Advances in Astronomy

Advances in Astronomy / 2019 / Article

Research Article | Open Access

Volume 2019 |Article ID 5641518 | https://doi.org/10.1155/2019/5641518

Jia-jia He, Jing-jing Wang, "New Photometric Investigation of the Solar-Type Shallow-Contact Binary HH Bootis", Advances in Astronomy, vol. 2019, Article ID 5641518, 18 pages, 2019. https://doi.org/10.1155/2019/5641518

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

Academic Editor: Yue Wang
Received17 Sep 2018
Accepted12 Dec 2018
Published06 Feb 2019

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 the , , , and 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 = 1.703(31) and a degree of contact factor of = . By including 109 new determined times of light minimum together with those compiled from the literature, it is detected that the diagram shows a cyclic oscillation with a period of = 6.58(11) yr and an amplitude of = 0.0018 d. The cyclic change may reveal the presence of an extremely cool third body orbiting the central binary.

1. Introduction

HH Boo (GSC03472-00641, NSVS 5100852) was first listed as a star with a magnitude of = and a colour index of = 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 = and , respectively. They gave a preliminary ephemeris for the primary minimum asThe 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 = 0.633(42), = 0.78(8) , and = 0.49(5) . 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 = d 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 = 7.39 yr and an amplitude of = 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 of 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].

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 about . 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 .

The first complete , , , and light curves were obtained during three nights on December 25, 27, and 30, 2010, with PI TE CCD camera mounted on the Xinglong 85 cm telescope. The effective field of view of the photometric system is 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.


Stars(mag)(mag)

HH Boo 11.80 11.021
GSC03472-00043 (C) 13.57 12.87
GSC03472-01201 (K) 14.38 13.66

The CCD photometric data obtained on December 25, 27, and 30, 2010, in , , , and bands are listed in Tables 25 and shown in Figure 3, respectively. The complete CCD light curves in the four bands with respect to the linear ephemeris,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 Grol et al. [31].


Hel. JD Hel. JDHel. JDHel. JD

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 -1.721


Hel. JD Hel. JDHel. JDHel. JD

56.31712-1.64456.40860-1.85658.39372-1.62661.34757-1.843
56.31920-1.60756.41042-1.85758.39554-1.60861.34939-1.838
56.32102-1.58456.41225-1.86458.39736-1.59561.35121-1.844
56.32285-1.56358.30797-1.79658.39919-1.56961.35302-1.852
56.32468-1.55058.30980-1.79958.40101-1.55161.35484-1.858
56.32649-1.52158.31163-1.82258.40284-1.53861.35666-1.866
56.32832-1.49458.31345-1.81958.40467-1.51561.35847-1.861
56.33015-1.47758.31528-1.82558.40648-1.50261.36029-1.860
56.33197-1.46158.31710-1.83358.40831-1.48961.36212-1.856
56.33380-1.43258.31893-1.83658.41013-1.48461.36394-1.863
56.33563-1.40458.32075-1.86158.41196-1.47461.36575-1.859
56.33744-1.40458.32257-1.85758.41379-1.47961.36757-1.861
56.33927-1.39358.32440-1.87858.41560-1.46661.36939-1.859
56.34109-1.38558.32622-1.86461.28028-1.48061.37121-1.855
56.34292-1.39158.32805-1.87061.28210-1.47961.37302-1.846
56.34475-1.38458.32987-1.87561.28391-1.46261.37484-1.833
56.34656-1.37758.33169-1.87461.28573-1.46961.37666-1.836
56.34839-1.38658.33352-1.87761.28755-1.48661.37848-1.834
56.35022-1.41458.33535-1.87561.28936-1.48261.38030-1.828
56.35204-1.39858.33716-1.87761.29118-1.48761.38212-1.826
56.35387-1.44158.33899-1.88161.29301-1.50061.38394-1.813
56.35568-1.45758.34081-1.86361.29483-1.53261.38575-1.808
56.35751-1.48858.34264-1.87761.29664-1.53961.38757-1.797
56.35934-1.50058.34447-1.86861.29846-1.54861.38939-1.793
56.36116-1.51558.34629-1.87261.30028-1.56761.39120-1.784
56.36299-1.54458.34811-1.86761.30210-1.58561.39303-1.776
56.36482-1.56358.34993-1.85461.30393-1.59761.39485-1.769
56.36663-1.57858.35176-1.86261.30574-1.61461.39667-1.765
56.36846-1.59958.35359-1.85861.30756-1.63361.39849-1.751
56.37028-1.61858.35541-1.86061.30938-1.65061.40030-1.744
56.37211-1.65158.35724-1.84161.31119-1.66561.40212-1.724
56.37394-1.66258.35906-1.82661.31301-1.68861.40394-1.719
56.37575-1.67958.36088-1.82961.31483-1.69361.40575-1.706
56.37758-1.69258.36271-1.81961.31665-1.70561.40758-1.699
56.37941-1.70958.36453-1.81161.31847-1.71761.40940-1.681
56.38123-1.72758.36635-1.81161.32029-1.73461.41122-1.669
56.38306-1.71858.36818-1.80561.32211-1.73861.41303-1.645
56.38488-1.74558.37000-1.79861.32393-1.74361.41485-1.631
56.38670-1.75458.37183-1.78461.32574-1.76361.41667-1.612
56.38853-1.76458.37365-1.77561.32756-1.75861.41848-1.593
56.39036-1.76958.37548-1.75561.32938-1.76961.42030-1.570
56.39218-1.77158.37730-1.75761.33119-1.79061.42213-1.548
56.39401-1.78958.37912-1.74161.33302-1.79961.42395-1.525
56.39583-1.79958.38095-1.72961.33484-1.79061.42576-1.503
56.39765-1.80658.38277-1.72361.33666-1.81361.42758-1.475
56.39948-1.81158.38460-1.70661.33847-1.81761.42940-1.462
56.40130-1.82758.38643-1.69861.34029-1.820
56.40313-1.83258.38824-1.67861.34211-1.822
56.40496-1.84658.39007-1.65561.34392-1.835
56.40677-1.84158.39189-1.63961.34574-1.834


