, the start and end of the observation, in order to better constrain the phenomenon. Also, think about putting his camera at the time (second) on the speaking clock, for example.
We said a little earlier that the 1989 combination was not followed enough to show anything. It is not perhaps not accurate; that’s at least what the Wiki page devoted to Alf Com says, but without any reference (by the way, there was error from one year to the date of the combination as shown on the same page …) ;dropoff window in reality, we could not find any text or paper stating the results of the 1989 observation campaign that would have to get a better idea of what to expect observers in 2015. When contacted about this, the AAVSO has not responded to the date we are publishing this article … Also, basing observations of this combination on the single prediction Muterspaugh and Hartkopf and be limited to one (very) short end of the monitoring window in January would probably demonstrate a valiant optimism. No doubt it better to subject themselves to a wider observation, from January 1 to March 1 for example. After all, during the winter, clear nights are not so many as that.
Calendar for Latitude 45 ° N and Longitude 0 °:
(Day / rising of Alf Com / altitude 20° / dawn / Alf Com high at dawn)
- 15 December : 00h20 20° : 02h20 : 05h46 / 54°
- 01 January : 23h09 20° : 01h13 : 05h53 / 61°
- 15 January : 22h14 20° : 00h18 : 05h51 / 62°
- 01 February : 21h07 20° : 23h07 : 05h40 / 58°
- 15 February : 20h12 20° : 22h13 : 05h24 / 54°
- 01 March : 19h17 20° : 21h17 : 05h02 / 49°
Assiduous photometric monitoring Alf Com throughout the period indicated is a fascinating project that would perhaps detect a marginal eclipse of the star with a little sensitive brightness decline that would otherwise be difficult or even undetectable objectivable to the eye. This would also help to identify, if we have this chance then to be under a beautiful starry sky at the right time, the beginning or end of the phenomenon,
which will be very gradual. It will, for this, have a little more equipment; but again, with the same low amateur can do an excellent job. A small motorized equatorial mount on which to mount a camera, a camera dedicated to global or entry-CCD equipped with a telephoto lens will be more than enough. The avowed aim is to achieve an accuracy of a few hundredths of magnitude. Alain Klotz (CESR, Toulouse) and Jean-François Le Borgne (Observatoire Midi-Pyrénées, Toulouse), in particular, have shown that a facility of this type, the uncertainty of the data could be as good as on a 0.03 mag star 11.5 in five minutes exposure (10 times 30 seconds), and much better even on the brightest stars (0.01 on a 7.0 mag star).
Klotz et Le Borgne : VTT (very tiny telescope) : Automatisation de l’observation d’étoiles variables brillantes, Note circulaire GEOS nc 1105, 2009.
There is pressing need this time to follow a rigorous methodology: the images have to be calibrated and instruments and computers at the time the second before each observation. A light optical defocus will spread the stellar images, in order to avoid saturation. Perform some tests beforehand; in particular, ensure that the light from a nearby star does not come to mingle on the images to that of Alf Com. One to three images continuously with an exposure time of a few seconds at most every five minutes (150 to 500 pictures per night) are expected to provide sufficient temporal resolution. If necessary, refer to the tutorials signed Christian Buil (IRIS): http://www.astrosurf.com/buil/iris/tutorial15/doc38_fr.htm
For a few more nights
The amateur astronomy (and professional) is a combat sport, or:
And now a little astronomy fiction …
In 1995, Michel Mayor and Didier Queloz demonstrated, using the spectrograph ELODIE T193 to the home of the OHP, the exoplanets were a reality by finding a « hot Jupiter » around the star 51 Pegasi 5.49 magnitude. Almost 2000 planets have since been discovered, in particular by the method of the analysis of radial velocities (spectroscopy) and by observing transits – especially -. Among this large population, about sixty planets orbiting binary stars, which is a lot and little faith. Little, because there is an observational bias, this type of research, known delicate yet there is little, having been undertaken belatedly. Several interesting cases were discovered using the Kepler satellite Kepler Kepler systems 16 and 34, for example, are systems quite extraordinary.
