The Astronomical Journal, 144:80 (8pp), 2012 September C 2012.
doi:10.1088/0004-6256/144/3/80
The American Astronomical Society. All rights reserved. Printed in the U.S.A.
SYSTEM ADS 48: VISUAL BINARY OR MULTIPLE SYSTEM Z. Cvetkovi´c, R. Pavlovi´c, S. Ninkovi´c, and M. Stojanovi´c Astronomical Observatory, Volgina 7, 11060 Belgrade 38, Serbia;
[email protected] Received 2012 May 24; accepted 2012 July 11; published 2012 August 9
ABSTRACT In this paper, we analyze seven components of system ADS 48. Its number in the Washington Double Star Catalog is 00057+4549. We use the measuring results from our CCD frames obtained between 1994 and 2011. Our aim is to establish which of these components are gravitationally bound, i.e., have an orbital motion around the mass center, and which of them are mutually very distant in space so that only their projections are close in the field of view. In addition to the measurements, we also apply different criteria based on celestial mechanics. Out of seven considered components, only the closest pair STT 547 AB is in orbital motion around the mass center. The other components, except that with the largest separation, are merely projected stars. The most distant component has common proper motion with pair AB. Key words: binaries: visual – stars: individual (ADS 48) – techniques: image processing ponent P was discovered by G. Popovi´c in 1994 (Popovi´c & Pavlovi´c 1997a) and 16 measurements for the pair designated as POP 217 AP are available. In the case of four other pairs of this system—POP 217 AQ, POP 217 AX, POP 217 AY, and POP 217 YG—the number of measurements is small (less than 10). They were observed within a short time interval between 1998 and 2006. The magnitude differences between the components for these four pairs are large (Δm > 5), the components Q, X, Y, and G are fainter than m = 14. They are not considered here. The complete measurements for this system were obtained from the Washington Database due to the courtesy of B. Mason to whom we owe our very sincere gratitude. Until now the orbits for the closest pair AB and the widest pair AF have been calculated. In the Sixth Catalog of Orbits of Visual Binary Stars, one can find two orbital solutions concerning AB: Popovi´c & Pavlovi´c (1996) and Kiyaeva et al. (2001). In the case of AF preliminary orbital elements have been given by Kiyaeva et al. (2001). The motion of the F component has been measured since 1897 and in the course of these 115 years neither its position angle nor the angular separation have changed. In almost all of the measurements the photographic method was applied, with an astrograph (Kiyaeva et al. 2001). The orbital period has been estimated to be 830 centuries. For the other four pairs—AC (Friedman et al. 2012), AE (Hartkopf & Mason 2011), and AD and AP (Cvetkovi´c 2011)—linear solutions have been determined and one can find them in the Catalog of Rectilinear Elements. In the present paper we want to examine the components of system ADS 48 listed in WDS, more precisely to establish if any of them together with the closest pair AB forms a gravitationally bound system. Such an analysis also includes the possibility of common kinematics.
1. INTRODUCTION Systematic observations of double stars have been carried out for about 200 years. The measuring techniques and methods have been inevitably changed and improved, from visual micrometric measurements toward high-angular-resolution techniques. The Washington Double Star Catalog (WDS)1 contains the data for more than 117,000 pairs, components of double or multiple stars, for which the relative coordinates, position angle, and angular separation have been measured. Out of this number, almost 102,000 pairs have been observed less than 10 times. Also, in the case of many pairs no change in position angle and/or angular separation over a sufficiently long time interval has been registered. Only for a small number of pairs, about 2100, have the orbital elements been calculated, i.e., a Keplerian motion has been confirmed. Their orbital elements can be found in the Sixth Catalog of Orbits of Visual Binary Stars.2 This is about 2% of the whole sample. In the case of more than 1200 pairs there are linear solutions given in the Catalog of Rectilinear Elements.3 In the case of such pairs there are, in principle, three possibilities: to be gravitationally bound, but with large orbital periods, to be kinematically similar (say, common-proper-motion pairs), and to be mere optical pairs. For the purpose of establishing which of the three possibilities is the true one, observations covering long time intervals or detailed analysis of their data are needed. An example of interest is a system registered in ADS—the Aitken Double Stars catalog (Aitken 1932)—as ADS 48. In WDS its number is 00057+4549 and there are measured relative coordinates between eleven components. The closest pair was discovered by O. Struve in 1876 (Struve 1878) and its designation is STT 547 AB after him. Up to now this pair has been measured 394 times. R. Furuhjelm in 1897, as cited in ADS, made the first measurement for the pair designated in WDS as STT 547 AF. In the early twentieth century S. W. Burnham in 1911 (Burnham 1913) made the first measurements for other three pairs in WDS designated as STT 547 AC, STT 547 AD, and STT 547 AE. The relative coordinates for these pairs have been measured from that time. The number of measurements for them are 10, 17, 23, and 36, respectively. The seventh com1 2 3
2. OBSERVATIONS From 2004 till now a group of astronomers from the Belgrade Observatory have stayed several times at the National Astronomical Observatory Rozhen (NAOR) in Bulgaria and taken frames of visual double and multiple stars. A series of observations of double and multiple stars at the Bulgarian NAOR have been made with a CCD camera attached to their 2 m telescope. Only in the observations from 2004 was the CCD camera Photometrics CE200A used. The chip dimensions are 1024 × 1024 pixels, and the pixel size is 24 μm × 24 μm.
http://www.usno.navy.mil/USNO/astrometry/optical-IR-prod/wds/WDS http://www.usno.navy.mil/USNO/astrometry/optical-IR-prod/wds/orb6 http://www.usno.navy.mil/USNO/astrometry/optical-IR-prod/wds/lin1
1
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Table 1 Basic Characteristics of the CCD Cameras; FOV is the Field-of-view Size CCD Camera
Pixel Array
Pixel Size (μm)
FOV (arcmin)
Apogee Alta U42 2048 × 2048 13.5 × 13.5 15.8 × 15.8 SBIG ST-10ME SBIG ST-6
Table 2 Parallaxes, Proper Motions, Magnitudes, and Spectral Types of the Seven Components of the System ADS 48, as well as Our Δm Values with Respect to Component A
(arcsec pixel−1 )
Component HIP Number
0.46 × 0.46
2184 × 1472
6.8 × 6.8
8.3 × 5.6
0.23 × 0.23
375 × 241
23 × 27
4.9 × 3.7
0.79 × 0.93
A B C D E F P
The angle corresponding to one pixel is 0.31 arcsec. All later observations have been performed with the CCD camera VersArray: 1300B. The chip dimensions for this camera are 1340 × 1300 pixels, the pixel size is 20 μm × 20 μm. The angle corresponding to one pixel is 0.26 arcsec. The results of observations performed in 2011 have been published in Pavlovi´c et al. (2005) and Cvetkovi´c et al. (2006, 2007, 2010, 2011). The results of observations performed during 2011 will be published in a future work (Z. Cvetkovi´c et al., in preparation). During the summer of 2011 the first observations of celestial bodies from the new Astronomical Station on the mountain of Vidojevica (ASV) took place. This station belongs to the Astronomical Observatory of Belgrade. It is located in southern Serbia near the town of Prokuplje. The geographic coordinates of the station are: 21◦ 33 20. 4 longitude, 43◦ 08 24. 6 latitude, and 1150 m altitude above the sea level. More details can be found online.4 The 60 cm telescope was purchased from Astro Optik—an Austrian company—which, in the meantime, has become a part of a much bigger company, Astro System Austria (ASA). The telescope has a German equatorial mounting and a Cassegrain optical system with optical elements constructed in the LOMO company in St. Petersburg, Russia. The primary mirror is parabolic with a diameter of D = 60 cm. The secondary mirror is hyperbolic with a diameter of D = 20 cm, making it a classical Cassegrain optical system. The telescope focal length is 600 cm. From 2011 June to 2012 April we carried out several series of CCD observations of visual double or multiple stars at ASV. For these series we used either SBIG ST-10ME or Apogee Alta U42 CCD cameras. Their basic characteristics are summarized in Table 1. The first column gives the camera type; the size (in pixel units) of the pixel array is given in Column 2 and pixel size in Column 3; Column 4 gives the field-of-view size; and the scale in arcseconds per pixel is given in Column 5. The first CCD frames of the ADS 48 multiple system at our disposal were obtained in 1994 (Popovi´c & Pavlovi´c 1997a). These observations were performed with a CCD ST-6 camera attached to the Large Zeiss Refractor at the Astronomical Observatory of Belgrade. The diameter of its lens is 65 cm and focal length 1055 cm. We also obtained frames of this system at NAOR in 2004, 2005, 2006, 2010, and 2011, as well as three times at ASV in 2011: in August and October by using the CCD cameras Apogee Alta U42 and in November by using SBIG ST-10ME camera. The selected CCD frames obtained from 1994 to 2011 are presented in Figure 1. The relative coordinates of components in frames were measured by using the AIP4WIN software (Berry & Burnell 2002).
μα cos δ (mas)
μδ (mas)
m
Sp
88.44 ± 1.56 887.48 −152.02 8.98 K6 88.44 ± 1.56 887.48 −152.02 9.15 M0 ... 0.0 0.0 12.70 . . . ... 2.3 −1.4 12.51 . . . ... 8.7 −9.1 11.75 . . . 88.88 ± 1.42 870.19 −150.45 10.19 M2e ... 0.1 3.9 10.19 . . .
Δm ... 0.05 5.32 3.11 3.14 0.92 4.26
its parallax πHIP = 88.44 ± 1.56 mas is given in the new Hipparcos astrometric catalog (van Leeuwen 2007). This pair has a large proper motion, μα cos δ = 887.48 mas yr−1 and μδ = −152.02 mas yr−1 . The apparent magnitudes of the components are 8.98 (A) and 9.15 (B); their spectral types are K6 and M0, respectively. The orbital period according to Popovi´c & Pavlovi´c (1996) is equal to 1550 years, whereas according to Kiyaeva et al. (2001) it is about three times as small, equal to 509 years. The observations cover an orbital arc of about 70◦ and both orbits yield good fits. The F component has the number 428 in the Hipparcos Catalog. It has nearly the same parallax (πHIP = 88.88 ± 1.42 mas) and proper-motion components (μα cos δ = 870.19 mas yr−1 and μδ = −150.45 mas yr−1 ) as pair AB. Its apparent magnitude is 10.19, and the spectral type is M2e. The separation between A and F is large, and its value is 328 . The F component is not visible (it is outside view field) in our frames, except in the frames obtained with the CCD camera Apogee Alta U42, which has a larger view field. In Figure 2 one selected CCD frame obtained with Apogee Alta U42 is presented. The other components, C, D, E, and P, have much smaller proper motions and they are fainter than the three former components (see Table 2). In the frame from 1994 (see Figure 1) only four components, A, B, E, and P, are visible. In the other frames one can also see components C and D, as well as the image of the star designated by us as R. It has no measurements of relative coordinates and in the WDS Catalog it is not registered as a component of the multiple system ADS 48. It is used here for the purpose of our study. In some frames it is possible to see another image of a faint nearby companion to component C. This pair has not been measured yet. In Table 2 we give the following data for the seven components of ADS 48: the first column contains the designation of the component; the second one the Hipparcos number—HIP; the Hipparcos parallax πHIP is given in Column 3; in Columns 4 and 5 are proper-motion components μα cos δ and μδ ; the apparent magnitude m is in Column 6; the spectral type Sp is in Column 7; and in the last column the magnitude difference Δm is determined. For the three components which have the HIP number the values of the parallax and of proper motion are taken from the new Hipparcos astrometric catalog (van Leeuwen 2007). The other components are identified in UCAC35 catalog and it is the source for the proper motions of these components. The magnitudes and spectral types are from WDS. It should be emphasized that the magnitudes of components C and P, as given in WDS, do not correspond to reality. From the CCD frames it is clearly seen that star P is fainter than D and E, whereas star C is fainter than all three. The magnitudes
3. SYSTEM ADS 48 Pair STT 547AB has number 473 in the Hipparcos Catalog. It is at a small heliocentric distance d = 11.3 pc, i.e., 4
473 473 ... ... ... 428 ...
πHIP (mas)
5
http://belissima.aob.rs/
2
http://www.nofs.navy.mil/data/fchpix/
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Figure 1. CCD frames of system ADS 48 obtained from 1994 to 2011 with different cameras and instruments. The straight line shows the relative motion of the AP pair compared to other stars in the field of view.
finds that the mean values of Δm for pairs STT 547 AC, AD, and AE are equal to 6.62, 4.88, and 4.55, respectively. This confirms what is obvious from the CCD frames, i.e., that star C is by about 2 mag fainter than D and E. As for star P magnitude, in addition to the WDS value there is also the discoverer’s estimate (Popovi´c & Pavlovi´c 1997b) according to which this magnitude
of these components given in WDS (Table 2) do not agree with the situation on the frames. In the Third Photometric Magnitude Difference Catalog6 the results of Δm determinations in J, H , and K bands from the 2MASS Catalog are contained. There one 6
http://www.usno.navy.mil/USNO/astrometry/optical-IR-prod/wds/dm3
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Figure 2. System ADS 48 (CCD frame obtained with Apogee Alta U42 camera) where one can see component F.
