IU Cancri: a solar-type contact binary with mass transfer

Eclipsing binaries are key objects for study, which can provide fundamental stellar properties and critical tests on the theories of stellar evolution and structure. The theory of thermal relaxation oscillations (see the review by Webbink 2003) postulates that a binary system can oscillate between contact and semi-detached states. Orbital period variations may provide some straightforward information, such as mass transfer and loss, and magnetic activity, and reveal an additional companion body around the binary star. Recently, the spectra of contact binaries, included in the LAMOST¹ (Luo et al. 2015) database, were statistically analyzed by Qian et al. (2017). Therefore, it is necessary to monitor some binary systems at special stages, which may provide some key observational evidence on the formation and evolution of contact binaries.

IU Cnc [α_J2000.0 = 09^h00^m59.06^s, δ_J2000.0 = +12° 58'51.87''] is an EW-type binary identified from the Northern sky Variability survey (Woźniak et al. 2004). Its light variability ranges from 11.80mag to 12.36mag. Kreiner (2004) determined an orbital period of 0.4216450 d, which was later updated to 0.4216475 d (Otero & Wils 2005). This short-period eclipsing binary was then successively listed in three catalogs derived from sky surveys (Avvakumova et al. 2013; Drake et al. 2014; Huber et al. 2016). From Gaia Data Release 2, the absolute stellar parallax for IU Cnc is 2.0684 ± 0.0422 mas (Gaia Collaboration 2018), which determines a distance of 483.5 ± 9.9 pc from Earth. Three spectra of IU Cnc are obtained from the LAMOST survey, which are displayed in Figure 1 The flare around the Hα line that was recorded on 2017 April 15 may be unremoved cosmic rays.

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The spectral information is listed in Table 1 The associated phases are computed by the epoch of the observed primary eclipse, HJD 2458080.3572 (see Table 4). From this table, the spectral type of the more massive component (i.e., the primary) should be G2, because its observed phase (i.e., 0.869) only approaches the primary eclipse, indicating it is a W-type contact binary (see Sect. 3). Except for several light minimum times, no photometry or period analysis for this solar-type binary IU Cnc has been published up to now.

New photometry of IU Cnc was acquired from November 2017 to March 2018, by employing the 80-cm telescope (Zheng et al. 2008) and the 85-cm telescope (Zhou et al. 2009) at Xinglong Station (XLs) of National Astronomical Observatories, Chinese Academy of Sciences (NAOC), and the 1.0-m telescope operated by Yunnan Astronomical Observatories (YNAO). These three telescopes are equipped with the standard Johnson UBVR_cI_c filters. All photometric reductions were carried out by using IRAF in standard mode, including bias and dark subtraction, and flat-field correction.

In the observing process, TYC 817-2361-1 (V = 11.21 ± 0.11 mag) and TYC 817-2308-1 (V = 11.43 ± 0.12 mag) were chosen as comparison and check stars, respectively. Detailed information about the observations is given in Table 2 The typical exposure times depended on weather. The standard error is determined by the magnitude difference between the comparison and check stars. The individual differential magnitudes (i.e., Δm = m_var – m_comp) with their associated Heliocentric Julian Dates (i.e., HJDs) in 2018 are listed in Table 3. The complete light curves, i.e., 577 data in B and 594 data in V, are displayed in the left panel of Figure 2 and the corresponding phases are computed by Equation (1) (see Sect. 3). The amplitudes of variable light are 0.472 mag in B and 0.506 mag in V bands. Two eclipses are shown in the right panel of Figure 2. From this figure, the primary eclipse is a total one with a duration of 37 min, implying that IU Cnc is a W-type contact binary. This kind of total eclipse occurs in other contact binaries, such as V343 Ori (Yang et al. 2008), AS CrB (Liu et al. 2017) and EF Dra (Yang 2012). The long duration of the total eclipse indicates that the mass ratio may be small or orbital inclination is large. From our new data, we determined several light minimum times, which are written in Table 4.

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For the eclipsing binary IU Cnc, no period analysis has been performed up till now. From the O – C gateway², we compiled all eclipse times together with seven newly observed ones.

Table 5 provides 24 available light minimum times, including five photoelectric and 19 CCD measurements. With the weights from observed errors, we update a new ephemeris as follows,

$$\begin{eqnarray}\begin{array}{ll}{\rm{Min}}.{\rm{I=HJD}} & 2452500.1058(20)\\ & +0.42164408(23)\times E,\end{array}\end{eqnarray} \tag{ 1 }$$

whose standard derivation in a parenthesis is in the unit of the last decimal place. The residuals, (O – C)_i, are listed in Table 5. The corresponding O – C curve is displayed in the upper panel of Figure 3 From this figure, the orbital period apparently shows a secular increase. A linear least-squares solution with weights leads to the following equation,

$$\begin{eqnarray}\begin{array}{lll}{(O-C)}_{i} & = & 0.0330(1)-7.53(1)\times {10}^{-6}E\\ & & +4.004(2)\times {10}^{-10}{E}^{2}.\end{array}\end{eqnarray} \tag{ 2 }$$

The final residuals, (O – C)_f, are also listed in Table 5, and are plotted in the lower panel of Figure 3. From the quadratic coefficient of Equation (2), we can easily determine a period increase rate of dP/dt = +6.93(4) × 10⁻⁷ d yr⁻¹.

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On five nights in February and March of 2018, we first obtained two-color light curves, which are used to derive the photometric solution by the 2015 version of the Wilson-Devinney Code³ (Wilson & Devinney 1971; Wilson & van Hamme 2016). As displayed in the left panel of Figure 2, IU Cnc is a total contact binary, whose geometric elements are reliable only from light curves. In the calculation, the limb darkening, gravity darkening, and albedo coefficients are taken from the literature (van Hamme 1993; Lucy 1967; Ruciński 1973). The adjustable parameters are listed as follows: T₁, Ω_1,2, L₁ and q.

The spectra of IU Cnc are displayed in Figure 1, whose phases are given in Table 1. For the W-subtype binary seen in Figure 2(a), the more massive component (i.e., the primary) is occulted by the less massive one (i.e., the secondary) at a deep eclipse time (i.e., zero phase). The observed spectrum should be attributed to radiation from the primary component. Therefore, the spectral type of the primary is G2. Its mean effective temperature of T_p = 6075 ± 120 K is taken from Table 1. Moreover, the spectral type of F9 may result from the spectrum being polluted by the secondary component.

Due to lack of a mass ratio, we first preformed a series of solutions deduced from BV light curves. The mass ratio ranges from 0.5 to 6.0 with a step of 0.5. The contact configuration is always assumed. The resulting residuals versus mass ratio (i.e., Σ and q) are displayed in Figure 4(a), where a minimum value of Σ occurs around q = 4. This indicates that IU Cnc is a W-subtype contact binary. Then we consider q as a free parameter. The final photometric solution is derived and listed in Table 6 The calculated light curves are shown in Figure 2(a) as solid lines. Their corresponding residuals (o – c) (i.e., observed values minus theoretical ones), are displayed in Figure 4(b). Although small distortions still exist around phase 0.5, the overall trend of BV observations is described by our photometric solution very well. This may be similar to another previously studied binary, WW Gem (Yang et al. 2014). The fill-out factor for this binary is f = 30.2% ± 0.3%.

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Table 6. Photometric Elements of the Contact Binary IU Cnc

Parameter	Star 1 (Sec.)	Star 2 (Pri.)
q = M2/M1	4.014 ± 0.004
i(°)	80.43 ± 0.12
T(K)	6272 ± 4	6075 ± 118a
A	0.5	0.5
g	0.32	0.32
X, Y	+0.649, +0.218	+0.649, +0.217
xB,yB	+0.831, +0.182	+0.832, +0.179
xV,yV	+0.751, +0.254	+0.752, +0.252
Ω	7.7395 ± 0.0053
bℓiB	0.2618 ± 0.0006	0.7382 ± 0.0015
ℓiV	0.2523 ± 0.0006	0.7477 ± 0.0018
rpole	0.2595 ± 0.0013	0.4810 ± 0.0020
rside	0.2717 ± 0.0014	0.5230 ± 0.0023
rback	0.3152 ± 0.0017	0.5505 ± 0.0029
$\Sigma {(O-C)}_{i}^{2}$	0.8587
f	30.2% ± 0.3%

^aThe mean effective temperature for Star 2 (i.e., the primary component) is taken from the LAMOST data. ^bℓ_i = L_i/(L₁ + L₂).

According to the spectral type of G2 for IU Cnc, the mass of the primary is adopted to be M_p = 1.0( ± 0.02) M_⊙ (Drilling & Landolt 2000), but the associated error depends on the uncertainty of its effective temperature. Combined with the photometric elements in Table 6, other absolute parameters for IU Cnc are given as follows, M_s = 0.25( ± 0.08) M_⊙, R_p = 1.36( ± 0.11) R_⊙, R_s = 0.74( ± 0.06) R_⊙, L_p = 2.24( ± 0.35) L_⊙, and L_s = 0.75( ± 0.11) L_⊙.

The orbital period of IU Cnc may be undergoing a secular increase as described by Equation (2). This situation appears in other W-type contact binaries, which are listed in Table 7 From this table, the period increase rate is typical for this kind of binary. The period increase may generally be attributed to mass transfer from the less massive component to the more massive one. Assuming conservative transfer, its mass transfer rate may be computed by the following equation (Singh & Chaubey 1986),

$$\begin{eqnarray}&&\frac{\dot{P}}{P}=3\frac{1-q}{q}\frac{{\dot{M}}_{{\rm{p}}}}{{M}_{{\rm{p}}}}\,,\end{eqnarray} \tag{ 3 }$$

where the mass ratio is q = M_s/M_p. Inserting , P, q and M_p into Equation (3), the rate of mass transfer is dM_p/dt = +1.82( ± 0.01) × 10⁻⁷ M_⊙ yr⁻¹. This will result in the mass ratio increasing with mass transfer, which causes the inner and outer critical Lagrangian surfaces to inflate. Finally, the Roche lobe of such a binary system approximates the inner critical Lagrangian surface. In this case, the binary will evolve into a "broken-contact" configuration as predicted by the thermal relaxation model (Webbink 2003).

Therefore, IU Cnct provides more good observational evidence supporting the thermal relaxation oscillation model (TRO; Webbink 2003), and resembles other binaries, such as DD Com (Zhu et al. 2010), II Per (Zhu et al.2009), RV Psc (He & Qian 2009) and UU Lyn (Zhu et al. 2007).

In future observations, it will be necessary to obtain radial velocity curves and more eclipse times for IU Cnc in order to determine the absolute parameters and to identify the orbital period increase.

All authors express thanks to the referee for his/her helpful comments. This research has received funding from the National Natural Science Foundation of China (Nos. 11873003 and 11473009), the Natural Science Research Project (No. KJ 2017A850) and the Outstanding Young Talents Program (No. gxyq2018161) of the Educational Department of Anhui Province. New photometry of IU Cnc is performed by using 80-cm and 85-cm telescopes at the XLS of NAOC. This work was partially supported by the Open Project Program of the Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences.