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Photometric and periodic investigations of W-type W UMa eclipsing binary BB Peg
New Astronomy 78 (2020) 101354
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Photometric and periodic investigations of W-type W UMa eclipsing binary BB Peg
T
Z. Kamalifara,b, A. Abedi⁎,a,b, K.Y. Roobiata,b a b
Department of Physics, Faculty of Sciences, University of Birjand, P.O.Box 97175/615, Birjand, Iran Dr. Mojtahedi Observatory, University of Birjand, Birjand, Iran
ARTICLE INFO
ABSTRACT
Keywords: Stars: binaries: close Stars: binaries: eclipsing Stars: individual (BB Peg)
In this study, photometry was conducted for the W UMa type eclipsing binary BB Peg through V and R Johnson filters during several nights in September and October 2016. The light curves were obtained at Dr. Mojtahedi Observatory, of the University of Birjand, Iran. Data reduction was performed using IRIS software. Orbital parameters were obtained by analyzing the light curves using PHOEBE software. The radial velocity information was then used to obtain the absolute parameters of the system. Some minimum light times were obtained forthe system and variations in the orbital period of BB Peg were analyzed by adding the new minimum light times to the O-C diagram to obtain a new ephemeris for the system. The period change appeared to be due to the lighttime effect. A justifiable fit was obtained using the third and fourth stars. However, this fit was not confirmed and it may need revision when further data are obtained. The variation could be attributed to other sources, such as magnetic cycles or non-conservative mass transfer from the system.
1. Introduction BB Peg (HIP 110493) is a W-subtype W UMa over-contact eclipsing binary system. The variability of this system was first noted by Hoffmeister (1931) and confirmed subsequently by other studies in the 1930s (Guthnick and Prager, 1932; Nikonov and Dobronravin, 1937; Piotrowski, 1936). The orbital period variability of BB Peg was first determined by Whitney (1943) and various processes have been proposed as the sources of these orbital period variations. The two most important processes are mass transfer between the components and the light-time effect (LTE) (Awadalla, 1988; Cerruti-Sola et al., 1981; Cerruti-Sola and Scaltriti, 1980; D’Angelo et al., 2006; Kalomeni et al., 2007; Pribulla and Rucinski, 2006; Qian, 2001). The first light curve for this system was analyzed by Cerruti-Sola et al. (1981) in two B and V Johnson–Cousins bands. The analyses of the BB Peg light curve performed by Giuricin et al. (1981) and Leung et al. (1985) classified this binary as belonging to the W-subtype W UMa system. In addition, these analyses showed that some hot or cold spots may exist on the surfaces of the components of this system due to the inequalities of the flux received from the system at phases 0.25 and 0.75. These results have been confirmed by other studies (Awadalla, 1988; Kalomeni et al., 2007; Senavci et al., 2014; Zola et al., 2005). The first spectroscopic
observations of this system were published by Hrivnak (1990) who determined the spectroscopic mass ratio as q = 0.34 for BB Peg. Lu and Rucinski (1999) obtained a mass ratio of 0.36 for this binary system according to new spectroscopy and radial velocity measurements. In 1981, Giuricin et al. proposed the spectral type as F8 for this system, while Pribulla et al. determined the spectral type as F2V for this system according to their spectroscopic observations at David Dunlap Observatory in 2009. 2. Photometric observations In this study, photometry was conducted at Dr. Mojtahedi Observatory, University of Birjand, Iran for the eclipsing binary system BB Peg during four nights in September and October 2016 through Johnson V and R filters using a 14-inch Schmidt-Cassegrain telescope with an ST-7 CCD camera attached. We used Maxim Dl1 software for controlling the CCD. In the field of view, we selected TYC 168-1525-1 as the comparison star (Senavci et al., 2014) and the coordinates are presented in Table 1. IRIS2 software was used for data reduction. In addition, we used the ephemeris presented by Hanna and Awadalla (2011) for calculating the orbital phases as follows.
Corresponding author. E-mail address: [email protected] (A. Abedi). 1 http://diffractionlimited.com 2 http://www.astrosurf.com ⁎
https://doi.org/10.1016/j.newast.2020.101354 Received 17 August 2019; Received in revised form 28 December 2019; Accepted 8 January 2020 Available online 10 January 2020 1384-1076/ © 2020 Elsevier B.V. All rights reserved.
New Astronomy 78 (2020) 101354
Z. Kamalifar, et al.
HJD (MinI ) = 2443764.33319 + 0.361502127 × E
(1)
3. Light curve analysis We studied the V and R light curves for BB Peg simultaneously using PHOEBE Legacy3 (Prsa and Zwitter, 2005). Moreover, we selected the initial mass ratio, q, of the system based on spectroscopic data (Lu and Rucinski, 1999). Next, we fixed the temperature of the primary star, T1 = 6355 K , based on spectroscopic observations (Pribulla et al., 2009) and set the effective temperature of the secondary star as the free parameter. Bolometric albedos and the gravity-darkening coefficients were then set to A1 = A2 = 0.5 (Rucinski, 1969) and g1 = g2 = 0.32 (Lucy, 1969), respectively. The limb-darkening coefficients were interpolated using data from the van Hamme tables (van Hamme, 1993) in PHOEBE software by selecting the logarithmic limb-darkening law. In addition, the asymmetries observed at phases 0.25 and 0.75 on the light curve indicated cold or hot spots on the surfaces of the components of BB Peg (O’Connell, 1951). We added two cold spots to the surface of the secondary star, and changed their size and position to obtain the best fit. Next, we reanalyzed the V and R band photometry simultaneously with spectroscopic data. The spectroscopic data were taken from Lu and Rucinski (1999), and the converged solutions were obtained. The results are listed in Table 2, where i denotes the orbital inclination, q is the mass ratio, T is the effective temperature, Ω is the surface potential, x and y are the limb darkening coefficients, L is the luminosity, Vγ is the center of mass velocity, and r represents the radii of the components. According to the definition of the filling factor, fover = in (Lucy and Wilson, 1979), the degree of contact for BB in out Peg was approximated as 28%, thereby implying that this system is over-contact. The estimated errors of the derived parameters generated by the WD code are quoted in Table 2, but all workers in this field know that they are significant underestimations of the real errors. Fig. 1 shows the observed V and R light curves as well as the best corresponding theoretical curves. Fig. 2 shows the three-dimensional configuration of BB Peg with two cold spots on the surfaces of the primary and secondary stars at some phases. Absolute parameters such as the mass, radius, and semi-major axis Km were calculated using the values of K1 = 265.42(9.20) s and
Fig. 1. V and R light curves obtained for BB Peg. Points are the original observations and solid lines are the theoretical light curves. Table 1 Positions and magnitudes of the variable and comparison stars. Type of star
Variable Comparison
BB Peg TYC 168-1525-1
magnitude
11.17 10.14
RA (J2000)
Dec (J2000)
h
m
s
∘
’
”
22 22
22 23
56.89 30.39
16 16
19 23
28.73 45.68
spectroscopy to compute the B-V color indices of the components because some modifications were needed to the effective temperature (Hilditch et al., 1988). According to Hilditch et al. (1988), the temperatures of the BB Peg components were corrected as T1 = 7130 K and T2 = 5007 K . We obtained the corrected color indices of these stars from the tables published by Worthey and Lee (2011) as (B V )1 = 0.247(21) and (B V ) 2 = 1.101(23) . Fig. 4 shows the locations of the components of the BB Peg system in the density-color diagram. ZAMS and TAMS lines are also plotted in Fig. 4 to clarify the identification of the evolutionary state of the system. Fig. 4 verifies the evolutionary state of the components of BB Peg binary system, which was deduced based on Fig. 3. Finally, based on statistical analyses of the orbital angular momentum and total masses of some binaries, Eker et al. (2006) obtained the critical orbital angular momentum for a contact binary systems as:
Km
K2 = 87.94(5.10) s obtained from the radial velocity curve fitted based on spectroscopic data and the orbital inclination produced by light curve analysis. Table 3 shows the absolute parameters. The bolometric luminosities of the components were calculated as L1 = 0.92(8) L and L2 = 2.04(12) L based on the effective temperature and radius of each component. The Hertzsprung–Russell (H–R) diagram is commonly used as a powerful tool for investigating the evolutionary state of stars. Fig. 3 shows the positions of the primary and secondary components of BB Peg in the H–R diagram. For comparison, some other W-type W UMa binaries are also shown in this figure, which was compiled by Yakut and Eggleton (2005). Moreover, the zero age main sequence (ZAMS) and terminal age main sequence (TAMS) lines are plotted in this diagram. According to Fig. 3, the secondary component is in the subgiant region and the primary is below the ZAMS line. Consequently, the primary component is denser than the main sequence stars. In addition to the H-R diagram, the evolutionary status of a binary system can be studied based on the mean densities and B-V color indices of the components (Mochnacki, 1981; 1984; 1985). The mean densities ( ¯1 and ¯2 ) of the BB Peg components were found using the absolute physical parameters listed in Table 3. It should be noted that due to the common envelope around the primary and secondary cores, we could not use the effective temperature obtained by light curve analysis or 3
Star name
log Jcr = 0.522(log M )2 + 1.664(log M ) + 51.315,
(2)
where M = M1 + M2 is the total mass of the system in solar mass units. The orbital angular momentum of BB Peg was calculated using the absolute physical parameters as (Hu et al., 2018):
J=
q G 2 (M1 + M2)5P (1 + q) 2 2
1 3
.
(3)
Using this equation, the logarithm of the angular momentum of BB Peg was obtained as 51.602. According to Fig. 5, BB Peg is located in a dense region of contact binaries and below the borderline. The position of BB Peg in this diagram confirms that it is a contact system. 4. Period study Based on our V and R CCD photometry data, we obtained four minimum light times for the BB Peg system. The method proposed by Kwee and van Woerden (1956) was used to obtaining these minima,
http://phoebe-project.org 2
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Table 2 Light curve solution for BB Peg. Parameter
This study R+V filter
Thisstudy R+V filter + radial velocity data
Leung et al. (1985)
Zola et al. (2005)
Kalomeni et al. (2007)
i( )
83.90(26) 3.141(19)
84.11(18) 2.753(23)
86.7(16) 2.811(27)
88.5(2) 2.589
85.0(5) 2.702(7)
6355 6121(10) 6.510(24) –
6355 6160(33) 6.145(29) −28.236(511)
6545(41) 6100 6.298(20) –
6100 5780(7) 5.936(3) –
6250 5955(30) 6.056(13) −28.1(2.2)
0.627 0.643 0.720 0.733 0.279 0.272 0.272 0.262 0.299(19)
0.627 0.641 0.720 0.736 0.279 0.273 0.272 0.264 0.312(51)
– – 0.65 0.65 – – – – –
– – – – – – – – 0.3436(12)
– – – – – – – – 0.32
0.306(21)
0.318(63)
0.338(10)
0.3506(16)
0.34
r1(pole) r1(side) r1(back) r2(pole) r2(side) r2(back) fover(%)
0.287(77) 0.302(95) 0.355(199) 0.471(68) 0.511(97) 0.544(128) 47
0.288(78) 0.302(94) 0.345(170) 0.459(72) 0.497(98) 0.530(130) 28
0.278(1) 0.290(2) 0.326(3) 0.447(1) 0.479(2) 0.507(2) 12
– 0.30363(28) – – 0.47778(30) – 21
0.2889(19) 0.3030(24) 0.3457(45) 0.4507(16) 0.4849(22) 0.5157(30) 34
T T2
0.90(3)
0.90(3)
Radius(rad) Longitude(rad) Latitude(rad)
0.35(6) 3.93(12) 1.05(12)
0.35(6) 3.93(12) 1.05(12)
T T2
0.9
0.9
0.35(6) 2.53(15) 0.87(11) 0.0102
0.35(6) 2.53(15) 0.87(11) 0.0356
∘
q=
m2 m1
T1(K) T2(K) 1=
V (
2
Km ) s
x1,R x2,R x1,V x2,V y1,R y2,R y1,V y2,V
L1 )R L1 + L2 L1 ( )V L1 + L2
(
Radius(rad) Longitude(rad) Latitude(rad)
=
(O--C )2 N
Spot 1 parameters
Spot 2 parameters
–
–
0.92(2)
– – –
– – –
0.25(2) 4.78(29) 1.05(16)
–
–
–
– – – –
– – – –
– – – –
Fig. 2. Theoretical configuration of BB Peg with two cold spots on the secondary component at phases 0.15, 0.75, and 0.95.
3
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Table 3 Absolute parameters calculated for BB Peg in the present study and the results obtained in other studies. Parameter
This study
Kalomeni et al. (2007)
Senavci et al. (2014)
M1(M⊙) M2(M⊙) R1(R⊙) R2(R⊙) a(R⊙)
0.41(11) 1.24(13) 0.79(7) 1.25(8) 2.52(10)
0.53 1.42 0.83 1.29 2.664
0.50(2) 1.40(4) 0.81(1) 1.28(2) 2.64(4)
Fig. 5. Position of BB Peg in the angular momentum-mass diagram. Clearly, BB Peg is under the Jcr borderline and this verifies its geometrical contact configuration. The sample data were taken from Eker et al. (2006). CAB denotes chromospherically active binaries; G, SG, and MS denote systems containing at least one giant, one subgiant, and systems in the main sequence, respectively.
HJD (MinI ) = 2443764.34215(17) + 0.361501468(31) × E 1.433(31) × 10
12
(4)
× E 2.
C )2 * w N
The value of for this fit was determined as = 0.00661. The new period for the system was obtained using the method proposed by Kalimeris et al. (1994). The new ephemeris for BB Peg was then obtained as : (O
Fig. 3. Position of BB Peg in the H-R diagram. The exsamples of W-type systems were taken from Yakut and Eggleton (2005). ZAMS and TAMS lines for solar metallicity were obtained from MESA-Web (http://mesa-web.asu.edu).
(5)
HJD (MinI ) = 2457664.42758(19) + 0.3615014(23) × E . In addition, the rate of the period variations was calculated as:
P=
2.90(15) × 10
9 days .
