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Light curve analyses of new eclipsing binary systems with eccentric orbits
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New Astronomy 13 (2008) 252–254 www.elsevier.com/locate/newast
Light curve analyses of new eclipsing binary systems with eccentric orbits _ Bulut *, O. Demircan I. C¸anakkale Onsekiz Mart University Observatory, 17100 Terziog˘lu Kampu¨su¨, C¸anakkale, Turkey Received 2 August 2007; received in revised form 11 September 2007; accepted 10 October 2007 Available online 23 October 2007 Communicated by P.S. Conti
Abstract A photometric study of seven new eclipsing binary systems with eccentric orbits, namely, V466 Car, V493 Car, V529 Car, MN TrA, V398 Lac, V402 Lac and V821 Cas, is presented. The photometric data analyzed were taken from the Hipparcos database. The secondary minima in all systems were shifted by different amounts from the phase 0.5 giving clear evidence of their eccentric orbits. The EBOP computer program based upon models by Nelson et al. [Popper, D.M., Etzel, P.E., 1981. AJ 86, 102] was used in the analysis of the photometric data to deduce the orbital geometry in space and the relative sizes and luminosities of the component stars. 2007 Elsevier B.V. All rights reserved. Keywords: Stars: binaries: close; Stars: binaries: eclipsing; Stars: individual: V466 Car, V493 Car, V529 Car, MN TrA, V398 Lac, V402 Lac,V821 Cas
1. Introduction If the major axis of the eccentric orbit of an eclipsing binary system is not close to the line of sight, then the secondary minimum is observed to have shifted from the phase 0.5. Such observations are used in practice as clear evidence of eccentric orbits. The Hipparcos (ESA, 1997) photometric database was surveyed for eclipsing binary light curves with shifted secondary minima. We thus detected seven new eclipsing binary systems with eccentric orbits. These are V466 Car, V493 Car, V529 Car, MN TrA, V398 Lac, V402 Lac and V821 Cas. The identification of these systems is listed in Table 1. The entries in the table were mostly extracted from the Variability Annex of the Hipparcos Catalogue (ESA, 1997). These systems are good candidates in testing theories of apsidal motion and of orbital circularisation in binary star systems.
*
Corresponding author. Tel.: +90 286 2180018x1414; fax: +90 286 2180549. _ Bulut). E-mail address: [email protected] (I. 1384-1076/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2007.10.003
The aim of the present work is to provide a preliminary set of parameters for the systems, which can be used as input parameters in the analysis of more precise light curves in the future, based on follow-up observations. 2. Analysis of the light curves The photometric observations (Hp magnitudes) for the selected systems were taken from the Epoch Photometry Annex of the Hipparcos database and the relevant light curves were constructed using the light elements (T0, P) given in Table 1. All observations were used and were assumed to have unit weight. For analysis of the Hipparcos light curves of the systems, we chose the Nelson–Davis–Etzel (NDE) model (Etzel, 1981; Popper and Etzel, 1981), and used the computer programme EBOP (Eclipsing Binary Orbit Program). This model proved to yield reliable photometric elements for detached binaries of spherical or slightly oblate stars (oblateness, 6 0.04). If the primary star (p) is defined to be the one eclipsed during the deepest minimum, the major parameters of EBOP to be determined by the iterative least-squares procedure are: the orbital inclination
_ Bulut, O. Demircan / New Astronomy 13 (2008) 252–254 I.
