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New light curve analysis and period changes of the overcontact binary EQ Tauri
New Astronomy 34 (2015) 262–265
Contents lists available at ScienceDirect
New Astronomy journal homepage: www.elsevier.com/locate/newast
New light curve analysis and period changes of the overcontact binary EQ Tauri A. Hasanzadeh a,b,⇑, F. Farsian a, M. Nemati a a b
The International Occultation Timing Association Middle East Section (IOTA/ME), Iran Institute of Geophysics, University of Tehran, Tehran, Iran
h i g h l i g h t s We carried out new observations of the eclipsing binary EQ Tauri and plotted light curves in BVR filters. We obtained times of light minimum and determined new ephemeris for primary minimum of EQ Tau. We calculated and plotted O–C diagram of EQ Tau and calculated the period changes. We analyzed the BVR light curves and determined some geometrical and physical parameters.
a r t i c l e
i n f o
Article history: Received 20 May 2014 Received in revised form 16 July 2014 Accepted 17 July 2014 Available online 27 July 2014 Communicated by E.P.J. van den Heuvel Keywords: Eclipsing Binaries EQ Tauri PHOEBE
a b s t r a c t A photometric CCD study of EQ Tauris was carried out in the R, V and B bands. These new data were analyzed by using the PHOEBE and Binary Marker 3 programs, which yielded the geometrical system parameters and mass and radius of both stars. We find these to confirm the results of Pribulla and Vanko (2002). Using these new data together with data from the literature, the orbital period variations were studied by using the Kalimeris method. We find the same timescale of variability of the orbital period as Pribulla and Vanko (2002), namely about 49 years. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction The eclipsing binary EQ Tau (GSC 01260-00909) was discovered as a variable star (HV 6189) by Shapley and Hughes (1940) and was studied by Tsesevich (1954) for the first time. Magalashvili and Kumsishvili (1971) presented photoelectric light curves from 1968 to 1969. Both of these studies concluded that the orbital period is 0.413 days but Whitney (1972) appears to be the first one to have determined the correct period of 0.341 days. The R light curve has since been obtained by Benbow and Mutel (1995). Spectroscopic observations and radial velocity analysis of the system were published by Rucinski et al. (2001). The changes in the orbital period of EQ Tau were analyzed by Qian and Ma (2001). Subsequently, two photoelectric light curve studies of EQ Tau were published by Pribulla et al. (2001) and Vanko et al. (2004). Yang and Liu (2002)
⇑ Corresponding author at: No. 105, Nazari st., 12 farvardin st., Enghelab sq., Tehran, Iran. E-mail address: [email protected] (A. Hasanzadeh). http://dx.doi.org/10.1016/j.newast.2014.07.013 1384-1076/Ó 2014 Elsevier B.V. All rights reserved.
obtained complete BV light curves using a CCD (Hrivnak et al., 2006). EQ Tauri belongs to the subtype A from W Ursae Majoris contact binary variables (Binnendijk, 1984). The mass of larger and warmer star is about 1.28 solar masses. It is covered during the main eclipse by cooler star with a mass of about 0.47 solar masses. This variable has an orbital inclination of 84° (degrees) which provides suitable conditions for studying this system.
2. Observations The observation of EQ Tau was carried out on October 13, 2012 at the Alborz observatory in Mahdasht, Iran with a 16-inch Cassegrain telescope and SBIG 11000 type CCD. This CCD has a 890 1339 pixel array with a pixel length of 27 lm. 130 images were taken with exposure times of 30 s in each of the V, B and R Johnson filters. The comparison star was GSC 01260-00575 which was used in Yang and Liu (2002) and Hrivnak et al. (2006) work.
263
A. Hasanzadeh et al. / New Astronomy 34 (2015) 262–265 Table 1 The variable, comparison and reference stars (From: SIMBAD query result EQ Tau). Stars
Name
RA
DEC
Magnitude (V)
Variable Comparison Reference
GSC 01260-00909 GSC 01260-00575 GSC 01260-01016
03 48 13 03 48 16 03 48 36
22 18 51 22 17 30 22 16 36
10.45–11.13 9.76 11.99
Table 3 EQ Tau light curve parameters.
Fig. 1. Light curves of EQ Tau in B, V, R.
The applied reference star is GSC 1260-01016, which was the second comparison star in Hrivnak et al. (2006) study. The variable, the comparison and the reference stars’ coordinates are shown in Table 1. 3. Light curve, time of minimum and period study In order to plot the light curve, we converted the extracted times by Maxim DL software from Julian date (JD) to Heliocentric Julian date (HJD). Then for converting this date to phase, the ephemeris in Eq. (1), which is obtained from Hrivnak et al. (2006), was used.
Min I ðHJDÞ ¼ 2452296:6941 þ 0:34134727 E
ð1Þ
The light curves in B, V and R filters, are shown in Fig. 1. In order to obtain the minimum time, Kwee and Woerden method was applied (Kwee and van Woerden, 1956).
Parameter
This study
q i (deg) T1 (K) T2 (K) O1 = O2 L1/(L1 + L2)V L1/(L1 + L2)B L1/(L1 + L2)R x1, x2 (V) y1, y2 (V) x1, x2 (B) y1, y2 (B) x1, x2 (R) y1, y2 (R) r1 (pole) r1 (side) r1 (back) r2 (pole) r2 (side) r2 (back) Spot colatitude (deg) Spot longitude (deg) Spot radius (deg) Tspot/Tstar
0.439 ± 0.001 84.54 ± 0.32 5800 ± 4 5730 ± 4 2.732 ± 0.003 0.6900 0.6928 0.6876 0.758 0.237 0.836 0.150 0.666 0.255 0.4294 0.4583 0.4873 0.2942 0.3075 0.3432 91 275 6 1.1
0.763 0.229 0.838 0.137 0.670 0.251
The minimum time for each filter was calculated and the average value for the first and second minimum is presented in Table 2. The O–C graph was plotted by using new minimum times and recorded minimum times from the literatures. We collected 197 visual and photographic data and 118 data achieved from CCD and photoelectric observations (Fig. 2).
Table 2 New times of minima for EQ Tau.
Min 1 Min 2
B filter +2450000 (HJD)
R filter +2450000 (HJD)
V filter +2450000 (HJD)
Average +2450000 (HJD)
O–C (days)
6214.34744 ± 0.00014 6214.51819 ± 0.00048
6214.34774 ± 0.00012 6214.51799 ± 0.00033
6214.34769 ± 0.00009 6214.51784 ± 0.00017
6214.34762 ± 0.00011 6214.51801 ± 0.00032
0.01128 0.01061
Fig. 2. O–C curve with the derived 6th order function fitted to the data.
264
A. Hasanzadeh et al. / New Astronomy 34 (2015) 262–265
Fig. 3. The observed (circles) and synthetic (solid line) light curves of EQ Tau in B, V, R filters.
and Vanko (2002) found a period around 50 years. In this study, the changes of period were calculated with the Kalimeris et al. (1994) method. In the Kalimeris method, first we divide the values of the horizontal column (Epoch) of the O–C curve by a constant number N:
EN ¼
Fig. 4. EQ Tau model with a small hot spot on component 1.
We calculated a new ephemeris based on recent CCD minimum times.
Min I ðHJDÞ ¼ 2452296:70707ð0:00019Þ þ 0:34134713ð0:000000036Þ E
ð2Þ
The timescale of the changes of this star’s period are not quite obvious. Yang and Liu (2002) reported it to be around 23 years. By including Kumsishvili and Magalashvili‘s data a periodicity of about 60 years was found (Hrivnak et al., 2006), while Pribulla
E N
ð3Þ
The number N should fulfill the condition jEN;max ; EN;min jh1. Then we fit a polynomial function to it. We assigned weight two for CCD and photoelectric observations and weight one for visual and photographic observations. A single polynomial of 6th order appears to fit very well to the data (Fig. 2). In the next step:
1 P P e ¼ f ðEN Þ f EN N
ð4Þ
(P Pe) was calculated, in which Pe is the orbital period in new ephemeris in Eq. (2).
265
A. Hasanzadeh et al. / New Astronomy 34 (2015) 262–265 Table 4 Absolute parameters for EQ Tau components and comparison with previous studies. The numbers in parentheses represent the standard error in the last digit(s). Parameter
Pribulla and Vanko (2002)
Yang and Liu (2002)
Hrivnak et al. (2006)
This study
M1 (M() M2 (M() R1 (R() R2 (R() log g1 log g2 L1 (L() L2 (L() f (% overcontact)
1.22(3) 0.54(1) 1.14(1) 0.79(1) 4.41(1) 4.38(1) 1.32(27) 0.62(13) 12
1.32(3) 0.59(2) 1.16(3) 0.82(3) 4.43(9) 4.38(9) 1.35(12) 0.64(6) 19
1.28(3) 0.57(1) 1.17(1) 0.81(1) 4.41(1) 4.38(1) 1.39(29) 0.63(13) 16
1.233(3) 0.541(3) 1.143(4) 0.788(4) 4.412(12) 4.378(12) 1.327(14) 0.610(14) 9.3
In this way the periodic change of the system during recent decades can be obtained. We found a periodicity of 49 years in our study. 4. Light curve analysis Light curves resulting from our observations in three B, V and R filters were analyzed using the Binary Marker 3 program (Bradstreet, 2005). The Observational data were given as the input to the program in order to derive the best fitting values of the potential, temperature, mass ratio, and orbital inclination angle in accordance with Hrivnak et al. (2006). Addition of a spot seemed essential in order to achieve a suitable fit. As Liu and Yang used hot and cold spots for resolving the light curve maximum asymmetry issue (Yang and Liu, 2002) (Table 3). We obtained a satisfactory result by putting a hot spot on the hotter component (Fig. 4). As a result, the geometrical parameters of the system were obtained for further studies and were then used for logging into the PHOEBE program (Prsa and Zwitter, 2005). In the next step, we used PHOEBE based on the Wilson– Devinney (WD) code for modeling and analyzing the light curve (Fig. 3). The values of bolometric albedo (A1,2 = 0.5) and gravitydarkening coefficients (g1,2 = 0.32) were assumed to be constant based on reported values for such systems (Rucinski, 1969; Lucy, 1967). The values of the limb-darkening coefficients (x1, x2, y1, y2) were calculated according to a logarithmic law (Van Hamme, 1993). There has not been evidence of a third light (l3 = 0). In order to achieve a suitable fit, other parameters such as the temperature of the first and second components (T1, T2), orbital inclination (i), mass ratio (q = m2/m1) and the surface potential (X) were studied and also our parameters have been compared with parameters in other papers (Table 3) and eventually the absolute parameters were obtained and comparisons with results from earlier studies are given (Table 4).
5. Conclusions A new light curve and observational data from EQ Tau is presented and we suggest the new ephemeris. The characteristic timescale for changes in the orbital period is of order 49 years. Physical parameters including mass, radius and luminous of the two stars were calculated using the modeling by the programs Binary Marker 3 and PHOEBE 0.31. Our results confirm the results of Pribulla and Vanko (2002) who find the same parameter values and the same timescale of variation of the orbital period. Acknowledgments We are so thankful to A. Poro, the President of International Occultation and Timing Association/Middle East Section who associated us and also supports of ISA. We are also grateful to S. Ostadnejad for her kind guidance. We are also grateful to the anonymous reviewer whose comments helped us to improve this paper. References Benbow, W., Mutel, R., 1995. IBVS 4187, 1. Binnendijk, L., 1984. Pub. A.S.P. 96, 646. Bradstreet, D.H., 2005. SASS 24, 23B. Hrivnak, B.J., Lu, W., Eaton, J., Kenning, D., 2006. AJ 132, 960. Kalimeris, A., Rovithis-Livaniou, H., Rovithis, P., 1994. A&A 282, 775. Kwee, K.K., van Woerden, H., 1956. B.A.N. 12, 327. Lucy, L.B., 1967. Z. Astrophys. 65, 89. Magalashvili, N.L., Kumsishvili, J.I., 1971. Abastumanskaia Astrofiz. Obs. Bull. 40, 2. Pribulla, T., Vanko, M., Parimucha, S., Chochol, D., 2001. IBVS 5056, 1. Pribulla, T., Vanko, M., 2002. Contrib. Astr. Obs. Skalnate Pleso 32, 79. Prsa, A., Zwitter, T., 2005. AJ 628, 426. Qian, S., Ma, Y., 2001. PASP 113, 754. Rucinski, S.M., 1969. Acta Astron. 19, 245. Rucinski, S.M., Lu, W., Mochnacki, S.W., Ogloza, W., Stachowski, G., 2001. AJ 122, 1974. Shapley, H., Hughes, E.M., 1940. Annu. Rep. 90, 163. Tsesevich, V.P., 1954. Izv. Astr. Obs. Odessa 4, 3. Van Hamme, W., 1993. AJ 106, 2096. Vanko, M., Parimucha, S., Pribulla, T., Chocol, D., 2004. Balt. Astron. 13, 151. Whitney, B.S., 1972. IBVS 633, 1. Yang, Y., Liu, Q., 2002. AJ 124, 3358.
Contents lists available at ScienceDirect
New Astronomy journal homepage: www.elsevier.com/locate/newast
New light curve analysis and period changes of the overcontact binary EQ Tauri A. Hasanzadeh a,b,⇑, F. Farsian a, M. Nemati a a b
The International Occultation Timing Association Middle East Section (IOTA/ME), Iran Institute of Geophysics, University of Tehran, Tehran, Iran
h i g h l i g h t s We carried out new observations of the eclipsing binary EQ Tauri and plotted light curves in BVR filters. We obtained times of light minimum and determined new ephemeris for primary minimum of EQ Tau. We calculated and plotted O–C diagram of EQ Tau and calculated the period changes. We analyzed the BVR light curves and determined some geometrical and physical parameters.
a r t i c l e
i n f o
Article history: Received 20 May 2014 Received in revised form 16 July 2014 Accepted 17 July 2014 Available online 27 July 2014 Communicated by E.P.J. van den Heuvel Keywords: Eclipsing Binaries EQ Tauri PHOEBE
a b s t r a c t A photometric CCD study of EQ Tauris was carried out in the R, V and B bands. These new data were analyzed by using the PHOEBE and Binary Marker 3 programs, which yielded the geometrical system parameters and mass and radius of both stars. We find these to confirm the results of Pribulla and Vanko (2002). Using these new data together with data from the literature, the orbital period variations were studied by using the Kalimeris method. We find the same timescale of variability of the orbital period as Pribulla and Vanko (2002), namely about 49 years. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction The eclipsing binary EQ Tau (GSC 01260-00909) was discovered as a variable star (HV 6189) by Shapley and Hughes (1940) and was studied by Tsesevich (1954) for the first time. Magalashvili and Kumsishvili (1971) presented photoelectric light curves from 1968 to 1969. Both of these studies concluded that the orbital period is 0.413 days but Whitney (1972) appears to be the first one to have determined the correct period of 0.341 days. The R light curve has since been obtained by Benbow and Mutel (1995). Spectroscopic observations and radial velocity analysis of the system were published by Rucinski et al. (2001). The changes in the orbital period of EQ Tau were analyzed by Qian and Ma (2001). Subsequently, two photoelectric light curve studies of EQ Tau were published by Pribulla et al. (2001) and Vanko et al. (2004). Yang and Liu (2002)
⇑ Corresponding author at: No. 105, Nazari st., 12 farvardin st., Enghelab sq., Tehran, Iran. E-mail address: [email protected] (A. Hasanzadeh). http://dx.doi.org/10.1016/j.newast.2014.07.013 1384-1076/Ó 2014 Elsevier B.V. All rights reserved.
obtained complete BV light curves using a CCD (Hrivnak et al., 2006). EQ Tauri belongs to the subtype A from W Ursae Majoris contact binary variables (Binnendijk, 1984). The mass of larger and warmer star is about 1.28 solar masses. It is covered during the main eclipse by cooler star with a mass of about 0.47 solar masses. This variable has an orbital inclination of 84° (degrees) which provides suitable conditions for studying this system.
2. Observations The observation of EQ Tau was carried out on October 13, 2012 at the Alborz observatory in Mahdasht, Iran with a 16-inch Cassegrain telescope and SBIG 11000 type CCD. This CCD has a 890 1339 pixel array with a pixel length of 27 lm. 130 images were taken with exposure times of 30 s in each of the V, B and R Johnson filters. The comparison star was GSC 01260-00575 which was used in Yang and Liu (2002) and Hrivnak et al. (2006) work.
263
A. Hasanzadeh et al. / New Astronomy 34 (2015) 262–265 Table 1 The variable, comparison and reference stars (From: SIMBAD query result EQ Tau). Stars
Name
RA
DEC
Magnitude (V)
Variable Comparison Reference
GSC 01260-00909 GSC 01260-00575 GSC 01260-01016
03 48 13 03 48 16 03 48 36
22 18 51 22 17 30 22 16 36
10.45–11.13 9.76 11.99
Table 3 EQ Tau light curve parameters.
Fig. 1. Light curves of EQ Tau in B, V, R.
The applied reference star is GSC 1260-01016, which was the second comparison star in Hrivnak et al. (2006) study. The variable, the comparison and the reference stars’ coordinates are shown in Table 1. 3. Light curve, time of minimum and period study In order to plot the light curve, we converted the extracted times by Maxim DL software from Julian date (JD) to Heliocentric Julian date (HJD). Then for converting this date to phase, the ephemeris in Eq. (1), which is obtained from Hrivnak et al. (2006), was used.
Min I ðHJDÞ ¼ 2452296:6941 þ 0:34134727 E
ð1Þ
The light curves in B, V and R filters, are shown in Fig. 1. In order to obtain the minimum time, Kwee and Woerden method was applied (Kwee and van Woerden, 1956).
Parameter
This study
q i (deg) T1 (K) T2 (K) O1 = O2 L1/(L1 + L2)V L1/(L1 + L2)B L1/(L1 + L2)R x1, x2 (V) y1, y2 (V) x1, x2 (B) y1, y2 (B) x1, x2 (R) y1, y2 (R) r1 (pole) r1 (side) r1 (back) r2 (pole) r2 (side) r2 (back) Spot colatitude (deg) Spot longitude (deg) Spot radius (deg) Tspot/Tstar
0.439 ± 0.001 84.54 ± 0.32 5800 ± 4 5730 ± 4 2.732 ± 0.003 0.6900 0.6928 0.6876 0.758 0.237 0.836 0.150 0.666 0.255 0.4294 0.4583 0.4873 0.2942 0.3075 0.3432 91 275 6 1.1
0.763 0.229 0.838 0.137 0.670 0.251
The minimum time for each filter was calculated and the average value for the first and second minimum is presented in Table 2. The O–C graph was plotted by using new minimum times and recorded minimum times from the literatures. We collected 197 visual and photographic data and 118 data achieved from CCD and photoelectric observations (Fig. 2).
Table 2 New times of minima for EQ Tau.
Min 1 Min 2
B filter +2450000 (HJD)
R filter +2450000 (HJD)
V filter +2450000 (HJD)
Average +2450000 (HJD)
O–C (days)
6214.34744 ± 0.00014 6214.51819 ± 0.00048
6214.34774 ± 0.00012 6214.51799 ± 0.00033
6214.34769 ± 0.00009 6214.51784 ± 0.00017
6214.34762 ± 0.00011 6214.51801 ± 0.00032
0.01128 0.01061
Fig. 2. O–C curve with the derived 6th order function fitted to the data.
264
A. Hasanzadeh et al. / New Astronomy 34 (2015) 262–265
Fig. 3. The observed (circles) and synthetic (solid line) light curves of EQ Tau in B, V, R filters.
and Vanko (2002) found a period around 50 years. In this study, the changes of period were calculated with the Kalimeris et al. (1994) method. In the Kalimeris method, first we divide the values of the horizontal column (Epoch) of the O–C curve by a constant number N:
EN ¼
Fig. 4. EQ Tau model with a small hot spot on component 1.
We calculated a new ephemeris based on recent CCD minimum times.
Min I ðHJDÞ ¼ 2452296:70707ð0:00019Þ þ 0:34134713ð0:000000036Þ E
ð2Þ
The timescale of the changes of this star’s period are not quite obvious. Yang and Liu (2002) reported it to be around 23 years. By including Kumsishvili and Magalashvili‘s data a periodicity of about 60 years was found (Hrivnak et al., 2006), while Pribulla
E N
ð3Þ
The number N should fulfill the condition jEN;max ; EN;min jh1. Then we fit a polynomial function to it. We assigned weight two for CCD and photoelectric observations and weight one for visual and photographic observations. A single polynomial of 6th order appears to fit very well to the data (Fig. 2). In the next step:
1 P P e ¼ f ðEN Þ f EN N
ð4Þ
(P Pe) was calculated, in which Pe is the orbital period in new ephemeris in Eq. (2).
265
A. Hasanzadeh et al. / New Astronomy 34 (2015) 262–265 Table 4 Absolute parameters for EQ Tau components and comparison with previous studies. The numbers in parentheses represent the standard error in the last digit(s). Parameter
Pribulla and Vanko (2002)
Yang and Liu (2002)
Hrivnak et al. (2006)
This study
M1 (M() M2 (M() R1 (R() R2 (R() log g1 log g2 L1 (L() L2 (L() f (% overcontact)
1.22(3) 0.54(1) 1.14(1) 0.79(1) 4.41(1) 4.38(1) 1.32(27) 0.62(13) 12
1.32(3) 0.59(2) 1.16(3) 0.82(3) 4.43(9) 4.38(9) 1.35(12) 0.64(6) 19
1.28(3) 0.57(1) 1.17(1) 0.81(1) 4.41(1) 4.38(1) 1.39(29) 0.63(13) 16
1.233(3) 0.541(3) 1.143(4) 0.788(4) 4.412(12) 4.378(12) 1.327(14) 0.610(14) 9.3
In this way the periodic change of the system during recent decades can be obtained. We found a periodicity of 49 years in our study. 4. Light curve analysis Light curves resulting from our observations in three B, V and R filters were analyzed using the Binary Marker 3 program (Bradstreet, 2005). The Observational data were given as the input to the program in order to derive the best fitting values of the potential, temperature, mass ratio, and orbital inclination angle in accordance with Hrivnak et al. (2006). Addition of a spot seemed essential in order to achieve a suitable fit. As Liu and Yang used hot and cold spots for resolving the light curve maximum asymmetry issue (Yang and Liu, 2002) (Table 3). We obtained a satisfactory result by putting a hot spot on the hotter component (Fig. 4). As a result, the geometrical parameters of the system were obtained for further studies and were then used for logging into the PHOEBE program (Prsa and Zwitter, 2005). In the next step, we used PHOEBE based on the Wilson– Devinney (WD) code for modeling and analyzing the light curve (Fig. 3). The values of bolometric albedo (A1,2 = 0.5) and gravitydarkening coefficients (g1,2 = 0.32) were assumed to be constant based on reported values for such systems (Rucinski, 1969; Lucy, 1967). The values of the limb-darkening coefficients (x1, x2, y1, y2) were calculated according to a logarithmic law (Van Hamme, 1993). There has not been evidence of a third light (l3 = 0). In order to achieve a suitable fit, other parameters such as the temperature of the first and second components (T1, T2), orbital inclination (i), mass ratio (q = m2/m1) and the surface potential (X) were studied and also our parameters have been compared with parameters in other papers (Table 3) and eventually the absolute parameters were obtained and comparisons with results from earlier studies are given (Table 4).
5. Conclusions A new light curve and observational data from EQ Tau is presented and we suggest the new ephemeris. The characteristic timescale for changes in the orbital period is of order 49 years. Physical parameters including mass, radius and luminous of the two stars were calculated using the modeling by the programs Binary Marker 3 and PHOEBE 0.31. Our results confirm the results of Pribulla and Vanko (2002) who find the same parameter values and the same timescale of variation of the orbital period. Acknowledgments We are so thankful to A. Poro, the President of International Occultation and Timing Association/Middle East Section who associated us and also supports of ISA. We are also grateful to S. Ostadnejad for her kind guidance. We are also grateful to the anonymous reviewer whose comments helped us to improve this paper. References Benbow, W., Mutel, R., 1995. IBVS 4187, 1. Binnendijk, L., 1984. Pub. A.S.P. 96, 646. Bradstreet, D.H., 2005. SASS 24, 23B. Hrivnak, B.J., Lu, W., Eaton, J., Kenning, D., 2006. AJ 132, 960. Kalimeris, A., Rovithis-Livaniou, H., Rovithis, P., 1994. A&A 282, 775. Kwee, K.K., van Woerden, H., 1956. B.A.N. 12, 327. Lucy, L.B., 1967. Z. Astrophys. 65, 89. Magalashvili, N.L., Kumsishvili, J.I., 1971. Abastumanskaia Astrofiz. Obs. Bull. 40, 2. Pribulla, T., Vanko, M., Parimucha, S., Chochol, D., 2001. IBVS 5056, 1. Pribulla, T., Vanko, M., 2002. Contrib. Astr. Obs. Skalnate Pleso 32, 79. Prsa, A., Zwitter, T., 2005. AJ 628, 426. Qian, S., Ma, Y., 2001. PASP 113, 754. Rucinski, S.M., 1969. Acta Astron. 19, 245. Rucinski, S.M., Lu, W., Mochnacki, S.W., Ogloza, W., Stachowski, G., 2001. AJ 122, 1974. Shapley, H., Hughes, E.M., 1940. Annu. Rep. 90, 163. Tsesevich, V.P., 1954. Izv. Astr. Obs. Odessa 4, 3. Van Hamme, W., 1993. AJ 106, 2096. Vanko, M., Parimucha, S., Pribulla, T., Chocol, D., 2004. Balt. Astron. 13, 151. Whitney, B.S., 1972. IBVS 633, 1. Yang, Y., Liu, Q., 2002. AJ 124, 3358.