New Photometric Investigation of the Solar-Type Shallow-Contact Binary HH Bootis

1Yunnan Observatories, Chinese Academy of Sciences (CAS), P. O. Box 110, 650216 Kunming, China 2Key Laboratory of the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, P. O. Box 110, 650216 Kunming, China 3Center for Astronomical Mega-Science, Chinese Academy of Sciences, Beijing 100012, China 4China University of Petroleum-Beijing at Karamay, Anding Road 355, 834000 Karamay, China


Introduction
HH Boo (GSC03472-00641, NSVS 5100852) was first listed as a star with a magnitude of  = 11.m 32 and a colour index of ( − ) = 0. m 45 in the TYCHO-2 Catalogue [24].The variability of HH Boo was discovered by Maciejewski et al. [2].They reported that HH Boo was a EW-type binary system with a period of almost 8 hours from 214 data points collected during 12 nights between April 19 and May 7, 2003.The depths of the primary and secondary minima on their light curves are Δ  = 0. m 50 and 0. m 39, respectively.They gave a preliminary ephemeris for the primary minimum as .= 2452764.50965(30) + 0.318618 (81) × .(1) The spectrum of HH Boo is most similar to G5III type from their optical spectra in the blue.The first radial-velocity studies of HH Boo have been done by Maciejewski & Ligeza [25].They estimate the radii and the masses and derive a mass ratio  2 / 1 = 0.633 (42),  1 sin 3  = 0.78(8) M ⊙ , and  2 sin 3  = 0.49(5) M ⊙ .Recently, a new period distribution for EW-type binaries was given by Qian et al. [26,27] based on the orbital periods of 40646 systems given in VSX (the international variable star index [28]).The period (0.319 d) of HH Boo is close to the peak of the distribution for EWs indicating that it is a typical EW-type binary.
The first photometric multicolor light curves in , , and  bands were published by Dal & Sipahi [16] that were obtained with 35 cm SchmidtCCassegrain type MEADE telescope at the Ege University Observatory.As shown in Figure 3 in their paper, their light curves showed a positive O'Connell effect [29] where the maxima following the primary minima are higher than the others.The asymmetries of the light curves may be caused by stellar dark-spot activities (e.g., [30]).They demonstrated that HH Boo is most likely a member of the A-type subclass of W UMa binaries and derived absolute parameters of HH Boo.A continuous decrease in the orbital period with a rate of / = −9.60 × 10 −7 d yr −1 was detected by them that was explained by either mass transfer from the secondary to the primary or mass loss from the system.HH Boo was later observed in 2011 and 2012 by using the 0.40 m Meade-LX200 GPS telescope at Ankara University Observatory [31] and new CCD light curves in  bands were obtained.Their light curves also show positive O'Connell effect.By analyzing their  light curves and published radial velocity data, they determined the parameters of the binary.They found that HH Boo is W-subclass contact system and the asymmetry of the light curves was interpreted by one cool star spot region located on the primary star (the hotter, less massive component).They reported that the − diagram showed a cyclic variation with a period of  3 = 7.39 yr and an amplitude of  3 = 0.00227 d.

Observations
2.1.Spectroscopy.To determine the spectrum of the solartype contact binary, the low-resolution spectrograms for HH Boo were observed by using the OMR spectrograph of the 2.16 m telescope at Xinglong station of National Astronomical Observatories (Xinglong-2.16m) in China on 2017 June 4.We chose a slit width of 1.  8 and the Grism-14 with a wavelength ranging from 3200 Å to 7500 Å ( [33]).The exposure time is 15 min.Reduction of the spectra was performed by using IRAF packages (IRAF is supported by the National Optical Astronomy Observatories (NOAO) in Tucson, Arizona http://iraf.noao.edu/iraf/web/iraf-homepage.html),including bias subtraction, flat-fielding, and cosmic-ray removal.Finally, the one-dimensional spectrum was extracted.Using the winmk software (http://www.appstate.edu/∼grayro/MK/winmk.htm), the normalized spectra are displayed in the upper pane of Figure 1.On the basis of the stellar spectral classification ( [32]), we determined its spectral type to be G2V, which is similar with G5III obtained by [2].

