A&A 422, 1023-1029 (2004)
DOI: 10.1051/0004-6361:20047172

Multicolour CCD measurements of nearby visual double stars. II[*]

A. Strigachev 1,2 - P. Lampens 2

1 - Institute of Astronomy, Bulgarian Academy of Sciences, 72 Tsarigradsko Shosse Blvd., 1784 Sofia, Bulgaria
2 - Royal Observatory of Belgium, Av. Circulaire 3, 1180 Brussels, Belgium

Received 30 January 2004 / Accepted 13 April 2004

We present accurate CCD astrometric and photometric data for 31 nearby visual double stars in the standard filters BVRI. The observations were collected with a 1.3-m telescope in 2001-2002[*]. The results consist of relative astrometric positions (epoch, angular separation and position angle) and differential BVRI photometry of the components. Mean errors are: 0.01 $^{\prime\prime}$ for the separation; 0.06$^\circ$ for the position angle; and 0 $.\!\!^{\rm m}$015 for the photometric data. Comparing the relative positions at different epochs, we evaluate the physical association of the systems. We additionally derive fractional masses and true separations for the most probable binary systems and, whenever orbits are available, also total and component masses.

Key words: stars: binaries: visual - techniques: photometric - stars: fundamental parameters

1 Introduction

This is the second paper devoted to CCD observations of nearby visual double stars performed at the Skinakas Observatory (Crete). In Paper I (Lampens & Strigachev 2001), we set the context of this research: our goal is to determine with a good accuracy the true separations, relative motions, masses (total and individual), luminosity ratios and temperature differences of the visual binaries in the immediate Solar neighbourhood. The determination of the distribution functions of these properties is known to provide observational constraints to the various scenarios of binary star formation and offers a direct calibration tool for basic stellar properties. We therefore need to accurately measure and monitor the (changing) astrometric parameters providing the fundamental data on the binaries as well as the individual properties of each component such as the magnitude and the colour indices. Accurate magnitude and colour differences of double stars allow the characterization of the evolutionary stage of the components as they allow one to derive basic properties of the system in the form of the luminosity and mass ratios and the temperature difference. It therefore remains surprising that colour differences, - if they exist at all - are seldom accurate, even for the nearest and brightest systems. Of course, the Hipparcos Catalogue provides a precise differential magnitude, $\Delta Hp$, for many visual binaries for the first time (ESA 1997). And while the recent Tycho Double Star Catalogue (Fabricius et al. 2002) allows one to derive the differences $\Delta B_{T}$ and $\Delta V_{T}$ (only if $\rho > 0.5\hbox{$^{\prime\prime}$ }$ and $\Delta m < 3$ mag), its accuracy is much lower and the information is not always complete. Note also that, from a comparison with ground-based CCD measurements, the Tycho-1 mag measurements of the components of double stars with separations up to $34\hbox{$^{\prime\prime}$ }$ (i.e. the width of the star mapper slits) were found to be contaminated by the companions (Halbwachs et al. 1997). For the construction of the Tycho-2 Catalogue, reprocessing with a dedicated tool for double star analysis was applied to visual double stars with separations between 0.8 and  $2.5\hbox{$^{\prime\prime}$ }$ only, whereas the components of the wider systems were still treated as independent entries (Fabricius et al. 2002).

In this work we present high-accuracy relative astrometry and BVRI differential photometric data for several tens of visual double stars from a programme that is based on the improved census of the Solar neighbourhood from the Hipparcos mission, which led to a significant change of the stellar content in the Solar vicinity (Jahreiss & Wielen 1998). The majority of our programme stars belongs to the intersection of the Catalogue of Nearby Stars (GJ, Gliese & Jahreiss 1991) and the Hipparcos Catalogue (ESA 1997) and have parallaxes larger than 0.04 $^{\prime\prime}$. They have been furthermore chosen among the systems with "intermediate'' angular separation (between 1 and 15 $^{\prime\prime}$) for which CCD observations can provide both accurate and complementary data on each of the components. Their absolute parallax measurements are very accurate. In a few cases however, we made use of the ground-based determined absolute parallaxes from The General Catalogue of Trigonometric Stellar Parallaxes (Van Altena et al. 1995) as they appear to be of higher accuracy than the Hipparcos ones.

The paper is organized as follows: firstly, we present the observations, the reduction method and the astrometric calibrations in Sect. 2. Next we show the resulting astrometric and photometric data (Sect. 3), followed by a discussion of the errors. In Sect. 4 we derive, wherever possible, true separations and masses for the probable physical binaries. Finally, conclusions are presented (Sect. 5).

2 Observations and reductions

2.1 Instrumentation and limitations

The observations were performed at the Skinakas Observatory of the Institute of Astronomy, University of Crete, Greece using the 1.3-m telescope equipped with a CCD camera. The telescope is an f/7.7 Modified Ritchey-Chrétien. The CCD is a Photometrics $1024\times1024$ SITe SI003B chip of grade 1 with a pixel size of 24 $\mu$m corresponding to a scale of $0.5\hbox{$^{\prime\prime}$ }$ on the sky. The usable field of view is $8.5\hbox{$^\prime$ }\times8.5\hbox{$^\prime$ }$.

The frames were taken from May to June 2001 and during August 2002 through standard Johnson B, V and Cousins R, I filters (Papadakis et al. 2003). Only visual double stars not brighter than mag 6 and with expected angular separations larger than or equal to about 1 $^{\prime\prime}$ were observed. These programme stars are listed in Table 1. Their angular separations range from 1 to 22 $\hbox{$^{\prime\prime}$ }$ while the differential V magnitudes are smaller than 4 $.\!\!^{\rm m}$0.

During the observations the exposure times were adjusted in order to get the highest possible counts for the primary (brighter) component without overexposing; they were usually a few seconds long. A set of three biases was taken regularly during each night, i.e. every few hours. Flat-fields were obtained during evening and/or morning twilights: a set of 5 to 6 flats per filter was taken every night. The open cluster NGC 6611 (=M 16) was chosen as the astrometric standard field. The seeing during these observations was $1.6\pm0.2\hbox{$^{\prime\prime}$ }$. The logbook of the observations is shown in Table 2.

Table 1: General information on the observed stars.

Table 3: Astrometric calibration.

2.2 The reduction method

All the primary reduction steps were performed using ESO-MIDAS standard routines. The frames were processed for bias and flat-field corrections. They include: subtraction of the residual bias pattern using a median master zero exposure frame, flat-fielding using a median master flat-field frame, and median cosmic ray cleaning.

Next we computed the angular separations (in pixels), the position angles and the magnitude differences in the various filters for the components of the double stars. For this we used a two-dimensional Moffat-Lorentz profile (Moffat 1982) fitting method. This dedicated tool was developed by Cuypers (1997) within the ESO-MIDAS environment and was also used in Paper I.

2.3 Astrometric calibration

To convert the angular positions to absolute units we applied the astrometric corrections as computed from stars observed in the field of NGC 6611. We used the following nine stars with the numbering 166, 197, 205, 223, 235, 246, 254, 280, 314, with the identification numbers and the coordinates following Hillenbrand et al. (1993). We measured their positions on the frames with standard ESO-MIDAS routines. A multi-linear regression fit was applied between the (x, y) positions and the catalogued ( $\alpha, \delta$) values to determine the scale and the orientation of the CCD chip, the latter being measured from the direction North towards East. The finally adopted values are presented in Cols. 3 and 5 of Table 3. In Col. 7 we list the Hipparcos numbers of the stars whose astrometric data were corrected with the corresponding values.

The thus computed scale is extremely close to the specifications of the telescope (Sect. 2.1) and to the value derived in Paper I (within the errors).

3 Presentation and discussion of the results

3.1 Astrometric and photometric results

The results consist of relative astrometric positions and differential photometry of the components.