(6)
year
Quasisinusoidal behavior was detected by plotting the O-C residuals obtained from the quadratic fit versus the epochs. This periodical variation may be attributed to LTE. We used the following equation to fit the LTE based on the residual O-C curve (Irwin, 1959):
(O
C )LTE = K
1 1
e2
cos2
×
1 e2 sin( + ) + e sin 1 + e cos
, (7)
where K, e, and ω are the amplitude, eccentricity, and longitude of the periastron of the third body orbit, respectively, and ν is the true anomaly of the third body. Moreover, the period of the ternary system was obtained using Period046 (Lenz and Breger, 2005). Sine-like variations were identified in the residuals after removing the quadratic fit and tertiary component LTE from the O-C data. A fourth component may produce these sine-like variations, and thus the period, orbital parameter, and minimum mass of the fourth component were calculated by re-using the method for the third body LTE. The results obtained for the third and fourth components are presented in Table 5, and the final O-C residuals are shown in the bottom panel in Fig. 6. It was not possible to find any systematic behavior in the final residuals, which implies that the parabolic curve and LTE of the third and fourth bodies fitted to the O-C values possibly have the required accuracy.
Fig. 4. Positions of the components of BB Peg in the color-density diagram. The examples of W-type system were taken from Yakut and Eggleton (2005). ZAMS and TAMS lines were added according to Fig. 3 in the study by Mochnacki (1981).
and the minimum light times and errors are given in Table 4. We collected all of the available times of the minima reported in the O-C Gateway database4 and AAVSO database5 from 1931 until now. Epoch and O-C were calculated using the linear ephemeris given by 1. The photographic (pg) and visual (vis) times of the minima are usually low precision compared with photoelectric (PE) or CCD data. Therefore, we used weights of 0.1 and 0.2 for vis and pg data, respectively, and a weight of 1 for PE and CCD data. The O-C diagram in the top panel in Fig. 6 was plotted based on 359 minima times (155 vis, 35 pg, 179 PE and CCD). The decrement in the orbital period of this system was deduced based on the downward parabolic shown in Fig. 6. We obtained the nonlinear ephemeris for the system using the least-squares method as:
4 5
5. Conclusion BB Peg can be categorized in the W subclass given its short period, nearly equal depth of the minima, and the continuous variations in the light curve for the W UMa type eclipsing binary system BB Peg as well as the mass ratio (q > 1) obtained for this system. We found that the system has a filling factor of 28%, which means that the stars fill the
http://var.astro.cz/ocgate/ www.aavso.org
6
4
https://www.univie.ac.at/tops/Period04
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previous studies (Leung et al., 1985; Zola et al., 2005; Kalomeni et al., 2007; Senavci et al., 2014). The presence of spots in this system was suggested previously by Leung et al. (1985), Kalomeni et al. (2007), and Senavci et al. (2014). We consider that two spots are present on the secondary star according to the results produced in this study due to the O’Connel effect (O’Connell, 1951) on the light curve and the better fit of the simulated curve based on the observational data. Fitting a parabola to the O-C curve data suggested that the period of this system decreases days with P = 2.90(15) × 10 9 year . Despite using more recent data, the
Table 4 Minimum light times of BB Peg in V and R bands. HJD
Band
Type
Standard error
2457664.42811 2457664.42760 2457641.47366 2457641.47314
V R V R
I I II II
0.00018 0.00019 0.00030 0.00034
positive values of P obtained in other studies (Cerruti-Sola and Scaltriti, 1980; Qian, 2001; Kalomeni et al., 2007) and the negative value obtained in the present are not highly trustworthy, so it is not possible to definitely comment on the causative factors. In fact, these findings were due to the high scattering of the data, which are generally vis data, and the low curvature of the O-C curve (P 10 8 10 9). Therefore, more accurate data are needed to determine the rate of change in the period and its causative factors with greater precision. However, the periodic behavior was clearly observed in the O-C curve, which can be explained by various reasons, such as the presence of additional components (Awadalla, 1988; Cerruti-Sola et al., 1981; Cerruti-Sola and Scaltriti, 1980; D’Angelo et al., 2006; Kalomeni et al., 2007; Pribulla and Rucinski, 2006; Qian, 2001) or magnetic activity (Hanna and Awadalla (2011)). In this study, we assumed that the periodic changes are due to the possible presence of third and fourth bodies in the BB Peg system. We determined minimum masses of 0.287 M⊙ and 0.10 M⊙ for the third and fourth components, respectively. The mass of a white dwarf varies within the range of 0.2 < MWD < 1.2 M⊙ (Kepler et al., 2007; Kilic et al., 2007), and the minimum mass obtained for the third body shows that it is probably a white dwarf, which is consistent with the findings reported by D’Angelo et al. (2006) and Pribulla and Rucinski (2006) who identified the effects of M-dwarfs with minimum masses of 0.18 M⊙ and 0.19 M⊙, respectively. The possibility of the presence of a fourth object was investigated in this study for the first time and we demonstrated that a giant planet or brown dwarf might exist in the system. Moreover, the effect of light from the third body could not be detected by light curve analysis, thereby suggesting that the third and fourth bodies are non-stellar objects, such as a white dwarf, brown dwarf, or giant planet.
Fig. 6. O-C diagram and residuals for BB Peg. In the top panel, the dotted (green) line represents a downward parabola, the dashed (blue) line represents the effects of mass transfer and third body LTE, and the solid (red) line represents the final curve fitted to O-C. In the bottom panel, the points denote the final residuals. (Please see electronic version for colored figure.) Table 5 Parameters for the third and fourth bodies. Parameter
Third body
P3 (years) e ω(∘) K(day) T0(HJD) a sin i(AU) f(m3) M3,min(M⊙)
= Fourth body
(O
P4 (years) e ω(∘) K(day) T0(HJD) a sin i(AU) f(m4) M4,min(M⊙)
=
(O
C )2 * w N
C )2 * w N
This study
Pribulla and Rucinski (2006)
Kalomeni et al. (2007)
35.17(31) 0.490(5) 226(2) 0.01004(5) 2,457,915 1.84(8) 0.00511 (68) 0.287(13) 0.00370
20.44 0.32(21) – 0.0092 – 0.83(9) 0.0014(5) 0.19 –
27.9(2) 0.56(30) 96(18) – 2,438,540(793) 0.96(15) 0.0010(5) 0.16 –
18.04(2) 0.170(5) 151(2) 0.00230(5) 2,450,572 0.40(1) 0.000205(13) 0.10(7) 0.00365
– – – – – – – – –
– – – – – – – – –
CRediT authorship contribution statement Z. Kamalifar: Visualization, Writing - original draft. A. Abedi: Conceptualization, Methodology, Validation, Investigation, Supervision, Project administration. K.Y. Roobiat: Formal analysis, Software. References Awadalla, N.S., 1988. Three-colours photoelectric observations of w uma-system bb pegasi. Astrophys. Space Sci. 140 (1), 137–159. https://doi.org/10.1007/BF00643538. Cerruti-Sola, M., Milano, L., Scaltriti, F., 1981. Bb peg : a w uma-w system with a high degree of overcontact. Astron. Astrophys. 101, 273. Cerruti-Sola, M., Scaltriti, E., 1980. Two-color photoelectric observations of the eclipsing binary bb peg. Astron. Astrophys. Suppl. Ser. 40, 85–89. D’Angelo, C., van Kerkwijk, M.H., Rucinski, S.M., 2006. Contact binaries with additional components. ii. a spectroscopic search for faint tertiaries. Astron. J. 132 (2), 650–662. https://doi.org/10.1086/505265. Eker, Z., Demircan, O., Bilir, S., Karatas, Y., 2006. Dynamical evolution of active detached binaries on the log(j0)log(m) diagram and contact binary formation. Mon. Not. R. Astron. Soc. 373 (4), 1483–1494. https://doi.org/10.1111/j.1365-2966.2006. 11073.x. Giuricin, G., Mardirossian, F., Mezzetti, M., 1981. Light curve synthesis for the eclipsing binary bb peg. Astron. Nachr. 302 (6), 285–286. https://doi.org/10.1002/asna. 2103020605. Guthnick, P., Prager, R., 1932. Benennung von ver anderlichen sternen. Astron. Nachr. 247 (7), 121–152. https://doi.org/10.1002/asna.19322470702. van Hamme, W., 1993. New limb-darkening coefficients for modeling binary star light curves. Astron. J. 106 (5), 2096. https://doi.org/10.1086/116788. Hanna, M.A., Awadalla, N.S., 2011. Orbital period variation and morphological light curve studies for the w uma binary bb pegasi. J. Korean Astron. Soc. 44 (3), 97.
