5 Evaluation of the catalogue

An interesting property of the catalogue follows from Fig. 2, which shows the sky distribution of the $20\,000$ known and $13\,000$ new systems in ecliptic coordinates. The known systems have a concentration towards the Galactic plane, as could be expected, while the new systems in addition show a concentration towards ecliptic latitude $\pm 47 \hbox{$^\circ$ }$, which is only barely visible for the known systems. Due to the nature of the Hipparcos scanning law (ESA 1997, vol. 1, Fig. 3.3.3), these latitudes received more than twice the average number of observations and can therefore provide a much better signal-to-noise ratio than the more sparsely observed ecliptic region. We may conclude that a uniform survey would have discovered many more new systems.

Figure 3: The distribution of separations for all present WDS systems (dashed line), for TDSC systems known in WDS (thin line) and for new systems (thick line). Only the smaller separations are shown.

The distribution of separations for known and new systems in TDSC is shown in Fig. 3, and the distribution for WDS systems (irrespective of magnitude) is included for comparison. For separations around 0.5 arcsec, the majority of the observed systems are new and outnumber the present WDS. The new systems mostly have separations between 0.4 and 1 arcsec, but there is a substantial number also around 2 arcsec. For separations between 0.4 and 2.3 arcsec we have observed the majority of the WDS systems.

5.1 Astrometric comparisons

Figure 4: Comparison of the relative astrometry between Hipparcos and new Tycho results for 2699 double stars.

In Fig. 4 we show a comparison of the relative astrometry between Hipparcos and the new Tycho solutions for 2699 double stars. The scatter increases toward smaller separations especially for the separation (panel a). For measured separations below 0.4-0.5 arcsec, as indicated by the line, this is particularly pronounced.

As an assessment of the quality of double star measures from Tycho-2, they have been compared to systems with calibration quality orbits (see the 5th Orbit Catalog, Hartkopf et al. 2001). While the orbit catalog contains many definitive orbits it also contains a like number of wider, long-period systems whose orbits, while describing the complete motion inexactly, provide perfectly reasonable ephemerides over the observation dates. Two examples of these are given in Figs. 5 and 6. The full list of residuals to calibration systems is presented in Table 2. The first four columns identify the system by providing the TDSC running number, the epoch 2000 coordinate, discovery designation, and Hipparcos number. All of these systems have a significant observational history, and these tend to be quite bright. Therefore, all of these systems have Hipparcos numbers. One might reasonably wonder how these Tycho-2 observations compare for the fainter systems (i.e., those with no Hipparcos number), however, that sort of comparison is not possible here, since typically only brighter systems have enough observations to be deemed "calibration quality''. Columns five through seven give the epoch of observation, the position angle (in degrees), and the separation (in seconds of arc). Columns eight and nine give the O-C orbit residuals (in $\theta$ and $\rho$) to the orbit referenced in column ten. The systematic over-estimating of separations in very close systems which has been noted for other techniques (Worley 1981) is perhaps also seen here, where the mean for the 18 close systems (i.e., $\rho$ < 1 $.\!\!^{\prime\prime}$0) is $(\rm O{-}C_{\rho}) =$ 0 $.\!\!^{\prime\prime}$02. The mean $\frac{\vert(\rm O{-}C_{\rho})\vert}{\rho} =$ 1.42%, which compares quite well with ground-based high angular resolution work. While close systems are measured, at separations less than about 1 arcsec the error can be considerable; as shown in Fig. 7. While these measures with larger errors are still of value in systems with few measures, their value in systems with many measures (especially those with contemporaneous double star observations) is more limited.