253
Table 1 Identifications of seven eclipsing binary systems with eccentric orbits in the Hipparcos photometric database Parameter
V466 Car
V493 Car
V529 Car
MN TrA
V398 Lac
V402 Lac
V821 Cas
HIP DM a(2000) d(2000) T0 (HJD) P (days) mV (mag) Dm (mag) B–V (mag) Sp d (pc) /II
40,666 CPD 59 1017 08 18 05.03 60 18 50.1 2,448,500.069 3.4560 7.27 0.28 0.013(11) B8/B9V 640(220) 0.37
48,832 CPD 59 1551 09 57 40.26 59 42 51.7 2,448,501.210 3.22940 8.89 0.29 0.037(21) B9IV 860(570) 0.63
54,026 CPD 62 1862 11 03 12.85 63 03 59.9 2,448,503.560 4.74450 8.13 0.30 0.448(12) B8V 430(130) 0.59
78,231 CPD 61 5428 15 58 28.33 62 03 37.6 2,448,501.361 2.37983 8.50 0.45 0.001(13) B9V
109,193 BD + 51 3251 22 07 12.42 +52 38 08.5 2,448,501. 570 5.40570 8.73 0.23 0.140(15) A0 840(560) 0.36
109,354 BD + 44 4059 22 09 15.19 +44 50 47.3 2,448,500.980 3.78200 6.73 0.07 0. 036(6) B9 239(40) 0.71
118,223 BD + 52 3571 23 58 49.18 +53 40 19.9 2,448,500.446 1.76975 8.26 0.33 0.110(15) A0 186(31) 0.47
0.45
HIP: Hipparcos identifier; DM: durchmusterung listing; a(2000): right ascension (2000); d(2000): declination (2000); T0: epoch in HJD; P: orbital period in days; mV: magnitude at maximum brightness (V); Dm: depth of primary minimum (Hp); B–V: colour index; Sp: spectral type; d: distance in pc; /II: phase of secondary minimum.
(O-C) + 8.90
Phase
MN TrA
Fig. 1. Hipparcos light curves and their theoretical representations together with corresponding (O–C) residuals.
_ Bulut, O. Demircan / New Astronomy 13 (2008) 252–254 I.
254 Table 2 Results of photometric analysis Parameter
V466 Car
V493 Car
V529 Car
MN TrA
V398 Lac
V402 Lac
V821 Cas
Js k rp rs i () Lp Ls e cos x e sin x e x () up = us / n r
0.554(74) 0.58 (11) 0.251(10) 0.144 81.18(2.12) 0.845 0.155 0.1912(24) 0.136(24) 0.235 215.46 0.408 0.0100(11) 112 0.011
0.941(63) 0.728 0.220(6) 0.160 80.20(39) 0.667 0.333 0.2035(26) 0.130(32) 0.242 32.69 0.408 0.0055(5) 121 0.017
0.755(44) 0.80(10) 0.218(8) 0.174 79.85(68) 0.678 0.322 0.1205(18) 0.056(24) 0.133 25.07 0.388 0.0410(8) 123 0.011
0.729(20) 0.824 (16) 0.164(2) 0.135 88.84(48) 0.669 0.331 0.0732(6) 0.035(14) 0.081 205.38 0.408 0.0038(1) 150 0.012
0.571 0.849 0.172 0.154 80.52(21) 0.688 0.312 0.2058(15) 0.180(20) 0.273 221.14 0.452 0.0088(6) 153 0.016
0.926 0.796 0.148(2) 0.118 79.22(18) 0.631 0.369 0.3069(14) 0.222(7) 0.379 35.93 0.408 0.0025(2) 155 0.009
0.622 0.690(67) 0.231(10) 0.159 81.79(68) 0.773 0.227 0.0650(17) 0.094(21) 0.115 124.62 0.452 0.0010(6) 205 0.018
angle (i), the relative radius of the primary star (rp) (in units of the semi-major axis of the orbit), the ratio of the radii (k = rs/rp), the central surface brightness of the secondary star (Js) in terms of that of the primary star (Jp ” 1), corresponding to effective temperatures. EBOP allows the eccentricity to be a variable parameter by introducing e cos x and e sin x as free parameters, where e is the orbital eccentricity and x the longitude of periastron. Several basic assumptions were made to solve the light curves of the systems. Theoretical limb darkening coefficients (up = us) were taken from Wade and Rucinski (1985) while the gravity darkening parameter (yp = ys) was assumed to have a monochromatic (radiative) dependence. The integration ring size was fixed to 5, no third light was included. Also, a phase zero-point correction (phase shift, /) and a photometric scale factor (the magnitude difference at quadrature) were included as free parameters in all solutions. In our preliminary analysis, we performed a grid search in k and found that r (the standard error of one observation expressed in magnitudes) minimized at a value of k. The initial values of e cos x were estimated from the observed displacement of the secondary eclipse from phase 0.5. The Hipparcos light curves and their theoretical representations together with the corresponding (O–C) residuals are shown in Fig. 1. The results of the photometric analysis are given in Table 2. In this table, n is the number of observational points. The theoretical representations of the light curves presented in Fig. 1 are based on the parameters of the light curve solutions as listed in Table 2.
puter program and their photometric elements (namely, orbital eccentricity (e), longitude of periastron, relative radius (rp,s), and orbital inclination (i)) were determined for the first time. These calculations are by no means final but can be used as initial parameters for future light curve analyses of these systems based on more precise follow-up observations. In particular, these solutions will be important to determine the change of the longitude of periastron angles, which may be used in turn to estimate the apsidal motion periods, and ultimately, the relativistic effect on apsidal motion and internal structure constants of the component stars. To obtain a more complete understanding of these systems, further more accurate photoelectric observations of the minima are necessary to firmly establish the apsidalmotion rate. Spectroscopic observations are also needed to obtain the absolute dimensions of the systems. Moreover, a spectroscopic determination of the luminosity ratio (Ls/Lp) will help to constrain the ratio of the radii, allowing for a more reliable determination of the internal-structure constants and system age. Finally, the determination of stellar rotational velocities may be used to test the degree of tidal synchronism.
Acknowledgement This work has been supported by Research Found of C ¸ anakkale Onsekiz Mart University (BAP) under the research project no. 2002/35.
3. Summary and discussion References In this study, we analyzed the photometric data from the Hipparcos database of seven systems (Table 1) to deduce orbital and physical parameters. The light curves of the seven selected systems based on Hipparcos photometry were analyzed with the EBOP com-
ESA, 1997. The Hipparcos and Tycho Catalogues, Noordwijk. Etzel, P.B., 1981. In: Carling, E.B., Kopal, Z. (Eds.), Photometric and Spectroscopic Binary Systems. Reidel, Dordrecht. Popper, D.M., Etzel, P.E., 1981. AJ 86, 102. Wade, R.A., Rucinski, S.M., 1985. A&AS 60, 471.
New Astronomy 13 (2008) 252–254 www.elsevier.com/locate/newast
Light curve analyses of new eclipsing binary systems with eccentric orbits _ Bulut *, O. Demircan I. C¸anakkale Onsekiz Mart University Observatory, 17100 Terziog˘lu Kampu¨su¨, C¸anakkale, Turkey Received 2 August 2007; received in revised form 11 September 2007; accepted 10 October 2007 Available online 23 October 2007 Communicated by P.S. Conti
Abstract A photometric study of seven new eclipsing binary systems with eccentric orbits, namely, V466 Car, V493 Car, V529 Car, MN TrA, V398 Lac, V402 Lac and V821 Cas, is presented. The photometric data analyzed were taken from the Hipparcos database. The secondary minima in all systems were shifted by different amounts from the phase 0.5 giving clear evidence of their eccentric orbits. The EBOP computer program based upon models by Nelson et al. [Popper, D.M., Etzel, P.E., 1981. AJ 86, 102] was used in the analysis of the photometric data to deduce the orbital geometry in space and the relative sizes and luminosities of the component stars. 2007 Elsevier B.V. All rights reserved. Keywords: Stars: binaries: close; Stars: binaries: eclipsing; Stars: individual: V466 Car, V493 Car, V529 Car, MN TrA, V398 Lac, V402 Lac,V821 Cas
1. Introduction If the major axis of the eccentric orbit of an eclipsing binary system is not close to the line of sight, then the secondary minimum is observed to have shifted from the phase 0.5. Such observations are used in practice as clear evidence of eccentric orbits. The Hipparcos (ESA, 1997) photometric database was surveyed for eclipsing binary light curves with shifted secondary minima. We thus detected seven new eclipsing binary systems with eccentric orbits. These are V466 Car, V493 Car, V529 Car, MN TrA, V398 Lac, V402 Lac and V821 Cas. The identification of these systems is listed in Table 1. The entries in the table were mostly extracted from the Variability Annex of the Hipparcos Catalogue (ESA, 1997). These systems are good candidates in testing theories of apsidal motion and of orbital circularisation in binary star systems.
*
Corresponding author. Tel.: +90 286 2180018x1414; fax: +90 286 2180549. _ Bulut). E-mail address: [email protected] (I. 1384-1076/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.newast.2007.10.003
The aim of the present work is to provide a preliminary set of parameters for the systems, which can be used as input parameters in the analysis of more precise light curves in the future, based on follow-up observations. 2. Analysis of the light curves The photometric observations (Hp magnitudes) for the selected systems were taken from the Epoch Photometry Annex of the Hipparcos database and the relevant light curves were constructed using the light elements (T0, P) given in Table 1. All observations were used and were assumed to have unit weight. For analysis of the Hipparcos light curves of the systems, we chose the Nelson–Davis–Etzel (NDE) model (Etzel, 1981; Popper and Etzel, 1981), and used the computer programme EBOP (Eclipsing Binary Orbit Program). This model proved to yield reliable photometric elements for detached binaries of spherical or slightly oblate stars (oblateness, 6 0.04). If the primary star (p) is defined to be the one eclipsed during the deepest minimum, the major parameters of EBOP to be determined by the iterative least-squares procedure are: the orbital inclination
_ Bulut, O. Demircan / New Astronomy 13 (2008) 252–254 I.
253
Table 1 Identifications of seven eclipsing binary systems with eccentric orbits in the Hipparcos photometric database Parameter
V466 Car
V493 Car
V529 Car
MN TrA
V398 Lac
V402 Lac
V821 Cas
HIP DM a(2000) d(2000) T0 (HJD) P (days) mV (mag) Dm (mag) B–V (mag) Sp d (pc) /II
40,666 CPD 59 1017 08 18 05.03 60 18 50.1 2,448,500.069 3.4560 7.27 0.28 0.013(11) B8/B9V 640(220) 0.37
48,832 CPD 59 1551 09 57 40.26 59 42 51.7 2,448,501.210 3.22940 8.89 0.29 0.037(21) B9IV 860(570) 0.63
54,026 CPD 62 1862 11 03 12.85 63 03 59.9 2,448,503.560 4.74450 8.13 0.30 0.448(12) B8V 430(130) 0.59
78,231 CPD 61 5428 15 58 28.33 62 03 37.6 2,448,501.361 2.37983 8.50 0.45 0.001(13) B9V
109,193 BD + 51 3251 22 07 12.42 +52 38 08.5 2,448,501. 570 5.40570 8.73 0.23 0.140(15) A0 840(560) 0.36
109,354 BD + 44 4059 22 09 15.19 +44 50 47.3 2,448,500.980 3.78200 6.73 0.07 0. 036(6) B9 239(40) 0.71
118,223 BD + 52 3571 23 58 49.18 +53 40 19.9 2,448,500.446 1.76975 8.26 0.33 0.110(15) A0 186(31) 0.47
0.45
HIP: Hipparcos identifier; DM: durchmusterung listing; a(2000): right ascension (2000); d(2000): declination (2000); T0: epoch in HJD; P: orbital period in days; mV: magnitude at maximum brightness (V); Dm: depth of primary minimum (Hp); B–V: colour index; Sp: spectral type; d: distance in pc; /II: phase of secondary minimum.
(O-C) + 8.90
Phase
MN TrA
Fig. 1. Hipparcos light curves and their theoretical representations together with corresponding (O–C) residuals.
_ Bulut, O. Demircan / New Astronomy 13 (2008) 252–254 I.