primary Roche lobes. The diagram in Fig. 4 also confirms this result, so the assumption of an over-contact system is fair. The actual errors of the calculated system parameters were greater than the values reported in the WD code output due to the scattering of the light curve data. Table 2 presents the identical errors reported for the output obtained using Phoebe software (which uses the WD code to simulate the light curve). The results obtained by simultaneously analyzing the R and B light curves and the spectroscopic data for the BB Peg eclipsing binary system (Tables 2 and 3) are in agreement with those reported in 5
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Z. Kamalifar, et al. https://doi.org/10.5303/JKAS.2011.44.3.097. Hilditch, R.W., King, D.J., McFarlane, T.M., 1988. The evolutionary state of contact and near-contact binary stars. Mon. Not. R. Astron. Soc. 231 (2), 341–352. https://doi. org/10.1093/mnras/231.2.341. Hoffmeister, C., 1931. 316 neue veriable. Astron. Nachr. 242 (7), 129–142. https://doi. org/10.1002/asna.19312420702. Hrivnak, B.J., 1990. Radial velocity studies of the w uma binaries bx peg and bb peg. Bull. Am. Astron. Soc. 22, 1291. Hu, K., Cai, J.-T., Yu, Y.-X., Xiang, F.-Y., 2018. First ccd photometric investigation of the eclipsing binary v737 per. New Astron. 65, 52–58. https://doi.org/10.1016/J. NEWAST.2018.06.007. Irwin, J.B., 1959. Standard light-time curves. Astron. J. 46, 149. https://doi.org/10. 1086/107913. Kalimeris, A., Rovithis-Livaniou, H., Rovithis, P., 1994. On the orbital period changes in contact binaries. Astron. Astrophys. 282 (3), 775–786. Kalomeni, B., Yakut, K., Keskin, V., Degirmenci, O.L., Ulas, B., Kose, O., 2007. Absolute properties of the binary system bb pegasi. Astron. J. 134 (2), 642–647. https://doi. org/10.1086/519493. Kepler, S.O., Kleinman, S.J., Nitta, A., Koester, D., Castanheira, B.G., Giovannini, O., Costa, A.F.M., Althaus, L., 2007. White dwarf mass distribution in the sdss. Mon. Not. R. Astron. Soc. 375 (4), 1315–1324. https://doi.org/10.1111/j.1365-2966.2006. 11388.x. Kilic, M., Prieto, C.A., Brown, W.R., Koester, D., 2007. The lowest mass white dwarf. Astrophys. J. 660 (2), 1451–1461. https://doi.org/10.1086/514327. Kwee, K.K., van Woerden, H., 1956. A method for computing accurately the epoch of minimum of an eclipsing variable. Bull. Astron. Inst. Neth. 12, 327. Lenz, P., Breger, M., 2005. Period04 user guide. Commun. Asteroseismol. 146, 53–136. https://doi.org/10.1553/cia146s53. Leung, K.-C., Zhai, D., Zhang, Y., 1985. Two very similar late-type contact systems - bx and bb pegasi. Astron. J. 90, 515. https://doi.org/10.1086/113759. Lu, W., Rucinski, S.M., 1999. Radial velocity studies of close binary stars. i. Astron. J. 118 (1), 515–526. https://doi.org/10.1086/300933. Lucy, L.B., 1969. Gravity-Darkening for Stars with Convective Envelopes. 65 EDP Sciences [etc.]. Lucy, L.B., Wilson, R.E., 1979. Observational tests of theories of contact binaries. Astrophys. J. 231, 502. https://doi.org/10.1086/157212. Mochnacki, S.W., 1981. Contact binary stars. Astrophys. J. 245, 650. https://doi.org/10.
1086/158841. Mochnacki, S.W., 1984. Accurate integrations of the roche model. Astrophys. J. Suppl. Ser. 55, 551. https://doi.org/10.1086/190967. Mochnacki, S.W., 1985. Erratum - accurate integrations of the roche model. Astrophys. J. Suppl. Ser. 59, 445. https://doi.org/10.1086/191080. Nikonov, V.B., Dobronravin, B., 1937. Bull. Abastumani Obs. 1 (11). O’Connell, D.J.K., 1951. The so-called periastron effect in eclipsing binaries. Monthly Notices of the Royal Astronomical Society 111 (6). https://doi.org/10.1093/mnras/ 111.6.642. 642–642 Piotrowski, S., 1936. Acta Astron. Ser. C 2 (157). Pribulla, T., Rucinski, S.M., 2006. Contact binaries with additional components. i. the extant data. Astron. J. 131 (6), 2986–3007. https://doi.org/10.1086/503871. Pribulla, T., Rucinski, S.M., Blake, R.M., Lu, W., Thomson, J.R., DeBond, H., Karmo, T., de Ridder, A., Ogloza, W., Stachowski, G., Siwak, M., 2009. Radial velocity studies of close binary stars. xv. Astron. J. 137 (3), 3655–3667. https://doi.org/10.1088/00046256/137/3/3655. Prsa, A., Zwitter, T., 2005. A computational guide to physics of eclipsing binaries. i. demonstrations and perspectives. Astrophys. J. 628 (1), 426–438. https://doi.org/10. 1086/430591. Qian, S., 2001. A possible relation between the period change and the mass ratio for wtype contact binaries. Mon. Not. R. Astron. Soc. 328 (2), 635–644. https://doi.org/ 10.1046/j.1365-8711.2001.04931.x. Rucinski, S.M., 1969. The proximity effects in close binary systems. ii. the bolometric reflection effect for stars with deep convective envelopes. Acta Astronomica 19, 245. Senavci, H.V., Yilmaz, M., Basturk, O., Ozavci, I., Caliskan, S., Kilicoglu, T., Tezcan, C.T., 2014. A tale on two close binaries in pegasus. Open Astron. 23 (2), 123–135. https:// doi.org/10.1515/astro-2017-0177. Whitney, B.S., 1943. Some eclipsing variable stars. Astron. J. 50, 131. https://doi.org/10. 1086/105750. Worthey, G., Lee, H., 2011. An empirical ubv ri jhk color-temperature calibration for stars. Astrophys. J. Suppl. Ser. 193 (1), 1. https://doi.org/10.1088/0067-0049/193/ 1/1. Yakut, K., Eggleton, P.P., 2005. Evolution of close binary systems. Astrophys. J. 629 (2), 1055–1074. https://doi.org/10.1086/431300. Zola, S., Kreiner, J.M., Zakrzewski, B., Kjurkchieva, D.P., Marchev, D.V., Baran, A., Rucinski, S.M., Ogloza, W., Siwak, M., Koziel, D., Drozdz, M., Pokrzywka, B., 2005. Physical parameters of components in close binary systems. v. Acta Astron. 55, 389.
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Photometric and periodic investigations of W-type W UMa eclipsing binary BB Peg
T
Z. Kamalifara,b, A. Abedi⁎,a,b, K.Y. Roobiata,b a b
Department of Physics, Faculty of Sciences, University of Birjand, P.O.Box 97175/615, Birjand, Iran Dr. Mojtahedi Observatory, University of Birjand, Birjand, Iran
ARTICLE INFO
ABSTRACT
Keywords: Stars: binaries: close Stars: binaries: eclipsing Stars: individual (BB Peg)
In this study, photometry was conducted for the W UMa type eclipsing binary BB Peg through V and R Johnson filters during several nights in September and October 2016. The light curves were obtained at Dr. Mojtahedi Observatory, of the University of Birjand, Iran. Data reduction was performed using IRIS software. Orbital parameters were obtained by analyzing the light curves using PHOEBE software. The radial velocity information was then used to obtain the absolute parameters of the system. Some minimum light times were obtained forthe system and variations in the orbital period of BB Peg were analyzed by adding the new minimum light times to the O-C diagram to obtain a new ephemeris for the system. The period change appeared to be due to the lighttime effect. A justifiable fit was obtained using the third and fourth stars. However, this fit was not confirmed and it may need revision when further data are obtained. The variation could be attributed to other sources, such as magnetic cycles or non-conservative mass transfer from the system.
1. Introduction BB Peg (HIP 110493) is a W-subtype W UMa over-contact eclipsing binary system. The variability of this system was first noted by Hoffmeister (1931) and confirmed subsequently by other studies in the 1930s (Guthnick and Prager, 1932; Nikonov and Dobronravin, 1937; Piotrowski, 1936). The orbital period variability of BB Peg was first determined by Whitney (1943) and various processes have been proposed as the sources of these orbital period variations. The two most important processes are mass transfer between the components and the light-time effect (LTE) (Awadalla, 1988; Cerruti-Sola et al., 1981; Cerruti-Sola and Scaltriti, 1980; D’Angelo et al., 2006; Kalomeni et al., 2007; Pribulla and Rucinski, 2006; Qian, 2001). The first light curve for this system was analyzed by Cerruti-Sola et al. (1981) in two B and V Johnson–Cousins bands. The analyses of the BB Peg light curve performed by Giuricin et al. (1981) and Leung et al. (1985) classified this binary as belonging to the W-subtype W UMa system. In addition, these analyses showed that some hot or cold spots may exist on the surfaces of the components of this system due to the inequalities of the flux received from the system at phases 0.25 and 0.75. These results have been confirmed by other studies (Awadalla, 1988; Kalomeni et al., 2007; Senavci et al., 2014; Zola et al., 2005). The first spectroscopic
observations of this system were published by Hrivnak (1990) who determined the spectroscopic mass ratio as q = 0.34 for BB Peg. Lu and Rucinski (1999) obtained a mass ratio of 0.36 for this binary system according to new spectroscopy and radial velocity measurements. In 1981, Giuricin et al. proposed the spectral type as F8 for this system, while Pribulla et al. determined the spectral type as F2V for this system according to their spectroscopic observations at David Dunlap Observatory in 2009. 2. Photometric observations In this study, photometry was conducted at Dr. Mojtahedi Observatory, University of Birjand, Iran for the eclipsing binary system BB Peg during four nights in September and October 2016 through Johnson V and R filters using a 14-inch Schmidt-Cassegrain telescope with an ST-7 CCD camera attached. We used Maxim Dl1 software for controlling the CCD. In the field of view, we selected TYC 168-1525-1 as the comparison star (Senavci et al., 2014) and the coordinates are presented in Table 1. IRIS2 software was used for data reduction. In addition, we used the ephemeris presented by Hanna and Awadalla (2011) for calculating the orbital phases as follows.
Corresponding author. E-mail address: [email protected] (A. Abedi). 1 http://diffractionlimited.com 2 http://www.astrosurf.com ⁎
https://doi.org/10.1016/j.newast.2020.101354 Received 17 August 2019; Received in revised form 28 December 2019; Accepted 8 January 2020 Available online 10 January 2020 1384-1076/ © 2020 Elsevier B.V. All rights reserved.
New Astronomy 78 (2020) 101354
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HJD (MinI ) = 2443764.33319 + 0.361502127 × E
(1)
3. Light curve analysis We studied the V and R light curves for BB Peg simultaneously using PHOEBE Legacy3 (Prsa and Zwitter, 2005). Moreover, we selected the initial mass ratio, q, of the system based on spectroscopic data (Lu and Rucinski, 1999). Next, we fixed the temperature of the primary star, T1 = 6355 K , based on spectroscopic observations (Pribulla et al., 2009) and set the effective temperature of the secondary star as the free parameter. Bolometric albedos and the gravity-darkening coefficients were then set to A1 = A2 = 0.5 (Rucinski, 1969) and g1 = g2 = 0.32 (Lucy, 1969), respectively. The limb-darkening coefficients were interpolated using data from the van Hamme tables (van Hamme, 1993) in PHOEBE software by selecting the logarithmic limb-darkening law. In addition, the asymmetries observed at phases 0.25 and 0.75 on the light curve indicated cold or hot spots on the surfaces of the components of BB Peg (O’Connell, 1951). We added two cold spots to the surface of the secondary star, and changed their size and position to obtain the best fit. Next, we reanalyzed the V and R band photometry simultaneously with spectroscopic data. The spectroscopic data were taken from Lu and Rucinski (1999), and the converged solutions were obtained. The results are listed in Table 2, where i denotes the orbital inclination, q is the mass ratio, T is the effective temperature, Ω is the surface potential, x and y are the limb darkening coefficients, L is the luminosity, Vγ is the center of mass velocity, and r represents the radii of the components. According to the definition of the filling factor, fover = in (Lucy and Wilson, 1979), the degree of contact for BB in out Peg was approximated as 28%, thereby implying that this system is over-contact. The estimated errors of the derived parameters generated by the WD code are quoted in Table 2, but all workers in this field know that they are significant underestimations of the real errors. Fig. 1 shows the observed V and R light curves as well as the best corresponding theoretical curves. Fig. 2 shows the three-dimensional configuration of BB Peg with two cold spots on the surfaces of the primary and secondary stars at some phases. Absolute parameters such as the mass, radius, and semi-major axis Km were calculated using the values of K1 = 265.42(9.20) s and
Fig. 1. V and R light curves obtained for BB Peg. Points are the original observations and solid lines are the theoretical light curves. Table 1 Positions and magnitudes of the variable and comparison stars. Type of star
Variable Comparison
BB Peg TYC 168-1525-1
magnitude
11.17 10.14
RA (J2000)
Dec (J2000)
h
m
s
∘
’
”
22 22
22 23
56.89 30.39
16 16
19 23
28.73 45.68
spectroscopy to compute the B-V color indices of the components because some modifications were needed to the effective temperature (Hilditch et al., 1988). According to Hilditch et al. (1988), the temperatures of the BB Peg components were corrected as T1 = 7130 K and T2 = 5007 K . We obtained the corrected color indices of these stars from the tables published by Worthey and Lee (2011) as (B V )1 = 0.247(21) and (B V ) 2 = 1.101(23) . Fig. 4 shows the locations of the components of the BB Peg system in the density-color diagram. ZAMS and TAMS lines are also plotted in Fig. 4 to clarify the identification of the evolutionary state of the system. Fig. 4 verifies the evolutionary state of the components of BB Peg binary system, which was deduced based on Fig. 3. Finally, based on statistical analyses of the orbital angular momentum and total masses of some binaries, Eker et al. (2006) obtained the critical orbital angular momentum for a contact binary systems as:
Km
K2 = 87.94(5.10) s obtained from the radial velocity curve fitted based on spectroscopic data and the orbital inclination produced by light curve analysis. Table 3 shows the absolute parameters. The bolometric luminosities of the components were calculated as L1 = 0.92(8) L and L2 = 2.04(12) L based on the effective temperature and radius of each component. The Hertzsprung–Russell (H–R) diagram is commonly used as a powerful tool for investigating the evolutionary state of stars. Fig. 3 shows the positions of the primary and secondary components of BB Peg in the H–R diagram. For comparison, some other W-type W UMa binaries are also shown in this figure, which was compiled by Yakut and Eggleton (2005). Moreover, the zero age main sequence (ZAMS) and terminal age main sequence (TAMS) lines are plotted in this diagram. According to Fig. 3, the secondary component is in the subgiant region and the primary is below the ZAMS line. Consequently, the primary component is denser than the main sequence stars. In addition to the H-R diagram, the evolutionary status of a binary system can be studied based on the mean densities and B-V color indices of the components (Mochnacki, 1981; 1984; 1985). The mean densities ( ¯1 and ¯2 ) of the BB Peg components were found using the absolute physical parameters listed in Table 3. It should be noted that due to the common envelope around the primary and secondary cores, we could not use the effective temperature obtained by light curve analysis or 3
Star name
log Jcr = 0.522(log M )2 + 1.664(log M ) + 51.315,
(2)
where M = M1 + M2 is the total mass of the system in solar mass units. The orbital angular momentum of BB Peg was calculated using the absolute physical parameters as (Hu et al., 2018):
J=
q G 2 (M1 + M2)5P (1 + q) 2 2
1 3
.