5.2 Photometric comparisons

For close Hipparcos doubles, $B_{\rm T}$, $V_{\rm T}$ photometry is given by Fabricius & Makarov (2000a), (FM for short). They have analysed the Tycho data, taking advantage of the very accurate Hipparcos astrometry to obtain Tycho photometry for 9473 components of 5173 systems. The separations are between 0.3 and 2.5 arcsec. In Fig. 8 we compare this special photometry with the TDSC photometry. The fainter stars are generally brighter in TDSC than in FM by some $0\hbox{$.\!\!^{\rm m}$ }1$, and the effect is more pronounced for B components than for A components. A few per cent of the stars, mostly B components, show large differences of $0\hbox{$.\!\!^{\rm m}$ }25$ or more. The faint B components get brighter and the bright B components fainter; for the A component it is the reverse. The colours are better behaved. The faint stars are perhaps $0\hbox{$.\!\!^{\rm m}$ }05$ redder in TDSC than in FM, but the number of outliers is quite modest. Figure 9 shows the distribution of the more than 5000 components in the comparison, with respect to magnitude and separation. The upper panel shows the distribution of stars with modest errors and the bottom panel shows the ones with larger errors. Large deviations occur almost entirely for small separations, and what is to be considered "small'' depends on the magnitude.

5.3 Hipparcos single stars resolved in TDSC

Somewhat unexpectedly, six of the TDSC doubles turned out to be unresolved in the Hipparcos Catalogue. The immediate worry, that they must be false detection and indicate a low reliability for TDSC, is fortunately unwarranted. Three of the stars, HIP 14388, 47053A and 93519 are already known as doubles in the WDS. For the other three, HIP 25085, 86869 and 98334, we tried to make new Hipparcos solutions from the published transit data using the same method as in Fabricius & Makarov (2000b). All three solutions confirm the TDSC relative positions, but they are at the same time suffering from various problems. For HIP 25085 we get a well behaved Hipparcos solution with a separation of 0.66 arcsec, but the magnitude difference is almost 4 mag, as compared to 0.2 mag in TDSC. One may speculate that the Hipparcos solution is weakened by a separation close to half the grid period. For HIP 86869, the new solution gives about the same magnitudes as in TDSC, but a proper motion of almost 300 mas/year for the fainter component, which must then be a foreground star. Finally, HIP 98334 is in fact a single star, but has been playing us an odd trick, possibly because it is a Mira variable. The corresponding TDSC entries have been removed.

  

Table 2: Tycho measures of calibration quality orbits.

$$\begin{tabular}{lll@{~}rccccccl} \hline \multicolumn{1}{c}{TD... ...-$}0.007 & Starikova (\cite{stari}) \\ \hline\\ \end{tabular}$$

$\parbox{17.2cm}{ $^1$ ~{Note that TDSC 227 A-B has two calibration q... ...her, though the Tycho data here fit the Heintz (\cite{hei93}) orbit better.}}$

Figure 5: The double star measures of TDSC 39584 (= STF1937AB = WDS15232+3017) are plotted against the definitive orbit of Mason et al. (1999). Double star measures made with a micrometer are illustrated as plus signs while measures made by speckle interferometry are dots. The open circle at lower right is the measure of Tycho. For clarity, all other measures within 5 degrees in position angle of the Tycho measure are omitted. Data points are connected with their predicted positions on the orbit by $\rm O{-}C$ lines. The broken line is the line of nodes and the axes of the figure are in arcseconds. The direction of motion is indicated in the lower right corner. Position angles are measured from north through east.

Figure 6: The double star measures of TDSC 10552 (= STT  93 = WDS05005+0506) are plotted against the provisional (but still calibration grade) orbit of Seymour & Mason (1999). All symbols are as Fig. 5.

Figure 7: Separation vs. % error in separation ( $\frac{\vert(\rm O{-}C)_{\rho}\vert}{\rho}$) for the closer systems listed in Table 2. At a little less than 1 arcsec the error drops to $\sim$10%.

Figure 8: Comparison of the TDSC photometry for about 2750 Hipparcos double stars, with supposedly more accurate photometry from Fabricius & Makarov (2000a). Outliers are indicated with triangles.

Figure 9: The distribution of the stars from Fig. 8 with respect to magnitude and separation. Panel  a) shows those with $V_{\rm T}$ differences below $0\hbox{$.\!\!^{\rm m}$ }25$, while panel  b) shows those with larger differences.