Study of Principal Catalogues of Visual Double Stars

The goal of this study is to develop a tool for detection of errors and misprints in principal catalogues of visual double stars. Modern statistical investigations of visual doubles (which are about 130 thousand, and they represent the most numerous observational type of binaries) are based almost exclusively on data, listed in those catalogues. So their correction is a challenging task, otherwise the statistics of visual binaries can be biased. Study of individual stars should also be based on correct data. We have presented tools to detect some of errors in the catalogues, especially, to indicate cases i) when positional information on components of a pair is contradictory, and ii) when a double star or its component is included in a catalogue twice, under different names.


Introduction
Heggie in his investigation of formation and evolution of binaries identified two classes of binary stars [1].He called these binaries as "soft" and "hard" binary stars.Actually this classification is analogues to "wide" and "close" binary stars respectively.There is no well defined boundary between close and wide binary systems.It differs from author to author according to the purpose and types of the data required.The operative parameter of a binary system is the semi-major axis a.Since its values vary over a wide range of several orders of magnitude, the exact form of semi-major axis distribution is not well known yet.According to [2]- [4] binary stars can be more or less classified as "close" when semi-major axis a ≤ 10 AU and "wide" when semi-major axis a ≥ 100 AU.
Close binary systems are very essential to study stellar properties to a high certainty.One of the types of close binary systems, eclipsing binary systems, are used to determine stellar parameters like masses and radii of components of binary systems [5].On the other hand, wide binary systems are essential systems to study star formation processes as well as an exceptionally useful tracer of local potential and tidal fields through which they traverse.Specifically, they have been used to place constraints on the nature of halo dark matter [6] and to explore the dynamical history of the Galaxy [7].Moreover, wide binaries used to constrain the mass of hypothetical MAssive Compact Halo Objects, so-called "MACHOs" [8].
Visual binaries represent the most numerous observational types of binary stars.Catalogues of visual binaries contain more than 10 5 pairs and provide us with astrometric, photometric and sometimes spectral information on the components.Consequently these data are extremely useful for statistical study and for construction of distributions on and relations between various observational and astrophysical parameters.However, catalogues of visual binaries are not error free.It is probably impossible to entirely fix the problem, but it is desirable to minimize the number of errors through various checks, to avoid any statistical investigations to be biased.
In this study we consider three principal catalogues of visual double stars, namely, The Washington Visual Double Star Catalog (WDS, [9]), the Catalog of Components of Double & Multiple stars (CCDM, [10]), and the Tycho Double Star Catalogue (TDSC, [11]).They contain information on about 130 thousand (i.e., almost all known) visual double and multiple stars.
All catalogues contain annoying bugs and misprints, and this especially concerns large compilative catalogues WDS and CCDM.Some types of errors can be discovered without attraction of external data sources.These are, in particular, the cases (i) when positional information on an additional component in a pair is contradictory, and (ii) when a binary or a component is included in a catalogue twice, under different names.
Constructed tools and results of their application to the cases (i) and (ii) mentioned above are reported in Sections 2 and 3, respectively.Distribution of dublications as well as other errors found in the catalogues are discussed in Section 4. Finally, in Section 5 we make our conclusions.

Positional Inconsistency in the Catalogues
Catalogues of visual double stars provide us, among other data (brightness of the components, their spectral types, proper motion and cross-identification), with coordinates of the reference ( 1 1 , α δ ) and the additional ( 2 2 , α δ ) components of the pair.Also, the studied catalogues provide user with positional angle ( θ ) and separation ( ρ ) of the additional component in a pair, i.e., its position relative to the reference component (with coordinates 1 1 , α δ ).From these data coordinates of the additional component ( 3 3 , α δ ) can also be calculated according to and compared with those, explicitely given in the catalogues ( 2 2 , α δ ), using a formula for calculation of angular distance between two points on the sky: It can be argued that if the distance d exceeds certain selected value 1 d , then the set ( 1 1 2 2 , , , , , contains inconsistent data.The value of 1 d depends on observational conditions, and should be estimated experimentally for every studied catalogue.