Multicolor CCD Photometric
Observations.HH Boo was monitored photometrically in 13 nights from December 25, 2010, to April 23, 2018, by using the next three telescopes: the 1.0 m telescope at Yunnan observatories (YNOs-1m), the 60 cm telescope at Yunnan observatories (YNOs-60cm), and the 85 cm telescope at Xinglong station of National Astronomical Observatories (Xinglong-85cm) in China.The camera attached on Cassegrain focus of the 1.0 m telescope is DW436 CCD from Andor Technology, whose field is about 7  .5 × 7  .5.The CCD camera used on the 60 cm telescope is the same as that used on the 1.0 m telescope but has a larger field of view, about 12  .5 × 12  .5.
The first complete , , , and  light curves were obtained during three nights on December 25, 27, and 30, 2010, with PI 512 × 512 TE CCD camera mounted on the Xinglong 85 cm telescope.The effective field of view of the photometric system is 14  .5 × 14  .5 at prime focus.The filter system was close to the standard Johnson-Cousin-Bessel  CCD photometric system [34].The integration times were 40 s, 30 s, 20 s, and 10 s for , , , and  bands, respectively.For each band, about 200 images were obtained ( = 197,  = 196,  = 196, and  = 196).One image of the  band is shown in Figure 2. GSC03472-00043 and GSC03472-01201 whose coordinates and magnitudes are listed in Table 1 were chosen as the comparison and the check star for HH Boo, respectively.The comparison and check stars are close enough to the variable that the range of air-mass difference between both of them was very small.Therefore, an extinction correction was not made.The PHOT task (which measures magnitudes for a list of stars) in the IRAF aperture photometry package was used to reduce the observed images, including a flat-fielding correction process.
The CCD photometric data obtained on December 25, 27, and 30, 2010, in , , , and  bands are listed in Tables 2-5 and shown in Figure 3, respectively.The complete CCD light curves in the four bands with respect to the linear ephemeris, .() = 2455556.34396+ 0 d .318666208× , (2)

Orbital Period Investigation
The changes in the orbital period of HH Boo have been investigated by several authors (e.g., [16,31]).Dal & Sipahi [16] found the period was decreasing at a rate of / = −9.60 ×   The black solid dots refer to the data collected by G ü rol et al. [31], the blue solid dots refer to the data by WASP database, the red solid dots refer to the data obtained by Nelson [21], Hubscher $ Lehmann [22] or Hubscher [23], and green solid dots refer to the data obtained by us.
10 −7 d yr −1 that could be explained by mass transfer or/and angular momentum loss via magnetic braking.Subsequently, G ü rol et al. [31] reported that the period of the binary showed a cyclic change by adding some eclipse times.However, the data did not cover the whole cycle of the  −  curve.
To investigate the period changes, we monitored the system since December 25, 2010.By using a least-squares parabolic fitting method, 30 individual CCD times of light minimum were determined and listed in Table 6.On the other hand, Wide Angle Search for Planets (WASP) is an international consortium of several academic organisations performing an ultrawide angle search for exoplanets using transit photometry [35,36].WASP database (https://wasp.cerit-sc.cz/)releases many photometric data of HH Boo obtained from 2004 to 2007.By using those data, 79 times of light minimum were obtained and are including in Table 7.
All available photoelectric and CCD times of light minimum were compiled and are shown in column 1 of Table 7.The ( − ) values (observational times of light minimumcalculational times of light minimum) calculated by (2) are also listed in column 6 of Table 7 and plotted in the upper panel of Figure 5.The black solid dots in the figure refer to the data collected by G ü rol et al. [31], the blue solid dots refer to eclipse times computed with WASP data, the red solid dots refer to the data obtained by Nelson [21], Hubscher & Lehmann [22] or Hubscher [23], and green solid dots refer to the data observed by us.As displayed in the figure, the  −  diagram may show a cyclic variation that could be explained by the light travel time effect via the presence of a third body (e.g., [37]).A least-squares solution yields the following ephemeris: ( With this ephemeris, a cyclic oscillation with a period of  3 = 6.58 (11) yr and an amplitude of  3 = 0.0018(1) d is determined.The residuals from (3) are showed in the lower panel of Figure 5 and listed in column 7 of Table 7.

Photometric Solutions
Photometric solutions of HH Boo were obtained by Dal & Sipahi [16] and G ü rol et al. [31].However, those light curves were obtained with two small telescopes and were showing a little large scatter.As shown in Figure 4, the light curves are in higher precision and almost symmetric, which enables determining reliable photometric parameters.To understand its geometrical structure and evolutionary state, the , , , and  light curves shown in Figure 4 were analyzed by using the W-D code [38][39][40][41].During the solution process, the effective temperature of star 1 was chosen as  1 = 5680 K according to our result G2V and G ü rol et al. [31].As shown in Figure 4, the depths of both minima are nearly the same indicating the nearly same temperature of both components.Therefore, we take the same values of the gravity-darkening coefficients and the bolometric albedo for both components, i.e., g 1 = g 2 = 0.32 [42] and A 1 = A 2 = 0.5 [43].The limb-darkening coefficients were used according to Claret & Gimenez [44] (x and y are the bolometric and bandpass limbdarkening coefficients).The adjustable parameters include the orbital inclination (); the mean temperature of star 2 ( 2 ); the monochromatic luminosity of star 1 ( 1 ,  1 ,  1 ,  1 ); and the dimensionless potential of star 1 (Ω 1 = Ω 2 , mode 3 for overcontact configuration).We chose the initial value of  as 1.70 obtained by G ü rol et al. [31] and made it as an adjustable parameter.Then, we performed a differential correction until it converged and final solutions were derived.The solution converged at  = 1.703 (31).The photometric solutions are listed in column 2 Table 8 and the theoretical light curves computed with those photometric parameters are plotted in Figure 6.The light curves are nearly symmetric and no spotted solution is needed.The solution reveals that HH Boo is a W-type shallow-contact binary with a degree of contact factor of  = 12.86%(0.73%)and a mass ratio of  = 1.703 (31).
The geometrical structures at phases 0.0, 0.25, 0.5, and 0.75 are shown in Figure 7.

Discussions and Conclusions
High-precision CCD light curves in , , , and  bands obtained in 2010 are presented and were analyzed by the W-D method.Our solution confirms that HH Boo is a W-type overcontact binary system with a mass ratio of  = 1.703 (31).The temperature of the less massive component is about Δ = 359 K higher than that of the more massive one.The fill-out factor is about 12.86%(±0.73%)indicating that HH Boo is a shallow-contact binary system.The observational properties of HH Boo are similar to some EW-type contact binaries such as AE Phe [45], V524 Mon [46], NSVS 2669503 [47], DE Lyn [48], AQ Boo [49], GK Aqr [50], and V532 Mon [51].All of them are W-type shallow-contact systems with  < 20% that are at the beginning phase of contact (e.g., [37]).They may be formed from detached EAs through a combination of Case A mass transfer and angular momentum loss via magnetic braking (e.g., [27,52]), and the magnetic braking is more weaker than that of Pulsar (e.g., [53,54]).As shown in Figure 4, our light curves observed in 2010 are symmetric that may indicate weak photospheric activity in the system (e.g., [55,56]).However, the light curves in , , and  bands obtained in 2011 by Dal & Sipahi [16] show a positive O'Connell effect (see Figure 3 in their paper).The  light curves published by G ü rol et al. [31] also show a positive O'Connell effect.These properties indicate that the light curve of HH Boo is variable.Our photometric solution reveals that HH Boo is a W-type subclass binary, while Dal & Sipahi [16] demonstrated that HH Boo is most likely a member of the A-type subclass of W UMa binaries.The solutions obtained by G ü rol et al. [31] suggest the EWtype binary is a W-type.They modeled the asymmetry of the maxima by using one cool star spot region located on the primary star.HH Boo is a solar-type contact binary (Sp.= G2V) with a period of 0.318666 days where both components rotate very fast.The variation of the light curve may be caused by the magnetic activities.
To study the variations in the orbital period, we monitored the binary for about 8 years and 30 individual eclipse times were obtained.Moreover, by using WASP data, 79 times of light minimum were derived.Our analyses show that the  −  diagram of HH Boo undergoes a cyclic oscillation.As shown in Figure 5, our data cover the whole cycle well.The cyclic oscillation could be more plausibly explained as the light-travel time effect via the presence of a third body (e.g., [57,58]).The period of the third body orbiting around

Figure 1 :
Figure 1: Normalized spectra of the eclipsing binary HH Boo from 3300 Å to 5700 Å, observed on 2017 June 4 with the 2.16 m telescope at the Xinglong station of National Astronomical Observatories of China.The lower pane is the spectrum data of G2V type star from the stellar spectral classification ([32]).

Figure 2 :
Figure 2: One CCD image about HH Boo obtained by 85 cm telescope at Xinglong station of National Astronomical Observatories (Xinglong-85cm) in China including variable (V), comparison (C), and check stars (K).

Figure 4 :Figure 5 :
Figure 4: CCD photometric light curves in the , , , and  bands obtained using the Xinglong 85 cm telescope in 2012.The magnitude differences between the comparison and the check stars are shown in the low pane.

iFigure 8 :
Figure 8: Relation between the orbital radius of the third body and the orbital inclination, and the mass and the orbital inclination for an assumed third body in HH Boo.

Table 1 :
Coordinates and magnitudes of HH Boo, the comparison, and the check stars.

Table 6 :
New CCD times of light minimum for HH Boo.

Table 7 :
( − ) values of light minimum times for HH Boo.