The Algol-type close binary system SZ Her revised

New Astronomy 35 (2015) 79–83

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The Algol-type close binary system SZ Her revised B. Hosseinzadeh a,⇑, R. Pazhouhesh a, K. Yakut b a b

Department of Physics, Faculty of Sciences, University of Birjand, Birjand, Iran _ Turkey Department of Astronomy and Space Sciences, University of Ege, Izmir,

h i g h l i g h t s  Modeling of SZ Her shows that the secondary component fills its Roche lobe.  The results showed that there is not convincing pulsational behavior in this binary star.  Study of the O  C diagram indicates the existence of a third and fourth body.  The minimum mass for the fourth body is close to brown dwarf mass limit.

a r t i c l e

i n f o

Article history: Received 10 June 2014 Received in revised form 1 September 2014 Accepted 14 September 2014 Available online 20 September 2014 Communicated by E.P.J van den Heuvel Keywords: Eclipsing binaries Fundamental parameters SZ Herculis

a b s t r a c t We present long term ground-based photometric variations of the Algol type binary system SZ Her. Modeling of the system shows that the secondary component is filling Roche lobe. The parameters for the primary and the secondary components have been determined as M1 ¼ 1:56  0:05 M ; M 2 ¼ 0:77 0:03 M , R1 ¼ 1:61  0:10 R ; R2 ¼ 1:55  0:09 R ; L1 ¼ 6:5  0:5 L , L2 ¼ 1:1  0:1 L while the separation of the components is a ¼ 4:9  0:3 R . Newly obtained parameters yield the distance of the system as 302  12 pc. We collected all the photometric and CCD times of mid-eclipse available in the literature and combined them with the newly obtained eight times of light minima. Analysis of the mid-eclipse ¼ þ3:1ð2Þ  108 days/yr that can be interpreted in terms of times indicate a period increase of dP dt dM the mass transfer rate as dt ¼ þ2:62ð3Þ  109 M =yr from the secondary to the primary component. The orbital period of the system oscillates with periods of 118 years and 30 years with corresponding semi-amplitudes of 0.0057 days and 0.0055 days, respectively. These changes were analyzed under the assumption of the existence of third and fourth bodies in the system. Ó 2014 Elsevier B.V. All rights reserved.

1. Introduction The system SZ Her (BD + 33o2930 = GSC 2610-1209 = HIP 86430 = TYC 2610-1209-1, V = 10.05 mag, Porb = 0.818 days) was discovered by Ceraski (1908) and Dunér et al. (1909) as a variable star. The first observational data of the system were obtained in 1902 Shapley (1913), Russell and Shapley (1914), Dugan (1923). For the first time Giuricin and Mardirossian (1981) analyzed two-color photoelectric light curve data of Broglia et al. (1955) and reported that the system is a semi-detached Algol-type binary with a mass ratio of q ¼ 0:4 and an orbital inclination of i ¼ 87 :9. Szekely (2003) and Dvorak (2010) performed CCD observations to investigate the pulsation behavior of the d Scuti type component in SZ Her. ⇑ Corresponding author. E-mail addresses: (B. Hosseinzadeh).

[email protected],

http://dx.doi.org/10.1016/j.newast.2014.09.005 1384-1076/Ó 2014 Elsevier B.V. All rights reserved.

[email protected]

Recently Lee et al. (2012) obtained multiband CCD photometric data of SZ Her. The authors concluded that the less massive component in the system fills its Roche lobe and the system SZ Her is indeed a classical Algol-type system. The authors reported a mass ratio of q ¼ 0:472, an inclination angle of i ¼ 87 :57, and DT ¼ 2381 K for the system. The orbital period variation of SZ Her has been the subject of many papers such as Kreiner (1971), Mallama (1980), Zavala (2002), Szekely (2003), Soydugan (2008), Lee et al. (2012) and Hinse et al. (2012). The observed period variation was attributed to a third body in the system in Szekely (2003) and Soydugan (2008) with an orbital period of 66 years and 71 years, respectively. Soydugan (2008) suggested that the timing residuals from the Light Time Effect (LITE) fit indicate fluctuations with small and variable amplitudes whose period was estimated to be about 20 years. In a recent study Lee et al. (2012) proposed the system SZ Her to be a quadruple. The authors estimated that the orbital period of SZ Her varies due to the combination of two periodic

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B. Hosseinzadeh et al. / New Astronomy 35 (2015) 79–83 Table 1 Coordinates and magnitudes for SZ Her, comparison and check stars. Star

GSC

RA (J2000)

SZ Her

2610-0129

17 39 36:81

þ32 56 46:7

10.05

0.35

Comparison

2610-1116

17h 39m 00:20s

þ32 540 36:000

9.79

1.09

Check

2610-0821

17h 39m 03:40s

þ32 580 56:5400

11.61

0.53

h

m

Dec (J2000) 

s

0

V (mag) 00

B  V (mag)

Table 2 Available data set of SZ Her. All data for four colors data sets can be found electronically at CDS. Filter

HJD + 2400000

Delta magnitude

B B B B B B B B B B .. .

2456097.28886 2456097.29168 2456097.30015 2456097.30581 2456097.32280 2456097.32562 2456097.33129 2456097.34258 2456097.34824 2456097.35674 .. .

0.553 0.551 0.553 0.563 0.567 0.558 0.562 0.562 0.559 0.547 .. .

Fig. 1. Light curves of SZ Her in the B, V, R, and I bandpasses that are plotted as (V  C) differential magnitudes versus orbital phase.At here the (V  C) means the Variable star’s magnitude minus Comparison star’s magnitude.

Fig. 2. (a) The O  C variation of SZ Her. The continuous line indicates the total effect of third and fourth stars. (b) The (O  C)II residuals after the subtraction of third body orbit. (c) shows the residuals after subtraction of the effects of the third and fourth components.

variations with a cycle lengths of P3 ¼ 85:8 years and P4 ¼ 42:5 years and semi-amplitudes of K 3 ¼ 0:013 days and K 4 ¼ 0:007 days, respectively. The corresponding masses were given as M 3 ¼ 0:22 M and M 4 ¼ 0:19 M . The orbital stability and LITE model of the system was revised by Hinse et al. (2012).

The authors studied the stability of the system using the osculating orbital elements given in Lee et al. (2012). The results show instabilities that lead to the escape of one of the proposed companions. In this study we revised light curve solution of SZ Her, the pulsation behavior of the component and period change analysis of this interesting binary system.

Table 3 Observed PE and CCD times of minimum light for SZ Her. A sample is shown here: the full version is provided as supplementary material to the online article. HJD

Method

Ref.

HJD

Method

Ref.

HJD

Method

Ref.

33463.2708 33501.723 34901.486 34905.5761 34923.5732 34987.3852

pe pe pe pe pe pe

1 2 1 1 1 3

53176.53844 53178.58273 53180.62827 53183.08448 53183.49127 53185.53634

ccd ccd ccd ccd ccd ccd

13 13 13 13 13 13

54581.62260 54588.16795 54589.8040 54592.25831 54604.12114 54616.8016

ccd ccd ccd ccd ccd ccd

13 13 21 13 13 13

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B. Hosseinzadeh et al. / New Astronomy 35 (2015) 79–83 Table 4 Orbital elements of the quadruple system SZ Her. The standard errors 1r, in the last digit are given in parentheses. Parameter

Unit

Table 6 The photometric parameters and 1r errors obtained from the solution of all available light curves. See text for details.

Value

LC1

LC2

LC3

q Fractional radius of primary Fractional radius of secondary

87.3(1) 4.902(9) 2.820 0.463(4) 0.3141(14) 0.3126(8)

87.4(1) 3.569(11) 2.820 0.432(1) 0.3266(10 0.307(6)

88.0(1) 3.611(7) 2.820 0.491(3) 0.3293(10) 0.3171(6)

Radiative parameters: T 1 (K) T 2 (K) Albedo A1 Albedo A2 Gravity brightening g 1 Gravity brightening g 2 l3

7262 4721(9) 1.0 0.59(3) 1.0 0.32 –

7262 4762(9) 1.0 0.77(1) 1.0 0.24 –

7262 4736(7) 1.0 0.80(1) 1.0 0.24 0.09

– 87(5) 82(5) 78(4)

93(4) 88(4) 83(4) 79(3)

93(4) 88(3) 83(3) 78(3)