It has been shown that the distribution of matter in binary systems was quite largely subject to the rule of coplanarity: when planets form around double stars, their orbital plane coincides with that of the parent stars. The process is complex, but it is broadly equivalent to that which is at work around single stars, except that there are privileged areas where bodies can form through accretion and remain (stable areas) and areas where planet formation may not take place because the relative velocities of the particles involved, too high, do not allow the accretion – the impacts are too violent.
There are two populations of planets around double stars (or multiple) type planets P (P for planetary) whose orbits are circumbinaires (they orbit the common center of gravity of the two stars companions and are therefore physically far their suns), and type of planets S (S for satellite) orbiting the primary star (circumprimaires orbits) or the secondary star (circumsecondaires orbits). Recent (type S) are, by necessity, much closer to their stars than the P-type planets, in generally narrow stability zones, within which the companion star gravitational force has little or no influence at all. The planets that have been discovered in binary systems to date are of two types. But their number is still largely insufficient for comprehensive studies to be erected on the subject. Discover new ones is highly expected by experts exoplanets.
Alf Com is quite interesting in that the inclination of the system is close to 90 °, as we have already said. It has been quite widely studied under the theoretical angle of the possibility of the existence of planets within it. Without going into details, just note that the extent of orbital stability zones were calculated in three studies for components A and B (1 and 2 studies are dated 2012, while the study is 3 oldest: 1998 references below). In all cases, the rating is considered a slightly different mass: spectral class F5 / F6.
Kind of stability zones S, outer limits in terms of semi-major axis, the internal limit being the star itself:
A: 1.465 AU (Study 1) or: 1.45 AU (Study 2) or: 1.49 AU (Study 3)
B: 1.339 AU (Study 1) or: 1.42 AU (Study 2) or: 1.45 AU (Study 3)
Revolution period calculated for a planet located on the outer edge of S-type stability zone:
A: 372 days (Study 1) or 555 days (Study 3)
B: 346-349 days (Study 1) or 544 days (Study 3)
As regards the P-type area of stability, it extends beyond 41.08 UA or UA 45 (semi-major axis) in the case of Alf Com for study 2 and 3. Period of revolution a planet located on the inner border of P-type stability zone: 182 years (study 3).
The situation is not clear so far, as it is actually possible planets may exist in the Alf Com system. Research has been carried out and probably some others may be pending at this moment, but we found no trace in the literature, and for good reason: there is stiff competition between research teams … To date, what we can say is that no planet is discovered and officially announced.
The star was necessarily monitored in terms of transits by several programs, but if no phenomenon of this type has yet been discovered in Alf Com, one can deduce that the likely absence of planet type « Jupiter hot « in the area quite immediately the two components, which does not exclude that the giant planets may be at greater distance. Another detail: most automated exoplanet research programs are designed so that they can monitor the broader population of stars possible; moderately faint stars being the prime target, this excludes, by definition, the bright stars, few and that is sacrificed, which appear as saturated images; there may have been incorrectly followed Alf Com to think from this point of view, there is not one that can be attempted to cross …
Being spectroscopic observations (radial velocity studies), nothing is clearly not established and the numbers can be found are quite contradictory and very ample sources said. The relative proximity of the two components of Alf Com seems herring. Probably can we conclude, once again, that no giant planet is close to one of the components. But all this is still « to be taken lightly » because observational difficulty is real, so that photometry spectroscopy.
Include the three studies which the boundaries of stability zones around Alf Com were drawn:
- Study 1 : Eggl S., Pilat-Lohinger E. et al : Circumstellar habitable zones of binary star systems in the solar neihborhood, Monthly notices of the RAS, 2012,
- Study 2 : Jaime L. G., Pichardo B. et Aguilar L. : Regions of dynamical stability for discs and planets in binary stars of the solar neighborhood, Monthly notices of the RAS, 2012.
- Study 3 : Holman M. et Wiegert P. : Long-term stability of planets in binary systems, arXiv, 1998.
And two articles of great interest, too, about the formation of planets in binary systems:
- Thebault P. (Lesia, Observatoire de Paris) et Haghighipour N. : Planet formation in binaries, arXiv 2014.
- Holman M. et Wiegert P. : Long-term stability in binary systems, arXiv 1998.
Christian Buil, tireless pioneer and passing skills, greatly innovated in the field, and demonstrated as early as 2005 that the detection of known exoplanets transits was within reach of the amateur, this sometimes with surprisingly small optical (telephoto 200mm f2.8), behind which were installed only single APN. The accuracy obtained in excellent conditions can then be equal to 0.001 magnitude. The XO professional project (McCullough et al: The XO Project: Searching for Extra-Solar Planet Transiting Candidates 2005) proved that it was possible even to discover exoplanets with very good but very small optical; and the gas giants of the series XO (XO-1b XO-5b) have they been discovered with lenses 200mm open 1.8 (110 mm diameter) and very short exposure time (a few tens of seconds, in automatic mode) – albeit from high altitude observatories.
Amateur determined may therefore consider systematic monitoring Alf Com during the winter 2014-2015, « just in case ». We start from the assumption that the forecast Muterspaugh and Hartkopf is essentially correct: in this case we have the S-type stability zone of a component of a binary system that will potentially pass before its companion star, which does has never been observed before. Or, at least, we will observe the scrolling of a « half planetary system » because, do not forget, the magnitude of the eclipse is only 0.50 maximum. In these conditions, only a planet whose orbit is slightly inclined relative to the common orbital plane can scroll and show transit. This is pretty good: it has been shown (Cited) in binary systems, even at an orbital zone of stability, the chances of formation and survival of a planet are a little better slightly outside the plane orbital.
The observation window will last until early summer, with a probability of positive observation will decrease to become zero when the S-type stability zone will fully show (about 180 days – estimate – before and after the conjunction of 24
January 2015, the phenomenon has started at the end of the summer of 2014 but it was impossible to observe because of the proximity of the Sun). A giant planet will be sought large radius or very large radius (several Jupiter), only likely to make its mark in silhouette in front of the disk of a star F5 or F6 kind, much brighter than the Sun; a planet located quite a distance from its sun and would not let legibly spectroscopy brand. The expected decrease in brightness is about 0.3% for a few hours for an object the size of Jupiter, a fairly low down in the end, since in reality it is the light of two stars F5 or F5F6 a couple, and not that of an isolated star, we raise our combined optical at the time of any transit. The difficulty is rather high. For comparison, when we observe the transit of the exoplanet type « hot Jupiter » TrES-3b, brightness lowers to 2.6% … but then monitored star of spectral type G, is only 12.40 and magnitude the signal is 1000 times lower than in the case of Alf Com; such transit is easily accessible with a telescope of 100 mm, however.
TrES-3b transit observed with a 100 mm / CCD :
Transit of HAT-P-23b, also observed with a 100 mm / CCD. The planet highlight is again a « hot Jupiter » 2.09 Jupiter masses and 1.368 Jovian radius; Brightness down during the phenomenon does not exceed 0.0076 magnitudes and monitored star of 11.94 magnitude of spectral class G5.
Transit HAP-P-7b observed with a telescope of 200 mm / CCD. The planet is still a « hot Jupiter » 1.8 Jovian Jovian mass and radius 1.42, orbiting in a little over 2 days around a star of spectral class F6 magnitude 10.5. The drop in brightness during transit is equal to 0.0067 magnitudes.