The astrometric data are listed in Table 4. The first column gives the Hipparcos identification number, followed by the epoch (Bessel year), the angular separation ($\rho$) and the position angle ($\theta$) measured from North to East, with the respective standard errors  $\sigma_{\rho}$ and $\sigma_{\theta}$. The values of $\rho$ and $\theta$ are the means of several frames measured in the different filters. The number of frames per filter typically equals 3 (cf. Table 2). The next columns show the comparison of the relative positions with the Hipparcos Catalogue data (at epoch 1991.25) in the sense ours minus Hipparcos. In the last column we mention if the system has a known orbit or shows a linear relative motion (in the case of an optical pair). Other remarks concern the quality of the Hipparcos double-star solution.

In Table 5 the following photometric data are listed: the V magnitude difference ($\Delta V$) and the colour differences (( $\Delta B-\Delta V$), ( $\Delta V- \Delta R$) and ( $\Delta V-\Delta I$)), together with their respective standard errors. We consider that these values reflect the colour differences between the components (e.g. $\Delta(B-V)$) very well.

Specific comments are needed for the following systems:

HIP 2552: the colour differences were computed between the B and the Aa components (Henry & McCarthy 1993).

HIP 17749/50: the colour differences were computed between the A and the BC components.

HIP 54952: component B is too far (at  $54.5\hbox{$^{\prime\prime}$ }$) and does not influence our measurements.

HIP 65011/12: the colour differences were computed between the C and the B components (ESA 1997). Note that Balega et al. (1999) resolved the latter into a close double (BAG 11 Aa) and that these components are called B and A in the Washington Double Star Catalog (Mason et al. 2001).

3.2 Errors of the astrometry

The error in relative position (cf. Table 4) includes the contributions of the standard error on the mean value and the error of the astrometric calibration following the law of propagation of errors and supposing all the measurements to be independent. The astrometric measurements have typical errors of 0.01-0.04 pixels (5-20 mas), depending on the angular separation and on the magnitude difference between the components (Lampens et al. 2001). Surprisingly, the largest differences are mostly found for the widest angular separations (i.e. $\ge$15 $\hbox{$^{\prime\prime}$ }$). This can be explained by the fact that the Hipparcos measurement is not always reliable in this range of separation (ESA 1997, Vol. 1, p. 80). The average accuracy of the stellar coordinates used for the astrometric calibration is 0.3 $\hbox{$^{\prime\prime}$ }$ according to Hillenbrand et al. (1993). The standard errors of the multi-linear regression are extremely small (of the order of 0.00001) and are thus insignificant. The values of the scale and the orientation in Table 3 are the means of 3 different observational runs. Their rms errors are a factor of 10 smaller than the standard errors on the means of the measurements themselves. Because the astrometric calibration obtained with NGC 6611 is of very high quality, the errors in relative position are mainly a reflection of the internal consistency between the various filters used.

Table 4: Astrometric results and comparison of the relative positions with the Hipparcos data (only available online at the CDS).

Table 5: Differential photometry (only available online at the CDS).

3.3 Errors of the photometry

The internal errors in magnitude difference $\Delta V$ in Table 5 are the standard errors of the mean value. The errors on the colours were computed taking into account the contribution of both filters.

In Fig. 1 we plotted the internal error of the magnitude difference $\Delta V$ as a function of angular separation for two classes of $\Delta V$ for illustration: one can see that errors $\ge$20 mmag are linked to either a larger $\Delta V$value and/or a smaller angular separation. The mean photometric error is 15 mmag for all observed separations and $\Delta V$values; it is however below 10 mmag in the more favourable cases.

\end{figure} Figure 1: Photometry error vs. angular separation (in arcsec).
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External photometric errors can be estimated by observing the same (non-variable) targets with the same instrument during different campaigns. The stars HIP 2552, 86282, 97292 and 110893 were already observed by us before (cf. Paper I). In three cases (HIP 2552, 86282 and 110893) we were able to compare with the previous measurements (there are not enough measurements of HIP 97292). This result is shown in Table 6. The difference $\delta$ is in the sense these data minus those of Paper I. The contribution of various possible error sources was considered. The mean of the differences in differential magnitude and colours weighted with respect to their errors as listed in Table 6 is $0.005\pm0.001$ mag. This is a test for the quoted internal errors and also shows that there are no significant magnitude changes for these stars over the two years interval (Note, however, that HIP 2552 A = V547 Cas and HIP 110893 B = DO Cep are known flare stars).

