Catalog of Rectilinear Elements

(last update: 21 Jul 2011)


William I. Hartkopf & Brian D. Mason
U.S. Naval Observatory, Washington, DC





Introduction & Purpose

Many systems in the Washington Double Star Catalog have shown significant relative motion since their discovery. The Catalog of Rectilinear Elements provides linear fits for those systems whose motion does not appear to be Keplerian. While a few of these may in fact be very long-period physical pairs whose orbital motion is not yet apparent, most are probably optical pairs (i.e., chance alignments of unrelated stars). These linear fits, then, just describe the relative proper motions between these pairs of stars.

The purposes of this catalog are threefold. First, the very well-defined motions of some of these systems means they may prove useful for scale calibration for imaging systems such as CCDs or photographic cameras. Also, these differential proper motions may allow us to improve upon proper motions of individual components. Finally, these linear fits, especially in comparison with Hipparcos proper motions, may be useful in searches for submotions due to closer components. These investigations are underway.


Definition of Terms

A very straightforward method was used to define the motion of the secondary star relative to the primary: 
Define:
            x = -sin(theta) * rho
            y =  cos(theta) * rho

and let (x0,y0,t0) or (rho0,theta0,t0) define the relative location and time of closest
approach
      
Solve for:
            x = xa * (t-t0) + x0
            y = ya * (t-t0) + y0
A standard weighted least squares fit is made, with weights of individual measures determined using the technique outlined in the Sixth Catalog of Orbits of Visual Binary Stars.


Catalog Files

Available files are as follows:
Figures are also provided for each system, and are linked from the main catalog by the letter "P" in one of the righthand columns. The figures include all measures in the WDS, as well as the linear fits whose elements are given in the main catalog (shown as a solid black line). Individual measures in these figures are color-coded as in the Orbit Catalog; green, blue, and purple indicate micrometric, interferometric, and photographic/CCD measures, respectively, while a red "H" or "T" indicates a measure from Hipparcos or Tycho. Measures are connected to their predicted locations by "O-C" lines; measures given zero weight are indicates by dotted O-C's.

For those pairs with two sets of proper motions in the WDS, a red line indicates the differential proper motion predicted by these values. Since most of these proper motions are from the Hipparcos or Tycho-2 catalogs, the red lines intersect the least-squares fit to the data at the Hipparcos epoch of 1991.25. The lengths of both the black and red lines correspond to a similar range of dates, usually roughly corresponding to the range of observation dates, unless T0 falls outside that range (a maximum date range of 1000 - 3000 was set to handle a few extreme cases).


Conclusion

Qualities of the fits vary considerably among the 1267 systems presented here; some undoubtedly need more data, while others have not shown enough motion for a meaningful fit to be made in our lifetime. These systems will be weeded out through further examination. Other systems in the WDS do show enough motion for a fit to be attempted; additional pairs will be added as they are discovered. Additional notes, astrometric data and proper motion information, as well as updated figures, will be added regularly, as well.

Note: The initial versions of this catalog did not include a reference code for each solution, as all were done "in house". However, publication of linear elements by others prompted the editors to make a slight format change in July 2011; all future solutions will now include such a code. The reference code for most of the solutions is at present this catalog itself - this code will be updated from time to time, as solutions for all pairs are recalculated.

Your comments regarding format, as well as notification of errors, are welcome.





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