WDS
It should be noted that WDS (unlike the other two catalogues) does not provide coordinates for the additional component ( 2 2 , α δ ).It means that the detection of fictitious data may be performed only for those members of multiple (triple and higher multiplicity) systems, which appear as the reference component in one pair and as the additional component in another one.For example, WDS provides data for the following pairs of the system WDS 00013+6021: AB, AC, AD, BD, and the task can be performed, consequently, only for component B. The summary WDS catalog posted on-line provides two sets of , θ ρ values, for the first and the last observations (the full WDS database includes all measures).We used the latter one in this study.For WDS we found 1 8 d = arcsec, and there are about 340 pairs in the catalogue, demonstrating an inconsis- tency in positional data for additional components.The reasons for that inconsistency are large orbital motion in relatively close pairs (especially in a case of large difference in epochs of observation), large proper motion difference in optical pairs, confusion between two closely spaced objects, positional angle θ ambiguity by 180 degrees, large and consequently imprecisely defined value of separation ρ , misprints in the catalogue.

CCDM
CCDM, though being smaller than WDS, is based on a similar set of observational data (in fact it was based on an earlier version of the WDS).On the other hand, WDS is constantly updated, while CCDM keeps observational data collected before 2002.Also, unlike WDS, the detection of fictitious data may be performed for all catalogued objects (as coordinates are provided for every component in CCDM).That is why when we set 1 d for CCDM to be 8 arcsec, we found 1070 pairs demonstrating inconsistency between catalogued secondary coordinates and ones, calculated from primary coordinates, positional angle and separation.
Here we do not consider pairs, where θ is indicated roughly in CCDM, in the format like "SF" (to the South and following, i.e., second quadrant) or "NP" (to the North and preceding, i.e., fourth quadrant).Note that there are also pairs in the WDS with θ only published as N, S, SF, NP, etc.These have been converted to coarse θ values such as 0, 45, 90, etc. Usually these quadrant-only position angles were published only for very early measures, so the "last" angles are nearly always more accurately measured values.

TDSC
TDSC is a homogeneous catalogue, and it contains observations performed with the same instrument.As a result for the majority of objects we found 1 d to be about 1.2 arcsec.This limit is exceeded by eight very wide ( ρ exceeds 10 arcmin) pairs only.For the extreme case 27.4 d = arcsec (TDCS 56356 = WDS 20452-3120AB, 78 ρ = arcmin).

Data Duplication in the Catalogues
Some star can happen to be a member of two different double (multiple) systems, included in a compilation catalogue of doubles.Moreover, a double star can be discovered by two different observers independently and, consequently, this pair appears twice in the catalogue, under different designations.This can be checked by coordinate comparison.Similarly to the case described in Section 2, angular distance between two points with celestial coordinates ( , x x α δ ) and ( , y y α δ ) can be calculated according to ( ) ( ) and compared to certain limiting value 2 d .If d does not exceed certain 2 d , one can conclude that ( , ( , y y α δ ) correspond to the same celestial object.
Again, 2 d value depends on observational conditions, and we should estimate it experimentally for every studied catalogue.Preliminary results were checked manually with the Binary star database (BDB, [12]), which allows us to visualize catalogued data, and SIMBAD.arcsec range.The absence of a strict border between these two cases can be explained by variations of the positional accuracy of the catalogued data.In some cases coordinates of the objects are known with relatively low preci-sion.It is true for overcrowded areas (e.g., Orion nebula), for very bright (e.g., α Cap) or very faint (e.g., WDS 19252-2900) stars, and for relatively wide ( 200 ρ > arcsec) pairs (e.g., WDS 09479+1319).It also happens when K-band or other infrared magnitudes are given in WDS (e.g., vicinity of RK86 reflection nebula) instead of the visual photometry.