is 14.5. We measured Δm (see Table 2) between the primary A and other six components from our CCD frames in V filter using the AIP4WIN software. Our magnitude differences show that components C and P are fainter than one finds in WDS. In the paper by (Lampens et al. 2007) we find for pair AP a magnitude difference of 4.11 in accordance with our value given in Table 2. In Figure 3 four linear fits concerning the pairs AC, AE, AD, and AP are presented. In the lower right (or left) corner the arrow indicates the sense of the motion for the secondaries C, E, D, and P with respect to the primary A. The linear fits for two pairs STT 547 AC and STT 547 AE have been taken from the Catalog of Rectilinear Elements maintained in the Washington Database. The other two linear fits for pairs STT 547 AD and STT 547 AP have been obtained by us. The linear solutions for the pairs AD and AP have been determined (Cvetkovi´c 2011) from a set of measurements also including the ones from the frames obtained at ASV. They are indicated by filled circles in Figure 3. The linear elements (equinox J2000) are listed in Table 3. The pair designation is given in Column 1, whereas Columns 2–8 show the linear elements: X0 and Y0 (coordinates of points with the closest relative separation, in arcseconds), XA and YA (components of velocity of relative motion of the secondary for one year, in arcseconds), T0 (epoch of the closest passage, in fractional Besselian year), ρ0 (the closest relative separation, in arcseconds), and θ0 (position angle of the closest passage, in degrees). The velocity V of relative motion of the secondary is given in Column 9. The reference for linear elements is given in the final column.
D, E, P, and R from our frames. The results are given in Table 4. In the table header we give the component pairs for which separations and position angles are measured. Column 1 gives the epoch of observation (expressed as a fractional Besselian year). In Columns 2–11 are the values ρ and θ for each pair. In the first part of the table there are the values found from the frames obtained at NAO Rozhen between 2004 and 2011 and, finally, in the second part of the table there are the values found from the frames obtained at ASV in 2011 August, October, and November. In the case of the frame from 1994 the coordinates ρ and θ could be measured for pair EP only. The obtained values are: 45.49 arcsec and 172.41 deg, respectively. The agreement with the values for ρ and θ for this pair given in Table 4 is good. From this table it can be seen that the values of both coordinates (ρ and θ ) for all pairs under consideration do not change with time, i.e., their relative positions are constant. As can be seen from Figure 3, both the separations ρ and the position angles θ of the pairs AC, AD, AE and AP change with time. The coordinates between the components of these pairs have been also measured from our frames for the considered time interval 1994–2011. The measured values are given in Table 5. The designations in this table are the same as in Table 4. If the measurements have been published yet, then we give the reference in the last column. Obviously, all components C, D, E, and P move in almost parallel directions (see θ0 values in Table 3) and in the same sense with respect to A (Figure 3). This confirms that in fact it is the A component (AB mass center) which moves in space with respect to other stars. To us of interest are XA and YA —the components of the velocity of the secondary with respect to the primary (Table 3). The values are almost the same for all four pairs (small differences are due to the differences in angles and separations). The velocities V are calculated and the agreement between these four values is apparent. If we calculate the proper motion of the mass center for the pair AB
4. RESULTS From the CCD frames at our disposal (see Figure 1) a relative motion of the P component with respect to the A component has been noticed. The orientation of the line passing through A and P is subject to noticeable changes. A careful inspection of the frames concerning system ADS 48 indicates that the configuration of its components C, D, E, and P and of star R remains constant. Because of this we have measured the separations ρ and position angles θ between all components C,
μ= 4
(μα cos δ)2 + (μδ )2 ,
(1)
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120
WDS 00057+4549
Cvetkovi´c et al.
STT 547AD
WDS 00057+4549
POP 217AP
4 100
+
0 80
60
-4
40 -8 20 E
N
-120
-100
E
-12
+
0
N
-80
-60
-40
-20
0
20
-8
-4
0
4
8
Figure 3. Linear fits for four pairs. Linear fits for STT 547 AE (Hartkopf & Mason 2011) and STT 547 AC (Friedman et al. 2012) taken from the Catalog of Rectilinear Elements (upper part). Our linear fits for STT 547 AD and STT 547 AP (Cvetkovi´c 2011; lower part). Table 3 Linear Elements and Velocity of the Pairs AC, AD, AE, and AP Pair STT 547 AC STT 547 AD STT 547 AE POP 217 AP
X0 ( )
XA ( /yr)
Y0 ( )
YA ( /yr)
T0 (yr)
ρ0 ( )
θ0 (◦ )
V ( /yr)
Reference
−5.6953 −14.4639 7.8411 1.7267
−0.8683 −0.8711 −0.8721 −0.8887
33.2358 82.0463 −52.1163 −9.4052
−0.1488 −0.1536 −0.1312 −0.1631
1891.28 1936.07 1988.75 2002.92
33.72 83.31 52.70 9.56
189.7 190.0 8.6 10.4
0.881 0.885 0.882 0.904
(Friedman et al. 2012) (Cvetkovi´c 2011) (Hartkopf & Mason 2011) (Cvetkovi´c 2011)
we obtain 0. 9 yr−1 , in an excellent agreement with the values of the relative-motion velocity V for the four components in linear solutions. This is another argument in favor of pair AB’s motion. Its proper motion is large, exceeding by two orders of magnitude the proper motions of the other components. Its orbital motion, considered within a short time interval (1994–2011), is not noticeable. Its proper motion is dominant. We overlapped our
CCD frames to have the components (C, D, E, P, and R) with invariable configuration at the same position (Figure 4). The motion of the AB pair in the view field is clearly seen. We have measured the separations ρ and position angles θ between component C and its faint nearby companion from our frames where it was possible. The measurements for this pair here denoted as STT 547 Ca,Cb are given in Table 6. The 5
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Table 4 Relative Coordinates of the Pairs with Invariable Configuration NAO Rozhen CD
CE
CP
Epoch
ρ ( )
2004.7950 2005.8301 2006.9574 2010.6844 2011.8212
... ... 63.83 63.79 63.82
... ... 331.17 331.21 331.19
... ... 122.36 122.33 122.34
... ... 234.36 234.42 234.43
2011.5803 2011.8048 2011.8355
63.75 63.73 63.79
331.39 331.51 331.21
122.25 122.09 122.30
234.57 234.50 234.44
θ (◦ )
ρ ( )
θ (◦ )
ρ ( )
CR θ (◦ )
ρ ( )
DE θ (◦ )
ρ ( )
θ (◦ )
... ... 109.00 108.97 108.96
... ... 255.96 255.99 255.98
... ... 191.88 191.85 191.86
... ... 289.22 289.25 289.25
144.41 144.55 144.56 144.50 144.49
28.32 28.28 28.36 28.42 28.41
108.90 108.78 108.90
256.15 256.14 255.98
191.68 191.68 191.72
289.41 289.38 289.28
144.43 144.30 144.45
28.58 28.48 28.43
ASV
NAO Rozhen DP Epoch 2004.7950 2005.8301 2006.9574 2010.6844 2011.8212
ρ ( )
DR θ (◦ )
111.22 ··· 111.37 111.35 111.33
42.31 ... 42.31 42.35 42.33
ρ ( )
EP θ (◦ )
150.52 150.53 150.58 150.58 150.56
ρ ( )
92.77 92.67 92.77 92.80 92.79
ER θ (◦ )
ρ ( )
PR θ (◦ )
ρ ( )
θ (◦ )
45.34 ··· 45.28 45.22 45.20
171.91 ... 172.00 172.07 172.11
157.36 157.29 157.37 157.28 157.26
148.66 148.64 148.71 148.73 148.73
117.09 ··· 117.15 117.13 117.15
319.86 ... 319.91 319.93 319.92
45.20 45.31 45.17
172.22 172.01 172.15
157.16 157.18 157.21
148.90 148.76 148.78
117.03 116.93 117.12
320.11 319.97 319.99
ASV 2011.5803 2011.8048 2011.8355
111.30 111.19 111.29
42.51 42.49 42.32
150.46 150.52 150.42
92.95 92.87 92.83
Table 5 Relative Coordinates of the Pairs with Variable Configuration NAO Rozhen AC Epoch
ρ ( )
AD θ (◦ )
ρ ( )
AE θ (◦ )
2004.7950 2005.8301 2006.9574 2010.6844 2011.8212
... 105.98 107.28 110.49 112.79
... 260.10 261.48 262.95 262.14
102.70 103.59 103.90 106.02 107.86
226.10 226.47 226.85 229.22 228.70
2011.5803 2011.8048 2011.8355
112.90 112.75 112.65
261.89 261.62 262.16
108.08 107.98 107.77
228.45 228.18 228.65
ρ ( )
AP θ (◦ )
54.24 54.54 54.84 55.86 56.95
ρ ( )
θ (◦ )
Reference
353.50 352.53 351.60 349.22 347.37
9.62 9.42 10.21 11.76 12.57
0.1 355.87 349.58 334.49 330.14
Pavlovi´c et al. (2005) Cvetkovi´c et al. (2006) Cvetkovi´c et al. (2007) Cvetkovi´c et al. (2011) this paper
347.15 346.84 347.56
12.50 12.60 12.54
329.93 329.96 330.79
this paper this paper this paper
ASV 56.99 57.12 56.98
From observations covering a sufficiently long time interval it will be possible to establish whether this is a gravitationally bound pair or an optical pair.
Table 6 Measurements of the Pair STT 547 Ca,Cb Epoch 2006.9574 2010.6844 2011.5803 2011.8212 2011.8355
ρ ( )
θ (◦ )
Δm
6.03 6.04 6.10 6.00 6.07
91.25 91.29 91.39 91.42 91.89
0.86 0.85 0.87 0.85 0.81
5. DETERMINING THE NATURE OF SYSTEM ADS 48 Bearing in mind what is said above about the motion of individual components of the system ADS 48 we want to discuss this matter in more detail. Since all measured pairs are rather wide, except AB, to answer the question concerning the nature of their motion we need observations covering very long time intervals. The only possibility is to apply existing criteria for establishing the nature of this system. These criteria are mostly based on some fundamental properties, such as the
designations in the first three columns are the same as in Tables 4 and 5, whereas in the last column we give our Δm between Ca and Cb. Within this short time interval the separation (similar separation to AB) and position angle do not show any changes. 6
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Figure 4. CCD frames obtained between 1994 and 2011 are overlapped in order to have at the same position images of the components (C, D, E, P, and R) for which the configuration is invariable. The motion of pair AB in the view field is clearly seen; the direction and sense are indicated by the arrow.
energy-conservation law, Kepler’s third law, etc, which should be obeyed by bound pairs. Since the F component has almost the same proper motion and parallax as pair AB, it is considered first. For the relative proper motion of the component F with respect to AB we obtained 17.36 mas yr−1 . The use of the Hipparcos parallax (Table 2) yields the corresponding tangential velocity of 0.93 km s−1 . The measured separation (328 ) at this heliocentric distance leads to a projected distance between F and AB of 3706 astronomical units. On the basis of their spectral types (K6, M0, and M2) and absolute magnitudes it follows that these three components are late main-sequence stars. Their total mass should be about 1.5 M (Lang 1992). With the values of mass and distance (in projection) we find 0.85 km s−1 for the escape velocity. These two velocity values are close to each other, but the former one is the lower limit, whereas the latter one is the upper limit. Therefore, it is not likely that the F component is bound to pair AB. According to Dommanget’s criterion (Dommanget 1955a, 1955b), one calculates the minimum parallax (maximum distance) for which the pair is still bound. In this case it is equal to 9.5 pc, a distance smaller than the actual one of 11.3 pc. This also favors that AB and F are not bound. The calculation of the maximum orbital velocity following the criterion Sinachopoulos & Mouzourakis (1992) yields 0.59 km s−1 , less than the tangential velocity found above. Then according to this criterion pair AB and component F are not bound. On the other hand since the tangential velocity is smaller than the triple maximum orbital velocity, according to the same criterion there is no confirmation for their optical nature.
Most likely, pair AB and component F are not bound but form a group with common proper motion. The other four components (C, D, E, and P) have quite different proper motion from AB. If they were at the same heliocentric distance as pair AB, then their absolute magnitudes would be 12.43 (C), 12.24 (D), 11.48 (E), and 12.93 (P). Consequently, they would have masses about 0.15 M . We applied the criterion (Sinachopoulos & Mouzourakis 1992) and obtained that the tangential velocity is much larger than the triple maximum orbital velocity in all four cases. Thus each of these components is an optical pair with AB. 6. CONCLUSION The relative coordinates obtained from our CCD frames for all pairs which contain neither A nor B (Table 4) are constant within the considered time interval, i.e., their configuration is invariable. Based on the linear solutions for four components we find that all of them have the same direction, sense, and relative velocity with respect to component A. The values of the relative velocity and proper motion of the A component agree very well with each other. These conclusions combined with the criteria based on celestial mechanics lead to the following: 1. within the system ADS 48 only stars A and B are gravitationally bound; 2. component F has common proper motion with A and B, but is not bound to them; 3. all other components considered here form optical pairs with AB. 7
The Astronomical Journal, 144:80 (8pp), 2012 September
Cvetkovi´c et al. Burnham, S. W. 1913, Publication No. 168 (Washington, DC: Carnegie institution of Washington) Cvetkovi´c, Z. 2011, IAU Comm. 26 Inf. Circ., 175, 1 Cvetkovi´c, Z., Novakovi´c, B., Strigachev, A., & Popovi´c, G. M. 2006, Serb. Astron. J., 172, 53 Cvetkovi´c, Z., Pavlovi´c, R., & Boeva, S. 2010, Serb. Astron. J., 180, 103 Cvetkovi´c, Z., Pavlovi´c, R., Damljanovi´c, G., & Boeva, S. 2011, AJ, 142, 73C Cvetkovi´c, Z., Pavlovi´c, R., Strigachev, A., Novakovi´c, B., & Popovi´c, G. M. 2007, Serb. Astron. J., 174, 83 Dommanget, J. 1955a, Bull. Astron., 20, 1 Dommanget, J. 1955b, Bull. Astron., 20, 183 Friedman, E. A., Mason, B. D., & Hartkopf, W. I. 2012, IAU Comm. 26 Inf. Circ., 176, 1 Hartkopf, W. I., & Mason, B. D. 2011, Catalog of Rectilinear Elements (v 2011.07.20) (http://www.usno.navy.mil/USNO/astrometry/ optical-IR-prod/wds/lin1) Kiyaeva, O. V., Kiselev, A. A., Polyakov, E. V., & Rafal’Skii, V. B. 2001, Astron. Lett., 27, 391 Lampens, P., Strigachev, A., & Duval, D. 2007, A&A, 464, 641 Lang, K. R. 1992, Astrophysical Data: Planet and Stars (New York: Springer) Pavlovi´c, R., Cvetkovi´c, Z., Olevi´c, D., et al. 2005, Serb. Astron. J., 171, 49 Popovi´c, G. M., & Pavlovi´c, R. 1996, Bull. Astron. Belgr., 153, 57 Popovi´c, G. M., & Pavlovi´c, R. 1997a, A&AS, 123, 487 Popovi´c, G. M., & Pavlovi´c, R. 1997b, Bull. Astron. Belgr., 155, 97 Sinachopoulos, D., & Mouzourakis, P. 1992, in ASP Conf. Ser. 32, Complementary Approaches to Double and Multiple Star Research, IAU Colloquium 135, ed. H. A. McAlister & W. I. Hartkopf (San Francisco, CA: ASP), 252 Struve, O. 1878, Pulkovo Obs., 9, 281 van Leeuwen, F. 2007, A&A, 474, 653
For the future work we suggest that pair STT 547 Ca,Cb be observed in order to establish whether this is a gravitationally bound pair or an optical pair. The authors from the Astronomical Observatory in Belgrade gratefully acknowledge the observing grant from the Institute of Astronomy and Rozhen National Astronomical Observatory, Bulgarian Academy of Sciences. We thank Dr. B. Mason for the data about this system sent to us. This research has made use of the USNOFS Image and Catalog Archive operated by the United States Naval Observatory, Flagstaff Station (http://www.nofs.navy.mil/data/fchpix/). The authors also thank the anonymous referee for valuable comments and suggestions. This research has been supported by the Ministry of Education and Science of the Republic of Serbia (project Nos. 176011, “Dynamics and kinematics of celestial bodies and systems,” and 176021, “Visible and Invisible Matter in Nearby Galaxies: Theory and Observations”). REFERENCES Aitken, R. G. 1932, New General Catalogue of Double Stars (Washington, DC: Carnegie Inst.) (ADS) Berry, R., & Burnell, J. 2002, The Handbook of Astronomical Image Processing, Includes AIP4WIN Software (Richmond, VA: Willmann-Bell)
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