254 Table 2 Results of photometric analysis Parameter
V466 Car
V493 Car
V529 Car
MN TrA
V398 Lac
V402 Lac
V821 Cas
Js k rp rs i () Lp Ls e cos x e sin x e x () up = us / n r
0.554(74) 0.58 (11) 0.251(10) 0.144 81.18(2.12) 0.845 0.155 0.1912(24) 0.136(24) 0.235 215.46 0.408 0.0100(11) 112 0.011
0.941(63) 0.728 0.220(6) 0.160 80.20(39) 0.667 0.333 0.2035(26) 0.130(32) 0.242 32.69 0.408 0.0055(5) 121 0.017
0.755(44) 0.80(10) 0.218(8) 0.174 79.85(68) 0.678 0.322 0.1205(18) 0.056(24) 0.133 25.07 0.388 0.0410(8) 123 0.011
0.729(20) 0.824 (16) 0.164(2) 0.135 88.84(48) 0.669 0.331 0.0732(6) 0.035(14) 0.081 205.38 0.408 0.0038(1) 150 0.012
0.571 0.849 0.172 0.154 80.52(21) 0.688 0.312 0.2058(15) 0.180(20) 0.273 221.14 0.452 0.0088(6) 153 0.016
0.926 0.796 0.148(2) 0.118 79.22(18) 0.631 0.369 0.3069(14) 0.222(7) 0.379 35.93 0.408 0.0025(2) 155 0.009
0.622 0.690(67) 0.231(10) 0.159 81.79(68) 0.773 0.227 0.0650(17) 0.094(21) 0.115 124.62 0.452 0.0010(6) 205 0.018
angle (i), the relative radius of the primary star (rp) (in units of the semi-major axis of the orbit), the ratio of the radii (k = rs/rp), the central surface brightness of the secondary star (Js) in terms of that of the primary star (Jp ” 1), corresponding to effective temperatures. EBOP allows the eccentricity to be a variable parameter by introducing e cos x and e sin x as free parameters, where e is the orbital eccentricity and x the longitude of periastron. Several basic assumptions were made to solve the light curves of the systems. Theoretical limb darkening coefficients (up = us) were taken from Wade and Rucinski (1985) while the gravity darkening parameter (yp = ys) was assumed to have a monochromatic (radiative) dependence. The integration ring size was fixed to 5, no third light was included. Also, a phase zero-point correction (phase shift, /) and a photometric scale factor (the magnitude difference at quadrature) were included as free parameters in all solutions. In our preliminary analysis, we performed a grid search in k and found that r (the standard error of one observation expressed in magnitudes) minimized at a value of k. The initial values of e cos x were estimated from the observed displacement of the secondary eclipse from phase 0.5. The Hipparcos light curves and their theoretical representations together with the corresponding (O–C) residuals are shown in Fig. 1. The results of the photometric analysis are given in Table 2. In this table, n is the number of observational points. The theoretical representations of the light curves presented in Fig. 1 are based on the parameters of the light curve solutions as listed in Table 2.
puter program and their photometric elements (namely, orbital eccentricity (e), longitude of periastron, relative radius (rp,s), and orbital inclination (i)) were determined for the first time. These calculations are by no means final but can be used as initial parameters for future light curve analyses of these systems based on more precise follow-up observations. In particular, these solutions will be important to determine the change of the longitude of periastron angles, which may be used in turn to estimate the apsidal motion periods, and ultimately, the relativistic effect on apsidal motion and internal structure constants of the component stars. To obtain a more complete understanding of these systems, further more accurate photoelectric observations of the minima are necessary to firmly establish the apsidalmotion rate. Spectroscopic observations are also needed to obtain the absolute dimensions of the systems. Moreover, a spectroscopic determination of the luminosity ratio (Ls/Lp) will help to constrain the ratio of the radii, allowing for a more reliable determination of the internal-structure constants and system age. Finally, the determination of stellar rotational velocities may be used to test the degree of tidal synchronism.
Acknowledgement This work has been supported by Research Found of C ¸ anakkale Onsekiz Mart University (BAP) under the research project no. 2002/35.
3. Summary and discussion References In this study, we analyzed the photometric data from the Hipparcos database of seven systems (Table 1) to deduce orbital and physical parameters. The light curves of the seven selected systems based on Hipparcos photometry were analyzed with the EBOP com-
ESA, 1997. The Hipparcos and Tycho Catalogues, Noordwijk. Etzel, P.B., 1981. In: Carling, E.B., Kopal, Z. (Eds.), Photometric and Spectroscopic Binary Systems. Reidel, Dordrecht. Popper, D.M., Etzel, P.E., 1981. AJ 86, 102. Wade, R.A., Rucinski, S.M., 1985. A&AS 60, 471.