4 Construction of the catalogue

The construction of the TDSC follows the same main principles as for Tycho-2, as described in Høg et al. (2000a), and uses the same astrometric and photometric calibrations. Here we restrict ourselves to TDSC specific questions.

We should, however, mention the problem of sidelobes. Due to the design of the Tycho instrument, with eight long slits (see ESA 1997, for details), sidelobes will cause a disturbance at characteristic distances from each star. This gives a risk of spurious detections of "new'' components or double stars, due to the sidelobes. We have checked relevant cases in an attempt to eliminate such mistakes.

4.1 Relative positions

In addition to the absolute positions given for each component, we also derive the traditional relative positions in terms of position angle and separation. Starting from the first component, the entire geometry of the system can easily be established from the relative positions only.

In the Hipparcos and Tycho Catalogues, the observed position for a star results from the combination of a large number of one-dimensional observations along different directions. This mean position therefore represents a slightly different epoch in right ascension and declination, and these epochs will differ from one star to the next, though only slightly for neighbouring stars. The separations and position angles we present here are computed for an epoch which is the mean of the four relevant epochs. As in the Hipparcos Catalogue, the position angles are given with respect to the ICRS pole. This is unlike traditional double star observations which are made relative to the pole of observation date. Standard errors of position angle and separation have been derived, taking the correlations between RA and Dec into account.

4.2 Photometry

The photometry in the catalogue is either copied across from Tycho-2 or new TDSC photometry, processed using the same set of calibrations as for Tycho-2. For the supplementary Hipparcos and Tycho-1 stars, which were copied across to the TDSC Supplement for completeness, the situation is more complex. For about half of them, $B_{\rm T}$, $V_{\rm T}$ photometry is taken from Tycho-1 or from Fabricius & Makarov (2000a). For the other half, only the Hipparcos magnitude, Hp, is given. A flag in the catalogue specifies the origin of the photometry.

4.3 TDSC identification

The stars in TDSC are identified by a running number which specifies the system, and a one- or two-character component designation.

 

 

Table 1: Distribution of number of components in each system, for the main TDSC catalogue, for new systems in the main catalogue, and for the supplement.

N	main	new	supplement	total
comp	catalogue	systems	catalogue
1	$32\,263$	-	4420	$28\,572$
2	$31\,785$	$13\,250$	166	$35\,432$
3	758	1	7	$1\,047$
4	76		1	132
5	7			16
6	3			8
7	1			1
8	0			1
11	1			1

The number of components in each system is shown in Table 1. Multiple systems in TDSC may well consist of more than one physical system. We have only looked at the WDS position to define the number of members in a system. E.g., a "triple'' system like TDSC 232 (WDS 00059+1805) consists of an A-B pair with high proper motion (200 mas/yr) and a C component at a large separation and with small proper motion. Nothing indicates a physical connection between the C component and the A-B pair.

Figure 2: The sky distribution in ecliptic coordinates of TDSC systems known in the present WDS (panel a)), and newly discovered systems b).

4.4 Component reversal

In the double star processing, the signal from one of the components is subtracted from the total signal at the assumed location of that component and with the assumed amplitudes, and the other component is then sought in the residual signal. The process is then repeated, but now the second component is subtracted and an improved position for the first is determined. As many iterations are made as required to obtain a stable solution. Unfortunately, a stable solution does not always mean a correct solution. Examples are known for close doubles, where we have found the bright component near the photocentre, leaving a rather strong residual signal on the opposite side of the primary. The secondary is then found with an error of $180\hbox{$^\circ$ }$ in position angle. Such erroneous solutions with "component reversal'' can be quite stable, and fulfill the convergence criterion.

For all relevant solutions, we computed alternative solutions assuming that the first suffered from component reversal. We then restarted the iterations, but starting from the alternative solution. If the second set of iterations converged to a different solution, the signal-to-noise ratios and the separation values were used to judge which was the correct solution. Despite this effort, we cannot exclude that a number of "reversed'' solutions have survived.

4.5 Notes

Notes are provided for some stars to explain peculiarities, particularly related to the identification. The value of the note flag indicates which kind of problem has been found. We distinguish between unclear or ambiguous WDS designations, WDS components we have apparently resolved, stars added to a WDS system and just general notes. The flag for resolved WDS components should also be seen as a warning that the new component may be spurious.