One strategy in the case of Alpha Comae Berenices: instrument stationary, unit poses 3 to 5 minutes with a camera, or – much better – a CCD in defocused mode, reduced sensitivity to minimum (maximum resolution ./ filter …) with an equal or higher optical 200mm. The report FD instrument is not a discriminating criterion to the extent the observed star is very bright and the signal / noise ratio at its best: so the rise (Barlow) if required / opportunity. Rest of the problem … the sky is sometimes unusually dry nights, transparent and photometric winter. Promote environmental chilling imagery significantly reducing the background noise.
Moreover, we must be clear: beyond the part of the dream, it is highly unlikely that an isolated amateur detects anything orbiting Alf Com; it is almost a professional job that requires weeks of diligent tracking; work that could be likened to looking for a needle in a haystack in which we are not even sure that there is a needle to find. Especially since the geometry of Alf Com system will only allow the survey, in the end, only one-third of the area could be a possible giant planet between December 2014 and June 2015. But who cares! This is a whole new way to push the « exoplanet investigation » beyond its normal limits, leading her outside the orbital plane of a binary, outside the transit area « ordinary, « and out of the area easily accessible by spectroscopy. In automatic mode, and in the context of international cooperation with ongoing monitoring of the star … everything would become almost possible … on paper! Anyway, the opportunity is unique: an attempt every 26 years, we have already said. And nothing to show at all, after weeks of observation, with a resolution of only a few millimagnitudes, asking the things worse, that would be greatly constrain the study of Alf Com system, which would be a good result yet a small group of committed fans.
To learn more about observing transits of exoplanets:
Buil, Christian : Observation of HD189733 b
Gary Bruce L., Exoplanet observing for amateur, Reductionist Publications, d/b/a, 2007.
(1) Cypris: The Cypriot name of the goddess Aphrodite.
(2) This observation, and seven made by Struve from 1829 to 1837 listed at WDS, are not included in the Observationes astronomical institutas in specula caesareae Dorpatensis, vol VII, gathering the Struve observations for the years 1827 to 1831. They are given in Duplicium Stellarum and multiplicium mensurae micrometricae, Saint Petersburg, 1837.
(3) On this subject, read: Herschel, William : On the method of observing the changes that happen to the fixed stars …, Philosophical Transactions, vol 86, 1796. See also: A Third Catalogue of the Comparative Brightness of the Stars … , Philosophical Transactions, vol 87, 1797, and: A Fourth Catalogue of the Comparative Brightness of the Stars, Philosophical Transactions, vol 89, 1799.
(4) The parallax of 61 Cygni, the first star whose distance was known, was measured by Bessel in 1838.
(5) Translation Christian Joye. The full text is appended below. Struve, Friedrich GW, Ueber den Doppelsterne nach auf der Sternwarte mit Dorpater Frauenhofers grossem Fernrohre von 1824 bis 1837 Angestellten Micrometermessungen, Saint Petersburg, 1837.
(6) In reality, Struve is mistaken: the period of ζ of Hercules, which is now well known, is equal to 34.45 years, and the orbital plane is inclined torque to 131 ° only. The separation between the two components, 2.95 and 5.40 mag, is never less than 0.5 ». So this is a configuration that is far removed from that by which presents the couple Alf Com AB. Perhaps the difference in brightness between the two components is it the source of the error ?
Friedrich Struve GW: Ueber Doppelsterne nach den auf der Sternwarte mit Dorpater Frauenhofers grossem Fernrohre von 1824 bis 1837 Angestellten Micrometermessungen, Saint Petersburg, 1837.
Full text. From a translation in french of the original text in german. Translation Christian Joye.
The most important result of my actions is finally in [the discovery of] changes the positions of double stars, associated with their movement in their orbits. I show that by comparing the results of my actions with older Herschel results we have:
58 double stars for which the change is certain,
39 double stars for which the change is likely,
66 double stars for which the change is possible.