(3)
Using this equation, the logarithm of the angular momentum of BB Peg was obtained as 51.602. According to Fig. 5, BB Peg is located in a dense region of contact binaries and below the borderline. The position of BB Peg in this diagram confirms that it is a contact system. 4. Period study Based on our V and R CCD photometry data, we obtained four minimum light times for the BB Peg system. The method proposed by Kwee and van Woerden (1956) was used to obtaining these minima,
http://phoebe-project.org 2
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Table 2 Light curve solution for BB Peg. Parameter
This study R+V filter
Thisstudy R+V filter + radial velocity data
Leung et al. (1985)
Zola et al. (2005)
Kalomeni et al. (2007)
i( )
83.90(26) 3.141(19)
84.11(18) 2.753(23)
86.7(16) 2.811(27)
88.5(2) 2.589
85.0(5) 2.702(7)
6355 6121(10) 6.510(24) –
6355 6160(33) 6.145(29) −28.236(511)
6545(41) 6100 6.298(20) –
6100 5780(7) 5.936(3) –
6250 5955(30) 6.056(13) −28.1(2.2)
0.627 0.643 0.720 0.733 0.279 0.272 0.272 0.262 0.299(19)
0.627 0.641 0.720 0.736 0.279 0.273 0.272 0.264 0.312(51)
– – 0.65 0.65 – – – – –
– – – – – – – – 0.3436(12)
– – – – – – – – 0.32
0.306(21)
0.318(63)
0.338(10)
0.3506(16)
0.34
r1(pole) r1(side) r1(back) r2(pole) r2(side) r2(back) fover(%)
0.287(77) 0.302(95) 0.355(199) 0.471(68) 0.511(97) 0.544(128) 47
0.288(78) 0.302(94) 0.345(170) 0.459(72) 0.497(98) 0.530(130) 28
0.278(1) 0.290(2) 0.326(3) 0.447(1) 0.479(2) 0.507(2) 12
– 0.30363(28) – – 0.47778(30) – 21
0.2889(19) 0.3030(24) 0.3457(45) 0.4507(16) 0.4849(22) 0.5157(30) 34
T T2
0.90(3)
0.90(3)
Radius(rad) Longitude(rad) Latitude(rad)
0.35(6) 3.93(12) 1.05(12)
0.35(6) 3.93(12) 1.05(12)
T T2
0.9
0.9
0.35(6) 2.53(15) 0.87(11) 0.0102
0.35(6) 2.53(15) 0.87(11) 0.0356
∘
q=
m2 m1
T1(K) T2(K) 1=
V (
2
Km ) s
x1,R x2,R x1,V x2,V y1,R y2,R y1,V y2,V
L1 )R L1 + L2 L1 ( )V L1 + L2
(
Radius(rad) Longitude(rad) Latitude(rad)
=
(O--C )2 N
Spot 1 parameters
Spot 2 parameters
–
–
0.92(2)
– – –
– – –
0.25(2) 4.78(29) 1.05(16)
–
–
–
– – – –
– – – –
– – – –
Fig. 2. Theoretical configuration of BB Peg with two cold spots on the secondary component at phases 0.15, 0.75, and 0.95.
3
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Table 3 Absolute parameters calculated for BB Peg in the present study and the results obtained in other studies. Parameter
This study
Kalomeni et al. (2007)
Senavci et al. (2014)
M1(M⊙) M2(M⊙) R1(R⊙) R2(R⊙) a(R⊙)
0.41(11) 1.24(13) 0.79(7) 1.25(8) 2.52(10)
0.53 1.42 0.83 1.29 2.664
0.50(2) 1.40(4) 0.81(1) 1.28(2) 2.64(4)
Fig. 5. Position of BB Peg in the angular momentum-mass diagram. Clearly, BB Peg is under the Jcr borderline and this verifies its geometrical contact configuration. The sample data were taken from Eker et al. (2006). CAB denotes chromospherically active binaries; G, SG, and MS denote systems containing at least one giant, one subgiant, and systems in the main sequence, respectively.
HJD (MinI ) = 2443764.34215(17) + 0.361501468(31) × E 1.433(31) × 10
12
(4)
× E 2.
C )2 * w N
The value of for this fit was determined as = 0.00661. The new period for the system was obtained using the method proposed by Kalimeris et al. (1994). The new ephemeris for BB Peg was then obtained as : (O
Fig. 3. Position of BB Peg in the H-R diagram. The exsamples of W-type systems were taken from Yakut and Eggleton (2005). ZAMS and TAMS lines for solar metallicity were obtained from MESA-Web (http://mesa-web.asu.edu).
(5)
HJD (MinI ) = 2457664.42758(19) + 0.3615014(23) × E . In addition, the rate of the period variations was calculated as:
P=
2.90(15) × 10
9 days .
(6)
year
Quasisinusoidal behavior was detected by plotting the O-C residuals obtained from the quadratic fit versus the epochs. This periodical variation may be attributed to LTE. We used the following equation to fit the LTE based on the residual O-C curve (Irwin, 1959):
(O
C )LTE = K
1 1
e2
cos2
×
1 e2 sin( + ) + e sin 1 + e cos
, (7)
where K, e, and ω are the amplitude, eccentricity, and longitude of the periastron of the third body orbit, respectively, and ν is the true anomaly of the third body. Moreover, the period of the ternary system was obtained using Period046 (Lenz and Breger, 2005). Sine-like variations were identified in the residuals after removing the quadratic fit and tertiary component LTE from the O-C data. A fourth component may produce these sine-like variations, and thus the period, orbital parameter, and minimum mass of the fourth component were calculated by re-using the method for the third body LTE. The results obtained for the third and fourth components are presented in Table 5, and the final O-C residuals are shown in the bottom panel in Fig. 6. It was not possible to find any systematic behavior in the final residuals, which implies that the parabolic curve and LTE of the third and fourth bodies fitted to the O-C values possibly have the required accuracy.
Fig. 4. Positions of the components of BB Peg in the color-density diagram. The examples of W-type system were taken from Yakut and Eggleton (2005). ZAMS and TAMS lines were added according to Fig. 3 in the study by Mochnacki (1981).
and the minimum light times and errors are given in Table 4. We collected all of the available times of the minima reported in the O-C Gateway database4 and AAVSO database5 from 1931 until now. Epoch and O-C were calculated using the linear ephemeris given by 1. The photographic (pg) and visual (vis) times of the minima are usually low precision compared with photoelectric (PE) or CCD data. Therefore, we used weights of 0.1 and 0.2 for vis and pg data, respectively, and a weight of 1 for PE and CCD data. The O-C diagram in the top panel in Fig. 6 was plotted based on 359 minima times (155 vis, 35 pg, 179 PE and CCD). The decrement in the orbital period of this system was deduced based on the downward parabolic shown in Fig. 6. We obtained the nonlinear ephemeris for the system using the least-squares method as:
4 5
5. Conclusion BB Peg can be categorized in the W subclass given its short period, nearly equal depth of the minima, and the continuous variations in the light curve for the W UMa type eclipsing binary system BB Peg as well as the mass ratio (q > 1) obtained for this system. We found that the system has a filling factor of 28%, which means that the stars fill the
http://var.astro.cz/ocgate/ www.aavso.org
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4
https://www.univie.ac.at/tops/Period04
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previous studies (Leung et al., 1985; Zola et al., 2005; Kalomeni et al., 2007; Senavci et al., 2014). The presence of spots in this system was suggested previously by Leung et al. (1985), Kalomeni et al. (2007), and Senavci et al. (2014). We consider that two spots are present on the secondary star according to the results produced in this study due to the O’Connel effect (O’Connell, 1951) on the light curve and the better fit of the simulated curve based on the observational data. Fitting a parabola to the O-C curve data suggested that the period of this system decreases days with P = 2.90(15) × 10 9 year . Despite using more recent data, the
Table 4 Minimum light times of BB Peg in V and R bands. HJD
Band
Type
Standard error
2457664.42811 2457664.42760 2457641.47366 2457641.47314
V R V R
I I II II
0.00018 0.00019 0.00030 0.00034
positive values of P obtained in other studies (Cerruti-Sola and Scaltriti, 1980; Qian, 2001; Kalomeni et al., 2007) and the negative value obtained in the present are not highly trustworthy, so it is not possible to definitely comment on the causative factors. In fact, these findings were due to the high scattering of the data, which are generally vis data, and the low curvature of the O-C curve (P 10 8 10 9). Therefore, more accurate data are needed to determine the rate of change in the period and its causative factors with greater precision. However, the periodic behavior was clearly observed in the O-C curve, which can be explained by various reasons, such as the presence of additional components (Awadalla, 1988; Cerruti-Sola et al., 1981; Cerruti-Sola and Scaltriti, 1980; D’Angelo et al., 2006; Kalomeni et al., 2007; Pribulla and Rucinski, 2006; Qian, 2001) or magnetic activity (Hanna and Awadalla (2011)). In this study, we assumed that the periodic changes are due to the possible presence of third and fourth bodies in the BB Peg system. We determined minimum masses of 0.287 M⊙ and 0.10 M⊙ for the third and fourth components, respectively. The mass of a white dwarf varies within the range of 0.2 < MWD < 1.2 M⊙ (Kepler et al., 2007; Kilic et al., 2007), and the minimum mass obtained for the third body shows that it is probably a white dwarf, which is consistent with the findings reported by D’Angelo et al. (2006) and Pribulla and Rucinski (2006) who identified the effects of M-dwarfs with minimum masses of 0.18 M⊙ and 0.19 M⊙, respectively. The possibility of the presence of a fourth object was investigated in this study for the first time and we demonstrated that a giant planet or brown dwarf might exist in the system. Moreover, the effect of light from the third body could not be detected by light curve analysis, thereby suggesting that the third and fourth bodies are non-stellar objects, such as a white dwarf, brown dwarf, or giant planet.
Fig. 6. O-C diagram and residuals for BB Peg. In the top panel, the dotted (green) line represents a downward parabola, the dashed (blue) line represents the effects of mass transfer and third body LTE, and the solid (red) line represents the final curve fitted to O-C. In the bottom panel, the points denote the final residuals. (Please see electronic version for colored figure.) Table 5 Parameters for the third and fourth bodies. Parameter
Third body
P3 (years) e ω(∘) K(day) T0(HJD) a sin i(AU) f(m3) M3,min(M⊙)
= Fourth body
(O
P4 (years) e ω(∘) K(day) T0(HJD) a sin i(AU) f(m4) M4,min(M⊙)
=
(O
C )2 * w N
C )2 * w N
This study
Pribulla and Rucinski (2006)
Kalomeni et al. (2007)
35.17(31) 0.490(5) 226(2) 0.01004(5) 2,457,915 1.84(8) 0.00511 (68) 0.287(13) 0.00370
20.44 0.32(21) – 0.0092 – 0.83(9) 0.0014(5) 0.19 –
27.9(2) 0.56(30) 96(18) – 2,438,540(793) 0.96(15) 0.0010(5) 0.16 –
18.04(2) 0.170(5) 151(2) 0.00230(5) 2,450,572 0.40(1) 0.000205(13) 0.10(7) 0.00365
– – – – – – – – –
– – – – – – – – –
CRediT authorship contribution statement Z. Kamalifar: Visualization, Writing - original draft. A. Abedi: Conceptualization, Methodology, Validation, Investigation, Supervision, Project administration. K.Y. Roobiat: Formal analysis, Software. References Awadalla, N.S., 1988. Three-colours photoelectric observations of w uma-system bb pegasi. Astrophys. Space Sci. 140 (1), 137–159. https://doi.org/10.1007/BF00643538. Cerruti-Sola, M., Milano, L., Scaltriti, F., 1981. Bb peg : a w uma-w system with a high degree of overcontact. Astron. Astrophys. 101, 273. Cerruti-Sola, M., Scaltriti, E., 1980. Two-color photoelectric observations of the eclipsing binary bb peg. Astron. Astrophys. Suppl. Ser. 40, 85–89. D’Angelo, C., van Kerkwijk, M.H., Rucinski, S.M., 2006. Contact binaries with additional components. ii. a spectroscopic search for faint tertiaries. Astron. J. 132 (2), 650–662. https://doi.org/10.1086/505265. Eker, Z., Demircan, O., Bilir, S., Karatas, Y., 2006. Dynamical evolution of active detached binaries on the log(j0)log(m) diagram and contact binary formation. Mon. Not. R. Astron. Soc. 373 (4), 1483–1494. https://doi.org/10.1111/j.1365-2966.2006. 11073.x. Giuricin, G., Mardirossian, F., Mezzetti, M., 1981. Light curve synthesis for the eclipsing binary bb peg. Astron. Nachr. 302 (6), 285–286. https://doi.org/10.1002/asna. 2103020605. Guthnick, P., Prager, R., 1932. Benennung von ver anderlichen sternen. Astron. Nachr. 247 (7), 121–152. https://doi.org/10.1002/asna.19322470702. van Hamme, W., 1993. New limb-darkening coefficients for modeling binary star light curves. Astron. J. 106 (5), 2096. https://doi.org/10.1086/116788. Hanna, M.A., Awadalla, N.S., 2011. Orbital period variation and morphological light curve studies for the w uma binary bb pegasi. J. Korean Astron. Soc. 44 (3), 97.
