The Third Photometric Magnitude Difference Catalog, maintained at the United States Naval Observatory, is a collection of magnitude difference measures for double stars and serves as a repository for double star observations where no astrometry is given. At the present time (8 July 2013) it consists of 5,391 measures of 2,954 systems with a mean Delta-m of 1.83. Additional magnitude information is available in the Fourth Interferometric Catalog which is available online. Due to the non-uniformity of filters and the possible variability of one or more components in a system no ``WDS-like'' summary line is provided. Rather, all the data are presented, and their interpretation is left as an ``exercise for the reader.'' A brief summary and statistical analysis of the contents of the catalog are presented.

The problem of obtaining accurate magnitude differences in binary star astronomy is a long-standing one. The crux of the problem, as in accurate binary star astrometry, is the lack of standards against which systems can be measured. Binary star astronomers have, since the time of John Herschel, maintained a consistency in the way in which fundamental astrometric data are published (usually, Besselian year, position angle, and separation in seconds of arc). However, the publication of photometric information has been uneven - while sometimes individual magnitudes or magnitude differences were estimated or measured, on other occasions catalog magnitudes were published with no indication of the source of the measurement, yielding no clear way to determine when a measure of photometry was made and when it was not.

Yet the importance of accurate differential photometry of binary stars cannot be overstated. While there has been more overlap of late between spectroscopic and visual binaries, historically the characteristics of visual binaries were known through orbital analysis and parallax, leading to a mass sum. A measure of Delta-m can place the individual components of a binary star system on an empirical mass/luminosity plot, which (although model dependent) can aid in the refinement and convergence of models of stellar characteristics. In addition, measurement of Delta-m at two or more wavelengths ties the masses and luminosities to an effective temperature.

When looking at publications providing binary star measurements which are primarily listings of relative astrometry, a measure citing a magnitude difference can typically be believed as a true measure. However, unless it is made explicitly clear in the publication, cases where magnitudes are published for both companions typically cannot be trusted. In considering measures contained in the Washington Double Star (WDS) Catalog, the only ones which can be trusted as bona fide Delta-m measures are those where only a magnitude difference is cited or where it is known that individual magnitudes of the components were measured (as was the case, for example, for Hipparcos and Tycho). Additional complications to these matters are the different (and often non-standard) central wavelengths and passbands of measurements, as well as the photometric variability of some of these companions.

In addition to this small subset of relatively reliable magnitude difference measurements, there are a few cases where the primary purpose of the work has been the measurement of photometry of the components of binary stars. Double-image photometers and micrometers were used from the late 19th Century (Pickering 1879) until the late-20th (Worley 1969); these permitted moderate Delta-m measurements over a wide range of separations, sometimes as close as half a second of arc, although both of these (and any other) techniques have a number of smaller Delta-m systems which serve to calibrate the technique against other standards. Kuiper (see Baize 1950) pioneered work in objective gratings which, although limited in the separations of systems for which they could effectively observe, were capable of measuring larger magnitude differences. This work culminated in measures by Lindenblad (1970) of the Sirius AB system. Wider systems have had a variety of techniques applied, including the area scanner observations by Rakos and Franz (see, e.g., Franz 1970), as well as more conventional photographic measures. This was standardized by Strand (1969). Recent efforts have used CCDs (e.g., Tokovinin & Shatskii 1995). A listing of the different techniques, their contribution and mean Delta-m is provided here.

Systems which are separated by an arcsecond or less are typically not observable by the aforementioned techniques. Unfortunately, it is often these systems which are the most astrophysically interesting. The occultation of stars by the Moon can be used to determine Delta-m measurements for quite close systems. However, these events are restricted to zodiacal band stars and are infrequent and unrepeatable occurrences. Also, the Delta-m determinations from lunar occultation have suffered from large errors and were often taken with non-standard filters (Mason 1996, 1997). In high angular resolution work, the ``fork'' algorithm (Bagnuolo & Sowell 1988) is only applicable to a photon-noise-limited detector with more than 5 photons per speckle, while the ``directed vector-autocorrelation'' has errors which are too large without laborious calibrations (which in turn, decreases observational efficiency by as much as a factor of 40; Mason et al. 1993). Full image reconstruction from non-redundant aperture masking or bispectrum analysis is possible; however, the intensification used with CCDs in most speckle observations seems to prevent accurate determination in all but photon-limited data (Roberts 1999). Some of these data from selected papers are included below. While the technique of adaptive optics appears quite promising (e.g., ten Brummelaar et al. 1996, 2000), it is quite labor intensive and has yet to see effective throughput. The most effective technique of late for measurement of the delta magnitude of close binaries has been the determination of V and B magnitudes of Hipparcos stars measured by the Tycho instrument (Fabricius & Makarov 2000).

Changes since the First Photometric Magnitude Difference Catalog

The WDS and Delta-M method files are now the same. This has resulted in the merging of similar techniques which were quite small in number.

Measures for which there is also an relative astrometric measurement have now been folded into the main WDS database. These measures now have a "D" code in the data line which indicates they are thought to be reliable magnitudes or magnitude differences. Thus, it more closely resembles the original, internal only, catalog of Charles Worley.

Measures in the Photometric Magnitude Difference Catalog have been collected, collated, and maintained as an internal USNO publication for over 30 years. Presented in order are the WDS 2000 coordinate, the discovery (and component) designation, the measured magnitude difference, the number of measures contributing in the mean, a reference code, a method code and a column of notes. These notes include but are not limited to wavelength characteristics (in nanometers) and error of the measurements (sigma). Links to the complete Delta-m Catalog are below, as are links to the reference list and a description of observing methods. All these materials are also included on a CDROM of USNO double star catalogs. Copies of this CDROM can be obtained from the authors.

• Available Files:
• The Delta-M Catalog
• Method Key to the above file
• Number and mean Delta-m for various methods
• Reference file

• Bagnuolo, Jr., W.G. & Sowell, J.R. 1988, AJ 96, 1056
• Baize, P. 1950, J. Obs. 33, 1
• ten Brummelaar, T.A., Mason, B.D., Bagnuolo, Jr., W.G., Hartkopf, W.I., McAlister, H.A., & Turner, N.H. 1996, AJ, 112, 1180
• ten Brummelaar, T.A., Mason, B.D., McAlister, H.A., Roberts, Jr., L.C., Turner, N.H., Hartkopf, W.I., & Bagnuolo, Jr., W.G. 2000, AJ, 119, 2403
• ESA 1997, The Hipparcos and Tycho Catalogues (ESA SP-1200) (Noordwijk: ESA)
• Fabricius, C. & Makarov, V.V. 2000, A&A 356, 141
• Franz, O.G. 1970, Lowell Obs. Bull., 17, 191
• Lindenblad, I.W. 1970, AJ 75, 841
• Mason, B.D. 1996, AJ 112, 2260
• Mason, B.D. 1997, AJ 114, 808
• Mason, B.D., McAlister, H.A., Hartkopf, W.I., & Bagnuolo, Jr., W.G. 1993, AJ 105, 220
• Pickering, E. 1879, Harvard Annals 11, 105
• Roberts, Jr., L.C. 1999, PASP, 111, 650
• Strand, K.A. 1969, Pub. USNO 18, Pt. 5
• Tokovinin, A.A. & Shatskii, N.I. 1995, Pisma Astron. Zhur. 21, 523
• Worley, C.E. 1969, AJ 74, 764

This catalog has been substantially improved by Hartmut Jahreiss pointing out an earlier Delta-m catalog of Stefan Wierzbinski (Contributions of the Wroclaw Astronomical Observatory No. 16, Wroclaw, Poland, 1969). While the calculated determinations of Wierzbinski are not included, the list of references in his catalog has allowed the identification of many WDS magnitude listings as delta-m measures, as well as the several references that were not previously included.

If the WDS and associated databases were helpful for your research work, the following acknowledgement would be appreciated: