Period Variation Study and Light Curve Analysis of the Eclipsing Binary GSC 02013-00288

The star IK Boo (= GSC 02013-00288, mag_B=12.16, B-V=0.81, FONAC.Catalogue, Kislyuk+1999) was reported by Akerlof et al. [1] as a newly discovered eclipsing binary system. Unfiltered CCD light curve with SBIG ST-7 camera attached to the 0.15m starfire reflector in Wald, Switzerland, was obtained by Blättler during 6 nights between JD 2453382 (2005, Jan 12) and JD 2453517 (2005, May 27)(Figure 1). Blättler and Diethlem [3] reported the system to be an eclipsing W UMa type with a magnitude range 11.42-11.76 (<mag>=11.69).

Fig. 1

Hanna and Awadalla [11] in a poster paper have presented the first set of complete light curves in BVRI filters observed photometrically during a clear night on 2013, May 1-2. They made a preliminary study for its period variations giving two new linear and quadratic ephemerides and deduced a decrease in the orbital period by a rate of −1.976 × 10⁻⁷ day/year.

The aim of this study is to analyze these light curves to determine the physical and geometrical elements for the system, to show any morphological variation due to star spot(s) activity found and to study the period variability of the system with some more details.

The observations of the W UMa eclipsing binary IK Boo were carried out through an EEV CCD 42-40 camera of multi-color BVRI standard Johnson filters attached to the Newtonian focus (F=4.0) of the 74-inch reflector telescope of the Kottamia observatory in Egypt, during a clear photoelectric night on 2013, May 1-2 i.e., HJD 2456414.0 (Hanna and Awadalla [11]). The exposure times, ranged from 20 s to 90 s, depend on the observing sky conditions and the filter used. The CCD camera has a format 2048 x 2048 pixels with a scale of 0^″.308 per pixel that was cooled by liquid nitrogen down to about -122^oC. The package of C-Muniwin, was used to reduce the CCD images.

The name and the coordinates of the variable star IK Boo (V), the comparison (C1), and the check (C2) stars are listed in Table 1, and their identification chart is shown in Figure 2. Also their magnitudes in different filters are presented in Table 2.

Table 1

The coordinates of IK Boo and the comparison stars

Table 2

The magnitude of IK Boo and the comparison stars in different filters

Fig. 2

A total of 71 observations in B, 86 observations in V, 89 in R and 89 in I filters, were obtained and listed in Table 7, where Δ (BVRI) denote magnitude differences in the sense, variable minus comparison. The light curves in different filters with the calculated corresponding phases are plotted in Figure 3. The phases have been calculated from ephemeris given by Hanna and Awadalla [11].

Fig. 3

The observed light curves of IK Boo indicate typical short period (7^h.27) W UMa eclipsing binary with narrow minima and broad maxima. To find the geometrical and physical parameters for the system, we proceed to solve the light curves simultaneously using the software PHOEBE (Prša and Zwitter [19]).

First, we have to determine the effective temperature of the primary star T₁, and the mass ratio q since there is no information about the mass ratio of the system in previous literature till now.

To determine the effective temperature, we used the observed colour index (B −V )_o = 0.81 from FONAK catalogue (Kislyuk, 1999) and the colour excess E(B — V) = 0.016 from the All Sky Imaging Survey AIS (Bianchi et al. [2]). Hence, the intrinsic colour index equals 0.794. Then, using tables of Cox [4] for the main sequence stars, a surface temperature 5190K was obtained for the primary component of IK Boo.

To determine the mass ratio q we have applied an extensive q-search procedure. We searched for solutions with mass ratios from 0.1 to 1.7. The relation between the resulted sum Σ of the weight square deviation (O — C)² and q is shown in Figure 4. The q-search of PHOEBE converged and resulted acceptable photometric solution for a contact configuration at about q_ph ≃ 0.657.

Fig. 4

Second, by using van Hamme’s [27] tables, the corresponding bolometric coefficient x₁ and x₂ were interpolated and found. Also, by following Lucy [17] and Rucinski [26], the gravity darkening exponent g₁ = g₂ = 0.32 and the bolometric albedo A₁ = A₂ = 0.5 were assumed for both components with a convective envelope. With the assumed initial parameters we continued the programme process, by using the "over contact mode" based on the shape of the light curves, till the solution converged. Finally, the solution with the standard errors obtained is tabulated for each filter in Table 3. The theoretical light curves are computed with the obtained parameters and plotted in Figure 3 as solid lines.

Table 3

The light curve fit parameters by PHOEBE for GSC 4405-00129

The fill-out factors of both components f₁ = f₂ ≃ −0.003, as obtained and listed in Table 3, imply that IK Boo is a contact binary system according to Lucy and Wilson [18]. The Roche lobe configuration of IK Boo is illustrated in Figure 5.

Fig. 5

Rucinski [23] has discussed the properties of W UMa-type systems in terms of their division into A- and W-types. He reported that for q nearer to the upper limit of the range 0.145 < q < 0.88, later spectral type G-K, for shallow envelopes Roche lobe configuration denoted by the fill-out factor f and for high colour index B − V ≥ 0.54; the system can be classified as W-type contact binary system. For IK Boo, the results show a q value ≃ 0.65, late spectral type K0 + K1.5 (corresponding to the obtained low temperatures T₁ = 5190,T₂ = 5000K), the Roche geometry configuration (Figure 5) where the fill out factor f = −0.003, and the colour index B −V = 0.796 > 0.54. Hence, one can deduce that IK Boo is likely to be of W-type W UMa system.

To follow the light curve variation for IK Boo, we measured the light curve levels at maxima and minima directly from Figure 3. Table 4 shows the magnitude difference between both maxima D_max. (O’Connell effect) and both minima D_min.; and the depths of the primary (A_p) and secondary (A_s) minima for the observed light curves in all bands (BVRI). Table 4 and Figure 3 show that the primary and secondary minima are deeper (A_p&A_s) in short wavelength and decreased with increasing the wave length, while the depth difference in minima is larger in V-band.

Table 4

Magnitude differences and minima depthes of IK Boo

Some of interesting in all light curves of IK Boo is the existence of a hump like distortion waves between phase 0.75 and 0.90 (Figure 3). This phenomenon displays when the primary goes free from the secondary and it has been recorded for the RS CVn binary systems as flare-like episodes (Zeilik, et al., [29]).

The first light elements was obtained by Blättler and Diethelm [3] by performing a linear regression to 10 times of minima obtained from ROTSE1 data. Later, Hanna and Awadalla [11] collected all the available time of minima together with their observed minima times and deduced two linear and quadratic ephemerides by constructing the O-C diagram. They have deduced a decrease in the orbital period of IK Boo by a rate dP/dt= −1.979 × 10⁻⁷ day/year. In this section we aimed to re-visit the period variation study of this system in some more details.

In order to study the period variation of IK Boo, we used all the minima times used in Hanna and Awadalla [11] together with two new minima observed recently by Hübscher and Lehmann [14]. They are all listed in Table 5.

Table 5

Time of Minima

We have constructed the O-C diagram as seen in the Figure 7 by using the light elements of Blättler and Diethelm [3]. Then, by using the linear and quadratic least squares methods, we obtained the following new linear and quadratic ephemerides:

Fig. 7

HJD(MinI)=2453382d.62805+0d.303117067E,$$\begin{array}{} \displaystyle HJD(Min I) =24 53382^{d}.62805+0^{d}.303117067 E, \end{array}$$(1)

with standard deviation (SD) =0.0025 day, correlation coefficient (r)=0.9609, and residual sum of squares = 1.68 × 10⁻⁴; and

HJD(MinI)=2453382d.62741+0d.303118999⋅E−6.96×10−11E2,$$\begin{array}{} \displaystyle HJD(Min I)=24 53382^{d}.62741 + 0^{d}.303118999\cdot E -6.96\times10^{-11}\, E^{2}, \end{array}$$(2)

with SD=0.0025 day, r=0.9636, and residual sum of squares = 1.57 × 10⁻⁴ associated with the period decrease rate dP/dt = −1.39 × 10⁻¹⁰d/cycle(= −1.68 × 10⁻⁷d/yr). Such period decrease rate is usually interpreted to be due to a transfer of matter from the more massive to the less massive component.

If the period decrease is caused by conservative mass transfer, then one can calculate the mass transfer between the binary components. On using the formula derived by Kreiner & Ziolkowski [16]:

dMdt=Mt⋅q3P(q2−1)⋅dPdt,$$\begin{array}{} \displaystyle \frac {\textrm{d}M}{\textrm{dt}}= \frac {M_{t}\cdot \,q}{3\,P\,(q^{2}-1)} \cdot\frac{\textrm{d}P}{\textrm{dt}}, \end{array}$$(3)

where, M_t = M₁ + M₂ and q = M₂/M₁, and by adopting the value 0.91 M_⊙ for M₁ by using Harmanec’s [12] table for main sequence stars where T₁ = 5190 K, consequently M₂= 0.59 M_⊙, where q_ph = 0.648 (Table 3). Hence, we have obtained the rate of mass transfer dP/dt (= 3.1 × 10⁻⁷ M_⊙/yr) from the more massive to the less massive star.

Eliminating the effect of mass transfer which is represented by the parabolic term of equation 2, we obtain the (O −C)₂ residual plot (Figure 8), which shows a significant orbital period variation. The dashed curve on Figure 8 represents the 4^th order polynomial fit to all the data (without the last two points since they have a severe upward bind) with SD = 0.002 and r = 0.612. We have performed such polynomial fit just to show the sine like variation which is usually interpreted to be due to the presence of a third body orbiting the binary or the effect of magnetic activity cycling as a result of star spot(s) activity. However, at present we cannot able to distinguish between the two possibilities due to that, the data available represents only one cycle. One cycle cannot confirm the third body hypothesis without either spectroscopic evidence or a presence of another cycle equals in duration to the first cycle. Strictly periodic sine variation behavior concerning the O −C diagram shape is an essential property to prove the LITE due to the presence of a third body. Hence, More photoelectric and spectroscopic observations are indeed required to decide among the two possibilities that causing the sine variation.

Fig. 8

The present (O −C)₂ values in Figure 8, considering all the data, clearly suggest a non-continuous variation. Following Qian’s [20] method, three clear jumps have taken place in the period of IK Boo within a time interval of about 9 years between the middle of Jan 12, 2005 (or JD = 2453382.6234) and the end of Mar 31, 2014 (or JD = 2456747.5323). Between these jumps, the period is assumed to have undergone a steady decrease. Similar systems, such as Y Psc, BO Mon, Z Per, and UU And have been studied by Qian [21,22], AT Peg by Hanna [9], BB Peg by Hanna and Awadalla [10]. Using the least squares method, a linear function in each portion is used to obtain the best fit to the (O −C)₂ values:

(O−C)2=ΔT+ΔP×E;$$\begin{array}{} \displaystyle (O-C)_{2}=\Delta T +\Delta P \times E; \end{array}$$(4)

the values ΔT and ΔP in each portion are listed in Table 6. The period at any cycle E has been computed with the following equation:

Table 6

Four linear fit sections, intervals, and the rates of change of the period of IK Boo

Table 7

BVRI-Observations of IK Boo

PRe(E)=PEph+ΔP+dPdE×E;$$\begin{array}{} \displaystyle P_{Re}(E)=P_{Eph} + \Delta P + \frac {dP}{dE} \times E; \end{array}$$(5)

results are shown in Figure 9, where we have plotted the difference between the real period P_Re(E) and the ephemeris period P_Eph (0^d.303117067) - in units of 10⁻6 day- as a function of time.

Fig. 9

From the study of the color indices we can conclude that the system is of late spectral type (K0+K1.5).

The system was found to have mass ratio q = 0.648 approaching the upper limit of the range 0.145 < q < 0.88 which is a W-type property, (note, q < 0.54 for A-type, Rucinski, [23]). In addition, the shapes of the light curves appear to have a moderate activity (seen between phase 0.75 and 0.9 of Figure 3).

The two spots were found on both components (Table 6, and Figure 6). The presence of star spots reveals the magnetic activity that characterizing the chromospheric activity in late W UMa and RS CVn stars.

Fig. 6

The schematic picture of the Roche lobe (Figure 5) showed moderate outer convective zone with common radiative envelope for both components which is a property of W-type W UMa systems (Rucinski, [23]).

The study of the O-C diagram of IK Boo showed a long term orbital period modulation decrease of rate dP/dt = −1.68 × 10⁻⁷d/yr, that can be interpreted to be due to mass transfer from the more to the less massive component.

The light curves solution showed presence of star spots on both components. Such magnetic activity is recommended to be the reason of the sine-like variation seen in the (O−C)₂ diagram (Figure 8). However, one cannot dismiss a probable detection of a third body orbiting the system, which can be proved by a periodic behaviour of the O-C diagram. The presence of a third body has to be supported by more observed minima time of mid-eclipse, and/or spectroscopic observations.

Spectroscopic observations for the binary system IK Boo are strongly recommended in order to determine its physical parameters and to verify the obtained photometric results. Also, observing more minima times are needed to re-study the period variability in order to decide among, is the alternating change in its period cyclic or periodic?