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

Authors: Jia-jia He; Jing-jing Wang
Journal: Advances in Astronomy
 (2019)

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## Abstract

The short-period solar-type contact binary HH Boo was monitored photometrically for about 8 years. It is found that the CCD light curves in theB, V, R, and I bands obtained in 2010 are symmetric, while the multicolor light curves observed in 2011 and 2012 by several investigators showed a positive O’Connell effect where the maxima following the primary minima are higher than the other ones. This indicates that the light curve of the solar-type contact binary is variable. By analyzing our multicolor light curves with the Wilson-Devinney code (W-D code), it is confirmed that HH Boo is a W-type shallow-contact binary system with a mass ratio of q = 1.703(31) and a degree of contact factor of f = 12.86%(0.73%). By including 109 new determined times of light minimum together with those compiled from the literature, it is detected that the O-C diagram shows a cyclic oscillation with a period of T3 = 6.58(11) yr and an amplitude of A3 = 0.0018(1) d. The cyclic change may reveal the presence of an extremely cool third body orbiting the central binary.


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## Body

## 1. Introduction

HH Boo (GSC03472-00641, NSVS 5100852) was first listed as a star with a magnitude ofV = 11.m32 and a colour index of (B-V) = 0.m45 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 ΔmV = 0.m50 and 0.m39, respectively. They gave a preliminary ephemeris for the primary minimum as(1)Min.I=2452764.5096530+0.31861881×E.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 M2/M1 = 0.633(42), M1sin3i = 0.78(8) M⊙, and M2sin3i = 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 inB, V, and R 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 dP/dt = -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 BVRI bands were obtained. Their light curves also show positive O’Connell effect. By analyzing their BVRI 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 O-C diagram showed a cyclic variation with a period ofT3 = 7.39 yr and an amplitude of A3 = 0.00227 d.


## 2. Observations

### 2.1. Spectroscopy

To determine the spectrum of the solar-type 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 of1.′′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].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]).


### 2.2. 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 about7′.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 completeB, V, R, and I 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 UBVRI CCD photometric system [34]. The integration times were 40 s, 30 s, 20 s, and 10 s for B, V, R, and I bands, respectively. For each band, about 200 images were obtained (B = 197, V = 196, R = 196, and I = 196). One image of the B 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.Table 1
Coordinates and magnitudes of HH Boo, the comparison, and the check stars.
Stars α 2000 δ 2000 B(mag) V(mag)  HH Boo 1 4 h 2 1 m 44.0750 9 s + 4 6 ∘ 41 ′ 59.3524 ′ ′ 11.80 11.021 GSC03472-00043 (C) 1 4 h 2 1 m 46.6002 3 s + 4 6 ∘ 43 ′ 49.4364 ′ ′ 13.57 12.87 GSC03472-01201 (K) 1 4 h 2 1 m 37.3118 0 s + 4 6 ∘ 46 ′ 18.5231 ′ ′ 14.38 13.66Figure 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).The CCD photometric data obtained on December 25, 27, and 30, 2010, inB, V, R, and I 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,(2)Min.IHJD=2455556.34396+0d.318666208×E,are shown in Figure 4. The magnitude differences between the comparison and the check stars are also shown in the low pane of this figure. The epoch in (2) is obtained by us (the mean value of four band light minima) and the period is from Gu¨rol et al. [31].Table 2
The observations inB band for HH Boo (Hel. JD 2,455,500+).
Hel. JD △ m Hel. JD △ m Hel. JD △ m Hel. JD △ m  56.31655 -1.504 56.40803 -1.753 58.39315 -1.516 61.34519 -1.740 56.31864 -1.490 56.40986 -1.751 58.39498 -1.498 61.34700 -1.732 56.32046 -1.465 56.41168 -1.756 58.39679 -1.490 61.34882 -1.742 56.32228 -1.447 58.30742 -1.692 58.39862 -1.469 61.35064 -1.745 56.32411 -1.424 58.30924 -1.712 58.40045 -1.444 61.35245 -1.745 56.32594 -1.402 58.31107 -1.700 58.40227 -1.427 61.35427 -1.747 56.32776 -1.379 58.31288 -1.714 58.40410 -1.413 61.35609 -1.755 56.32958 -1.353 58.31471 -1.729 58.40592 -1.398 61.35792 -1.759 56.33140 -1.334 58.31654 -1.728 58.40774 -1.373 61.35974 -1.757 56.33323 -1.306 58.31836 -1.750 58.40957 -1.367 61.36155 -1.763 56.33506 -1.288 58.32019 -1.757 58.41139 -1.357 61.36337 -1.753 56.33688 -1.278 58.32202 -1.746 58.41322 -1.348 61.36519 -1.756 56.33870 -1.260 58.32383 -1.760 58.41505 -1.348 61.36700 -1.760 56.34053 -1.255 58.32566 -1.765 58.41686 -1.348 61.36882 -1.750 56.34235 -1.242 58.32748 -1.766 61.27971 -1.353 61.37064 -1.748 56.34418 -1.241 58.32931 -1.773 61.28153 -1.360 61.37246 -1.751 56.34601 -1.250 58.33114 -1.773 61.28335 -1.349 61.37428 -1.738 56.34783 -1.245 58.33295 -1.775 61.28516 -1.343 61.37610 -1.730 56.34965 -1.275 58.33478 -1.782 61.28699 -1.343 61.37792 -1.727 56.35147 -1.292 58.33660 -1.778 61.28881 -1.356 61.37973 -1.727 56.35330 -1.298 58.33843 -1.774 61.29063 -1.354 61.38155 -1.720 56.35513 -1.314 58.34026 -1.789 61.29244 -1.366 61.38337 -1.713 56.35695 -1.347 58.34207 -1.768 61.29426 -1.400 61.38519 -1.708 56.35877 -1.359 58.34390 -1.775 61.29608 -1.406 61.38701 -1.696 56.36060 -1.385 58.34572 -1.775 61.29789 -1.424 61.38883 -1.691 56.36242 -1.420 58.34755 -1.766 61.29972 -1.434 61.39065 -1.675 56.36425 -1.436 58.34938 -1.767 61.30154 -1.463 61.39247 -1.669 56.36607 -1.464 58.35119 -1.771 61.30336 -1.477 61.39428 -1.664 56.36789 -1.485 58.35302 -1.750 61.30517 -1.491 61.39610 -1.650 56.36972 -1.500 58.35485 -1.750 61.30699 -1.513 61.39792 -1.639 56.37154 -1.520 58.35667 -1.748 61.30881 -1.530 61.39974 -1.638 56.37337 -1.543 58.35850 -1.737 61.31063 -1.551 61.40156 -1.622 56.37520 -1.556 58.36031 -1.738 61.31246 -1.559 61.40338 -1.607 56.37702 -1.581 58.36214 -1.723 61.31427 -1.574 61.40520 -1.591 56.37884 -1.591 58.36397 -1.714 61.31609 -1.588 61.40702 -1.586 56.38067 -1.607 58.36579 -1.714 61.31791 -1.605 61.40883 -1.571 56.38249 -1.620 58.36762 -1.701 61.31972 -1.612 61.41065 -1.560 56.38432 -1.626 58.36943 -1.688 61.32154 -1.630 61.41247 -1.537 56.38614 -1.645 58.37126 -1.681 61.32336 -1.635 61.41428 -1.518 56.38796 -1.650 58.37309 -1.667 61.32518 -1.647 61.41611 -1.495 56.38979 -1.660 58.37491 -1.657 61.32700 -1.644 61.41793 -1.480 56.39162 -1.683 58.37674 -1.651 61.32882 -1.668 61.41975 -1.454 56.39344 -1.687 58.37855 -1.637 61.33064 -1.677 61.42156 -1.429 56.39527 -1.693 58.38038 -1.623 61.33246 -1.681 61.42338 -1.412 56.39708 -1.703 58.38221 -1.613 61.33427 -1.699 61.42520 -1.387 56.39891 -1.712 58.38403 -1.605 61.33609 -1.694 61.42701 -1.358 56.40074 -1.726 58.38586 -1.586 61.33791 -1.716 61.42883 -1.336 56.40256 -1.732 58.38768 -1.568 61.33972 -1.710 56.40439 -1.737 58.38950 -1.552 61.34154 -1.722 56.40621 -1.737 58.39133 -1.534 61.34337 -1.721Table 3
The observations inV band for HH Boo (Hel. JD 2,455,500+).
Hel. JD △ m Hel. JD △ m Hel. JD △ m Hel. JD △ m 56.31712 -1.644 56.40860 -1.856 58.39372 -1.626 61.34757 -1.843 56.31920 -1.607 56.41042 -1.857 58.39554 -1.608 61.34939 -1.838 56.32102 -1.584 56.41225 -1.864 58.39736 -1.595 61.35121 -1.844 56.32285 -1.563 58.30797 -1.796 58.39919 -1.569 61.35302 -1.852 56.32468 -1.550 58.30980 -1.799 58.40101 -1.551 61.35484 -1.858 56.32649 -1.521 58.31163 -1.822 58.40284 -1.538 61.35666 -1.866 56.32832 -1.494 58.31345 -1.819 58.40467 -1.515 61.35847 -1.861 56.33015 -1.477 58.31528 -1.825 58.40648 -1.502 61.36029 -1.860 56.33197 -1.461 58.31710 -1.833 58.40831 -1.489 61.36212 -1.856 56.33380 -1.432 58.31893 -1.836 58.41013 -1.484 61.36394 -1.863 56.33563 -1.404 58.32075 -1.861 58.41196 -1.474 61.36575 -1.859 56.33744 -1.404 58.32257 -1.857 58.41379 -1.479 61.36757 -1.861 56.33927 -1.393 58.32440 -1.878 58.41560 -1.466 61.36939 -1.859 56.34109 -1.385 58.32622 -1.864 61.28028 -1.480 61.37121 -1.855 56.34292 -1.391 58.32805 -1.870 61.28210 -1.479 61.37302 -1.846 56.34475 -1.384 58.32987 -1.875 61.28391 -1.462 61.37484 -1.833 56.34656 -1.377 58.33169 -1.874 61.28573 -1.469 61.37666 -1.836 56.34839 -1.386 58.33352 -1.877 61.28755 -1.486 61.37848 -1.834 56.35022 -1.414 58.33535 -1.875 61.28936 -1.482 61.38030 -1.828 56.35204 -1.398 58.33716 -1.877 61.29118 -1.487 61.38212 -1.826 56.35387 -1.441 58.33899 -1.881 61.29301 -1.500 61.38394 -1.813 56.35568 -1.457 58.34081 -1.863 61.29483 -1.532 61.38575 -1.808 56.35751 -1.488 58.34264 -1.877 61.29664 -1.539 61.38757 -1.797 56.35934 -1.500 58.34447 -1.868 61.29846 -1.548 61.38939 -1.793 56.36116 -1.515 58.34629 -1.872 61.30028 -1.567 61.39120 -1.784 56.36299 -1.544 58.34811 -1.867 61.30210 -1.585 61.39303 -1.776 56.36482 -1.563 58.34993 -1.854 61.30393 -1.597 61.39485 -1.769 56.36663 -1.578 58.35176 -1.862 61.30574 -1.614 61.39667 -1.765 56.36846 -1.599 58.35359 -1.858 61.30756 -1.633 61.39849 -1.751 56.37028 -1.618 58.35541 -1.860 61.30938 -1.650 61.40030 -1.744 56.37211 -1.651 58.35724 -1.841 61.31119 -1.665 61.40212 -1.724 56.37394 -1.662 58.35906 -1.826 61.31301 -1.688 61.40394 -1.719 56.37575 -1.679 58.36088 -1.829 61.31483 -1.693 61.40575 -1.706 56.37758 -1.692 58.36271 -1.819 61.31665 -1.705 61.40758 -1.699 56.37941 -1.709 58.36453 -1.811 61.31847 -1.717 61.40940 -1.681 56.38123 -1.727 58.36635 -1.811 61.32029 -1.734 61.41122 -1.669 56.38306 -1.718 58.36818 -1.805 61.32211 -1.738 61.41303 -1.645 56.38488 -1.745 58.37000 -1.798 61.32393 -1.743 61.41485 -1.631 56.38670 -1.754 58.37183 -1.784 61.32574 -1.763 61.41667 -1.612 56.38853 -1.764 58.37365 -1.775 61.32756 -1.758 61.41848 -1.593 56.39036 -1.769 58.37548 -1.755 61.32938 -1.769 61.42030 -1.570 56.39218 -1.771 58.37730 -1.757 61.33119 -1.790 61.42213 -1.548 56.39401 -1.789 58.37912 -1.741 61.33302 -1.799 61.42395 -1.525 56.39583 -1.799 58.38095 -1.729 61.33484 -1.790 61.42576 -1.503 56.39765 -1.806 58.38277 -1.723 61.33666 -1.813 61.42758 -1.475 56.39948 -1.811 58.38460 -1.706 61.33847 -1.817 61.42940 -1.462 56.40130 -1.827 58.38643 -1.698 61.34029 -1.820 56.40313 -1.832 58.38824 -1.678 61.34211 -1.822 56.40496 -1.846 58.39007 -1.655 61.34392 -1.835 56.40677 -1.841 58.39189 -1.639 61.34574 -1.834Table 4
The observations inR band for HH Boo (Hel. JD 2,455,500+).
Hel. JD △ m Hel. JD △ m Hel. JD △ m Hel. JD △ m  56.31757 -1.722 56.40905 -1.944 58.39417 -1.721 61.34801 -1.935 56.31965 -1.693 56.41087 -1.937 58.39599 -1.699 61.34983 -1.946 56.32147 -1.687 56.41270 -1.946 58.39781 -1.682 61.35166 -1.931 56.32330 -1.660 58.30843 -1.893 58.39964 -1.658 61.35347 -1.947 56.32513 -1.644 58.31026 -1.895 58.40146 -1.639 61.35529 -1.958 56.32695 -1.628 58.31207 -1.881 58.40329 -1.623 61.35711 -1.945 56.32877 -1.593 58.31390 -1.924 58.40510 -1.613 61.35892 -1.936 56.33059 -1.580 58.31573 -1.905 58.40693 -1.604 61.36074 -1.939 56.33242 -1.554 58.31755 -1.915 58.40876 -1.591 61.36256 -1.935 56.33425 -1.556 58.31938 -1.925 58.41058 -1.580 61.36438 -1.949 56.33607 -1.523 58.32119 -1.954 58.41241 -1.570 61.36619 -1.949 56.33790 -1.509 58.32302 -1.947 58.41423 -1.574 61.36801 -1.940 56.33972 -1.499 58.32485 -1.950 58.41605 -1.565 61.36984 -1.943 56.34154 -1.493 58.32667 -1.940 61.28072 -1.583 61.37166 -1.936 56.34337 -1.481 58.32850 -1.946 61.28254 -1.576 61.37347 -1.937 56.34519 -1.486 58.33033 -1.959 61.28436 -1.581 61.37529 -1.928 56.34701 -1.495 58.33214 -1.956 61.28618 -1.569 61.37711 -1.935 56.34884 -1.508 58.33397 -1.962 61.28800 -1.574 61.37893 -1.921 56.35066 -1.513 58.33579 -1.965 61.28982 -1.582 61.38075 -1.919 56.35249 -1.526 58.33762 -1.967 61.29163 -1.592 61.38257 -1.907 56.35432 -1.550 58.33944 -1.963 61.29345 -1.624 61.38439 -1.897 56.35614 -1.555 58.34126 -1.959 61.29528 -1.616 61.38620 -1.898 56.35796 -1.606 58.34309 -1.957 61.29710 -1.637 61.38802 -1.886 56.35979 -1.610 58.34491 -1.951 61.29891 -1.648 61.38984 -1.881 56.36161 -1.641 58.34674 -1.946 61.30073 -1.670 61.39166 -1.870 56.36344 -1.654 58.34857 -1.942 61.30255 -1.686 61.39347 -1.863 56.36526 -1.667 58.35038 -1.963 61.30436 -1.707 61.39529 -1.854 56.36708 -1.695 58.35221 -1.951 61.30618 -1.713 61.39712 -1.852 56.36891 -1.711 58.35404 -1.941 61.30801 -1.727 61.39894 -1.832 56.37073 -1.737 58.35586 -1.931 61.30983 -1.745 61.40075 -1.831 56.37256 -1.736 58.35769 -1.924 61.31164 -1.764 61.40257 -1.824 56.37439 -1.751 58.35950 -1.928 61.31346 -1.779 61.40439 -1.812 56.37620 -1.785 58.36133 -1.919 61.31528 -1.791 61.40621 -1.796 56.37803 -1.795 58.36316 -1.908 61.31710 -1.799 61.40802 -1.786 56.37985 -1.804 58.36498 -1.910 61.31891 -1.818 61.40984 -1.773 56.38168 -1.813 58.36681 -1.900 61.32073 -1.825 61.41167 -1.752 56.38351 -1.831 58.36862 -1.875 61.32256 -1.834 61.41349 -1.741 56.38533 -1.849 58.37045 -1.876 61.32438 -1.836 61.41530 -1.722 56.38715 -1.846 58.37228 -1.873 61.32619 -1.857 61.41712 -1.704 56.38898 -1.864 58.37410 -1.867 61.32801 -1.859 61.41894 -1.683 56.39080 -1.865 58.37593 -1.840 61.32983 -1.860 61.42075 -1.663 56.39263 -1.879 58.37774 -1.844 61.33165 -1.883 61.42257 -1.649 56.39446 -1.881 58.37957 -1.832 61.33346 -1.881 61.42439 -1.627 56.39627 -1.887 58.38140 -1.819 61.33528 -1.904 61.42622 -1.607 56.39810 -1.897 58.38322 -1.807 61.33710 -1.900 61.42803 -1.584 56.39993 -1.901 58.38505 -1.794 61.33893 -1.906 61.42985 -1.567 56.40175 -1.913 58.38686 -1.777 61.34074 -1.911 56.40358 -1.922 58.38869 -1.762 61.34256 -1.920 56.40539 -1.924 58.39052 -1.741 61.34438 -1.928 56.40722 -1.931 58.39234 -1.742 61.34619 -1.920Table 5
The observations inI band for HH Boo (Hel. JD 2,455,500+).
Hel. JD △ m Hel. JD △ m Hel. JD △ m Hel. JD △ m  56.31796 -1.828 56.40938 -2.026 58.39450 -1.812 61.34835 -2.028 56.31998 -1.809 56.41121 -2.038 58.39632 -1.798 61.35016 -2.030 56.32181 -1.800 56.41303 -2.034 58.39815 -1.776 61.35198 -2.026 56.32364 -1.793 58.30876 -1.985 58.39997 -1.764 61.35380 -2.036 56.32545 -1.750 58.31059 -1.993 58.40180 -1.747 61.35561 -2.032 56.32728 -1.721 58.31241 -2.003 58.40362 -1.734 61.35744 -2.042 56.32911 -1.711 58.31424 -2.030 58.40544 -1.727 61.35926 -2.035 56.33093 -1.701 58.31605 -2.004 58.40727 -1.703 61.36108 -2.038 56.33276 -1.671 58.31788 -2.027 58.40909 -1.700 61.36290 -2.040 56.33458 -1.638 58.31971 -2.020 58.41092 -1.679 61.36471 -2.040 56.33640 -1.636 58.32153 -2.022 58.41274 -1.682 61.36653 -2.025 56.33823 -1.630 58.32336 -2.020 58.41456 -1.671 61.36835 -2.031 56.34005 -1.635 58.32518 -2.035 58.41639 -1.679 61.37016 -2.036 56.34188 -1.613 58.32700 -2.043 61.28105 -1.679 61.37198 -2.018 56.34371 -1.634 58.32883 -2.058 61.28287 -1.676 61.37381 -2.026 56.34552 -1.602 58.33065 -2.037 61.28469 -1.665 61.37563 -2.017 56.34735 -1.633 58.33248 -2.063 61.28651 -1.684 61.37744 -2.012 56.34918 -1.628 58.33431 -2.063 61.28833 -1.681 61.37926 -2.004 56.35100 -1.660 58.33612 -2.058 61.29015 -1.700 61.38108 -1.997 56.35283 -1.629 58.33795 -2.056 61.29197 -1.721 61.38289 -1.997 56.35464 -1.685 58.33977 -2.036 61.29379 -1.711 61.38471 -1.989 56.35647 -1.689 58.34160 -2.050 61.29560 -1.729 61.38653 -1.989 56.35830 -1.684 58.34343 -2.045 61.29742 -1.722 61.38836 -1.976 56.36012 -1.728 58.34524 -2.038 61.29925 -1.745 61.39017 -1.974 56.36194 -1.726 58.34707 -2.020 61.30107 -1.774 61.39199 -1.964 56.36377 -1.762 58.34889 -2.041 61.30288 -1.792 61.39381 -1.960 56.36559 -1.795 58.35072 -2.013 61.30470 -1.811 61.39563 -1.957 56.36742 -1.802 58.35255 -2.038 61.30652 -1.823 61.39744 -1.943 56.36924 -1.820 58.35436 -2.023 61.30833 -1.836 61.39926 -1.928 56.37107 -1.840 58.35619 -2.024 61.31015 -1.840 61.40108 -1.934 56.37290 -1.857 58.35802 -2.017 61.31197 -1.865 61.40291 -1.912 56.37471 -1.874 58.35984 -2.025 61.31380 -1.875 61.40472 -1.904 56.37654 -1.872 58.36167 -2.017 61.31561 -1.898 61.40654 -1.901 56.37837 -1.884 58.36348 -2.004 61.31743 -1.923 61.40836 -1.876 56.38019 -1.905 58.36531 -1.970 61.31925 -1.914 61.41018 -1.875 56.38202 -1.914 58.36714 -1.993 61.32107 -1.921 61.41199 -1.859 56.38384 -1.930 58.36896 -1.975 61.32288 -1.927 61.41381 -1.840 56.38566 -1.944 58.37079 -1.974 61.32470 -1.937 61.41563 -1.826 56.38749 -1.960 58.37261 -1.957 61.32652 -1.963 61.41745 -1.807 56.38932 -1.958 58.37443 -1.953 61.32833 -1.944 61.41927 -1.788 56.39113 -1.956 58.37626 -1.957 61.33016 -1.956 61.42109 -1.770 56.39296 -1.975 58.37808 -1.928 61.33198 -1.967 61.42291 -1.757 56.39479 -1.979 58.37991 -1.923 61.33380 -1.983 61.42472 -1.731 56.39661 -1.985 58.38173 -1.920 61.33561 -1.997 61.42654 -1.725 56.39844 -1.996 58.38355 -1.901 61.33743 -1.991 61.42836 -1.688 56.40026 -2.000 58.38538 -1.879 61.33925 -2.003 61.43017 -1.680 56.40208 -2.017 58.38720 -1.878 61.34107 -1.990 56.40391 -2.017 58.38903 -1.865 61.34288 -2.007 56.40573 -2.022 58.39085 -1.841 61.34471 -2.011 56.40756 -2.022 58.39267 -1.829 61.34653 -2.016Figure 3
CCD photometric observations for HH Boo in theB, V, R, and I bands observed on December 25, 27, and 30, 2010 by the 85 cm telescope at Xinglong station of National Astronomical Observatories (Xinglong-85cm) in China.Figure 4
CCD photometric light curves in theB, V, R, and I 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.


## 2.1. Spectroscopy

To determine the spectrum of the solar-type 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 of1.′′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].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]).


## 2.2. 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 about7′.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 completeB, V, R, and I 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 UBVRI CCD photometric system [34]. The integration times were 40 s, 30 s, 20 s, and 10 s for B, V, R, and I bands, respectively. For each band, about 200 images were obtained (B = 197, V = 196, R = 196, and I = 196). One image of the B 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.Table 1
Coordinates and magnitudes of HH Boo, the comparison, and the check stars.
Stars α 2000 δ 2000 B(mag) V(mag)  HH Boo 1 4 h 2 1 m 44.0750 9 s + 4 6 ∘ 41 ′ 59.3524 ′ ′ 11.80 11.021 GSC03472-00043 (C) 1 4 h 2 1 m 46.6002 3 s + 4 6 ∘ 43 ′ 49.4364 ′ ′ 13.57 12.87 GSC03472-01201 (K) 1 4 h 2 1 m 37.3118 0 s + 4 6 ∘ 46 ′ 18.5231 ′ ′ 14.38 13.66Figure 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).The CCD photometric data obtained on December 25, 27, and 30, 2010, inB, V, R, and I 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,(2)Min.IHJD=2455556.34396+0d.318666208×E,are shown in Figure 4. The magnitude differences between the comparison and the check stars are also shown in the low pane of this figure. The epoch in (2) is obtained by us (the mean value of four band light minima) and the period is from Gu¨rol et al. [31].Table 2
The observations inB band for HH Boo (Hel. JD 2,455,500+).
Hel. JD △ m Hel. JD △ m Hel. JD △ m Hel. JD △ m  56.31655 -1.504 56.40803 -1.753 58.39315 -1.516 61.34519 -1.740 56.31864 -1.490 56.40986 -1.751 58.39498 -1.498 61.34700 -1.732 56.32046 -1.465 56.41168 -1.756 58.39679 -1.490 61.34882 -1.742 56.32228 -1.447 58.30742 -1.692 58.39862 -1.469 61.35064 -1.745 56.32411 -1.424 58.30924 -1.712 58.40045 -1.444 61.35245 -1.745 56.32594 -1.402 58.31107 -1.700 58.40227 -1.427 61.35427 -1.747 56.32776 -1.379 58.31288 -1.714 58.40410 -1.413 61.35609 -1.755 56.32958 -1.353 58.31471 -1.729 58.40592 -1.398 61.35792 -1.759 56.33140 -1.334 58.31654 -1.728 58.40774 -1.373 61.35974 -1.757 56.33323 -1.306 58.31836 -1.750 58.40957 -1.367 61.36155 -1.763 56.33506 -1.288 58.32019 -1.757 58.41139 -1.357 61.36337 -1.753 56.33688 -1.278 58.32202 -1.746 58.41322 -1.348 61.36519 -1.756 56.33870 -1.260 58.32383 -1.760 58.41505 -1.348 61.36700 -1.760 56.34053 -1.255 58.32566 -1.765 58.41686 -1.348 61.36882 -1.750 56.34235 -1.242 58.32748 -1.766 61.27971 -1.353 61.37064 -1.748 56.34418 -1.241 58.32931 -1.773 61.28153 -1.360 61.37246 -1.751 56.34601 -1.250 58.33114 -1.773 61.28335 -1.349 61.37428 -1.738 56.34783 -1.245 58.33295 -1.775 61.28516 -1.343 61.37610 -1.730 56.34965 -1.275 58.33478 -1.782 61.28699 -1.343 61.37792 -1.727 56.35147 -1.292 58.33660 -1.778 61.28881 -1.356 61.37973 -1.727 56.35330 -1.298 58.33843 -1.774 61.29063 -1.354 61.38155 -1.720 56.35513 -1.314 58.34026 -1.789 61.29244 -1.366 61.38337 -1.713 56.35695 -1.347 58.34207 -1.768 61.29426 -1.400 61.38519 -1.708 56.35877 -1.359 58.34390 -1.775 61.29608 -1.406 61.38701 -1.696 56.36060 -1.385 58.34572 -1.775 61.29789 -1.424 61.38883 -1.691 56.36242 -1.420 58.34755 -1.766 61.29972 -1.434 61.39065 -1.675 56.36425 -1.436 58.34938 -1.767 61.30154 -1.463 61.39247 -1.669 56.36607 -1.464 58.35119 -1.771 61.30336 -1.477 61.39428 -1.664 56.36789 -1.485 58.35302 -1.750 61.30517 -1.491 61.39610 -1.650 56.36972 -1.500 58.35485 -1.750 61.30699 -1.513 61.39792 -1.639 56.37154 -1.520 58.35667 -1.748 61.30881 -1.530 61.39974 -1.638 56.37337 -1.543 58.35850 -1.737 61.31063 -1.551 61.40156 -1.622 56.37520 -1.556 58.36031 -1.738 61.31246 -1.559 61.40338 -1.607 56.37702 -1.581 58.36214 -1.723 61.31427 -1.574 61.40520 -1.591 56.37884 -1.591 58.36397 -1.714 61.31609 -1.588 61.40702 -1.586 56.38067 -1.607 58.36579 -1.714 61.31791 -1.605 61.40883 -1.571 56.38249 -1.620 58.36762 -1.701 61.31972 -1.612 61.41065 -1.560 56.38432 -1.626 58.36943 -1.688 61.32154 -1.630 61.41247 -1.537 56.38614 -1.645 58.37126 -1.681 61.32336 -1.635 61.41428 -1.518 56.38796 -1.650 58.37309 -1.667 61.32518 -1.647 61.41611 -1.495 56.38979 -1.660 58.37491 -1.657 61.32700 -1.644 61.41793 -1.480 56.39162 -1.683 58.37674 -1.651 61.32882 -1.668 61.41975 -1.454 56.39344 -1.687 58.37855 -1.637 61.33064 -1.677 61.42156 -1.429 56.39527 -1.693 58.38038 -1.623 61.33246 -1.681 61.42338 -1.412 56.39708 -1.703 58.38221 -1.613 61.33427 -1.699 61.42520 -1.387 56.39891 -1.712 58.38403 -1.605 61.33609 -1.694 61.42701 -1.358 56.40074 -1.726 58.38586 -1.586 61.33791 -1.716 61.42883 -1.336 56.40256 -1.732 58.38768 -1.568 61.33972 -1.710 56.40439 -1.737 58.38950 -1.552 61.34154 -1.722 56.40621 -1.737 58.39133 -1.534 61.34337 -1.721Table 3
The observations inV band for HH Boo (Hel. JD 2,455,500+).
Hel. JD △ m Hel. JD △ m Hel. JD △ m Hel. JD △ m 56.31712 -1.644 56.40860 -1.856 58.39372 -1.626 61.34757 -1.843 56.31920 -1.607 56.41042 -1.857 58.39554 -1.608 61.34939 -1.838 56.32102 -1.584 56.41225 -1.864 58.39736 -1.595 61.35121 -1.844 56.32285 -1.563 58.30797 -1.796 58.39919 -1.569 61.35302 -1.852 56.32468 -1.550 58.30980 -1.799 58.40101 -1.551 61.35484 -1.858 56.32649 -1.521 58.31163 -1.822 58.40284 -1.538 61.35666 -1.866 56.32832 -1.494 58.31345 -1.819 58.40467 -1.515 61.35847 -1.861 56.33015 -1.477 58.31528 -1.825 58.40648 -1.502 61.36029 -1.860 56.33197 -1.461 58.31710 -1.833 58.40831 -1.489 61.36212 -1.856 56.33380 -1.432 58.31893 -1.836 58.41013 -1.484 61.36394 -1.863 56.33563 -1.404 58.32075 -1.861 58.41196 -1.474 61.36575 -1.859 56.33744 -1.404 58.32257 -1.857 58.41379 -1.479 61.36757 -1.861 56.33927 -1.393 58.32440 -1.878 58.41560 -1.466 61.36939 -1.859 56.34109 -1.385 58.32622 -1.864 61.28028 -1.480 61.37121 -1.855 56.34292 -1.391 58.32805 -1.870 61.28210 -1.479 61.37302 -1.846 56.34475 -1.384 58.32987 -1.875 61.28391 -1.462 61.37484 -1.833 56.34656 -1.377 58.33169 -1.874 61.28573 -1.469 61.37666 -1.836 56.34839 -1.386 58.33352 -1.877 61.28755 -1.486 61.37848 -1.834 56.35022 -1.414 58.33535 -1.875 61.28936 -1.482 61.38030 -1.828 56.35204 -1.398 58.33716 -1.877 61.29118 -1.487 61.38212 -1.826 56.35387 -1.441 58.33899 -1.881 61.29301 -1.500 61.38394 -1.813 56.35568 -1.457 58.34081 -1.863 61.29483 -1.532 61.38575 -1.808 56.35751 -1.488 58.34264 -1.877 61.29664 -1.539 61.38757 -1.797 56.35934 -1.500 58.34447 -1.868 61.29846 -1.548 61.38939 -1.793 56.36116 -1.515 58.34629 -1.872 61.30028 -1.567 61.39120 -1.784 56.36299 -1.544 58.34811 -1.867 61.30210 -1.585 61.39303 -1.776 56.36482 -1.563 58.34993 -1.854 61.30393 -1.597 61.39485 -1.769 56.36663 -1.578 58.35176 -1.862 61.30574 -1.614 61.39667 -1.765 56.36846 -1.599 58.35359 -1.858 61.30756 -1.633 61.39849 -1.751 56.37028 -1.618 58.35541 -1.860 61.30938 -1.650 61.40030 -1.744 56.37211 -1.651 58.35724 -1.841 61.31119 -1.665 61.40212 -1.724 56.37394 -1.662 58.35906 -1.826 61.31301 -1.688 61.40394 -1.719 56.37575 -1.679 58.36088 -1.829 61.31483 -1.693 61.40575 -1.706 56.37758 -1.692 58.36271 -1.819 61.31665 -1.705 61.40758 -1.699 56.37941 -1.709 58.36453 -1.811 61.31847 -1.717 61.40940 -1.681 56.38123 -1.727 58.36635 -1.811 61.32029 -1.734 61.41122 -1.669 56.38306 -1.718 58.36818 -1.805 61.32211 -1.738 61.41303 -1.645 56.38488 -1.745 58.37000 -1.798 61.32393 -1.743 61.41485 -1.631 56.38670 -1.754 58.37183 -1.784 61.32574 -1.763 61.41667 -1.612 56.38853 -1.764 58.37365 -1.775 61.32756 -1.758 61.41848 -1.593 56.39036 -1.769 58.37548 -1.755 61.32938 -1.769 61.42030 -1.570 56.39218 -1.771 58.37730 -1.757 61.33119 -1.790 61.42213 -1.548 56.39401 -1.789 58.37912 -1.741 61.33302 -1.799 61.42395 -1.525 56.39583 -1.799 58.38095 -1.729 61.33484 -1.790 61.42576 -1.503 56.39765 -1.806 58.38277 -1.723 61.33666 -1.813 61.42758 -1.475 56.39948 -1.811 58.38460 -1.706 61.33847 -1.817 61.42940 -1.462 56.40130 -1.827 58.38643 -1.698 61.34029 -1.820 56.40313 -1.832 58.38824 -1.678 61.34211 -1.822 56.40496 -1.846 58.39007 -1.655 61.34392 -1.835 56.40677 -1.841 58.39189 -1.639 61.34574 -1.834Table 4
The observations inR band for HH Boo (Hel. JD 2,455,500+).
Hel. JD △ m Hel. JD △ m Hel. JD △ m Hel. JD △ m  56.31757 -1.722 56.40905 -1.944 58.39417 -1.721 61.34801 -1.935 56.31965 -1.693 56.41087 -1.937 58.39599 -1.699 61.34983 -1.946 56.32147 -1.687 56.41270 -1.946 58.39781 -1.682 61.35166 -1.931 56.32330 -1.660 58.30843 -1.893 58.39964 -1.658 61.35347 -1.947 56.32513 -1.644 58.31026 -1.895 58.40146 -1.639 61.35529 -1.958 56.32695 -1.628 58.31207 -1.881 58.40329 -1.623 61.35711 -1.945 56.32877 -1.593 58.31390 -1.924 58.40510 -1.613 61.35892 -1.936 56.33059 -1.580 58.31573 -1.905 58.40693 -1.604 61.36074 -1.939 56.33242 -1.554 58.31755 -1.915 58.40876 -1.591 61.36256 -1.935 56.33425 -1.556 58.31938 -1.925 58.41058 -1.580 61.36438 -1.949 56.33607 -1.523 58.32119 -1.954 58.41241 -1.570 61.36619 -1.949 56.33790 -1.509 58.32302 -1.947 58.41423 -1.574 61.36801 -1.940 56.33972 -1.499 58.32485 -1.950 58.41605 -1.565 61.36984 -1.943 56.34154 -1.493 58.32667 -1.940 61.28072 -1.583 61.37166 -1.936 56.34337 -1.481 58.32850 -1.946 61.28254 -1.576 61.37347 -1.937 56.34519 -1.486 58.33033 -1.959 61.28436 -1.581 61.37529 -1.928 56.34701 -1.495 58.33214 -1.956 61.28618 -1.569 61.37711 -1.935 56.34884 -1.508 58.33397 -1.962 61.28800 -1.574 61.37893 -1.921 56.35066 -1.513 58.33579 -1.965 61.28982 -1.582 61.38075 -1.919 56.35249 -1.526 58.33762 -1.967 61.29163 -1.592 61.38257 -1.907 56.35432 -1.550 58.33944 -1.963 61.29345 -1.624 61.38439 -1.897 56.35614 -1.555 58.34126 -1.959 61.29528 -1.616 61.38620 -1.898 56.35796 -1.606 58.34309 -1.957 61.29710 -1.637 61.38802 -1.886 56.35979 -1.610 58.34491 -1.951 61.29891 -1.648 61.38984 -1.881 56.36161 -1.641 58.34674 -1.946 61.30073 -1.670 61.39166 -1.870 56.36344 -1.654 58.34857 -1.942 61.30255 -1.686 61.39347 -1.863 56.36526 -1.667 58.35038 -1.963 61.30436 -1.707 61.39529 -1.854 56.36708 -1.695 58.35221 -1.951 61.30618 -1.713 61.39712 -1.852 56.36891 -1.711 58.35404 -1.941 61.30801 -1.727 61.39894 -1.832 56.37073 -1.737 58.35586 -1.931 61.30983 -1.745 61.40075 -1.831 56.37256 -1.736 58.35769 -1.924 61.31164 -1.764 61.40257 -1.824 56.37439 -1.751 58.35950 -1.928 61.31346 -1.779 61.40439 -1.812 56.37620 -1.785 58.36133 -1.919 61.31528 -1.791 61.40621 -1.796 56.37803 -1.795 58.36316 -1.908 61.31710 -1.799 61.40802 -1.786 56.37985 -1.804 58.36498 -1.910 61.31891 -1.818 61.40984 -1.773 56.38168 -1.813 58.36681 -1.900 61.32073 -1.825 61.41167 -1.752 56.38351 -1.831 58.36862 -1.875 61.32256 -1.834 61.41349 -1.741 56.38533 -1.849 58.37045 -1.876 61.32438 -1.836 61.41530 -1.722 56.38715 -1.846 58.37228 -1.873 61.32619 -1.857 61.41712 -1.704 56.38898 -1.864 58.37410 -1.867 61.32801 -1.859 61.41894 -1.683 56.39080 -1.865 58.37593 -1.840 61.32983 -1.860 61.42075 -1.663 56.39263 -1.879 58.37774 -1.844 61.33165 -1.883 61.42257 -1.649 56.39446 -1.881 58.37957 -1.832 61.33346 -1.881 61.42439 -1.627 56.39627 -1.887 58.38140 -1.819 61.33528 -1.904 61.42622 -1.607 56.39810 -1.897 58.38322 -1.807 61.33710 -1.900 61.42803 -1.584 56.39993 -1.901 58.38505 -1.794 61.33893 -1.906 61.42985 -1.567 56.40175 -1.913 58.38686 -1.777 61.34074 -1.911 56.40358 -1.922 58.38869 -1.762 61.34256 -1.920 56.40539 -1.924 58.39052 -1.741 61.34438 -1.928 56.40722 -1.931 58.39234 -1.742 61.34619 -1.920Table 5
The observations inI band for HH Boo (Hel. JD 2,455,500+).
Hel. JD △ m Hel. JD △ m Hel. JD △ m Hel. JD △ m  56.31796 -1.828 56.40938 -2.026 58.39450 -1.812 61.34835 -2.028 56.31998 -1.809 56.41121 -2.038 58.39632 -1.798 61.35016 -2.030 56.32181 -1.800 56.41303 -2.034 58.39815 -1.776 61.35198 -2.026 56.32364 -1.793 58.30876 -1.985 58.39997 -1.764 61.35380 -2.036 56.32545 -1.750 58.31059 -1.993 58.40180 -1.747 61.35561 -2.032 56.32728 -1.721 58.31241 -2.003 58.40362 -1.734 61.35744 -2.042 56.32911 -1.711 58.31424 -2.030 58.40544 -1.727 61.35926 -2.035 56.33093 -1.701 58.31605 -2.004 58.40727 -1.703 61.36108 -2.038 56.33276 -1.671 58.31788 -2.027 58.40909 -1.700 61.36290 -2.040 56.33458 -1.638 58.31971 -2.020 58.41092 -1.679 61.36471 -2.040 56.33640 -1.636 58.32153 -2.022 58.41274 -1.682 61.36653 -2.025 56.33823 -1.630 58.32336 -2.020 58.41456 -1.671 61.36835 -2.031 56.34005 -1.635 58.32518 -2.035 58.41639 -1.679 61.37016 -2.036 56.34188 -1.613 58.32700 -2.043 61.28105 -1.679 61.37198 -2.018 56.34371 -1.634 58.32883 -2.058 61.28287 -1.676 61.37381 -2.026 56.34552 -1.602 58.33065 -2.037 61.28469 -1.665 61.37563 -2.017 56.34735 -1.633 58.33248 -2.063 61.28651 -1.684 61.37744 -2.012 56.34918 -1.628 58.33431 -2.063 61.28833 -1.681 61.37926 -2.004 56.35100 -1.660 58.33612 -2.058 61.29015 -1.700 61.38108 -1.997 56.35283 -1.629 58.33795 -2.056 61.29197 -1.721 61.38289 -1.997 56.35464 -1.685 58.33977 -2.036 61.29379 -1.711 61.38471 -1.989 56.35647 -1.689 58.34160 -2.050 61.29560 -1.729 61.38653 -1.989 56.35830 -1.684 58.34343 -2.045 61.29742 -1.722 61.38836 -1.976 56.36012 -1.728 58.34524 -2.038 61.29925 -1.745 61.39017 -1.974 56.36194 -1.726 58.34707 -2.020 61.30107 -1.774 61.39199 -1.964 56.36377 -1.762 58.34889 -2.041 61.30288 -1.792 61.39381 -1.960 56.36559 -1.795 58.35072 -2.013 61.30470 -1.811 61.39563 -1.957 56.36742 -1.802 58.35255 -2.038 61.30652 -1.823 61.39744 -1.943 56.36924 -1.820 58.35436 -2.023 61.30833 -1.836 61.39926 -1.928 56.37107 -1.840 58.35619 -2.024 61.31015 -1.840 61.40108 -1.934 56.37290 -1.857 58.35802 -2.017 61.31197 -1.865 61.40291 -1.912 56.37471 -1.874 58.35984 -2.025 61.31380 -1.875 61.40472 -1.904 56.37654 -1.872 58.36167 -2.017 61.31561 -1.898 61.40654 -1.901 56.37837 -1.884 58.36348 -2.004 61.31743 -1.923 61.40836 -1.876 56.38019 -1.905 58.36531 -1.970 61.31925 -1.914 61.41018 -1.875 56.38202 -1.914 58.36714 -1.993 61.32107 -1.921 61.41199 -1.859 56.38384 -1.930 58.36896 -1.975 61.32288 -1.927 61.41381 -1.840 56.38566 -1.944 58.37079 -1.974 61.32470 -1.937 61.41563 -1.826 56.38749 -1.960 58.37261 -1.957 61.32652 -1.963 61.41745 -1.807 56.38932 -1.958 58.37443 -1.953 61.32833 -1.944 61.41927 -1.788 56.39113 -1.956 58.37626 -1.957 61.33016 -1.956 61.42109 -1.770 56.39296 -1.975 58.37808 -1.928 61.33198 -1.967 61.42291 -1.757 56.39479 -1.979 58.37991 -1.923 61.33380 -1.983 61.42472 -1.731 56.39661 -1.985 58.38173 -1.920 61.33561 -1.997 61.42654 -1.725 56.39844 -1.996 58.38355 -1.901 61.33743 -1.991 61.42836 -1.688 56.40026 -2.000 58.38538 -1.879 61.33925 -2.003 61.43017 -1.680 56.40208 -2.017 58.38720 -1.878 61.34107 -1.990 56.40391 -2.017 58.38903 -1.865 61.34288 -2.007 56.40573 -2.022 58.39085 -1.841 61.34471 -2.011 56.40756 -2.022 58.39267 -1.829 61.34653 -2.016Figure 3
CCD photometric observations for HH Boo in theB, V, R, and I bands observed on December 25, 27, and 30, 2010 by the 85 cm telescope at Xinglong station of National Astronomical Observatories (Xinglong-85cm) in China.Figure 4
CCD photometric light curves in theB, V, R, and I 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.


## 3. 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 dP/dt = -9.60×10-7 d yr-1 that could be explained by mass transfer or/and angular momentum loss via magnetic braking. Subsequently, Gu¨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 O-C 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.Table 6
New CCD times of light minimum for HH Boo.
JD (Hel.) Error (days) Method Min. Filter tel  2455556.34380 0.00017 CCD I B Xinglong-85cm 2455556.34381 0.00017 CCD I V Xinglong-85cm 2455556.34407 0.00023 CCD I I Xinglong-85cm 2455556.34416 0.00021 CCD I R Xinglong-85cm 2455561.28404 0.00131 CCD II V Xinglong-85cm 2455561.28436 0.00084 CCD II I Xinglong-85cm 2455561.28459 0.00118 CCD II B Xinglong-85cm 2455561.28462 0.00020 CCD II R Xinglong-85cm 2455918.35009 0.00022 CCD I R YNOs-1m 2456308.39843 0.00010 CCD I I YNOs-1m 2456308.39843 0.00013 CCD I N YNOs-1m 2456308.39862 0.00014 CCD I R YNOs-1m 2456348.23149 0.00016 CCD I I YNOs-1m 2456348.23163 0.00017 CCD I R YNOs-1m 2456348.23171 0.00014 CCD I N YNOs-1m 2456735.40805 0.00016 CCD I R YNOs-1m 2456735.40841 0.00016 CCD I I YNOs-1m 2457068.41899 0.00017 CCD I R YNOs-1m 2457068.41935 0.00015 CCD I I YNOs-1m 2457075.43087 0.00019 CCD I I YNOs-60cm 2457075.43087 0.00021 CCD I R YNOs-60cm 2457079.25398 0.00013 CCD I I YNOs-1m 2457097.25817 0.00042 CCD II R YNOs-60cm 2457097.25829 0.00032 CCD II I YNOs-1m 2457408.43508 0.00035 CCD I V YNOs-60cm 2457408.43544 0.00041 CCD I R YNOs-60cm 2457496.38545 0.00021 CCD I N YNOs-60cm 2458232.18458 0.00019 CCD I V YNOs-60cm 2458232.18467 0.00019 CCD I I YNOs-60cm 2458232.18479 0.00016 CCD I R YNOs-60cmTable 7
( O - C ) values of light minimum times for HH Boo.
2450000+ Error Method Ecl. type E ( O - C ) Residual Reference 1274.74700 - CCD p -13436 0.00221 -0.00002 ROSTE 2749.53280 0.0007 CCDV p -8808 0.00080 -0.00150 [1] 2764.50965 0.0003 CCDV p -8761 0.00034 -0.00189 [2] 3141.49120 0.00018 CCD p -7578 -0.00024 -0.00130 WASP 3142.60748 0.00032 CCD s -7574.5 0.00071 -0.00035 WASP 3143.40329 0.00021 CCD p -7572 -0.00014 -0.00120 WASP 3143.56365 0.00021 CCD s -7571.5 0.00088 -0.00018 WASP 3146.43139 0.00022 CCD s -7562.5 0.00063 -0.00043 WASP 3146.58931 0.00021 CCD p -7562 -0.00079 -0.00184 WASP 3828.53655 0.00085 CCD p -5422 0.00077 -0.00173 WASP 3831.56531 0.00033 CCD s -5412.5 0.00220 -0.00031 WASP 3832.52147 0.00035 CCD s -5409.5 0.00236 -0.00016 WASP 3832.68037 0.00037 CCD p -5409 0.00193 -0.00059 WASP 3833.47630 0.00024 CCD s -5406.5 0.00119 -0.00133 WASP 3833.63582 0.00028 CCD p -5406 0.00138 -0.00114 WASP 3837.45964 0.00031 CCD p -5394 0.00121 -0.00134 WASP 3851.63893 0.00022 CCD s -5349.5 -0.00015 -0.00276 WASP 3852.43511 0.00027 CCD p -5347 -0.00064 -0.00324 WASP 3852.59499 0.0002 CCD s -5346.5 -0.00009 -0.00270 WASP 3854.50736 0.0001 CCD s -5340.5 0.00028 -0.00233 WASP 3855.62182 0.00036 CCD p -5337 -0.00059 -0.00321 WASP 3856.57777 0.00013 CCD p -5334 -0.00064 -0.00326 WASP 4135.73391 0.00033 CCD p -4458 0.00391 0.00007 WASP 4140.67398 0.00024 CCD s -4442.5 0.00465 0.00080 WASP 4146.72875 0.00018 CCD s -4423.5 0.00476 0.00089 WASP 4147.68467 0.00025 CCD s -4420.5 0.00468 0.00081 WASP 4148.64060 0.0008 pe Ir s -4417.5 0.00461 0.00073 [3] 4150.71103 0.00025 CCD p -4411 0.00371 -0.00016 WASP 4157.72238 0.00015 CCD p -4389 0.00441 0.00050 WASP 4158.67807 0.00019 CCD p -4386 0.00410 0.00018 WASP 4160.58917 0.00021 CCD p -4380 0.00320 -0.00071 WASP 4161.70444 0.00038 CCD s -4376.5 0.00314 -0.00078 WASP 4162.66210 0.00029 CCD s -4373.5 0.00480 0.00087 WASP 4163.61836 0.00029 CCD s -4370.5 0.00506 0.00113 WASP 4165.68839 0.00022 CCD p -4364 0.00376 -0.00017 WASP 4169.67442 0.0005 CCD s -4351.5 0.00646 0.00251 WASP 4171.58470 0.00028 CCD s -4345.5 0.00475 0.00079 WASP 4190.54484 0.00021 CCD p -4286 0.00425 0.00022 WASP 4191.50030 0.00022 CCD p -4283 0.00371 -0.00031 WASP 4195.48520 0.00027 CCD s -4270.5 0.00528 0.00124 WASP 4202.49498 0.00029 CCD s -4248.5 0.00440 0.00034 WASP 4203.61289 0.00045 CCD p -4245 0.00698 0.00292 WASP 4204.56612 0.0002 CCD p -4242 0.00421 0.00015 WASP 4210.46262 0.00029 CCD s -4223.5 0.00539 0.00130 WASP 4210.62021 0.00026 CCD p -4223 0.00365 -0.00043 WASP 4214.44519 0.00021 CCD p -4211 0.00463 0.00053 WASP 4214.60510 0.00025 CCD s -4210.5 0.00521 0.00111 WASP 4216.51700 0.00037 CCD s -4204.5 0.00511 0.00101 WASP 4216.67541 0.00018 CCD p -4204 0.00419 0.00008 WASP 4217.47321 0.00028 CCD s -4201.5 0.00532 0.00121 WASP 4218.42927 0.00032 CCD s -4198.5 0.00538 0.00127 WASP 4218.58703 0.00032 CCD p -4198 0.00381 -0.00029 WASP 4219.54349 0.00037 CCD p -4195 0.00427 0.00016 WASP 4220.49855 0.00035 CCD p -4192 0.00333 -0.00077 WASP 4221.45434 0.00039 CCD p -4189 0.00313 -0.00099 WASP 4222.57230 0.00043 CCD s -4185.5 0.00575 0.00163 WASP 4223.52943 0.00028 CCD s -4182.5 0.00688 0.00276 WASP 4225.59797 0.00022 CCD p -4176 0.00409 -0.00003 WASP 4226.39570 0.00018 CCD s -4173.5 0.00516 0.00102 WASP 4227.50877 0.0005 CCD p -4170 0.00290 -0.00123 WASP 4230.53933 0.00056 CCD s -4160.5 0.00613 0.00198 WASP 4231.49453 0.00028 CCD s -4157.5 0.00533 0.00118 WASP 4232.45050 0.00026 CCD s -4154.5 0.00530 0.00115 WASP 4232.60834 0.00042 CCD p -4154 0.00381 -0.00034 WASP 4233.40675 0.00019 CCD s -4151.5 0.00555 0.00140 WASP 4233.56434 0.0003 CCD p -4151 0.00381 -0.00034 WASP 4234.52039 0.00056 CCD p -4148 0.00386 -0.00029 WASP 4235.47573 0.00059 CCD p -4145 0.00320 -0.00095 WASP 4236.43240 0.00033 CCD p -4142 0.00387 -0.00028 WASP 4236.59275 0.00037 CCD s -4141.5 0.00489 0.00072 WASP 4247.58620 0.00022 CCD p -4107 0.00436 0.00016 WASP 4249.49716 0.00069 CCD p -4101 0.00332 -0.00087 WASP 4250.45245 0.00079 CCD p -4098 0.00261 -0.00158 WASP 4251.40960 0.00023 CCD p -4095 0.00376 -0.00044 WASP 4252.52722 0.00036 CCD s -4091.5 0.00605 0.00184 WASP 4254.43799 0.00026 CCD s -4085.5 0.00482 0.00061 WASP 4256.50781 0.00031 CCD p -4079 0.00331 -0.00090 WASP 4257.46464 0.00027 CCD p -4076 0.00414 -0.00007 WASP 4260.49383 0.00047 CCD s -4066.5 0.00600 0.00177 WASP 4261.44916 0.0003 CCD s -4063.5 0.00534 0.00110 WASP 4265.43134 0.00027 CCD p -4051 0.00419 -0.00005 WASP 4513.51360 0.0004 pe Ir s -3272.5 0.00481 0.00022 [4] 4599.39352 0.0004 CCD -R p -3003 0.00418 -0.00034 [5] 4912.32330 0.0008 pe Ir p -2021 0.00375 0.00001 [4] 4912.48350 0.0003 pe Ir s -2020.5 0.00461 0.00088 [4] 4937.33920 0.0002 pe Ir s -1942.5 0.00435 0.00071 [4] 4958.68870 0.0009 peV s -1875.5 0.00321 -0.00033 [6] 4958.84900 0.003 peV p -1875 0.00418 0.00063 [6] 5243.89200 0.0002 peV s -980.5 0.00026 -0.00203 [7] 5259.98480 0.0002 CCD p -930 0.00041 -0.00180 [8] 5322.44278 0.0001 CCDBVRI p -734 -0.00018 -0.00214 [9] 5384.42480 0.0042 CCD -Ir s -539.5 0.00126 -0.00045 [10] 5542.32650 0.006 CCD DSLR p -44 0.00385 0.00261 [11] 5556.34380 0.00017 CCDB p 0 -0.00016 -0.00136 The present paper 5556.34381 0.00017 CCDV p 0 -0.00015 -0.00135 The present paper 5556.34407 0.00023 CCDI p 0 0.00011 -0.00109 The present paper 5556.34416 0.00021 CCDR p 0 0.00020 -0.00100 The present paper 5561.28404 0.00131 CCDV s 15.5 0.00075 -0.00044 The present paper 5561.28436 0.00084 CCDI s 15.5 0.00107 -0.00012 The present paper 5561.28459 0.00118 CCDB s 15.5 0.00130 0.00010 The present paper 5561.28462 0.0002 CCDR s 15.5 0.00133 0.00013 The present paper 5602.55080 0.0006 CCD p 145 0.00024 -0.00087 [12] 5609.40300 0.001 CCD s 166.5 0.00112 0.00001 [12] 5637.44590 0.0006 CCD s 254.5 0.00139 0.00032 [12] 5644.93360 0.0003 peV p 278 0.00043 -0.00061 [9] 5645.41280 0.0002 CCD s 279.5 0.00163 0.00058 [12] 5645.57080 0.0003 CCD p 280 0.00030 -0.00074 [12] 5647.48300 0.0005 CCD p 286 0.00050 -0.00054 [12] 5648.43860 0.0012 CCD p 289 0.00011 -0.00094 [12] 5676.48120 0.0002 CCD -Ir p 377 0.00008 -0.00093 [13] 5678.39290 0.0002 CCD p 383 -0.00022 -0.00123 [14] 5678.55380 0.0004 CCD s 383.5 0.00135 0.00033 [14] 5680.78530 0.0002 peV s 390.5 0.00219 0.00117 [9] 5682.37810 0.0004 CCD s 395.5 0.00165 0.00064 [14] 5682.53560 0.0003 CCD p 396 -0.00018 -0.00119 [14] 5686.36749 0.0008 CCD p 408 0.00772 0.00670 [15] 5716.47670 0.0003 CCDR s 502.5 0.00297 0.00198 [16] 5716.47680 0.0005 CCDB s 502.5 0.00307 0.00208 [16] 5716.47680 0.0002 CCDV s 502.5 0.00307 0.00208 [16] 5743.40260 0.0003 CCDR p 587 0.00158 0.00059 [16] 5743.40320 0.0004 CCDB p 587 0.00218 0.00119 [16] 5743.40380 0.0002 CCDV p 587 0.00278 0.00179 [16] 5747.38630 0.0005 CCDR s 599.5 0.00195 0.00096 [16] 5747.38710 0.0003 CCDB s 599.5 0.00275 0.00176 [16] 5747.38740 0.0002 CCDV s 599.5 0.00305 0.00206 [16] 5751.36960 0.0003 CCDR p 612 0.00192 0.00093 [16] 5751.37000 0.0003 CCDB p 612 0.00232 0.00133 [16] 5751.37000 0.0003 CCDV p 612 0.00232 0.00133 [16] 5751.37010 0.0002 CCDR p 612 0.00242 0.00143 [16] 5751.37020 0.0003 CCDB p 612 0.00252 0.00153 [16] 5751.37020 0.0004 CCDV p 612 0.00252 0.00153 [16] 5918.35009 0.00022 CCDR p 1136 0.00132 0.00019 The present paper 6011.87780 0.0004 CCDV s 1429.5 0.00050 -0.00084 [17] 6012.35700 0.0001 CCD o p 1431 0.00170 0.00035 [10] 6013.47198 0.0001 CCD s 1434.5 0.00134 0.00000 [15] 6013.47350 0.0005 CCD -Ir s 1434.5 0.00286 0.00152 [10] 6013.62918 0.0001 CCD p 1435 -0.00079 -0.00213 [15] 6013.63230 0.0011 CCD -Ir p 1435 0.00233 0.00098 [10] 6046.29570 0.0001 CCDBVI s 1537.5 0.00245 0.00100 [18] 6046.45370 0.0002 CCDBVI p 1538 0.00111 -0.00032 [18] 6065.41660 0.0014 CCD -Ir s 1597.5 0.00337 0.00187 [19] 6076.72610 0.0004 CCDV p 1633 0.00022 -0.00131 [17] 6091.38590 0.00006 CCDBVRI p 1679 0.00138 -0.00020 [20] 6092.34290 0.00008 CCDBVRI p 1682 0.00238 0.00079 [20] 6092.50240 0.00015 CCDBVRI s 1682.5 0.00255 0.00095 [20] 6308.39843 0.0001 CCDI p 2360 0.00222 -0.00023 The present paper 6308.39843 0.00013 CCD N p 2360 0.00222 -0.00023 The present paper 6308.39862 0.00014 CCDR p 2360 0.00241 -0.00004 The present paper 6348.23149 0.00016 CCDI p 2485 0.00200 -0.00063 The present paper 6348.23163 0.00017 CCDR p 2485 0.00214 -0.00049 The present paper 6348.23171 0.00014 CCD N p 2485 0.00222 -0.00041 The present paper 6690.95850 0.0002 CCD C s 3560.5 0.00351 -0.00054 [21] 6735.40805 0.00016 CCDR p 3700 -0.00088 -0.00506 The present paper 6735.40841 0.00016 CCDI p 3700 -0.00052 -0.00470 The present paper 6764.41270 0.0017 CCD -I p 3791 0.00515 0.00088 [22] 6764.57170 0.0004 CCD -I s 3791.5 0.00481 0.00055 [22] 6772.37860 0.0017 CCD -I p 3816 0.00439 0.00010 [22] 6772.53810 0.0031 CCD -I s 3816.5 0.00456 0.00027 [22] 7068.41899 0.00017 CCDI p 4745 0.00387 -0.00067 [22] 7068.41935 0.00015 CCDR p 4745 0.00423 -0.00031 [22] 7075.43087 0.00019 CCDI p 4767 0.00510 0.00055 The present paper 7075.43087 0.00021 CCDR p 4767 0.00510 0.00055 The present paper 7079.25398 0.00013 CCDI p 4779 0.00421 -0.00033 The present paper 7097.25817 0.00042 CCDI s 4835.5 0.00376 -0.00076 The present paper 7097.25829 0.00032 CCDR s 4835.5 0.00388 -0.00064 The present paper 7100.44860 0.0037 CCD -I s 4845.5 0.00753 0.00300 [23] 7100.60440 0.0009 CCD -I p 4846 0.00400 -0.00052 [23] 7408.43508 0.00035 CCDV p 5812 0.00312 -0.00059 The present paper 7408.43544 0.00041 CCDR p 5812 0.00348 -0.00023 The present paper 7496.38545 0.00021 CCD N p 6088 0.00162 -0.00173 The present paper 8232.18458 0.00019 CCDV p 8397 0.00047 -0.00051 The present paper 8232.18467 0.00019 CCDI p 8397 0.00056 -0.00042 The present paper 8232.18479 0.00016 CCDR p 8397 0.00068 -0.00030 The present paperAll available photoelectric and CCD times of light minimum were compiled and are shown in column 1 of Table7. The (O-C) values (observational times of light minimum-calculational 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 Gu¨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 O-C 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: (3)O-C=0.00241+0.00000000416×E-0.00061sin⁡0.00083314E-0.001718cos⁡0.00083314E.With this ephemeris, a cyclic oscillation with a period of T3 = 6.58(11) yr and an amplitude of A3 = 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.Figure 5
( O - C ) diagram of the short-period close binary HH Boo based on all the primary and secondary available photoelectric and CCD times of light minimum. Theblack solid line showed a cyclic period variation with a period of 6.58 yr. Residuals after the cyclic change was removed are shown in thelower panel. Theblack solid dots refer to the data collected by Gu¨rol et al. [31], theblue solid dots refer to the data by WASP database, thered solid dots refer to the data obtained by Nelson [21], Hubscher $ Lehmann [22] or Hubscher [23], andgreen solid dots refer to the data obtained by us.


## 4. Photometric Solutions

Photometric solutions of HH Boo were obtained by Dal & Sipahi [16] and Gu¨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 B, V, R, and I light curves shown in Figure 4 were analyzed by using the W-D code [38–41]. During the solution process, the effective temperature of star 1 was chosen as T1 = 5680 K according to our result G2V and Gu¨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., g1 = g2 = 0.32 [42] and A1 = A2 = 0.5 [43]. The limb-darkening coefficients were used according to Claret & Gimenez [44] (x and y are the bolometric and bandpass limb-darkening coefficients).The adjustable parameters include the orbital inclination (i); the mean temperature of star 2 (T2); the monochromatic luminosity of star 1 (L1B, L1V, L1R, L1I); and the dimensionless potential of star 1 (Ω1 = Ω2, mode 3 for overcontact configuration). We chose the initial value of q as 1.70 obtained by Gu¨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 q = 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 f = 12.86%(0.73%) and a mass ratio of q = 1.703(31). The geometrical structures at phases 0.0, 0.25, 0.5, and 0.75 are shown in Figure 7.Table 8
Photometric solutions analyzed using the W-D code.
Parameters Photometric elements  orbital inclination i 69.084(95) mass ratiom2/m1 1.703(31) primary temperatureT1 5680K temperature ratioT2/T1 0.9368(15) Luminosity ratioL1/(L1 + L2) in band B 0.4886(14) Luminosity ratioL2/(L1 + L2) in band B 0.5114(14) Luminosity ratioL1/(L1 + L2) in band V 0.4625(11) Luminosity ratioL2/(L1 + L2) in band V 0.5375(11) Luminosity ratioL1/(L1 + L2) in band R 0.44920(93) Luminosity ratioL2/(L1 + L2) in band R 0.55080(93) Luminosity ratioL1/(L1 + L2) in band I 0.43946(81) Luminosity ratioL2/(L1 + L2) in band I 0.56054(81) Modified dimensionless surface potential of star 1: 4.7504(43) Modified dimensionless surface potential of star 2: 4.7504(43) fillout factor 0.1286(73) Radius of star 1 (relative to semimajor axis) in pole direction 0.31974(42) Radius of star 2 (relative to semimajor axis) in pole direction 0.40786(41) Radius of star 1 (relative to semimajor axis) in side direction 0.33523(51) Radius of star 2 (relative to semimajor axis) in side direction 0.43333(52) Radius of star 1 (relative to semimajor axis) in back direction 0.37208(79) Radius of star 2 (relative to semimajor axis) in back direction 0.46513(71) Equal-volume radius of star 1 (relative to semimajor axis)R1: 0.34436(33) Equal-volume radius of star 2 (relative to semimajor axis)R2: 0.43735(32) Radius ratioR2/R1: 1.2700(15)Figure 6
Observed light curves of HH Boo inB, V, R, and I bands and their fits by theoretical light curves by using the W-D code.Figure 7
Geometrical structure of the A-type intermediate contact binary HH Boo at phases 0.00, 0.25, 0.50, and 0.75.


## 5. Discussions and Conclusions

High-precision CCD light curves inB, V, R, and I 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 q = 1.703(31). The temperature of the less massive component is about ΔT = 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 f<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 Figure4, 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 B, V, and R bands obtained in 2011 by Dal & Sipahi [16] show a positive O’Connell effect (see Figure 3 in their paper). The BVRI light curves published by Gu¨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 Gu¨rol et al. [31] suggest the EW-type 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 theO-C 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 the eclipsing pair of HH Boo is about 6.58 years. With the semiamplitude of the O-C oscillation, the value a12′sin⁡i′ is calculated to be 0.31(3) AU. Then, by using the following equation,(4)fm=4π2GT2a12′sin⁡i′3=m3sin⁡i′3M1+M2+m32,a small mass function of f(m) = 0.00065(22) M⊙ is determined. Combined with the masses of the two components M1 = 0.627 M⊙, M2 = 1.068 M⊙ obtained by Gu¨rol et al. [31], the relations between the orbital inclination and the orbital radius and the mass of the assumed third body in HH Boo are shown in Figure 8. As shown in this figure, the minimal mass of the additional body is 0.129 M⊙ indicating that it is an extremely cool star. By using the same method, some substellar objects orbiting evolved binaries were reported (e.g., [57, 59]). During the photometric solution, no third light is detected. This means that the orbital inclination of the third component could not be extremely lower. However, to further understand the properties of the variation of the light curves and the orbital periods, long-term photometric monitoring is needed.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.



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*Source: 5641518-2019-02-06.xml*