These changes are not related to a movement of the stars, but rather to a change in relative positions of a star with respect to the other, so as a consequence of their physical connection. This leads to the conclusion that most of the observed changes, ie 48 out of the 58 listed above, is rooted in [the relative positioning of the stars] and, among others, more change is observed when they closer than when it recede. The observation of the latter leads to an important proposal which can be written as:
« The orderly classification of double stars as the apparent distance between the two suns should not be based on appearance alone, but must take into account the angle at which they are observed, and this, whatever the distance. There are many more type 1 double stars separated by less than 1 « and somewhat distant from one another, that type stars 2. Their mutual attraction is the only evidence highlighted by a moving faster and shorter. do you even lift
Savary, Encke, Herschel II [John, son of William] and Mädler managed to calculate the orbits of some double stars from observations assuming the simple laws of Kepler could apply. Is precisely known periods of 4 double stars has traveled a full period, almost, since the Herschel measurements. For 3 other double stars with sufficient precision we know their grace period for comments on some of their trajectory.
These stars are:
η Corona Borealis, 43-year period,
ζ of Cancer, 56 years,
ξ of the Great Bear, 60 years,
ρ of the Serpent, 80 years,
σ Corona Borealis, 200 years,
Castor period of 215 years,
γ of the Virgin, a period of 513 years.
It is remarkable that the suns can rotate around other suns so quickly, with a period of the same order as the planet Uranus takes to browse its orbit around the sun. We must conclude that either these suns are closer Uranus our sun, or that the total mass of the two stars, because of their speed is significantly greater than the mass of our sun. Comments should be discussed further and will lead to an obvious conclusion. Regarding the orbits of double stars, it seems that of ξ of the Big Dipper, as measured by Mädler, is the most reliable. If we knew the parallax of these 2 stars and consequently their distance from Earth, we could calculate the elements of the orbit and in particular flattening. For the moment, we are reduced to estimate, according to the latest information, one of the stars is about 2 million AU us. ξ of the Big Dipper is a star of 4th magnitude to which it is estimated the distance to 7 ½ million AU. Under these assumptions, and with a lot of arbitrariness, we can infer the relationship between mass and magnitude of these stars, and from their apparent magnitudes, describe these double stars as follows:
ξ of the Big Dipper is a double star whose two stars have masses equal to 117 times and 42 times that of the Sun, and therefore equal to 159 times that of our sun together. If we take these two bodies the same density as the sun, their diameters are respectively 4 and 3 ½ 9/10 times that of the sun. Their orbit is elliptical with a 60 ½ years. On this path, the average distance is 83 2/5 AU, almost 4 ½ times the distance Uranus-Sun. The minimum distance of 50 AU and the maximum distance of 117 AU. The inclination of their plane of movement is 37 ° 45 ‘relative to the ecliptic. Their apparent diameters, given the distance, are for 2 star: 1/400 « and 1/565″. By observing these two stars in our best telescope with a resolution of ½ », and in view of the atmospheric dispersion of light in the instrument and the eye, it must be discernible.
Among the seven periods listed above, the period of η Corona Borealis is the shortest with 43 years.
It is found that these stars are closest to each other, since their apparent distance, even at maximum magnification remains less than one second. Many other double stars are even closer, this suggests that the period should be shorter. One can imagine that very short periods must exist for many double stars. It is not implausible that for ζ Hercules, the period is 14 years and for 42 of Coma Berenices it is perhaps even shorter [note: the original text quotes the star 42 of the Corona Borealis, which does not exist]. In a few centuries, astronomy reach a much richer level of knowledge in this area for which I have laid the foundation through my work.
Very short periods for double stars are observable changes in their position relative to the surrounding stars. But also for the double star longer period, it should be seen in a short time they change position when the eccentricity of their orbits is great.
To conclude I will speak of remarkable observations I have made in this area.
Already in my 1827 catalog, I spoke of 15 double stars listed by Herschel, I saw as triple star. I can describe this with the power and quality of the optics of Dorpat telescope, although it is possible that one or the other of these close companions could be seen by Herschel; these stars were hiding each other. Herschel had noticed this overlap phenomenon of a fixed star by another 2 star ζ δ Hercules and the Swan, where he saw a fellow in 1780 he could not find 20 years later. It is only since 1825 that I could find this companion, but in a different place.
