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New Astronomy 15 (2010) 150–154
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The data mining II: An analysis of 33 eclipsing binary light-curves observed by the INTEGRAL/OMC P. Zasche * ´ a, Universidad Nacional Autónoma de México, A.P. 70-264, México, DF 04510, Mexico Instituto de Astronomı Astronomical Institute, Faculty of Mathematics and Physics, Charles University Prague, CZ-180 00 Praha 8, V Holešovicˇkách 2, Czech Republic
a r t i c l e
i n f o
Article history: Received 22 June 2009 Accepted 26 June 2009 Available online 1 July 2009 Communicated by P.S. Conti PACS: 97.10.q 97.80.d 97.80.Hn
a b s t r a c t Thirty-three eclipsing binaries were selected for an analysis from a huge database of observations made by the INTEGRAL/OMC camera. The photometric data were processed and analyzed, resulting in a first light-curve study of these neglected eclipsing binaries. The system CY Lac was discovered to be an eccentric one. In several systems from this sample even their orbital periods have been confirmed or modified. Due to missing spectroscopic study of these stars, further detailed analyses are still needed. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Stars: binaries: eclipsing Stars: individual: V408 Aql V964 Aql V1426 Aql V1450 Aql LP Ara DQ Car DR Car BZ Cas V654 Cas PQ Cen V379 Cen V Cir DO Cyg DP Cyg V536 Cyg V537 Cyg V616 Cyg V642 Cyg V703 Cyg V359 Her CY Lac YY Nor HM Nor V537 Oph BS Sco V569 Sco V714 Sco BN Sgr V780 Sgr V2168 Sgr XY Vel YY Vel AZ Vel Stars: fundamental parameters ´ a, Universidad Nacional Autónoma de México, A.P. 70-264, México, DF 04510, Mexico. Fax: +420 221912577. * Address: Instituto de Astronomı E-mail address: [email protected] 1384-1076/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2009.06.005
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P. Zasche / New Astronomy 15 (2010) 150–154
1. Introduction The INTEGRAL (INTErnational Gamma-Ray Astrophysics Laboratory) satellite produces many observations since its launch in 2002, not only in gamma part of the spectra. The onboard OMC (Optical Monitoring Camera) was designed to obtain the observations in optical V passband. These observations are in fact only a by-product of the mission, but nowadays there are many observations available. Despite the fact that the database of these measurements is freely available on internet, the analyses are still very rare. The most recent one using the OMC data is that by Jurcsik et al. (2009) about a new b Cep star. This investigation is directly following our previous papers (Zasche, 2008 and Zasche, 2009). The selection criteria used here were also the same: maximum number of data points and nonexistence of any detailed light-curve analysis of the particular system. There were 33 systems selected for the present paper.
2. Analysis of the individual systems All observations of these systems were carried out by the same instrument (50 mm OMC telescope) and the same filter (standard Johnson’s V filter). Time span of the observations ranges from November 2002 to October 2008. A transformation of the time scale has been done following the equation JulianDate ISDCJulianDate ¼ 2; 451; 544:5. Only a few outliers from each data set were excluded. The PHOEBE programme (see e.g. Prša and Zwitter, 2005), based on the Wilson–Devinney algorithm (Wilson and Devinney, 1971), was used for the analysis.
Due to missing information about the stars, and having only the light-curves in one filter, some of the parameters have to be fixed. At first, for all systems we have used the ‘‘Detached binary” mode (in Wilson & Devinney mode 2) and also the ‘‘Semidetached with the secondary component filling its Roche lobe” (mode 5 in Wilson & Devinney) for computing. For both modes a ‘‘q-search method” was used, which means trying to find the best fit with different values of the mass ratio q ranging from 0 to 1 with a step 0.1. The limb-darkening coefficients were interpolated from van Hamme’s tables (see van Hamme, 1993), the linear cosine law was used. The values of the gravity brightening and bolometric albedo coefficients were set at their suggested values for convective atmospheres (see Lucy, 1968), i.e. G1 ¼ G2 ¼ 0:32; A1 ¼ A2 ¼ 0:5. In all cases (except for CY Lac) the orbital eccentricity was set to 0 (circular orbit). Therefore, the quantities which could be directly calculated from the light curve are the following: The luminosity ratio L1 =L2 , the temperature ratio T 1 =T 2 , the inclination i, ephemerides of the system, the Kopal’s modified potentials X1 and X2 , the synchronicity parameters F 1 and F 2 , the third light l3 , and the mass ratio q. Using the parameters introduced above, one could also derive the value of the radii ratio R1 =R2 . The distinguishing between the minima has been done only according to the observational point of view, which means that the deeper one is the primary one. This results in a fact that the primary component could be neither the larger one, nor the more massive one. In two cases the secondary components result to be the more luminous ones (V1450 Aql and V714 Sco), and in several cases also the more massive ones. All of the basic information about the analyzed systems are introduced in Table 1, where are the B and V magnitudes from
Table 1 Basic information about the analyzed systems, taken from the literature. Star
Mag B GCVS
V408 Aql V964 Aql V1426 Aql V1450 Aql LP Ara DQ Car DR Car BZ Cas V654 Cas PQ Cen V379 Cen V Cir DO Cyg DP Cyg V536 Cyg V537 Cyg V616 Cyg V642 Cyg V703 Cyg V359 Her CY Lac YY Nor HM Nor V537 Oph BS Sco V569 Sco V714 Sco BN Sgr V780 Sgr V2168 Sgr XY Vel YY Vel AZ Vel
14.10 13.20 9.63 9.28 10.48 11.3 11.80 11.4 10.50 8.80 10.80 11.2 13.20 11.90 11.4 13.80 12.90 13.50 10.30 11.53 13.20 11.5 12.50 11.1 10.70 12.20 9.60 12.80 12.50 11.50 11.3 12.70
Mag V GCVS
(B-V) GCVS
(B-V) Nomad
9.18
0.45
0.790 0.360 0.433
G0
8.99
0.29
0.272
A0V+A?
