Double Star Astronomy
Part 3: Double Star Datasets
The systematic search for double stars was stimulated by two achievements of William Herschel: the publication in 1782 and 1784 of catalogs that report pair magnitudes, colors, separation and relative position; and his demonstration, in Account of the Changes that have happened, during the last 25 years, in the Relative Situation of Double-Stars; with an Investigation of the Cause to which they are owing (1803), that double stars were "not merely double in appearance, but must be allowed to be real binary combinations of two stars, intimately held together by the bond of mutual attraction."
Herschel's search was inspired by the idea that two stars lying along the same line of sight, one much farther from Earth than the other, might reveal stellar distances through the Earth's orbital parallax. (In the event, this was achieved for two of the closest stars to Earth: 61 Cygni, measured by Friedrich Bessel in 1838, and Vega measured by Wilhelm Struve in 1839.) But once the fact of gravitational connection was affirmed, double stars became a major research focus of 19th century astronomers. Ambitious major double star catalogs were published by John Herschel and Friedrich Wilhelm Struve, and important early catalogs were compiled by James South, James Dunlop, Otto Struve and many others.
Eventually the gravitational dance of double stars provided the key to the stellar mass luminosity relationship, which in turn unlocked the fundamental principles of stellar evolution. More recently, the large proportion of double stars and the wide variation in their dynamical properties have established the view that double stars are intimately involved with star formation processes.
At present double stars are identified and measured primarily through general stellar surveys (such as the United States Naval Observatory's astrometric surveys and space missions such as Hipparcos, 2MASS and the recently launched GAIA) or as incidental discoveries in research directed to other topics.
To begin at the beginning, there are a number of historical (19th and early 20th century) double star catalogs whose designations of specific double stars have remained as the primary identification label for amateur astronomers (excepting only the Bayer/Flamsteed designations). These include the following:
The linked Summary of 98 Double Star Catalogs lists the catalogs that have contributed 98% of the potential targets for visual double star work. These comprise the canon of amateur double star observing. The remaining 670 catalogs in WDS contribute few or no double star targets to amateur observing lists.
The one letter to four letter catalog abbreviations used in the Washington Double Star Catalog (WDS) maintained at the United States Naval Observatory are now the standard synonyms for all double star catalogs. These originate in the Index Catalogue of Visual Double Stars (IDS) published by Lick Observatory in 1963, and they specifically supersede the 19th century use of Greek letters to denote the more important catalogs, a system perpetuated in all 20th century amateur references. These include William Olcott's Field Book of the Skies (various editions from 1929, now out of print), Robert Burnham Jr.'s Burnham's Celestial Handbook: An Observer's Guide to the Universe Beyond the Solar System (1966), or the Sky Catalogue 2000.0: Volume 2, Double Stars, Variable Stars and Nonstellar Objects by Alan Hirshfeld & Roger Sinnott (1985). (The few planetarium software packages that include a double star list all adopt the WDS naming conventions and WDS identifiers.) The professional astronomical literature commonly relies on the 10 digit WDS ID number, which is simply the right ascension and declination (with sign) of the target in the J2000 epoch celestial coordinates, or the Henry Draper (HD), Hipparcos (HIP) or USNO Astrometric (UCAC4) ID numbers. Spectroscopic binary stars are normally referenced by HD number.
The diagram (right) plots the cumulative catalog identifications by the visual magnitude of the cataloged primary star for the "classical" double star catalogs of John Herschel (HJ), F.W. Struve (STF+STFA+STFB), Otto Struve (STT+STTA), Sherburne Burnham (BU) and Henry Aitken (A). The median catalog magnitude is around 8th or 9th magnitude and (with the exception of John Herschel and Aitken) there is a limited number of entries fainter than 10.0. The catalogs by the amateur astronomers T.E. Espin and Robert Jonckheere (pronounced YONK-heeruh) extend to fainter pairs that will be of interest to observers with 250mm or larger apertures.
