ESTABLECER LA OFERTA Y DEMANDA DEL MANGOSTINO EN EL DEPARTAMENTO DEL META

The first mention of the term “double star” was made in Ptolemy’s Star Catalog (2nd century AD), to identifyν1 andν2 Sagittarii asδιπλoυς (Heintz 1978). While this pair, separated by

14′

in our sky, is not physically related, its appearance as a double star is consistent with the modern definition of the term. In fact, when astronomers began telescopically studying dou- ble stars, starting with Galileo’s observations of the double star Mizar in about the year 1617 (which was independently measured and published by Riccioli in 1650), they presumed that these stars were not physical associations, but rather chance alignments of stars separated by a great distance along the line of sight. In 1767, John Mitchell first argued that the law of probabilities suggested that double stars are likely to be gravitationally bound (Aitken 1964). The earliest organized studies of double stars were initiated by Christian Mayer and Sir William Herschel in the last quarter of the eighteenth century. Mayer published the first catalog of double stars in his 1779 book, and Herschel undertook a systematic search for double stars at around the same time. Once again, these astronomers assumed that they were studying chance alignments of stars separated by large distances, and they hoped to measure differential proper motions to derive a parallax to the nearer star, as was proposed by Galileo. In any case, this began an era of careful measurements of the separations be- tween double stars using micrometers. By 1802, Herschel, based on his own observations,

and the persistent input from Mitchell, separated his observations into optical double stars (chance alignments of unbound stars) and binary stars (gravitationally bound pairs), and his publication in the following year demonstrated that orbital motion was the only reasonable choice in describing his observations for six pairs, including Castor.

Double star astronomy continued over the ages through stalwarts such as Sir John Her- schel (William’s son), Sir James South, and Sherburne W. Burnham to F. G. Wilhelm Struve, who is credited with taking this science to a new level with the publication of the Mensu- rae Micrometricae, a fundamental catalog of double stars, in 1837. In this catalog, Struve adopted John Herschel’s earlier suggestions of recording the epoch of each observation, and measuring the position angle of the pair’s separation in degrees from 0 to 360, starting at north and going towards east. These conventions are followed for double star work to this day. The early work of double star astronomy continued with other legends in this field such as Otto Struve (Wilhelm’s son), W. R. Dawes, and Admiral W. H. Smythe through the mid 1800s, and by this time, methods had been developed to derive orbital elements from the observations of Visual Binaries (VB).

The modern era of double star astronomy was heralded by S. W. Burnham, who, over an active 40-year career beginning around 1870, made remarkable contributions to all of the modern developments in double star astronomy, including the discovery and observation of spectroscopic binaries, the demonstration that some variable stars are eclipsing binary systems, and the application of photographic methods to the measurement of visual double stars, all while discovering 1,340 new double stars and contributing many thousands of high-

quality measures (Aitken 1964). Remarkably, Burnham measured pairs with separations down to 0′′.

2 and ones with large brightness differences between the components. In 1895, Robert G. Aitken started working in this field and conducted the first systematic study of double stars for the purpose of deriving multiplicity statistics. Visual double star worked flourished in the coming decades with significant contributions from Gerard Kuiper, Robert Jonckheere, Paul Couteau, Charles Worley, and Wulff Heintz (H. McAlister 2008, private communication). Worley transferred the Lick “Index Catalog” to the United States Naval Observatory (USNO), creating the Washington Double Star Catalog1 _{(WDS), a current}

online double star resource that is continually updated under the direction of Brian Mason at the USNO. Meanwhile, lunar occultation events had been used for over a hundred years to determine the angular diameters of stars (Evans 1950, 1952) and vector separations of close binaries (Innes 1901; Nather & Evans 1970; Edwards et al. 1980). Observations of double stars in the southern hemisphere were started in the late nineteenth century by Robert Innes, and continued with significant contributions by Willem van den Bos, William S. Finsen, and Richard Rossiter. Recent notable contributors to visual double stars include Willem Luyten, who systematically measured proper motions of fast-moving stars and discovered about 2,000 common proper motion pairs, Antoine Labeyrie, who introduced the technique of speckle interferometry (Labeyrie 1970), and Harold McAlister, who used this technique to discover almost 300 new pairs and contributed about 35,000 double star measures. Recent adaptive optic surveys have enabled the detection of doubles with very high brightness

differences between the components at closer separations than previously possible, enabling the detection of substellar companions such as brown dwarfs (e.g., Liu et al. 2002).

The history of double stars traced above relates to visual doubles, one in which the two components of the system are resolved and their angular separation, or a component thereof, measured. As noted, these can be optical or physical. There are however, other techniques of identifying and characterizing binaries, and these involve studying periodic variations in the spectral lines or apparent brightnesses. The first spectroscopic binary was discovered by E. C. Pickering, with the announcement of Mizar as a double-lined spectroscopic binary (SB2) in 1889, in which the spectral lines of an apparently single star were seen as a pair of lines which moved relative to each other in a periodic manner due to the Doppler effect. Essentially, what Pickering saw was the shifting of the light from the components of the binary as they orbited each other, moving towards shorter wavelength (blue-shift) when a component moved towards us, and towards longer wavelengths (red-shift) when the component moved away from us. As the stars orbit their center-of-mass, when one star moves towards us, the other moves away, and so the characteristic pattern of movement is very telling and can be used to deduce characteristics of the stars and their orbits. Many astronomers and observatory programs have contributed to the study of spectroscopic binaries, notable among them, Roger Griffin, who pioneered the field by developing a technique for measuring stellar velocities to 1 km s−1_{precision (Griffin 1967) and recently published his 200}th_{paper using this}

technique (Griffin 2008), the CORAVEL survey (Baranne et al. 1979, DM91), and Carney & Latham (1987).

As early as 1782, John Goodricke had discovered that Algol (β Persei) showed periodic variations in its apparent brightness and explained this behavior as a partial eclipse by an unseen darker companion in orbit around the brighter primary. In 1889, H. C. Vogel confirmed this theory by demonstrating that the spectral lines of this star showed a periodic shift consistent with the brightness changes. Due to the relative faintness of the companion, its spectral lines were not seen, so only one set of spectral lines moved periodically towards shorter and longer wavelengths, consistent with the eclipses. Hence Algol was the first star to be seen as a single-lined spectroscopic binary (SB1).

Studying planets around stars other that the Sun is a relatively new field in astronomy, and the most fruitful techniques involve the detection and characterization of planets by studying minute shifts in the parent star’s spectral lines as a result of its wobble around the center of mass of its solar system, or by studying the tiny drop in its brightness due to eclipses from an unseen planet. Radial velocities are now routinely being measured to a few m s−1 _{(Baranne et al. 1996; Butler et al. 1996) and have enabled the detection of almost 300}

planets around other stars2_{, enabling statistical analyses of orbital and physical properties}

(Butler et al. 2006; Udry & Santos 2007). On the other hand, detecting planets via eclipses or transits requires photometric precision below 1% and is recently gaining momentum, with over 50 planets detected to-date, either as a follow-up of spectroscopically identified planets (Charbonneau et al. 2000) or through photometric surveys (e.g., Udalski et al. 2002), some of which are run with robotic telescopes (Bakos et al. 2002; Pollacco et al. 2006) or from space (Moutou et al. 2008).