10.2 11.1
0.28 0.2
11.4 10.9
0.5
B8 A0 B5 A0 B3-B5V
8.1 10.7 10.7
0.70 0.10 0.5
10.6
0.8
10.03 11.32
0.27 0.21
11.1
0.4
10.7
0.4
0.253 0.203 0.060 0.399 0.363 0.192 -0.007 0.637 0.346 0.130 0.386 0.884 0.250 0.230 -0.570 0.305 0.041 0.270 0.400 0.140 0.391 0.641
9.28
11.1
0.32
0.2
0.566 0.390 0.680 0.549 0.113 0.260
Sp.
B5Vn A0
A-B
F0 B5
B5V A3 G2-5
Sp. S&K
q S&K
Type S&K
(A2)+[G8IV] (A3)+[G0IV]
0.170 0.410
EA/SD EA/SD
B8+[A8] A0+[G1IV] B5+[G0IV] A0+[G1.5IV]
0.090 0.240 0.260 0.320
EA/DS EA/SD EA/SD EA/SD
(A8)+[K0IV] B5V+[A3] (B0)+[B3] A0+[G2IV] (A2)+[K6IV] (A2)+[K1IV] A(5)+[G8IV] (B7)+[F4] (A5)+[K0IV]
0.260 0.350 0.490 0.200 0.200 0.120 0.130 0.370 0.150
E/SD EA/SD EB/DM EA/SD EA/SD EA/SD EA/SD EA/SD EA/SD
F0+[G9IV] B5V+[F0] (B9)+[G0IV] (A5)+[K0IV] (F0)+[F0] B5V+[G2IV] A3+[A4] (A7)+[G7IV] F6+[K0IV] (A5)+[G2IV]
0.320 0.300 0.400 0.150 1.000 0.280 0.940 0.330 0.400 0.110
EA/SD EA/SD EA/SD EA/SD EA/DW EA/SD EA/DM EA/SD EA/SD EA/SD
(A5)+[G8IV] (A2)+[K1IV] (A8)+[F5]
0.210 0.220 0.500
EA/SD EA/SD EA/SD
Minima 16 4 10
0 3 0 49 3 4 26 83 2 16 20 33 15 3 141 0 0 0 2 0 14 0 3 0 1 4 0 2
Mag OMC
Mag MinI
Mag MinII
Data
13.08 13.73 9.14
14.20 14.89 9.60
13.23 14.04 9.31
822 511 823
8.87
9.16
9.11
2234
10.05 11.04 11.34 11.27 10.85 10.63 8.78 10.74 10.74 12.85 11.26 10.64 12.89 12.61 12.90 9.95 11.35 12.73 11.22 12.19 10.59 10.68 11.92 9.28 13.35 13.30 11.94 11.03 12.58
11.01 11.67 12.76 12.36 11.86 11.60 9.84 11.68 11.60 14.28 13.02 10.97 14.10 14.48 14.54 10.58 11.71 15.13 14.02 12.69 12.42 11.52 12.66 10.10 14.37 15.08 13.81 11.81 14.04
10.49 11.60 11.57 11.41 10.91 10.70 9.10 11.03 10.79 13.13 11.33 10.67 12.98 12.67 13.04 10.04 11.68 12.91 11.34 12.60 10.70 11.46 12.51 9.42 13.43 13.42 12.07 11.10 12.96
541 567 556 560 585 379 258 441 636 641 624 625 544 728 692 505 557 494 496 498 549 520 576 869 912 511 583 541 620
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P. Zasche / New Astronomy 15 (2010) 150–154
the GCVS (Kukarkin et al., 1971 and Malkov et al., 2006), the B V values from the GCVS and also from the NOMAD catalogue (Zacharias et al., 2004). The spectral types are taken from the published literature and also from the Svechnikov and Kuznetsova (S&K,
Svechnikov and Kuznetsova, 1990). The estimated mass ratio and also the type of the eclipsing binary have been taken from S&K (EA stands for the Algol type, while EB for the b Lyrae type, SD for semi-detached systems, DS for detached ones with subgiant
1.1
1.2 1.2
0.6
0.4
0.4
V408 Aql −0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
1.2
1
1
0.9
0.8
Flux
1.1
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
V1450 Aql
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.4
0.3
0.8
V1426 Aql
0.6 −0.7
0.3
−0.6
−0.5
−0.4
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
Phase
1.1 1 0.9 0.8 0.7
0.6
0.8
0.9
0.7
V964 Aql
0.2 −0.7
0.3
Flux
−0.6
Flux
0.8
0.6
−0.7
Flux
1
1
0.8
Flux
Flux
1
0.6
LP Ara
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
DQ Car
0.5 −0.7
0.3
−0.3
Phase
1.2 1
Flux
Flux
0.8
0.2
−0.7
−0.6
−0.5
0.4 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
0.8 0.6
0.6
DR Car
BZ Cas
−0.7
−0.6
−0.5
0.4 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
V654 Cas
−0.7
0.3
−0.6
−0.5
−0.4
−0.3
−0.4
−0.3
Phase
1.2
1
1
0.9
1 Flux
0.8 0.7 0.6
0.8
Flux
Flux
0.6 0.4
Flux
1
1
0.8
0.6
0.5
PQ Cen
0.4
−0.7
−0.6
−0.5
0.4 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
0.8 0.6
V379 Cen
−0.7
−0.6
−0.5
−0.4
0.4 −0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
V Cir
−0.7
−0.6
−0.5
Phase
1.4
0.4
DO Cyg
0.4 −0.7
−0.6
−0.5
0.2 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
Flux
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
V536 Cyg
−0.7
0.3
−0.6
−0.5
−0.4
−0.3
Phase
1 1
0.9
0.8
0.8
Flux
Flux
0.95
0.6
0.85
0.4
V537 Cyg
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.2 −0.7
0.3
1.1
1
1
0.8
0.9
Flux
1.2
0.6
−0.6
−0.5
−0.4
0.2 −0.3
−0.2
Phase
−0.1
0
0.1
0.2
V703 Cyg
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
−0.6
−0.5
−0.6
−0.5
−0.4
−0.3
Phase
1
0.8
0.6
V642 Cyg
−0.7
0.3
0.9 0.8
0.7
0.4
0.6 0.4
V616 Cyg
Flux
0.8
−0.6
0.2
1.2
1
0.75
0.6 0.4
DP Cyg
−0.7
1.05
Flux
0.8 0.6
0.6
Flux
0.8
1
0.8
0.2
1
1.2
Flux
Flux
1
V359 Her
−0.7
−0.6
−0.5
−0.4
CY Lac
0.7 −0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
Fig. 1. The light-curves of the analyzed systems.
−0.7
−0.4
−0.3
Phase
153
1.2
1.2
1
1
1
0.8
0.8
0.9
0.6
0.6 0.4
0.4 0.2
1.1
Flux
Flux
Flux
P. Zasche / New Astronomy 15 (2010) 150–154
0.2
YY Nor
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
0.7
HM Nor
0 −0.7
−0.6
−0.5
0.8
0.6 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
V537 Oph
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
Phase
1.1 1
1
1 0.9
0.6
0.6
0.4 0.2
0.8
Flux
Flux
Flux
0.8
BS Sco
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
V569 Sco −0.6
−0.5
−0.4
−0.3
−0.2
Phase
0.5 −0.1
0
0.1
0.2
0.3
1
0.6
BN Sgr
−0.7
−0.6
−0.5
0.4 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
−0.7
1.2
Flux
Flux
−0.4
−0.2
Phase
−0.1
0
0.1
0.2
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
−0.6
−0.5
−0.4
−0.3
−0.4
−0.3
Phase
1
0.6
−0.7
V2168 Sgr
0.8
0.8
0.5
Phase
0.6
−0.7
0.3
0.7
XY Vel
−0.3
0.8
0.2 −0.3
1
0.6
0.2
−0.5
0.9
0.8
0.4
−0.6
1.1
1
−0.4
0.4
V780 Sgr
Flux
0.5
0.8
Flux
Flux
Flux
0.6
−0.5
1
0.9
0.7
−0.6
1.2
1
0.8
V714 Sco
−0.7
1.2
1.1
0.7 0.6
0.4 −0.7
0.3
0.8
0.6 0.4
YY Vel
−0.7
−0.6
−0.5
0.2 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
AZ Vel
−0.7
−0.6
−0.5
Phase
Fig. 2. The light-curves of the analyzed systems.
secondary, and DM for detached main sequence ones).’Minima’ stands for the number of published times of minima and the last four columns introduce the actual OMC magnitudes in Johnson’s V filter, the depths of both primary and also secondary minima in V filter, and finally the number of data points used for this analysis. The results are introduced in Figs. 1 and 2 and Table 2, where are given all relevant parameters of the analyzed systems: HJD0 and P are the ephemerides of the system, i stands for the inclination, q denoted the mass ratio, the ‘Type’ refers the mode used for the best solution (‘D’ for a detached na ‘SD’ for a semi-detached one, see above), Xi stands for the Kopal’s modified potentials, T i for the effective temperatures, Li for the luminosities, Ri for the radii, F i for the synchronicity parameters, and xi for the limb-darkening coefficients (the linear cosine law was used), respectively. Inclinations smaller than 90° mean that the binary rotates counter-clockwise as projected onto a plane of sky. Only two systems (V780 Sgr and AZ Vel) have their respective orbital periods shorter than 1 day and CY Lac was found to be the eccentric eclipsing binary. In some systems their orbital periods were found to be different from the values published in the literature (e.g. in GCVS). The most reliable information about its orbital elements was found in the online ‘O-C gateway’1 (Paschke and Brat, 2006). The parameters of CY Lac are the following: the eccentricity e ¼ 0:2565 and the argument of periastron x ¼ 2:575 rad. In this system both primary and secondary minima have approximately equal depths, so the primary and secondary components (and also both minima) could be interchanged. This is the only case, where (due to its eccentricity) the value of HJD0 in Table 2 does not refer to the time of minimum light suitable for future observations. One 1
see http://var.astro.cz/ocgate/.
time of minimum light for this system has been derived: 2454248:8262 0:0049. Another interesting fact of this sample is that about one half of the investigated systems have the luminosity of the third unseen body above a statistically significant value about 5%. This result is not surprising, because e.g. Pribulla and Rucinski (2006) also discovered that more than 50% of binaries exist in multiple systems. One could speculate about a prospective future discovery of such components in these systems. Due to missing detailed analysis (spectroscopic, interferometric, etc.), the only possible way how to discover these bodies nowadays is the period analysis of their times of minima variations. In the system BZ Cas such an analysis exists and the third body was discovered with orbital period about 61 yr, see Erdem et al. (2007).
3. Discussion and conclusions The light-curve analyses of 33 selected systems have been carried out. Using the light-curves observed by the Optical Monitoring Camera onboard the INTEGRAL satellite, one can estimate the basic physical parameters of these systems. Despite this fact, the parameters are still only the preliminary ones, affected by relatively large errors and some of the relevant parameters were fixed at their suggested values. The detailed analysis is still needed, especially spectroscopic one, or another more detailed light curve one in different filters. Together with a prospective radial-velocity study, the final picture of these systems could be done. Particularly, the systems V1450 Aql and CY Lac seem to be the most interesting ones. The first one is massive semi-detached system, which shows total eclipses and the second one due to its eccentric orbit.
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P. Zasche / New Astronomy 15 (2010) 150–154
Table 2 The light-curve parameters of the individual systems, as derived from our analysis. Parameter Star
HJD0 2450000þ
P [days]
i[deg]
q ¼ M2 =M1
Type
X1
X2
T 1 =T 2
L1 ½%
L2 ½%
L3 ½%
R1 =R2
F1
F2
x1
x2
V408 Aql V964 Aql V1426 Aql V1450 Aql LP Ara DQ Car DR Car BZ Cas V654 Cas PQ Cen V379 Cen V Cir DO Cyg DP Cyg V536 Cyg V537 Cyg V616 Cyg V642 Cyg V703 Cyg V359 Her CY Lac YY Nor HM Nor V537 Oph BS Sco V569 Sco V714 Sco BN Sgr V780 Sgr V2168 Sgr XY Vel YY Vel AZ Vel
2742.574 2729.309 2709.109 2740.317 2674.116 2825.284 3146.403 3551.758 2656.527 2831.836 2651.290 3062.298 4087.345 2746.748 2836.598 3347.884 2653.970 2761.959 3125.944 3574.180 4094.814 2726.466 2726.068 3606.987 2876.953 2673.110 2743.254 2751.347 2746.065 3118.315 2998.041 2824.859 2805.448
2.83503997 1.26290000 1.17515945 4.81261051 8.53282038 1.73367847 3.99577477 2.12646842 4.94207240 1.05718895 1.87469639 4.40923643 1.70999742 2.34691815 6.01045459 4.75843337 1.32665076 4.44652373 4.14529239 1.75576649 8.35974636 1.69498989 4.42628455 1.14718255 7.62241175 1.04724351 1.39644612 2.51976721 0.86031002 2.06886580 2.51019823 4.16420826 0.77578092
89.094 85.342 77.683 93.106 77.079 92.179 97.608 95.307 79.681 87.357 89.393 91.678 84.467 86.792 84.108 77.032 82.405 90.046 85.315 79.273 83.474 87.133 76.341 80.989 86.533 88.826 88.728 76.280 84.031 86.908 88.230 78.788 89.973
0.6 0.5 0.7 1.5 0.2 0.8 0.7 0.6 0.3 0.4 0.6 0.6 0.4 0.3 0.5 0.9 0.6 0.8 0.7 0.8 0.6 0.6 0.2 0.7 2.7 1.2 1.2 1.0 0.9 1.2 0.7 0.7 0.5
SD SD SD SD SD D SD D SD D D D D SD D SD D D D SD D D SD D SD D D SD D D D D SD
6.0478 3.1582 4.9504 10.9790 4.7800 7.1553 5.4403 3.7192 5.9987 3.4249 3.9956 5.5716 4.7945 3.1773 6.3426 6.6202 3.9833 6.8413 6.4209 4.0204 8.4176 4.7717 6.8694 4.3997 8.1521 4.5470 6.0192 5.3627 5.7484 6.1918 6.3452 7.0504 3.1843
– – – – – 5.9273 – 3.0535 – 2.7701 3.2835 5.1156 2.9291 – 3.2831 – 3.0757 4.3267 4.1021 – 7.7674 3.2341 – 3.7075 – 4.7905 5.7818 – 3.8418 6.5589 4.5978 3.6171 –
1.815 0.993 1.367 1.040 1.143 0.841 2.197 1.548 2.532 2.307 1.331 1.655 2.078 1.795 1.727 1.863 1.423 2.549 2.043 1.350 1.498 2.097 1.336 1.213 3.274 0.981 1.012 1.532 1.069 1.478 0.764 1.909 0.987
63.75 84.54 68.58 19.41 70.52 52.68 70.65 74.75 72.26 81.34 66.22 84.16 66.11 87.17 82.58 65.70 82.80 81.49 79.22 65.38 57.81 83.80 89.57 47.30 88.42 50.78 47.06 65.84 59.96 89.89 86.95 62.23 78.45
14.96 11.90 29.21 73.20 29.48 43.71 29.35 9.74 10.51 3.54 20.52 15.84 5.09 12.83 12.81 8.52 5.16 6.35 16.04 5.34 42.19 16.20 10.43 43.48 6.40 49.22 52.94 11.54 12.28 9.78 4.32 20.99 21.55
21.29 3.57 2.21 7.39 0.00 3.61 0.00 15.51 17.24 15.12 13.26 0.00 28.80 0.00 4.61 25.78 12.04 12.16 4.74 29.28 0.00 0.00 0.00 9.22 5.18 0.00 0.00 22.63 27.76 0.33 8.73 16.78 0.00
0.713 1.196 0.940 0.396 1.135 1.036 0.725 0.988 0.593 1.204 1.061 1.425 0.834 1.205 0.656 0.766 0.918 0.656 0.738 0.955 0.672 0.774 0.569 0.969 0.826 0.974 0.835 0.674 0.636 0.953 0.972 0.560 1.097
5.106 1.485 0.000 9.906 3.748 5.332 0.000 0.000 0.000 0.000 1.838 3.755 0.504 1.272 1.161 4.261 1.111 2.180 0.000 1.089 3.154 0.000 3.199 1.411 2.835 0.894 0.696 3.282 0.000 1.976 5.371 4.581 0.000
1.883 0.000 3.187 2.634 2.316 0.000 2.220 0.207 0.388 0.544 0.880 0.000 1.498 0.000 1.826 3.605 0.768 1.552 0.000 1.687 4.941 1.271 0.133 1.458 5.084 0.760 1.088 0.662 0.319 1.597 2.438 1.468 0.168
0.499 0.690 0.472 0.457 0.500 0.350 0.292 0.319 0.285 0.500 0.514 0.074 0.291 0.529 0.579 0.436 0.502 0.316 0.440 0.532 0.406 0.319 0.544 0.528 0.309 0.454 0.442 0.531 0.357 0.450 0.823 0.406 0.406
0.787 0.682 0.635 0.478 0.500 0.309 0.472 0.452 0.537 0.255 0.563 0.279 0.533 0.814 0.500 0.707 0.746 0.611 0.797 0.757 0.549 0.522 0.764 0.665 0.587 0.444 0.449 0.689 0.378 0.555 0.613 0.653 0.403
Acknowledgements Based on data from the OMC Archive at LAEFF, pre-processed by ISDC. This investigation was supported by the Research Program MSMT 0021620860 of the Ministry of Education of Czech Republic and also by the Mexican grant PAPIIT IN113308. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and of NASA’s Astrophysics Data System Bibliographic Services. References Erdem, A., Soydugan, F., Dog˘ru, S.S., Özkardesß, B., Dog˘ru, D., Tüysüz, M., Demircan, O., 2007. New Astronomy 12, 613.
Jurcsik, J., Sodor, A., Hajdu, G., 2009. Information Bulletin on Variable Stars 5881, 1. Kukarkin, B.V., Kholopov, P.N., Pskovsky, Y.P., Efremov, Y.N., Kukarkina, N.P., Kurochkin, N.E., & Medvedeva, G.I., 1971. General Catalogue of Variable Stars, third ed. Lucy, L.B., 1968. ApJ 151, 1123. Malkov, O.Y., Oblak, E., Snegireva, E.A., Torra, J., 2006. A&A 446, 785. Paschke, A., Brat, L., 2006. Open European Journal on Variable Stars 23, 13. Pribulla, T., Rucinski, S.M., 2006. AJ 131, 2986. Prša, A., Zwitter, T., 2005. ApJ 628, 42. Svechnikov, M.A., Kuznetsova, E.F., 1990. Sverdlovsk: Izd-vo Ural’skogo universiteta, 1990. van Hamme, W., 1993. AJ 106, 2096. Wilson, R.E., Devinney, E.J., 1971. ApJ 166, 605. Zacharias, N., Monet, D.G., Levine, S.E., Urban, S.E., Gaume, R., Wycoff, G.L., 2004. Bulletin of the American Astronomical Society 36, 1418. Zasche, P., 2008. New Astronomy 13, 481. Zasche, P., 2009. New Astronomy 14, 129.
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New Astronomy journal homepage: www.elsevier.com/locate/newast
The data mining II: An analysis of 33 eclipsing binary light-curves observed by the INTEGRAL/OMC P. Zasche * ´ a, Universidad Nacional Autónoma de México, A.P. 70-264, México, DF 04510, Mexico Instituto de Astronomı Astronomical Institute, Faculty of Mathematics and Physics, Charles University Prague, CZ-180 00 Praha 8, V Holešovicˇkách 2, Czech Republic
a r t i c l e
i n f o
Article history: Received 22 June 2009 Accepted 26 June 2009 Available online 1 July 2009 Communicated by P.S. Conti PACS: 97.10.q 97.80.d 97.80.Hn
a b s t r a c t Thirty-three eclipsing binaries were selected for an analysis from a huge database of observations made by the INTEGRAL/OMC camera. The photometric data were processed and analyzed, resulting in a first light-curve study of these neglected eclipsing binaries. The system CY Lac was discovered to be an eccentric one. In several systems from this sample even their orbital periods have been confirmed or modified. Due to missing spectroscopic study of these stars, further detailed analyses are still needed. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Stars: binaries: eclipsing Stars: individual: V408 Aql V964 Aql V1426 Aql V1450 Aql LP Ara DQ Car DR Car BZ Cas V654 Cas PQ Cen V379 Cen V Cir DO Cyg DP Cyg V536 Cyg V537 Cyg V616 Cyg V642 Cyg V703 Cyg V359 Her CY Lac YY Nor HM Nor V537 Oph BS Sco V569 Sco V714 Sco BN Sgr V780 Sgr V2168 Sgr XY Vel YY Vel AZ Vel Stars: fundamental parameters ´ a, Universidad Nacional Autónoma de México, A.P. 70-264, México, DF 04510, Mexico. Fax: +420 221912577. * Address: Instituto de Astronomı E-mail address: [email protected] 1384-1076/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2009.06.005
151
P. Zasche / New Astronomy 15 (2010) 150–154
1. Introduction The INTEGRAL (INTErnational Gamma-Ray Astrophysics Laboratory) satellite produces many observations since its launch in 2002, not only in gamma part of the spectra. The onboard OMC (Optical Monitoring Camera) was designed to obtain the observations in optical V passband. These observations are in fact only a by-product of the mission, but nowadays there are many observations available. Despite the fact that the database of these measurements is freely available on internet, the analyses are still very rare. The most recent one using the OMC data is that by Jurcsik et al. (2009) about a new b Cep star. This investigation is directly following our previous papers (Zasche, 2008 and Zasche, 2009). The selection criteria used here were also the same: maximum number of data points and nonexistence of any detailed light-curve analysis of the particular system. There were 33 systems selected for the present paper.
2. Analysis of the individual systems All observations of these systems were carried out by the same instrument (50 mm OMC telescope) and the same filter (standard Johnson’s V filter). Time span of the observations ranges from November 2002 to October 2008. A transformation of the time scale has been done following the equation JulianDate ISDCJulianDate ¼ 2; 451; 544:5. Only a few outliers from each data set were excluded. The PHOEBE programme (see e.g. Prša and Zwitter, 2005), based on the Wilson–Devinney algorithm (Wilson and Devinney, 1971), was used for the analysis.
Due to missing information about the stars, and having only the light-curves in one filter, some of the parameters have to be fixed. At first, for all systems we have used the ‘‘Detached binary” mode (in Wilson & Devinney mode 2) and also the ‘‘Semidetached with the secondary component filling its Roche lobe” (mode 5 in Wilson & Devinney) for computing. For both modes a ‘‘q-search method” was used, which means trying to find the best fit with different values of the mass ratio q ranging from 0 to 1 with a step 0.1. The limb-darkening coefficients were interpolated from van Hamme’s tables (see van Hamme, 1993), the linear cosine law was used. The values of the gravity brightening and bolometric albedo coefficients were set at their suggested values for convective atmospheres (see Lucy, 1968), i.e. G1 ¼ G2 ¼ 0:32; A1 ¼ A2 ¼ 0:5. In all cases (except for CY Lac) the orbital eccentricity was set to 0 (circular orbit). Therefore, the quantities which could be directly calculated from the light curve are the following: The luminosity ratio L1 =L2 , the temperature ratio T 1 =T 2 , the inclination i, ephemerides of the system, the Kopal’s modified potentials X1 and X2 , the synchronicity parameters F 1 and F 2 , the third light l3 , and the mass ratio q. Using the parameters introduced above, one could also derive the value of the radii ratio R1 =R2 . The distinguishing between the minima has been done only according to the observational point of view, which means that the deeper one is the primary one. This results in a fact that the primary component could be neither the larger one, nor the more massive one. In two cases the secondary components result to be the more luminous ones (V1450 Aql and V714 Sco), and in several cases also the more massive ones. All of the basic information about the analyzed systems are introduced in Table 1, where are the B and V magnitudes from
Table 1 Basic information about the analyzed systems, taken from the literature. Star
Mag B GCVS
V408 Aql V964 Aql V1426 Aql V1450 Aql LP Ara DQ Car DR Car BZ Cas V654 Cas PQ Cen V379 Cen V Cir DO Cyg DP Cyg V536 Cyg V537 Cyg V616 Cyg V642 Cyg V703 Cyg V359 Her CY Lac YY Nor HM Nor V537 Oph BS Sco V569 Sco V714 Sco BN Sgr V780 Sgr V2168 Sgr XY Vel YY Vel AZ Vel
14.10 13.20 9.63 9.28 10.48 11.3 11.80 11.4 10.50 8.80 10.80 11.2 13.20 11.90 11.4 13.80 12.90 13.50 10.30 11.53 13.20 11.5 12.50 11.1 10.70 12.20 9.60 12.80 12.50 11.50 11.3 12.70
Mag V GCVS
(B-V) GCVS
(B-V) Nomad
9.18
0.45
0.790 0.360 0.433
G0
8.99
0.29
0.272
A0V+A?
10.2 11.1
0.28 0.2
11.4 10.9
0.5
B8 A0 B5 A0 B3-B5V
8.1 10.7 10.7
0.70 0.10 0.5
10.6
0.8
10.03 11.32
0.27 0.21
11.1
0.4
10.7
0.4
0.253 0.203 0.060 0.399 0.363 0.192 -0.007 0.637 0.346 0.130 0.386 0.884 0.250 0.230 -0.570 0.305 0.041 0.270 0.400 0.140 0.391 0.641
9.28
11.1
0.32
0.2
0.566 0.390 0.680 0.549 0.113 0.260
Sp.
B5Vn A0
A-B
F0 B5
B5V A3 G2-5
Sp. S&K
q S&K
Type S&K
(A2)+[G8IV] (A3)+[G0IV]
0.170 0.410
EA/SD EA/SD
B8+[A8] A0+[G1IV] B5+[G0IV] A0+[G1.5IV]
0.090 0.240 0.260 0.320
EA/DS EA/SD EA/SD EA/SD
(A8)+[K0IV] B5V+[A3] (B0)+[B3] A0+[G2IV] (A2)+[K6IV] (A2)+[K1IV] A(5)+[G8IV] (B7)+[F4] (A5)+[K0IV]
0.260 0.350 0.490 0.200 0.200 0.120 0.130 0.370 0.150
E/SD EA/SD EB/DM EA/SD EA/SD EA/SD EA/SD EA/SD EA/SD
F0+[G9IV] B5V+[F0] (B9)+[G0IV] (A5)+[K0IV] (F0)+[F0] B5V+[G2IV] A3+[A4] (A7)+[G7IV] F6+[K0IV] (A5)+[G2IV]
0.320 0.300 0.400 0.150 1.000 0.280 0.940 0.330 0.400 0.110
EA/SD EA/SD EA/SD EA/SD EA/DW EA/SD EA/DM EA/SD EA/SD EA/SD
(A5)+[G8IV] (A2)+[K1IV] (A8)+[F5]
0.210 0.220 0.500
EA/SD EA/SD EA/SD
Minima 16 4 10
0 3 0 49 3 4 26 83 2 16 20 33 15 3 141 0 0 0 2 0 14 0 3 0 1 4 0 2
Mag OMC
Mag MinI
Mag MinII
Data
13.08 13.73 9.14
14.20 14.89 9.60
13.23 14.04 9.31
822 511 823
8.87
9.16
9.11
2234
10.05 11.04 11.34 11.27 10.85 10.63 8.78 10.74 10.74 12.85 11.26 10.64 12.89 12.61 12.90 9.95 11.35 12.73 11.22 12.19 10.59 10.68 11.92 9.28 13.35 13.30 11.94 11.03 12.58
11.01 11.67 12.76 12.36 11.86 11.60 9.84 11.68 11.60 14.28 13.02 10.97 14.10 14.48 14.54 10.58 11.71 15.13 14.02 12.69 12.42 11.52 12.66 10.10 14.37 15.08 13.81 11.81 14.04
10.49 11.60 11.57 11.41 10.91 10.70 9.10 11.03 10.79 13.13 11.33 10.67 12.98 12.67 13.04 10.04 11.68 12.91 11.34 12.60 10.70 11.46 12.51 9.42 13.43 13.42 12.07 11.10 12.96
541 567 556 560 585 379 258 441 636 641 624 625 544 728 692 505 557 494 496 498 549 520 576 869 912 511 583 541 620
152
P. Zasche / New Astronomy 15 (2010) 150–154
the GCVS (Kukarkin et al., 1971 and Malkov et al., 2006), the B V values from the GCVS and also from the NOMAD catalogue (Zacharias et al., 2004). The spectral types are taken from the published literature and also from the Svechnikov and Kuznetsova (S&K,
Svechnikov and Kuznetsova, 1990). The estimated mass ratio and also the type of the eclipsing binary have been taken from S&K (EA stands for the Algol type, while EB for the b Lyrae type, SD for semi-detached systems, DS for detached ones with subgiant
1.1
1.2 1.2
0.6
0.4
0.4
V408 Aql −0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
1.2
1
1
0.9
0.8
Flux
1.1
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
V1450 Aql
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.4
0.3
0.8
V1426 Aql
0.6 −0.7
0.3
−0.6
−0.5
−0.4
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
Phase
1.1 1 0.9 0.8 0.7
0.6
0.8
0.9
0.7
V964 Aql
0.2 −0.7
0.3
Flux
−0.6
Flux
0.8
0.6
−0.7
Flux
1
1
0.8
Flux
Flux
1
0.6
LP Ara
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
DQ Car
0.5 −0.7
0.3
−0.3
Phase
1.2 1
Flux
Flux
0.8
0.2
−0.7
−0.6
−0.5
0.4 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
0.8 0.6
0.6
DR Car
BZ Cas
−0.7
−0.6
−0.5
0.4 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
V654 Cas
−0.7
0.3
−0.6
−0.5
−0.4
−0.3
−0.4
−0.3
Phase
1.2
1
1
0.9
1 Flux
0.8 0.7 0.6
0.8
Flux
Flux
0.6 0.4
Flux
1
1
0.8
0.6
0.5
PQ Cen
0.4
−0.7
−0.6
−0.5
0.4 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
0.8 0.6
V379 Cen
−0.7
−0.6
−0.5
−0.4
0.4 −0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
V Cir
−0.7
−0.6
−0.5
Phase
1.4
0.4
DO Cyg
0.4 −0.7
−0.6
−0.5
0.2 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
Flux
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
V536 Cyg
−0.7
0.3
−0.6
−0.5
−0.4
−0.3
Phase
1 1
0.9
0.8
0.8
Flux
Flux
0.95
0.6
0.85
0.4
V537 Cyg
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.2 −0.7
0.3
1.1
1
1
0.8
0.9
Flux
1.2
0.6
−0.6
−0.5
−0.4
0.2 −0.3
−0.2
Phase
−0.1
0
0.1
0.2
V703 Cyg
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
−0.6
−0.5
−0.6
−0.5
−0.4
−0.3
Phase
1
0.8
0.6
V642 Cyg
−0.7
0.3
0.9 0.8
0.7
0.4
0.6 0.4
V616 Cyg
Flux
0.8
−0.6
0.2
1.2
1
0.75
0.6 0.4
DP Cyg
−0.7
1.05
Flux
0.8 0.6
0.6
Flux
0.8
1
0.8
0.2
1
1.2
Flux
Flux
1
V359 Her
−0.7
−0.6
−0.5
−0.4
CY Lac
0.7 −0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
Fig. 1. The light-curves of the analyzed systems.
−0.7
−0.4
−0.3
Phase
153
1.2
1.2
1
1
1
0.8
0.8
0.9
0.6
0.6 0.4
0.4 0.2
1.1
Flux
Flux
Flux
P. Zasche / New Astronomy 15 (2010) 150–154
0.2
YY Nor
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
0.7
HM Nor
0 −0.7
−0.6
−0.5
0.8
0.6 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
V537 Oph
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
−0.2
−0.1
0
0.1
0.2
0.3
Phase
1.1 1
1
1 0.9
0.6
0.6
0.4 0.2
0.8
Flux
Flux
Flux
0.8
BS Sco
−0.7
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
V569 Sco −0.6
−0.5
−0.4
−0.3
−0.2
Phase
0.5 −0.1
0
0.1
0.2
0.3
1
0.6
BN Sgr
−0.7
−0.6
−0.5
0.4 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
−0.7
1.2
Flux
Flux
−0.4
−0.2
Phase
−0.1
0
0.1
0.2
−0.6
−0.5
−0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
−0.6
−0.5
−0.4
−0.3
−0.4
−0.3
Phase
1
0.6
−0.7
V2168 Sgr
0.8
0.8
0.5
Phase
0.6
−0.7
0.3
0.7
XY Vel
−0.3
0.8
0.2 −0.3
1
0.6
0.2
−0.5
0.9
0.8
0.4
−0.6
1.1
1
−0.4
0.4
V780 Sgr
Flux
0.5
0.8
Flux
Flux
Flux
0.6
−0.5
1
0.9
0.7
−0.6
1.2
1
0.8
V714 Sco
−0.7
1.2
1.1
0.7 0.6
0.4 −0.7
0.3
0.8
0.6 0.4
YY Vel
−0.7
−0.6
−0.5
0.2 −0.4
−0.3
−0.2
Phase
−0.1
0
0.1
0.2
0.3
AZ Vel
−0.7
−0.6
−0.5
Phase
Fig. 2. The light-curves of the analyzed systems.
secondary, and DM for detached main sequence ones).’Minima’ stands for the number of published times of minima and the last four columns introduce the actual OMC magnitudes in Johnson’s V filter, the depths of both primary and also secondary minima in V filter, and finally the number of data points used for this analysis. The results are introduced in Figs. 1 and 2 and Table 2, where are given all relevant parameters of the analyzed systems: HJD0 and P are the ephemerides of the system, i stands for the inclination, q denoted the mass ratio, the ‘Type’ refers the mode used for the best solution (‘D’ for a detached na ‘SD’ for a semi-detached one, see above), Xi stands for the Kopal’s modified potentials, T i for the effective temperatures, Li for the luminosities, Ri for the radii, F i for the synchronicity parameters, and xi for the limb-darkening coefficients (the linear cosine law was used), respectively. Inclinations smaller than 90° mean that the binary rotates counter-clockwise as projected onto a plane of sky. Only two systems (V780 Sgr and AZ Vel) have their respective orbital periods shorter than 1 day and CY Lac was found to be the eccentric eclipsing binary. In some systems their orbital periods were found to be different from the values published in the literature (e.g. in GCVS). The most reliable information about its orbital elements was found in the online ‘O-C gateway’1 (Paschke and Brat, 2006). The parameters of CY Lac are the following: the eccentricity e ¼ 0:2565 and the argument of periastron x ¼ 2:575 rad. In this system both primary and secondary minima have approximately equal depths, so the primary and secondary components (and also both minima) could be interchanged. This is the only case, where (due to its eccentricity) the value of HJD0 in Table 2 does not refer to the time of minimum light suitable for future observations. One 1
see http://var.astro.cz/ocgate/.
time of minimum light for this system has been derived: 2454248:8262 0:0049. Another interesting fact of this sample is that about one half of the investigated systems have the luminosity of the third unseen body above a statistically significant value about 5%. This result is not surprising, because e.g. Pribulla and Rucinski (2006) also discovered that more than 50% of binaries exist in multiple systems. One could speculate about a prospective future discovery of such components in these systems. Due to missing detailed analysis (spectroscopic, interferometric, etc.), the only possible way how to discover these bodies nowadays is the period analysis of their times of minima variations. In the system BZ Cas such an analysis exists and the third body was discovered with orbital period about 61 yr, see Erdem et al. (2007).
3. Discussion and conclusions The light-curve analyses of 33 selected systems have been carried out. Using the light-curves observed by the Optical Monitoring Camera onboard the INTEGRAL satellite, one can estimate the basic physical parameters of these systems. Despite this fact, the parameters are still only the preliminary ones, affected by relatively large errors and some of the relevant parameters were fixed at their suggested values. The detailed analysis is still needed, especially spectroscopic one, or another more detailed light curve one in different filters. Together with a prospective radial-velocity study, the final picture of these systems could be done. Particularly, the systems V1450 Aql and CY Lac seem to be the most interesting ones. The first one is massive semi-detached system, which shows total eclipses and the second one due to its eccentric orbit.
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P. Zasche / New Astronomy 15 (2010) 150–154
Table 2 The light-curve parameters of the individual systems, as derived from our analysis. Parameter Star
HJD0 2450000þ
P [days]
i[deg]
q ¼ M2 =M1
Type
X1
X2
T 1 =T 2
L1 ½%
L2 ½%
L3 ½%
R1 =R2
F1
F2
x1
x2
V408 Aql V964 Aql V1426 Aql V1450 Aql LP Ara DQ Car DR Car BZ Cas V654 Cas PQ Cen V379 Cen V Cir DO Cyg DP Cyg V536 Cyg V537 Cyg V616 Cyg V642 Cyg V703 Cyg V359 Her CY Lac YY Nor HM Nor V537 Oph BS Sco V569 Sco V714 Sco BN Sgr V780 Sgr V2168 Sgr XY Vel YY Vel AZ Vel
2742.574 2729.309 2709.109 2740.317 2674.116 2825.284 3146.403 3551.758 2656.527 2831.836 2651.290 3062.298 4087.345 2746.748 2836.598 3347.884 2653.970 2761.959 3125.944 3574.180 4094.814 2726.466 2726.068 3606.987 2876.953 2673.110 2743.254 2751.347 2746.065 3118.315 2998.041 2824.859 2805.448
2.83503997 1.26290000 1.17515945 4.81261051 8.53282038 1.73367847 3.99577477 2.12646842 4.94207240 1.05718895 1.87469639 4.40923643 1.70999742 2.34691815 6.01045459 4.75843337 1.32665076 4.44652373 4.14529239 1.75576649 8.35974636 1.69498989 4.42628455 1.14718255 7.62241175 1.04724351 1.39644612 2.51976721 0.86031002 2.06886580 2.51019823 4.16420826 0.77578092
89.094 85.342 77.683 93.106 77.079 92.179 97.608 95.307 79.681 87.357 89.393 91.678 84.467 86.792 84.108 77.032 82.405 90.046 85.315 79.273 83.474 87.133 76.341 80.989 86.533 88.826 88.728 76.280 84.031 86.908 88.230 78.788 89.973
0.6 0.5 0.7 1.5 0.2 0.8 0.7 0.6 0.3 0.4 0.6 0.6 0.4 0.3 0.5 0.9 0.6 0.8 0.7 0.8 0.6 0.6 0.2 0.7 2.7 1.2 1.2 1.0 0.9 1.2 0.7 0.7 0.5
SD SD SD SD SD D SD D SD D D D D SD D SD D D D SD D D SD D SD D D SD D D D D SD
6.0478 3.1582 4.9504 10.9790 4.7800 7.1553 5.4403 3.7192 5.9987 3.4249 3.9956 5.5716 4.7945 3.1773 6.3426 6.6202 3.9833 6.8413 6.4209 4.0204 8.4176 4.7717 6.8694 4.3997 8.1521 4.5470 6.0192 5.3627 5.7484 6.1918 6.3452 7.0504 3.1843
– – – – – 5.9273 – 3.0535 – 2.7701 3.2835 5.1156 2.9291 – 3.2831 – 3.0757 4.3267 4.1021 – 7.7674 3.2341 – 3.7075 – 4.7905 5.7818 – 3.8418 6.5589 4.5978 3.6171 –
1.815 0.993 1.367 1.040 1.143 0.841 2.197 1.548 2.532 2.307 1.331 1.655 2.078 1.795 1.727 1.863 1.423 2.549 2.043 1.350 1.498 2.097 1.336 1.213 3.274 0.981 1.012 1.532 1.069 1.478 0.764 1.909 0.987
63.75 84.54 68.58 19.41 70.52 52.68 70.65 74.75 72.26 81.34 66.22 84.16 66.11 87.17 82.58 65.70 82.80 81.49 79.22 65.38 57.81 83.80 89.57 47.30 88.42 50.78 47.06 65.84 59.96 89.89 86.95 62.23 78.45
14.96 11.90 29.21 73.20 29.48 43.71 29.35 9.74 10.51 3.54 20.52 15.84 5.09 12.83 12.81 8.52 5.16 6.35 16.04 5.34 42.19 16.20 10.43 43.48 6.40 49.22 52.94 11.54 12.28 9.78 4.32 20.99 21.55
21.29 3.57 2.21 7.39 0.00 3.61 0.00 15.51 17.24 15.12 13.26 0.00 28.80 0.00 4.61 25.78 12.04 12.16 4.74 29.28 0.00 0.00 0.00 9.22 5.18 0.00 0.00 22.63 27.76 0.33 8.73 16.78 0.00
0.713 1.196 0.940 0.396 1.135 1.036 0.725 0.988 0.593 1.204 1.061 1.425 0.834 1.205 0.656 0.766 0.918 0.656 0.738 0.955 0.672 0.774 0.569 0.969 0.826 0.974 0.835 0.674 0.636 0.953 0.972 0.560 1.097
5.106 1.485 0.000 9.906 3.748 5.332 0.000 0.000 0.000 0.000 1.838 3.755 0.504 1.272 1.161 4.261 1.111 2.180 0.000 1.089 3.154 0.000 3.199 1.411 2.835 0.894 0.696 3.282 0.000 1.976 5.371 4.581 0.000
1.883 0.000 3.187 2.634 2.316 0.000 2.220 0.207 0.388 0.544 0.880 0.000 1.498 0.000 1.826 3.605 0.768 1.552 0.000 1.687 4.941 1.271 0.133 1.458 5.084 0.760 1.088 0.662 0.319 1.597 2.438 1.468 0.168
0.499 0.690 0.472 0.457 0.500 0.350 0.292 0.319 0.285 0.500 0.514 0.074 0.291 0.529 0.579 0.436 0.502 0.316 0.440 0.532 0.406 0.319 0.544 0.528 0.309 0.454 0.442 0.531 0.357 0.450 0.823 0.406 0.406
0.787 0.682 0.635 0.478 0.500 0.309 0.472 0.452 0.537 0.255 0.563 0.279 0.533 0.814 0.500 0.707 0.746 0.611 0.797 0.757 0.549 0.522 0.764 0.665 0.587 0.444 0.449 0.689 0.378 0.555 0.613 0.653 0.403
Acknowledgements Based on data from the OMC Archive at LAEFF, pre-processed by ISDC. This investigation was supported by the Research Program MSMT 0021620860 of the Ministry of Education of Czech Republic and also by the Mexican grant PAPIIT IN113308. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and of NASA’s Astrophysics Data System Bibliographic Services. References Erdem, A., Soydugan, F., Dog˘ru, S.S., Özkardesß, B., Dog˘ru, D., Tüysüz, M., Demircan, O., 2007. New Astronomy 12, 613.
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