WDS
Duplication cases can be classified according to the following scheme.
• Both components of a catalogued double star are included in another, also catalogued, multiple system.Those two stars can constitute (e.g., WDS 23243 + 6216 = WDS 23248 + 6217 CD, Figure 2) or cannot constitute (e.g., WDS 23288 + 0703 A and B are WDS 23287 + 0703 C and B, respectively, Figure 3) a pair in the multiple system.
All of these cases should be taken into account in statistical research of visual binaries.We have reported on these errors to the WDS authors, and necessary corrections were made in the WDS catalogue.

CCDM
For CCDM we estimate 2 d to be about 11 arcsec, and in 19 cases components are included in two different binary/multiple systems in the catalogue (Figure 6 and Figure 7).

TDSC
Owing to its homogeneity, we did not find duplications in TDSC, at least at the level of 2 50 d ≈ arcsec.The only exception is TDSC 29583 A = TDSC 29584 A.

Data Duplication
It is instructive to compare distributions of duplication cases found in Sections 3.1 and 3.2 on component separation ρ .They are shown in Figure 8 and Figure 9, respectively.One can see that the maximum of the WDS distribution is shifted to the smaller ρ in comparison with thr CCDM distribution, as WDS includes more modern and more precise observations and, consequently, can resolve closer pairs.Note also the difference of Y-axis scale in Figure 8 and Figure 9.

Other Errors in the Catalogues
Sometimes catalogued positional angle θ can be ambiguous by 180 degrees.This is not always observer"s error.In some cases magnitude difference is too small for the observer to tell.It may also depend on the observing technique used-if the stars have different colors, the brighter star in B may not be the brighter star in R. Some of such cases can be indicated in WDS.As it was mentioned above, WDS provides two sets of ( , θ ρ ) values, for the first and the last observations.So, if the difference between θ values, obtained at the first and at the last observations, is close to 180 degree, it looks questionable.One can select pairs, where difference between 180 degree and last first θ θ − does not exceed some 3 d .To avoid pairs with high orbital motion, one   All errors found in WDS were reported to the authors of this constantly updated catalogue.TDSC contains cross-identification with WDS, but we have found that TDSC is apparently incorrect in identifying some objects with WDS objects, and, consequently, at least parts of the WDS names listed in TDSC are not correct.So we urge to be wary of WDS identifiers in TDSC.We note that TDSC contains data on 64894 systems, despite the fact that the latter number is 65210.
It should be noted also that our analysis has revealed about 70 errors (misprints) in CCDM, and the list of the errors is submitted to VizieR.

Conclusions
In this paper we developed methods of detection of errors in catalogues of double stars and presented results of their application to three principal catalogues of visual double and multiple stars, WDS, CCDM and TDSC.
Reports on the errors, detected in the studied catalogues, were sent to authors of the catalogues or to VizieR database.In some cases we could indicate a reason for the detected errors and suggest a way for correction.All lists of detected errors are available upon request.

Figure 4 .
Figure 4. Duplication case 3. Two catalogued double stars are in fact the same pair of objects.

Figure 8 .
Figure 8. Distribution of duplications WDS on the separation.

Figure 9 .
Figure 9. Distribution of duplications in CCDM on the separation.can consider only pairs with 10 ρ >arcsec.If one takes 3 15 d = degree, the resulting list contains 72 entries.Ten of them are happened to be pairs with large proper motions differences (and consequently with correct catalogued data), but other pairs contain erroneous data.To make the estimations more reliable, observation epoch difference can be taken into account.All errors found in WDS were reported to the authors of this constantly updated catalogue.TDSC contains cross-identification with WDS, but we have found that TDSC is apparently incorrect in identifying some objects with WDS objects, and, consequently, at least parts of the WDS names listed in TDSC are not correct.So we urge to be wary of WDS identifiers in TDSC.We note that TDSC contains data on 64894 systems, despite the fact that the latter number is 65210.It should be noted also that our analysis has revealed about 70 errors (misprints) in CCDM, and the list of the errors is submitted to VizieR.