primary Roche lobes. The diagram in Fig. 4 also confirms this result, so the assumption of an over-contact system is fair. The actual errors of the calculated system parameters were greater than the values reported in the WD code output due to the scattering of the light curve data. Table 2 presents the identical errors reported for the output obtained using Phoebe software (which uses the WD code to simulate the light curve). The results obtained by simultaneously analyzing the R and B light curves and the spectroscopic data for the BB Peg eclipsing binary system (Tables 2 and 3) are in agreement with those reported in 5
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Z. Kamalifar, et al. https://doi.org/10.5303/JKAS.2011.44.3.097. Hilditch, R.W., King, D.J., McFarlane, T.M., 1988. The evolutionary state of contact and near-contact binary stars. Mon. Not. R. Astron. Soc. 231 (2), 341–352. https://doi. org/10.1093/mnras/231.2.341. Hoffmeister, C., 1931. 316 neue veriable. Astron. Nachr. 242 (7), 129–142. https://doi. org/10.1002/asna.19312420702. Hrivnak, B.J., 1990. Radial velocity studies of the w uma binaries bx peg and bb peg. Bull. Am. Astron. Soc. 22, 1291. Hu, K., Cai, J.-T., Yu, Y.-X., Xiang, F.-Y., 2018. First ccd photometric investigation of the eclipsing binary v737 per. New Astron. 65, 52–58. https://doi.org/10.1016/J. NEWAST.2018.06.007. Irwin, J.B., 1959. Standard light-time curves. Astron. J. 46, 149. https://doi.org/10. 1086/107913. Kalimeris, A., Rovithis-Livaniou, H., Rovithis, P., 1994. On the orbital period changes in contact binaries. Astron. Astrophys. 282 (3), 775–786. Kalomeni, B., Yakut, K., Keskin, V., Degirmenci, O.L., Ulas, B., Kose, O., 2007. Absolute properties of the binary system bb pegasi. Astron. J. 134 (2), 642–647. https://doi. org/10.1086/519493. Kepler, S.O., Kleinman, S.J., Nitta, A., Koester, D., Castanheira, B.G., Giovannini, O., Costa, A.F.M., Althaus, L., 2007. White dwarf mass distribution in the sdss. Mon. Not. R. Astron. Soc. 375 (4), 1315–1324. https://doi.org/10.1111/j.1365-2966.2006. 11388.x. Kilic, M., Prieto, C.A., Brown, W.R., Koester, D., 2007. The lowest mass white dwarf. Astrophys. J. 660 (2), 1451–1461. https://doi.org/10.1086/514327. Kwee, K.K., van Woerden, H., 1956. A method for computing accurately the epoch of minimum of an eclipsing variable. Bull. Astron. Inst. Neth. 12, 327. Lenz, P., Breger, M., 2005. Period04 user guide. Commun. Asteroseismol. 146, 53–136. https://doi.org/10.1553/cia146s53. Leung, K.-C., Zhai, D., Zhang, Y., 1985. Two very similar late-type contact systems - bx and bb pegasi. Astron. J. 90, 515. https://doi.org/10.1086/113759. Lu, W., Rucinski, S.M., 1999. Radial velocity studies of close binary stars. i. Astron. J. 118 (1), 515–526. https://doi.org/10.1086/300933. Lucy, L.B., 1969. Gravity-Darkening for Stars with Convective Envelopes. 65 EDP Sciences [etc.]. Lucy, L.B., Wilson, R.E., 1979. Observational tests of theories of contact binaries. Astrophys. J. 231, 502. https://doi.org/10.1086/157212. Mochnacki, S.W., 1981. Contact binary stars. Astrophys. J. 245, 650. https://doi.org/10.
1086/158841. Mochnacki, S.W., 1984. Accurate integrations of the roche model. Astrophys. J. Suppl. Ser. 55, 551. https://doi.org/10.1086/190967. Mochnacki, S.W., 1985. Erratum - accurate integrations of the roche model. Astrophys. J. Suppl. Ser. 59, 445. https://doi.org/10.1086/191080. Nikonov, V.B., Dobronravin, B., 1937. Bull. Abastumani Obs. 1 (11). O’Connell, D.J.K., 1951. The so-called periastron effect in eclipsing binaries. Monthly Notices of the Royal Astronomical Society 111 (6). https://doi.org/10.1093/mnras/ 111.6.642. 642–642 Piotrowski, S., 1936. Acta Astron. Ser. C 2 (157). Pribulla, T., Rucinski, S.M., 2006. Contact binaries with additional components. i. the extant data. Astron. J. 131 (6), 2986–3007. https://doi.org/10.1086/503871. Pribulla, T., Rucinski, S.M., Blake, R.M., Lu, W., Thomson, J.R., DeBond, H., Karmo, T., de Ridder, A., Ogloza, W., Stachowski, G., Siwak, M., 2009. Radial velocity studies of close binary stars. xv. Astron. J. 137 (3), 3655–3667. https://doi.org/10.1088/00046256/137/3/3655. Prsa, A., Zwitter, T., 2005. A computational guide to physics of eclipsing binaries. i. demonstrations and perspectives. Astrophys. J. 628 (1), 426–438. https://doi.org/10. 1086/430591. Qian, S., 2001. A possible relation between the period change and the mass ratio for wtype contact binaries. Mon. Not. R. Astron. Soc. 328 (2), 635–644. https://doi.org/ 10.1046/j.1365-8711.2001.04931.x. Rucinski, S.M., 1969. The proximity effects in close binary systems. ii. the bolometric reflection effect for stars with deep convective envelopes. Acta Astronomica 19, 245. Senavci, H.V., Yilmaz, M., Basturk, O., Ozavci, I., Caliskan, S., Kilicoglu, T., Tezcan, C.T., 2014. A tale on two close binaries in pegasus. Open Astron. 23 (2), 123–135. https:// doi.org/10.1515/astro-2017-0177. Whitney, B.S., 1943. Some eclipsing variable stars. Astron. J. 50, 131. https://doi.org/10. 1086/105750. Worthey, G., Lee, H., 2011. An empirical ubv ri jhk color-temperature calibration for stars. Astrophys. J. Suppl. Ser. 193 (1), 1. https://doi.org/10.1088/0067-0049/193/ 1/1. Yakut, K., Eggleton, P.P., 2005. Evolution of close binary systems. Astrophys. J. 629 (2), 1055–1074. https://doi.org/10.1086/431300. Zola, S., Kreiner, J.M., Zakrzewski, B., Kjurkchieva, D.P., Marchev, D.V., Baran, A., Rucinski, S.M., Ogloza, W., Siwak, M., Koziel, D., Drozdz, M., Pokrzywka, B., 2005. Physical parameters of components in close binary systems. v. Acta Astron. 55, 389.
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