– 12.30 17.38 21.97

6.82 11.69 16.40 20.67

6.88 11.89 16.78 21.19

Parameter Binary system – Star AB Initial epoch, To Period, Pbin Period change ratio, Mass transfer ratio,

dP dt dM dt

Star C Initial epoch, To(C) Orbital period, P C Amplitude, AC Eccentricity, e Longitude of the periastron, x0C Mass function, f ðmC Þ Minimum mass, MCðminÞ Mass, MC;i0 ¼60 Star D Initial epoch, To(D) Orbital period, P D Amplitude, AD Eccentricity, e Longitude of the periastron, x0D Mass function, f ðmD Þ Minimum mass, MD(min) Mass, MD;i0 ¼60

HJD day day yr1

24 34987.3852(72) 0.818095712647(33)

M yr1

þ2:62ð3Þ  109

HJD yr day

24 31024(1608) 30(2) 0.0055(8) 0.76(7) 0.0006 0.003428(6) 0.29 0.34

° M M M HJD yr day ° M M M

þ3:1ð2Þ  108

24 08097.547(43630.646) 118 0.0057(34) 0.73(30) 120 0.000089(3) 0.083 0.09799(9)

Geometric parameters: i (°)

X1 X2

Luminosity ratio:

L1 (%) L1 þL2 þl3

B V R I Luminosity ratio:

L2 (%) L1 þL2 þl3

B V R I

3. Eclipse timings and period study 2. New observations New B; V; R, and I band CCD observations of SZ Her were obtained on ten nights between June and October 2012 at the Ege University and Birjand University Observatories with a 40 cm telescope using an Apogee CCD U47 and a 35 cm Schmidt–Gassegrain telescope using an SBIG CCD ST-7XE, respectively. We selected GSC 2610-1116 (V ¼ 9m :79; B  V ¼ 1m :09) and GSC 2610-0821 (V = 11m :61; B  V ¼ 0m :53) as comparison and check stars, respectively. During the observations, we collected a total of 238 differential magnitudes in B, 445 in V, 530 in R, and 503 in I bands. The observations cover the entire orbit of the binary for each filter. Bias, dark, and twilight flat field frames were taken with the CCD camera to calibrate the images of the stars using standard techniques. IRAF (DIGIPHOT/APPHOT) packages were used in data reduction. Standard deviations of the data were calculated to be 0m.019, 0m.018, 0m.018, and 0m.018 for B; V; R, and I bands, respectively. Some parameters for the variable, comparison and check stars are given in Table 1. All the data are listed in Table 2. The light curves of SZ Her obtained in this study are plotted in Fig. 1 as the (V  C) differential magnitudes versus orbital phase. In this study eight new times of minima light have been obtained and collated with those published (Table 3) with their errors.

In this study, four primary and four secondary times of minima were calculated using the method of Kwee and van Woerden (1956). For ephemeris computations, we have collected a total of 157 timings (18 photoelectric, and 139 CCD). As mentioned in the Introduction, a single light-time effect ephemeris due to a third body, was reported as a reason of the period change by Szekely (2003) and Soydugan (2008) while Lee et al. (2012) suggested it to be a quadruple system which according to Hinse et al. (2012) should be unstable and should not exist. We solve the O  C curve and find a parabolic variation which can be ascribed to mass transfer between the components. Weighted least-squares method was used. The ðO  CÞI represents residuals after the parabolic variation has been subtracted. In Fig. 2 full circles represent times of primary minima and open circles those of the secondary minima. The residuals ðO  CÞI are plotted in Fig. 2. The continuous line indicates the total effect of the third and fourth bodies in Fig.2(a). The ðO  CÞII in the middle of curve shows the residuals distribution after the subtraction of the third body in Fig.2(b) and the ðO  CÞIII shows the final residuals from the best fit shown in Fig.2(c). We used Eq. 0 (1) during the O  C analysis where T0, E, P0, a12 ; i , e0 and x0 are the starting epoch for the primary minimum, integer eclipse cycle (Epoch number), orbital period of the eclipsing binary, semi-major axis, inclination, eccentricity and longitude of the periastron of the

Table 5 Available light curves of SZ Her. JD⁄ refers to the time interval of data taken. Light curves are LC1: Szekely (2003), LC2: Lee et al. (2012), LC3: This study. ID

Year

JD⁄ (2400000+)

Filters

Type

Comparison(s)

Npoints

LC1

2002

52446.3-52450.5

V, R, I

ccd

V:997, R:1000, I:1002

LC2

2008

54525.2-54604.2

B, V, R, I

ccd

LC3

2012

56155.6-56212.3

B, V, R, I

ccd

GSC GSC GSC GSC GSC GSC

2610-1214 2610-1417 2610-1116 2610-0821 2610-1116 2610.0821

B:435, V:437, R:439, I:417 B:238, V:445, R:530, I:503

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B. Hosseinzadeh et al. / New Astronomy 35 (2015) 79–83 Table 7 Absolute parameters of SZ Her. The standard 1r errors in the last digit are given in parentheses. Parameter

Unit

Primary

Secondary

Mass (M) Radius (R) Temperature (Teff) Luminosity (L) Surface gravity (log g) Absolute bol. magnitude (Mb) Absolute vis. magnitude (MV) Separation between stars (a) Distance (d)

M R K L CGS mag mag R pc

1.56(5) 1.61(10) 7262 6.5(5) 4.22(1) 2.70 2.69 4.9(3) 302(12)

0.77(3) 1.55(9) 4735(21) 1.1(1) 3.94(2) 4.64 5.10

4. Light curves solution

Fig. 3. Light curves of the system (see text for details).

orbit, respectively and m0 is the true anomaly. The epoch of periastron passage T 0 and the period P 0 of the orbit of the three-body system are hidden parameters in Eq. (1) (see Kalomeni et al. (2007) for details). The results indicate the existence of a third body with a 30 years orbital period orbiting the binary system as well as the existence of a fourth body with a 118 years period. The minimum masses of the third and fourth components are obtained to be 0.29 M and 0.083 M , respectively. The parameters obtained for these bodies are listed in Table 4. 0

1 dP 2 a12 sin i E þ Min I ¼ T o þ Po E þ 2 dE c " # 02 1e 0 0 0 0 sin ðv þ x Þ þ e sin x  1 þ e0 cos v 0

ð1Þ

The Phoebe code (Prša and Zwitter, 2005) that follows the 2003 version of the W–D code (Wilson and Devinney, 1971) was used to model the new BVRI light curves of the system. According to theoretical models and previous studies, some parameters could be fixed, while others are adjusted during subsequent iterations. The temperature of the primary component was assumed to be T 1 ¼ 7262 K from Lee et al. (2012)’s study. The gravity-darkening exponents were taken at standard values of g 1 ¼ 1:0 for radiative atmosphere from von Zeipel (1924) and g 2 ¼ 0:32 for convective atmosphere from Lucy (1967). The bolometric albedos of the components were fixed to A1 ¼ 1:0 and A2 ¼ 0:5 for a radiative and convective atmospheres, following Rucin´ski (1969). Synchronous rotation for both components of the system and a circular orbit were adopted. We used the logarithmic limb-darkening law with the coefficients adopted from van Hamme (1993) for the model atmosphere option. During each iteration step, the adjustable parameters were surface temperature of the secondary component (T 2 ), orbital inclination (i), dimensionless surface potentials of primary (X1 ), mass ratio of the system (q ¼ m2 =m1 ) and the fractional luminosity of the primary component (L1 ). Also we searched third light contribution (l3 ) in order to check the probability of a third component. q-search was Performed by Lee et al. (2012) and the authors published the mass ratio as 0.49 which was used as initial value in our analysis The q values were regarded as a free parameter together with the albedos and gravity-darkening exponents. The Journal of the all available light curves for SZ Her is given in Table 5. The parameters obtained from the analysis are summarized in Table 6 and the theoretical light curves are shown in Fig. 3. The light curves obtained in this study are analysed together with those of Szekely (2003) and Lee et al. (2012). The results are listed in Table 6 while the light variations are shown in Figs. 3(a)–(c). We calculated the absolute physical parameters for SZ Her using the Table V in Torres et al. (2010). Bolometric corrections for the components obtained from Cox (2000) are listed in Table 7.

5. Conclusion SZ Hercules was listed as a candidate system with a possible d Scuti component by Soydugan (2008). He used the eclipsing binaries’s spectral type (A–F) as criterion. We searched for short-period pulsations in the data of this system. For this, we subtracted the theoretical LCs from the observed ones in order to remove the proximity effects (reflection and ellipticity). The frequency analysis was made on the LC residuals with Period04 (Lenz and Breger, 2005) software that is based on classical Fourier analysis. The result shows that there is not convincing pulsational behavior in this binary system.

B. Hosseinzadeh et al. / New Astronomy 35 (2015) 79–83

The published data of the system in the literature have been combined with those obtained in this study and analyzed together. Unlike previous studies of SZ Her, in this study we used only the most accurate (photoelectric and CCD data) minima times that the results indicate the existence of a third body with a 30 yrs orbital period around the binary system as well as the existence of a fourth body with a 118 yrs period. Our period analysis results are somewhat different from the results of Lee et al. (2012) and Hinse et al. (2012). The minimum masses of these bodies are obtained to be 0.29 M and 0.083 M, respectively. The minimum mass for the Star D is close to brown dwarf mass limit. The parameters obtained for these bodies are listed in Table 4. The binary orbital elements were obtained from multicolour light curve analysis. The results indicate that the secondary component star fills its Roche lobe undergoing a phase of mass transfer and the prominent light is from the primary component. The orbital parameters listed in Table 6 are obtained from the light curve solutions. The mass, temperature and spectral type of the primary component have been determined using the tables of Torres et al. (2010), Yakut and Eggleton (2005) and Cox (2000) because of the absence of a spectroscopic data. The mass of the primary was assumed to be 1:56 M in accordance with the values given in the literature. The mass ratio of the system is obtained to be 0:491. This results in a secondary mass of 0.77 M. The absolute physical parameters are listed in Table 7. The results are consistent with the similar systems on the M–R, M–L and the H–R diagrams given by Yakut and Eggleton (2005). Acknowledgments This study is a part of PhD thesis of B. Hosseinzadeh at the University of Birjand, Iran. This research has made use of the Simbad database, operated at CDS, Strasbourg, France. The authors would like to thank to Birjand University Observatory and Ege University

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Observatory for the observing time. K.Y. acknowledges support by _ Turkish Scientific and Technical Research Council (TUBITAK111T270). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.newast.2014. 09.005. References Broglia, P., Masani, A., Pestarino, E., 1955. MmSAI 26, 321. Ceraski, W., 1908. AN 179, 291. Cox A.N., 2000. asqu.book. Dugan, R.S., 1923. ApJ 58, 164. Dunér, N.C., Hartwig, E., Müller, G., 1909. AN 182, 321. Dvorak, S.W., 2010. IBVS 5938, 1. Giuricin, G., Mardirossian, F., 1981. A&AS 45, 85. Hinse, T.C., Goz´dziewski, K., Lee, J.W., Haghighipour, N., Lee, C.-U., 2012. AJ 144, 34. Kalomeni, B., Yakut, K., Keskin, V., Deg˘irmenci, Ö.L., Ulasß, B., Köse, O., 2007. AJ 134, 642. Kreiner, J.M., 1971. AcA 21, 365. Kwee, K.K., van Woerden, H., 1956. BAN 12, 327. Lee, J.W., Lee, C.-U., Kim, S.-L., Kim, H.-I., Park, J.-H., 2012. AJ 143, 34. Lenz, P., Breger, M., 2005. CoAst 146, 53. Lucy, L.B., 1967. ZA 65, 89. Mallama, A.D., 1980. ApJS 44, 241. Prša, A., Zwitter, T., 2005. ApJ 628, 426. Rucin´ski, S.M., 1969. AcA 19, 245. Russell, H.N., Shapley, H., 1914. ApJ 40, 417. Shapley, H., 1913. ApJ 38, 158. Soydugan, F., 2008. AN 329, 587. Szekely, P., 2003. IBVS 5467, 1. Torres, G., Andersen, J., Giménez, A., 2010. A&ARv 18, 67. van Hamme, W., 1993. AJ 106, 2096. von Zeipel, H., 1924. MNRAS 84, 702. Wilson, R.E., Devinney, E.J., 1971. ApJ 166, 605. Yakut, K., Eggleton, P.P., 2005. ApJ 629, 1055. Zavala, R.T. et al., 2002. AJ 123, 450.