Each double star catalog has its own (often idiosyncratic) inclusion criteria, affected by observing strategy and the instrument(s) used. William Herschel examined every star with a Bayer or Flamsteed designation, and stars near these target stars, in his first two catalogs; the third ("N") catalog lists stars encountered during his systematic sweeps of the sky for galactic star counts, nebulae surveys and (along the ecliptic) in search of new planets. John Herschel is the only observer to survey systematically the entire sky, using a 470mm (18.5") aperture speculum reflector (with a light grasp equivalent to a modern 355mm or 14" or reflector) from observing sites in England and South Africa. F.W. Struve examined every star clearly visible in the 65 mm finder scope of his 230mm (9") refractor, and stars nearby; Sherburne Burnham simply examined random areas of sky using his personal or observatory instruments. Most catalogs were made by northern hemisphere observers and are therefore usually truncated at a declination of 30°. Numerous southern hemisphere discoveries were made by John Herschel, Willem van den Bos, R.T.A. Innes (WDS code I) and R.A. Rossiter (WDS code RST).
A few catalogs, such as STFB, BUP and STTA, focus on very wide or known high proper motion pairs, and several catalogs or catalog sections (e.g., STT 540 to STT 600) include wide and likely optical pairs of very unequal magnitude, probably selected because they could be used to measure the proper motion of the brighter star in relation to the fainter ("more distant") component.
What information should a catalog of visual double stars contain? Surprisingly little, as double stars can be compactly described. Double star catalogs generally are limited to the list of parameters or indicators below; the information labeled in green is provided in almost every double star catalog I have examined and is the bare minimum necessary in a useful reference.
Catalog designation an alphanumeric identifier for a specific double star as identified in a specific double star catalog. Because the WDS, UCAC and other modern system identifiers can be nine or more digits long (plus declination sign), most references use the historical catalog label, either in the obsolete 19th century form (e.g., ΟΣ 144) or the now standard alphanumeric code (STT 144).
Most of this information is published for every catalogued double star in the Washington Double Star Catalog (WDS), maintained by the United States Naval Observatory (USNO) in Washington, D.C. by Brian Mason and William Hartkopf. This is the most up to date and standard reference for known or suspected visual double stars. The WDS lists all known components of a possible system, including pairs or components known to be optical (so that they will not be "rediscovered"), the date and number of measurements made of the system and the earliest and latest measurements of position angle and separation. Orbital elements such as period, semimajor axis and eccentricity are available in the Sixth Catalog of Orbits of Visual Binary Stars (1983), also maintained by the USNO.
The standard method of positional measurement since Herschel's time is to indicate the separation between the two stars (denoted ρ) in arcseconds, and the "clock face" position angle (denoted θ) on the celestial sphere in counterclockwise degrees measured from a line to celestial north.
The diagram (below) shows the effect of telescope optics on the apparent position angle: an "inverting" refracting or reflecting telescope rotates the apparent orientation by 180°, and a mirror diagonal reverts the east/west orientation to produce a mirror image around the telescope's optical axis.
A traditional shorthand for the position of a component star is to indicate whether the component is north or south, and west (preceding) or east (following) in relation to the primary star. These four cardinal directions can be combined to divide the positional locations into octants north following (n.f.), south following (s.f.), south preceding (s.p.) and north preceding (n.p.) in addition to the four cardinal directions. This orientation scheme is very easy to establish with an equatorial mount, and (when combined with a rough estimate of angular distance) provides a convenient way to notate the general location of objects of interest in the field around an identified double star.
When this method is used to define position angle measurements, angular measurements are made from a line parallel to the celestial equator, that is, the drift path of the star in a stationary telescope. Thus, 15° north following is equivalent to θ = 75°, and 15° north preceding to θ = 285° in the modern system.
Component Labeling. As positional measurements must apply to pairwise (binary) combinations, a standard labeling method is necessary to indicate which components of multiple stars are being measured.
Visual components are designated by capital letters, with letter A assigned to the brightest (apparently most massive) star. Lowercase letters are assigned to companions of any of these stars (these are often spectroscopic or "visual" interferometric pairs) and numbers are assigned to the companions of those companions. The historically assigned catalog names and component letter designations are retained even when a component or pair is later found to be optical.
The complete labeling guidelines and illustrative examples are available at the Washington Multiplicity Catalog web site. In brief, components are labeled with capital letters in order of discovery (AB, AC, etc.), then (often spectroscopic or interferometric) components of these stars by lowercase letters (Aa,Ab, Ca,Cb, etc.) and if necessary by numbers (Ca1,Ca2, etc.).
Component designations are omitted when the double star is a binary, and many amateur catalogs list only the brightest pair within a multiple regardless of the actual number of components a problem explored below. Amateur astronomical references sometimes use the Aitken (ADS) or Smithsonian Astrophysical Observatory (SAO) catalog numbers, although these are now rarely used in professional astronomical publications.
What Does WDS Contain?
The January, 2015 Washington Double Star Catalog comprises about 130,000 individual records or pairs, and 111,000 unique WDS numbers unique stellar targets and associated components. Two basic questions we can ask about this trove of discoveries are: how many unique IDs in the WDS are not double stars, and how many are within reach of amateur instruments?
Many of the "components" listed for stars whose proper motion or parallax measurements were of interest to 19th century astronomers are actually field stars used as astrometric reference points. There can be a dozen or more of these "components" listed for fast moving pairs (61 Cygni, Kruger 60) or nearby bright stars (Vega, Procyon), and double stars identified in a rich field or embedded in a star cluster such as Praesepe or the Pleiades. The late items in the Otto Struve (STT) catalog are all potential proper motion pairs, and F.W. Struve, Sherburne Burnham and others published separate catalogs of similar targets.
But we can't proceed by anecdote in this way: we need a general method to distinguish double stars, optical pairs and pair asterisms across the entire WDS.
Statistical tests have in the past been a primary tool to filter double star catalogs. If we adopt the tests devised by R.G. Aitken or Sinachoupoulos & Mouzourakis, then roughly 61,000 pairs pass one or the other test but only 12,000 pass them both; that's 11700 unique WDS IDs (11% of total). This introduces the conclusion that is borne out by evidence: less than half the unique IDs in WDS can be identified as physical.
In the past few decades astronomers have developed highly accurate measurements of many star systems. Using this new information, we can identify physical systems as those with a projected separation (based on the parallax distance of the primary star) that is less than 5000 AU, a small divergence in the relative proper motion of the components, a flag in WDS that indicates a physical pair based on CPM analyses or parallax evidence (or both) reported in the astronomical literature, or a calculated orbit of "preliminary" to "definitive" quality. These positive criteria can be contrasted with a projected separation greater than 50,000 AU, evidence that the pair is optical (a linear solution, divergent proper motions, discrepant parallax distances, or an "optical" or "bogus" WDS flag), to produce an overall numerical "physicality" score. We can then use this score to identify pairs within WDS that have the highest probability of being physical systems or pair asterisms, or those that are ambiguous optical pairs lacking evidence either way.
The table (below) shows the results of this analysis. The "all pairs" column gives the tallies across every pair (record) in the WDS catalog, and indicates how many pass the editorial Aitken test, which is essentially a projected orbital radius scaled to stellar luminosity.
As the table shows, using the physicality score, the total WDS catalog breaks roughly into thirds (physical, optical, asterism). The proportion of likely physical systems changes only slightly when the Aitken test is added, and although the test usefully rejects about three-fourths of the pair asterisms it adds more optical pairs. Rather than preferentially selecting high probability physical systems, the Aitken test is no more effective at that task than a random selection of pairs from the WDS catalog. This illustrates the inadequacy of any selection criterion, including a statistical test, that relies on visual appearance.
To assess the catalog available to the amateur visual astronomer, we can adopt Paul Couteau's suggestion that the domain of visual double stars is limited to pairs with components no fainter than magnitude 10. His rationale: "experience shows us that, whatever the aperture, magnitude 10 is a barrier. In a large instrument the images lose their sharpness and break up. Light is lost in the diffraction rings, and the eye does not receive very much more illumination."
Because magnitude implies an aperture dependent magnitude limit, and because smaller apertures are less sensitive to thermal currents and seeing, the magnitude limit suggests the largest aperture necessary for visual double star astronomy. If we calculate the minimum aperture needed to make a magnitude 10 star comfortably visible with the direct (foveal) vision necessary to resolve very close pairs, we get an aperture of 200 to 250 mm.
The third column of the table (NC) shows the breakout for pairs in WDS that are within the "Couteau limits" of ≤ 10.5 for the primary and ≤ 12.5 for a secondary and excluding pairs separated by less than 0.5" that are unresolved in a 250mm telescope again with or without the Aitken filter.
Although this trims the WDS catalog to about 40% it does not appreciably change the proportions between physical systems, optical pairs and pair asterisms. (Note that the Aitken test identifies high probability physical pairs with much higher efficiency in this subsample primarily by rejecting optical pairs with very faint, wide components.) This implies that the "Couteau limits" subsample is a representative subset of the whole, as the diagram (right) illustrates.
The plot presents the average separation and average sum of component magnitudes within each of the 780 separate catalogs included in WDS (excluding interferometric or astrometric pairs where the component magnitude is missing). The catalogs that comprise the amateur double star literature are indicated as orange dots. All these are above the magnitude 10.5 limit with an average separation of around 20", as is the central concentration of all other catalogs (white dots). (The 5 "amateur" catalogs below m.10.5 are catalogs of wide, common proper motion pairs.)
No matter how we slice and dice the data, the evidence suggests that a bit more than one third of the pairs in WDS can be described as physical, and only about 15% are within the "Couteau limits" accessible to amateur apertures. All the rest over 84,000 pairs, 63% of the total are either pair asterisms or lack any physical evidence to clarify their nature one way or the other.
Double Star References
As explained above, the only authoritative and reliable source of double star information is the online (summary) version of the Washington Double Star Catalog, which is updated almost daily with corrections or recent measurements and is currently (2014) undergoing a major revision. The historical positional measures of specific targets are available from the USNO on request, but currently the total archive of WDS measures is not available.
SIMBAD, the authoritative online resource of astronomical data, has not fully integrated WDS IDs into its query results for individual star systems and does not in any case provide the latest positional data.
Atlases and Checklists. My experience has led me to the conclusion that there is no printed reference adequate to the needs of a serious double star astronomer (see "Catalog Quality" below). However, for the novice or casual observer, there are several good choices.
Most basic or general interest "sky guides" include short lists of double stars, a tradition that extends from Olcott's Field Book of the Skies back to Rev. T.W. Webb's Celestial Objects for Common Telescopes (1859) and Admiral William H. Smyth's Cycle of Celestial Objects (1844, reprinted in part as "The Bedford Catalog"). These books are ruby port in cut crystal decanters, mildly pleasant for sipping and musing on ye olden times gone bye, but not for drinking deeply. However the observing checklists in Webb, organized by constellation, provide often useful comments on the color or configuration of hundreds of double stars, most of them objects in the Wilhelm Struve (STF) catalog which catalog is, by the way, the backbone of every amateur double star observing checklist.
Among modern references, Norton's Star Atlas and Reference Handbook (now in its 20th edition, 2004) combines eight double page, easy to read and beautifully designed star charts with matching tables of "Interesting Objects", including a separate table of about two dozen double stars for each atlas section (roughly 250 doubles in all). Many other astronomy publications provide incidental listings: the Peterson A Field Guide to the Stars and Planets (2006) lists about six dozen doubles in an appendix table, and the Observer's Handbook published annually by the Royal Astronomical Society of Canada lists a few hundred attractive and colorful targets. Periodicals such as Sky & Telescope typically run a monthly column that suggests interesting objects (including double stars) visible at different times of the year.
The next step up is where difficulties arise. The hideously expensive reprint of the Sky Catalogue 2000.0 is now almost three decades old, and the ceremonious decimal epoch of the title indicates updated celestial coordinates only. The tabulated double star positional measurements simply copy the contents of the 1976 "magnetic tape" (!) version of the IDS published in 1963, itself largely compiled from the double star catalogs by Robert Aitken (ADS, 1932) and Sherburne Burnham (BDS, 1906). Many of the included doubles are in fact optical randomly aligned stars that are actually far distant from each other.
Even worse is Burnham's Celestial Handbook, which does not reveal its source for double star measurements (most likely either IDS or ADS) and is also based on celestial coordinates accurate in 1950 but now (because of the Earth's precession) sufficiently out of date to frustrate visual search and GOTO pointing.
Paul Couteau's very informative Observing Visual Double Stars (1978) is an advanced review of visual double star techniques. It appends a checklist of 740 challenging double stars "accessible to a mirror of 40 cm" (16 inches): most of these are under 5 arcseconds separation and many are under 1 arcsecond. Like the previous references, it is based on the outmoded 1950 celestial coordinates, and without knowing exactly which star to study closely it can be difficult to identify a faint subarcsecond pair in a populated star field.
Among modern references, the double star astronomer can work with the stars flagged as double (by a small line through the star icon) in the large format Sky Atlas 2000.0 (1998) by Wil Tirion & Roger Sinnott or the more compact and slightly smaller scale Sky & Telescope's Pocket Sky Atlas by Sinnott. These stars can have Bayer/Flamsteed labels but no double star designation, so you must search WDS to find matching celestial coordinates and magnitude to identify the target and its positional measurements.
Sissy Haas's Double Stars for Small Telescopes (2007) is a carefully compiled introductory reference to double star observing, with a list of 2100 traditional double star targets including position angle, spectral type of primary, status as binary or optical pair (although I have found that these designations are untrustworthy), and effusive notes on star color.
The Cambridge Double Star Atlas (2009) by Jim Mullaney (now out of print but available used) is useful for the superb star charts by Wil Tirion and a somewhat larger selection (over 2300) of double star targets and a reliable and informative introduction to observing principles. Unfortunately the target list omits position angle as "too confusing" (!) for the amateur, adopts magnitude and separation data from the 1960's era IDS data (via the Sky Catalogue 2000.0), and mixes optical and physical systems indiscriminately: compared to the Haas guide it actually contains a larger proportion of optical pairs (61% to 42%, by my audit) and a smaller proportion of physical pairs (36% to 49%). Similar errors and lapses affect the checklist of 500 stars found in Mullaney's Double and Multiple Stars and How to Observe Them (2005).
The Cambridge Double Star Atlas (2nd ed.) (2016) by Bruce MacEvoy (that's me) retains the Tirion star charts but relabeled to follow a target list selection of 2500 double stars of which 90% are high probability physical systems and none are known pair asterisms so far as current data allow these to be identified. The introduction provides more information about the physical aspects of double stars, orbital dynamics and star formation, as well as more detailed advice on visual observing and an extensive bibliography. The target list includes both separation and position angle in the most recent data, primary star distance in parsecs, spectral types of both components when available, and both HD and SAO numbers for the primary star. This is the first and (currently) still only double star guide that expressly excludes optical pairs and pair asterisms from its catalog.
One point worth emphasizing: the magnitude descriptions of double stars in WDS (and publications based on it) become increasingly inaccurate at magnitudes below v.mag. ~8.0, apparently because these rely more on visual rather than photometric estimates. The extent of the problem will become clear if you inspect a list of "matched" doubles of decreasing magnitude according to the magnitudes listed in WDS. As you work through the list toward fainter targets you will encounter several that appear out of sequence, brighter or dimmer than the pairs listed at a brighter magnitude.
Astronomy Software. The following short list of astronomy software packages is by no means inclusive, but suggests the variety of tools available and the neglect of double star astronomy. For most lookup, targeting, charting and identification needs, the best choices are obviously AstroPlanner or DeepSky Planner.
As explained above, the only authoritative and reliable source of double star information is the online version of the Washington Double Star Catalog. All other sources, regardless of their origin or date of publication, must be considered suspect. This is a fact I have learned by experience.
In most areas of visual astronomy, the data are more or less fixed. The physical, dimensional and appearance features of galaxies, clusters or nebulae in the NGC, IC, Messier and similar catalogs are unchanging across centuries, and the data have been thoroughly scrubbed and revised over several decades. (The thousands of new pairs discovered by Hubble and other space telescopes are compiled under new catalog designations with a comparable stability and accuracy.) In contrast, double star catalogs are continuously expanded by new discoveries, and the pairs already cataloged are gradually or quickly changing across decades or less. Both considerations favor the use of WDS.
I became aware of the problem while working through the observing checklist in the Mullaney edition of the Cambridge Double Star Atlas (2009). I began to notice that double stars didn't seem to match the separation and magnitude measurements. Pairs I should have been able to split easily I couldn't, and pairs I could easily split were listed as near or below my resolution limit. Stars appeared brighter or dimmer, and the contrast between pairs more or less pronounced, than the data indicated.
Comparing the CDSA data to the current WDS, I found the CDSA data were either obsolete or inaccurate. I began to check systems in WDS as I worked through the list, largely to confirm visual judgments of magnitude, separation and PA, as part of training my binary eye. On average I discovered about 20 errors for every page in the CDSA list; the image (right) suggests the extent of the difficulties.
The problem is just as severe in other resources. Planetarium software often omits double star information entirely, or does not document the source used for the information it includes. The last significant print catalog, the Sky Catalog 2000, was published over two decades ago (and based on information that is even older) and is limited to a primary visual magnitude of 7.5, which (as described above) omits more than half the systems included in all the classic 19th century catalogs.
Online resources are no better. As one example: Duane Frybarger's nifty Double Star List Generator is based on the Saguaro Astronomy Club double star database, apparently based on an outdated version of the WDS.
How accurate is the Saguaro dataset? I queried a random bandwidth 4" to 0.4" separation in a random constellation (Cassiopeia) and checked the first ten hits against the current version of the WDS. Here's what I found:
HU 502 v.mag, spectral type don't match WDS
... and those are just the first ten items in a list chosen at random. Clearly, if you are going to use third party data, whether as a book or a dataset, then you can easily get 89º or 179º degrees of misinformation.
Nor are software publishers any better. One very highly regarded planetarium program contains data for position angles that appear to have been taken from the WDS values for the first measurement of the system, rather than the most recent measurement (typically within the past decade). As a result, every system in the traditional catalogs is described as it appeared in the 19th century!
Acute binary observation relies on accurate data: can I split that pair, or not? Is the companion too faint, or hidden in the first diffraction ring? Without accurate data, you just can't test and develop your optical and visual limits, or conduct any meaningful research project.
The serious double star astronomer has only three alternatives: (1) download (or access via web page) the latest version of the Washington Double Star Catalog, linked from the WDS home page and updated frequently as new measurements are received or errors are reported; (2) access the data through Stelle Doppie, on online query tool of WDS and other datasets scrupulously compiled and maintained by Gianluca Sordiglioni; or (3) download my carefully edited spreadsheet version of the WDS, published annually and described in detail on this site's home page. Then compare several dozen randomly selected targets in WDS to the information in whatever alternative data source is being considered for use, in order to verify the accuracy and reliability of this alternative source. In the present situation I would simply save myself the effort to reach disappointment and use the WDS without hesitation.
The Binary Bias
Perhaps the worst feature of print double star guides or annotated star atlases (such as Norton's Star Atlas and Observer's Handbook) available to the amateur astronomer is the binary bias. This is the identification of multiple star systems as binary systems through the use of a single catalog designation and the report of a single pair measurement, and the misconception this creates that "double stars are just two stars".
The extent of the problem can be evaluated by counting the number WDS ID numbers that index multiple components (table, below). This indicates that roughly 1 in 10 "double" stars actually comprise 3 or more components a proportion that remains roughly constant no matter what limiting magnitude (telescope aperture) is used.
This bias is the result of the traditional focus on binary pairs in orbital solutions and as probes of stellar mass and luminosity. Even when a physical system is known to have multiple components, most publications list only the brightest or most easily resolved pair as a matter of convenient tabulation. This convenience becomes a conviction for many double star observers, particularly those who focus on the "esthetic" aspect of star color and the challenge of splitting a close pair.
One example of this problem is STF 1964 in Corona Borealis, which is listed in all popular catalogs as a binary with a separation of about 15 arcseconds. This is the appearance it presents in a medium aperture telescope at a magnification of about 150x (diagram, below left). However, with a larger aperture, or good seeing and higher magnification (1350x is used for the diagram, below right, but a much lower power is sufficient), it resolves into a "double double" system in fact, one of the tiniest double doubles in the catalog.
This is a modest example, as the two pairs are separated by about 1.5" and the faintest component (B) is magnitude 9.9, which puts this system out of reach of apertures below 100mm (4"). But in most cases the "missing" component(s) are both bright and rather distant from the primary, and the omission is simply the result of the traditional catalog biases and the self limiting observer habits they encourage.
Double Stars for Small Telescopes: More than 2,100 Stellar Gems for Backyard Observers by Sissy Haas (2007) a generally accurate, complete and enthusiastic reference for the amateur astronomer; obviously a labor of love and diligence.
Cambridge Double Star Atlas (2nd ed.) by Bruce MacEvoy & Wil Tirion (2016) probably Tirion's most successful star atlas combined with the first target list to focus exclusively on "high probability" physical systems.
Sky & Telescope's Pocket Sky Atlas by Roger Sinnott (2006) compact, legible, comprehensive, well indexed, sturdy, spiral bound: the atlas highly recommended by pretty much every astronomer who owns one.
Double Stars by Wulff Heintz (1978) an indispensible general reference to double star astronomy history, methods, mathematics, dynamics and evolution. Very expensive if purchased as a book, but available for free at the link.
Last revised 09/26/16 ©2016 Bruce MacEvoy