2 Observations and data reduction

   
2.1 The sample

We have repeatedly observed 21 systems in Taurus-Auriga detected as binaries by Leinert et al. (1993) and Köhler & Leinert (1998) and 11 systems in Scorpius-Centaurus detected by Köhler et al. (2000). Furthermore, we re-observed two binaries found by Ghez et al. (1997a). These are HM Anon in the ChamaeleonI association, and HN Lup in the Lupus SFR. We combine our data with results taken from literature (see Sect. 2.6). In particular twelve systems discussed by G95 are also objects of our study.

   
2.2 Observations

The objects in Taurus-Auriga were observed with the 3.5m-telescope on Calar Alto. After September 1993 these observations used the NIR array camera MAGIC. Previous measurements were obtained with a device for one-dimensional speckle interferometry described by Leinert & Haas (1989). The observations of young binaries in southern SFRs were carried out at the ESO New Technology Telescope (NTT) at La Silla that is also a 3.5m-telescope. The instrument used for these observations was the NIR array camera SHARP I of the Max-Planck Institute for Extraterrestrial Physics (Hofmann et al. 1992). Both cameras are capable of obtaining fast sequences of short exposures with integration times $\tau\approx 0.1\,{\rm s}$, which is crucial for the applied data reduction process (see Sect. 2.3).

Most of the data were obtained in the K-band at $\lambda=2.2~\mu{\rm m}$. Some observations used the J-band at $\lambda=1.25~\mu{\rm m}$ and the H-band at $\lambda=1.65~\mu{\rm m}$. In these cases the main goal of the observations was to obtain resolved photometry of the components at those wavelenghts. In the course of data reduction we could however show that highly precise relative astrometry can also be derived from observations in J and H (see Sect. 2.4 for the determination of binary parameters).

   
2.3 Speckle interferometry

At the presumed distance of the objects (between 140 and 190pc, see Sect. 3.1 and Table 1) orbital motion measurable within a few years can only be expected for the closest pairs with projected separations of $d\le 0\hbox{$.\!\!^{\prime\prime}$ }5$. Therefore, high angular resolution techniques are necessary that overcome the effects of atmospheric turbulence and yield the diffraction-limited information about the objects. For this purpose, we have used speckle interferometry.

Sequences of $\approx$1000 short exposures ( $\tau\approx 0.1\,{\rm s}$) are taken for the object and a nearby point source, the reference star. The integration time is shorter than the coherence time of the turbulent atmosphere, so the turbulence is "frozen'', and the images are noisy, but principally diffraction limited. After Fourier transforming these "data cubes'', the power spectrum of the image is deconvolved with that of the reference star to obtain the modulus of the complex visibility. The phase is reconstructed using the Knox-Thompson algorithm (Knox & Thompson 1974) and the bispectrum method (Lohmann et al. 1983). The complex visibility is the Fourier transform of the object brightness distribution. For a sufficiently bright object it will contain the diffraction-limited information.

   
2.4 Determination of binary parameters

Modulus and phase of the complex visibility are characteristic strip patterns for a binary, as shown in Fig. 1 (first row) for the XZ Tau system. The position angle of the companion is orientated perpendicular to these patterns and towards higher values of phase. The distance between two strips is inversely proportional to the projected separation of the components, and the amplitude of the patterns denotes the flux ratio. Position angle, projected separation and flux ratio are determined by constructing an artificial complex visibility from a set of these parameters (second row in Fig. 1) and fitting it to the data (third row in Fig. 1). This fit uses the Amoeba algorithm (Press et al. 1994). The errors of the binary parameters are estimated by applying this fitting procedure to different subsets of the data.

Figure 1: The first row shows modulus (left) and bispectrum-phase (right) of the complex visibility for the binary XZ Tau, derived from data obtained on 29 Sep. 1996 at the 3.5m-telescope on Calar Alto with the NIR array camera MAGIC at $\lambda=2.2~\mu{\rm m}$. The second row is the modulus and phase of an artificial complex visibility that is fitted to the data. This fit is indicated in the third row in a one-dimensional projection towards the connection line of the components (perpendicular to the strip patterns in Fourier space). The circle around the strip patterns corresponds to the Nyquist spatial frequency, $7.0\,{\rm arcsec}^{-1}$ for the adopted pixel scale

   
2.5 Pixel scale and detector orientation

To obtain position angle and projected separation as astronomical quantities they must be transformed from the array onto the sky by calibrating them with pixel scale and orientation of the detector. Minimizing the uncertainties that result from this calibration is crucial for a highly accurate determination of the components' relative astrometry that is proposed here. We determine pixel scale and detector orientation from astrometric fits to images of the Orion Trapezium cluster where precise astrometry has been derived by McCaughrean & Stauffer (1994). Typical errors are $0.1^{\circ}$for the detector orientation and $10^{-4}\,{\rm arcsec/pixel}$for the pixel scale that is $\approx$ $0\hbox{$.\!\!^{\prime\prime}$ }07/{\rm pixel}$ for MAGIC and $\approx$ $0\hbox{$.\!\!^{\prime\prime}$ }05/{\rm pixel}$ for SHARP I.

This precise calibration exists for all observations obtained by the authors since July 1995. For calibrating data from previous observing runs we used visual binary stars with well-known orbits. We observed these stars afterwards and calibrated their separation and position angle with the help of the Trapezium cluster. Thus, we have placed all our (two-dimensional) speckle observations into a consistent system of pixel scale and detector orientation.

   
2.6 The database

In Table A.1 the derived position angles, projected separations and flux ratios are presented. For the subsequent analysis (Sect. 3) the relative positions are combined with data taken from literature. Twelve of our systems have also been discussed by G95. For some binaries there are additional measurements obtained by HST imaging, the HST Fine Guidance Sensors or adaptive optics (see references in Table A.1). The finding that our relative astrometry fits very well with that obtained by other groups further supports the idea that the position angles and projected separations are as precise as is indicated by the errors given in Table A.1.

 

 

Table 1: Adopted distances to stars in nearby SFRs

SFR	Distance[pc]	Reference
Taurus-Auriga	$142 \pm 14$	Wichmann et al. (1998)
Scorpius-Centaurus	$145 \pm 2$	de Zeeuw et al. (1999)
ChamaeleonI	$160 \pm 17$	Wichmann et al. (1998)
Lupus	$190 \pm 27$	Wichmann et al. (1998)

 

 

Table 2: Projected relative velocities of the companions with respect to the primaries in cartesian and polar coordinates. The adopted v is the mean of the total velocities derived from (v_x, v_y) and $(v_{\rho }, v_{\phi })$. Note that $v_{\rho }$ is given with respect to the main component and not relative to the observer

System	$v_x[\rm km\,s^{-1}]$	$v_y[\rm km\,s^{-1}]$	$v_{\rho}[\rm km\,s^{-1}]$	$v_{\phi}[\rm km\,s^{-1}]$	$v[\rm km\,s^{-1}]$	$\bar{d}$[AU]
V 773 Tau	-1.35 $\pm$ 2.47	15.64 $\pm$ 6.87	-8.37 $\pm$ 6.82	8.41 $\pm$ 2.83	13.78 $\pm$ 7.34	14.9
LkCa 3	4.54 $\pm$ 1.92	1.16 $\pm$ 1.07	-0.60 $\pm$ 1.49	-2.98 $\pm$ 1.62	3.86 $\pm$ 2.20	68.7
FO Tau	3.67 $\pm$ 1.63	-5.62 $\pm$ 1.52	-1.48 $\pm$ 1.36	5.63 $\pm$ 1.72	6.27 $\pm$ 2.21	22.3
CZ Tau	-4.83 $\pm$ 1.46	-1.97 $\pm$ 2.22	-2.72 $\pm$ 2.27	4.98 $\pm$ 1.43	5.45 $\pm$ 2.67	45.3
FS Tau	-9.26 $\pm$ 2.87	2.06 $\pm$ 1.44	-1.88 $\pm$ 1.54	6.61 $\pm$ 2.77	8.18 $\pm$ 3.19	35.6
FW Tau	8.11 $\pm$ 2.12	-7.69 $\pm$ 2.22	-7.77 $\pm$ 2.24	6.87 $\pm$ 1.67	10.77 $\pm$ 2.93	15.8
LkH$\alpha$ 331	-3.77 $\pm$ 2.21	2.51 $\pm$ 1.04	-1.55 $\pm$ 1.65	1.76 $\pm$ 1.77	3.44 $\pm$ 2.43	40.3
XZ Tau	2.14 $\pm$ 1.03	4.25 $\pm$ 1.32	-0.35 $\pm$ 0.50	-5.03 $\pm$ 1.52	4.90 $\pm$ 1.64	43.2
HK Tau G2	0.41 $\pm$ 0.34	-2.06 $\pm$ 1.92	5.00 $\pm$ 1.80	-2.05 $\pm$ 1.92	3.75 $\pm$ 1.95	26.3
GG Tau Aa	-0.62 $\pm$ 0.69	-6.59 $\pm$ 1.82	0.41 $\pm$ 0.72	-4.71 $\pm$ 1.80	5.67 $\pm$ 1.94	35.8
UZ Tau/w	3.20 $\pm$ 1.31	1.36 $\pm$ 1.24	1.21 $\pm$ 1.32	2.76 $\pm$ 1.24	3.24 $\pm$ 1.81	50.9
GH Tau	8.61 $\pm$ 2.96	-2.97 $\pm$ 2.14	-1.42 $\pm$ 3.18	-3.19 $\pm$ 1.92	6.30 $\pm$ 3.68	45.0
Elias 12	-13.79 $\pm$ 3.95	-0.65 $\pm$ 1.71	-6.05 $\pm$ 3.67	-4.68 $\pm$ 2.56	10.73 $\pm$ 4.39	49.3
IS Tau	-4.55 $\pm$ 2.35	0.45 $\pm$ 1.92	0.21 $\pm$ 1.93	3.24 $\pm$ 2.37	3.91 $\pm$ 3.04	31.7
IW Tau	-2.50 $\pm$ 0.55	-1.14 $\pm$ 1.91	2.50 $\pm$ 0.47	2.79 $\pm$ 1.80	3.24 $\pm$ 1.97	39.6
LkH$\alpha$ 332/G2	2.31 $\pm$ 1.80	7.68 $\pm$ 3.23	-5.58 $\pm$ 2.46	3.72 $\pm$ 2.07	7.36 $\pm$ 3.45	36.5
LkH$\alpha$ 332/G1	-1.66 $\pm$ 1.62	0.54 $\pm$ 1.23	2.86 $\pm$ 1.06	5.50 $\pm$ 1.76	3.97 $\pm$ 2.04	32.2
LkH$\alpha$ 332	2.91 $\pm$ 3.54	1.21 $\pm$ 1.20	-0.30 $\pm$ 3.69	-0.83 $\pm$ 0.60	2.02 $\pm$ 3.74	47.0
BD+26718B Aa	-6.98 $\pm$ 2.14	5.40 $\pm$ 1.66	-8.26 $\pm$ 2.70	-0.35 $\pm$ 0.12	8.55 $\pm$ 2.71	67.5
BD+26718B Bb	0.98 $\pm$ 3.60	1.06 $\pm$ 1.51	2.07 $\pm$ 3.48	3.02 $\pm$ 1.84	2.55 $\pm$ 3.92	23.3
BD+17724B	0.49 $\pm$ 1.64	10.83 $\pm$ 6.20	-0.41 $\pm$ 3.88	-4.02 $\pm$ 5.15	7.44 $\pm$ 6.43	12.8
NTTS155808-2219	0.75 $\pm$ 2.64	-4.06 $\pm$ 2.06	3.43 $\pm$ 2.13	2.31 $\pm$ 1.72	4.13 $\pm$ 3.05	29.4
NTTS155913-2233	1.60 $\pm$ 0.80	-5.38 $\pm$ 2.03	3.09 $\pm$ 0.90	-5.30 $\pm$ 1.85	5.87 $\pm$ 2.11	43.3
NTTS160735-1857	0.89 $\pm$ 2.51	-6.38 $\pm$ 2.24	0.17 $\pm$ 1.91	-6.44 $\pm$ 2.28	6.44 $\pm$ 3.18	43.4
NTTS160946-1851	-1.02 $\pm$ 0.64	0.09 $\pm$ 0.61	0.18 $\pm$ 0.65	1.04 $\pm$ 0.64	1.04 $\pm$ 0.90	30.5
HM Anon	1.04 $\pm$ 9.33	-7.04 $\pm$ 8.94	-2.65 $\pm$ 7.43	6.61 $\pm$ 6.42	7.12 $\pm$ 11.37	42.1
HN Lup	7.42 $\pm$ 3.30	-0.94 $\pm$ 3.21	1.57 $\pm$ 3.33	-7.32 $\pm$ 3.15	7.48 $\pm$ 4.60	46.3
RXJ1546.1-2804	22.34 $\pm$ 1.58	2.86 $\pm$ 4.86	-3.77 $\pm$ 1.84	-24.40 $\pm$ 7.21	23.60 $\pm$ 6.28	14.3
RXJ1549.3-2600	-0.83 $\pm$ 1.33	-0.45 $\pm$ 1.23	-0.17 $\pm$ 1.40	0.92 $\pm$ 0.46	0.94 $\pm$ 1.64	23.7
RXJ1600.5-2027	-4.02 $\pm$ 1.61	1.10 $\pm$ 1.42	1.88 $\pm$ 1.69	-3.72 $\pm$ 1.21	4.17 $\pm$ 2.12	28.2
RXJ1601.7-2049	2.04 $\pm$ 1.75	1.56 $\pm$ 1.73	0.00 $\pm$ 1.37	-2.57 $\pm$ 1.77	2.57 $\pm$ 2.11	29.7
RXJ1601.8-2445	8.43 $\pm$ 4.55	1.46 $\pm$ 4.76	7.79 $\pm$ 3.53	-3.59 $\pm$ 5.74	8.56 $\pm$ 6.66	13.3
RXJ1603.9-2031B	-2.03 $\pm$ 2.93	-9.58 $\pm$ 1.73	-4.28 $\pm$ 2.11	-8.95 $\pm$ 3.19	9.86 $\pm$ 3.61	15.8
RXJ1604.3-2130B	-2.98 $\pm$ 1.82	-2.52 $\pm$ 1.43	1.03 $\pm$ 1.55	3.78 $\pm$ 1.67	3.91 $\pm$ 2.13	12.3