In the same way as the star Herschel, I analyzed with micrometric measures and resolved 20 stars of my catalog, increasing the number of double stars near one another. This is undoubtedly due to the possibility of a better resolution and higher magnification related to optimal conditions. And therefore, it can be argued that a number of stars will be resolved only later, as they are really too close to each other right now. The star of the Snake τ is a notable example. Herschel had seen twice. My introduction to the 1827 catalog, I noted that this was the only star Herschel catalog for which the power of Dorpat telescope was put into default. The admirable reliability with which Herschel led his observations was rented many times, so I have no reason to imagine a mistake on his part. So I considered wise to follow that star diligently over a long period. Already in 1827 I pointed my telescope the star, two years earlier, was perfectly round. A small change in its form was no longer any doubt in 1835 and, in 1836, I recognized two separate stars. I needed a huge magnification to separate light from two different stars who obviously were very close to each other. It is easy to understand that, see 2 suns superposition phenomenon forming a double star, seen by us earthlings, is particularly difficult when the direction of their movement is facing the earth and we can only see the intensity, so to speak.
My observations on the basis of their trajectories and their movements and phenomena that they generate, can be summarized into 3 types:
1) There are stars that have been observed in the past as double stars that are so close that one can hardly guess lengthening or simply observe. Eg The Star Atlas of the Pleiades, η Hercules, ω Lion, γ Corona Borealis, γ of the Virgin, and the star No. 2173 of my catalog. Among these stars, the penultimate is remarkable because, despite its long period of 500 years, and due to its high eccentricity and extraordinary angular velocity, orientation has changed over the last 2 years (1834-1836) of not less than 80 degrees and above 130 degrees since 1822. at the same time, the gap was reduced from 3 « to 3/10 ». The star that already for over 100 years appeared as a double with a small telescope, is now easily visible with the biggest telescope. Herschel had published the star appeared as easily doubled since the observatory. A Dorpat and Berlin, it appears qu’allongée, as with the seat in Munich.
2) There are the stars that previously were simple and have become double. Among them, the Serpent and τ ε Petit Cheval. Other stars from single to double, as 44 of Bouvier and many others.
3) There is a connection between the two phenomena. I have here two remarkable cases. ζ Hercules: in 6 years the companion star has completely disappeared and reappeared on the other side. The star 42 of Coma Berenices was twofold from 1827 to 1829 and is now larger than a single star sentence. In 1833, even with a magnification of 1,000 times, I saw a simple round shape without distortion. But in 1835, the star has increased again; and she appeared twice, well separated in 1836. It is likely that the companion star has not yet reached its end position, but will return to its former position in 8 years. It is difficult to estimate accurately because the light comes from stars that are too little spaced from one another, and it is also possible that there is a brightness change.
For more information (historical background)
Bayle Pierre – Dictionnaire historique et critique, tome premier. Leide, 1730.
Bevan Edwyn R. – The house of Ptolemy. A history of hellenistic Egypt under the Ptolemaic dynasty. 1927, Chicago 1968.
Callimaque – Oeuvres de Callimaque, traduction nouvelle avec notes de Joseph Trabucco. Paris, 1934.
Dobias Lalou Catherine – Figures féminines en Libye antique : les reines. 2012
The Lagides Queens : les Bérénice.
La dynastie Lagide.
Struve, Friedrich G. W. :
Tartu Observatorium (Dorpat) :
Bayerischen Staatsbibliothek : texts in latin, german and french from Struve, Friedrich G. W.
Struve, Friedrich G. W.: Catalogus novus stellarum duplicium et multiplicium : maxima ex parte in specula Universitatis Caesareae Dorpatensis per magnum telescopium achromaticum Fraunhoferi detectarum ; Doparti 1827.
Struve, Friedrich G. W., a short biography :
Herschel William : Double star catalogues