Table 6: Differences of differential magnitude and colours over two years (1999-2001).

4 Determination of total and component masses and of true separations

From the colour differences presented in Table 5 and the joint UBV photometry of the systems available in the General Catalogue of Photometric Data (mean values for $(B-V)_{\rm AB}$ or for the measured component colours $(B-V)_{\rm A} (B-V)_{\rm B}$ from Mermilliod et al. 1997), applying Eq. (3) of Mermilliod et al. (1992), we derived the individual colours of the components. We then made use of the bolometric corrections listed as a function of (B-V) for main-sequence stars in Table 3 by Flower (1996). We computed the fractional mass, $\beta =M_{\rm B}/M_{\rm A+B}$, of the probable physical binaries of the sample via the relation:

\begin{displaymath}\beta = 1 / \left(1+10^{\Delta M_{\rm Bol}/(2.5 ~\rm K)}\right), \end{displaymath}

and the mass-luminosity relation with slope $K=3.82 \pm 0.07$ (Lampens et al. 1998). For binaries on the lower part of the main sequence (0.18  $M_{\odot}< M_{\rm A+B} < 0.5 ~M_{\odot}$as in the case of HIP 110893), we used the slope of 1.59 as derived by Henry & McCarthy (1993).

The global and component colours, the differences in bolometric correction, $\Delta M_{\rm Bol}$, as well as the resulting fractional masses are presented in Table 7. For HIP 2552 and HIP 86282 we compared these values with those of Paper I: the differences are smaller than 0.004. The distance between the primaries and their components (true separation in astronomical units) is also mentioned in Table 7. The quoted error includes the contribution of the standard error of both the angular separation and the parallax (mostly Hipparcos).

The published orbital elements (Hartkopf et al. 2001) are listed in Table 8. In Table 9 we give the sum and the component masses for systems with both known orbits and fractional masses. The majority of these orbits has a quality grade which is bad (grade 4 or 5) except for HIP 67422 and HIP 110893 (grade 2). In the latter cases the residuals are of order 50-70 mas. The relative positions of HIP 473, HIP 18512, HIP 65343, HIP 91768 and, to some extent, also HIP 110893 show large offsets with respect to their published orbits. The listed period, P, and semi-major axis, a, have been used to compute the sum of the masses of the components (except for HIP 13642, which in our case seems to show a relative linear motion, see Table 4). The relative error on the sum of the masses, $E_{\cal M_{A+B}}$, as derived from Kepler's third law,

\begin{displaymath}E_{\cal M_{A+B}}=\pm \sqrt{E^{2}_{a^{3}/P^{2}}+9E^{2}_{\pi}},\end{displaymath}

- where $\pi$ is the parallax - depends on the relative error $E_{\pi}$ (times a factor 3) and on the relative error Ea3/P2. The contribution of the relative error of the ratio (a3/P2) is usually small compared to the one of the parallax but should not be neglected in the case of a nearby system. One can deduce from the formula above that, in order to reach a relative accuracy of 10% on the mass sum, the relative error of a3/P2 should not exceed 1% if $E_{\pi}$ equals 3.3% (the latter being valid only for systems within 17 pc, i.e. having a parallax >0.060 $\hbox{$^{\prime\prime}$ }$, given the standard Hipparcos parallax accuracy of 2 mas. This situation illustrates the typical case for the orbital pairs listed in Table 9. HIP 65343, HIP 66492 and HIP 79492 have slightly larger errors of respectively 4%, 6% and 3.9%). Considering that the majority of the orbits are of grade 4 ("preliminary'') or 5 ("indeterminate'') a relative error Ea3/P2 of at least 10% must be adopted based on a statistical comparison between orbit grades (assigned by Worley & Heintz 1983) and the relative error Ea3/P2 (called "quality index'' by Ruymaekers 1999). The comparison indeed showed that only 25% of the orbits rated grade 4 and none of the orbits rated grade 5 corresponded to Ea3/P2 < 10% (Table 3.5 in Ruymaekers 1999). When no errors on the orbital elements are published, we adopted a minimal error of 15% (orbits with grade 4 and 5) and of 10% (two orbits with grade 2) for Ea3/P2. Thus the error $\sigma(\cal M_{A+B})$ is generally a lower limit. Else, we mention the relative sum mass errors following the error propagation law as was previously done (e.g. HIP 110893). Except for two cases (HIP 67422 and HIP 110893), the relative sum mass error will therefore never be smaller than 15%.

Table 7: Component colours, $\Delta M_{\rm Bol}$, fractional masses and estimated true separations.

Table 8: Parameters and residuals (of the relative positions) with respect to known orbits.

5 Conclusions

In this paper we presented high-accuracy astrometric and photometric results of multicolour CCD observations for 31 visual double stars in the Solar neighbourhood. As already mentioned in Paper I, the 1.3-m telescope at the Skinakas Observatory equipped with a professional CCD camera allows one to obtain high-quality data on "intermediate'' visual double stars, with an angular separation >1.4 $\hbox{$^{\prime\prime}$ }$. The mean internal errors are $0.01\pm 0.001$ $^{\prime\prime}$ in angular separation, $0.06\pm 0.005$$^\circ$ in position angle and $0\hbox{$.\!\!^{\rm m}$ }015\pm0.001$ in differential photometry. A comparison with some previous measurements shows that the quoted errors are consistent.

From a comparison of the new relative positions with the Hipparcos ones (with a minimum epoch difference of over 10 years) we can classify the 31 visual double stars as follows: 3 are optical pairs (HIP 3937, HIP 10531/29 - with ambiguous Hipparcos solution - and HIP 97292); 12 have known orbits (Table 8); HIP 13642 has a parabolic orbit (Hopmann 1967) but the data also fit a relative linear motion; 3 have a stable configuration (HIP 63253, HIP 83020 and HIP 86282); 3 have ambiguous Hipparcos solutions (HIP 21088, HIP 87768 and HIP 97241). The remaining 10 show a relative motion.

Comparing with the corresponding ephemeris positions, we conclude that the relative positions of HIP 473, HIP 18512, HIP 65343, HIP 91768 and, to some extent, also HIP 110893 show large offsets with respect to their latest published orbits. These binaries still need to be monitored in the future to improve the accuracy of the orbital parameters, and in particular of the ratio (a3/P2) to have more reliable mass determinations for these nearby systems.

We computed the differences $\Delta B$, $\Delta V$, $\Delta R$ and $\Delta I$ between the components, allowing us to derive at least one colour difference for all these double stars except for one case (HIP 79492). We stress the fact that in 12 of these 31 cases, no $\Delta B_{T}$ values exist in the Tycho Double Star Catalogue (Fabricius et al. 2002). Based on the newly derived component colours, we computed the differences in bolometric magnitude and determined the true separations and the fractional masses whenever joint photometric data were also found in the literature for 10 of the 12 orbital pairs and for 8 visual double stars showing evidence of relative motion as well as for one yet unclassified case (HIP 87768, a wide pair discovered during the Hipparcos mission but with a very poor solution), i.e. for those systems of the sample showing evidence of a relative (orbital) motion.

Finally, we also derived the sum and the component masses for 10 of the 12 visual binaries whose orbital parameters are known and published. Among these, 2 are fully consistent with a previous determination while 8 are new.

Table 9: Sum and component mass determinations.


We thank Prof. Y. Papamastorakis, Director of the Skinakas Observatory, and Dr. I. Papadakis for the allocated telescope time. A. Strigachev gratefully acknowledges a grant from the Belgian Federal Science Policy (formerly Office for Scientific, Federal and Cultural Affairs) in the framework of the project "Multicolour photometry and astrometry of double and multiple stars''. We also thank the anonymous referee for very useful comments which helped to improve the paper. This research made use of the SIMBAD and VIZIER databases, operated at CDS, Strasbourg, France, as well as the Double Star Library maintained at the U.S. Naval Observatory, Washington, DC (http://ad.usno.navy.mil/wds/dsl.html).



Online Material

Table 2: Log of observations.

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