Hel. JD Hel. JDHel. JDHel. JD

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 -1.920


Hel. JD Hel. JDHel. JDHel. JD

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 -2.016

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 = d that could be explained by mass transfer or/and angular momentum loss via magnetic braking. Subsequently, Grol 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.


JD (Hel.)Error (days)MethodMin.Filtertel

2455556.343800.00017CCDIBXinglong-85cm
2455556.343810.00017CCDIVXinglong-85cm
2455556.344070.00023CCDIIXinglong-85cm
2455556.344160.00021CCDIRXinglong-85cm
2455561.284040.00131CCDIIVXinglong-85cm
2455561.284360.00084CCDIIIXinglong-85cm
2455561.284590.00118CCDIIBXinglong-85cm
2455561.284620.00020CCDIIRXinglong-85cm
2455918.350090.00022CCDIRYNOs-1m
2456308.398430.00010CCDIIYNOs-1m
2456308.398430.00013CCDINYNOs-1m
2456308.398620.00014CCDIRYNOs-1m
2456348.231490.00016CCDIIYNOs-1m
2456348.231630.00017CCDIRYNOs-1m
2456348.231710.00014CCDINYNOs-1m
2456735.408050.00016CCDIRYNOs-1m
2456735.408410.00016CCDIIYNOs-1m
2457068.418990.00017CCDIRYNOs-1m
2457068.419350.00015CCDIIYNOs-1m
2457075.430870.00019CCDIIYNOs-60cm
2457075.430870.00021CCDIRYNOs-60cm
2457079.253980.00013CCDIIYNOs-1m
2457097.258170.00042CCDIIRYNOs-60cm
2457097.258290.00032CCDIIIYNOs-1m
2457408.435080.00035CCDIVYNOs-60cm
2457408.435440.00041CCDIRYNOs-60cm
2457496.385450.00021CCDINYNOs-60cm
2458232.184580.00019CCDIVYNOs-60cm
2458232.184670.00019CCDIIYNOs-60cm
2458232.184790.00016CCDIRYNOs-60cm


2450000+ErrorMethodEcl. typeResidualReference

1274.74700-CCDp-134360.00221-0.00002ROSTE
2749.532800.0007CCD p-88080.00080-0.00150[1]
2764.509650.0003CCD p-87610.00034-0.00189[2]
3141.491200.00018CCDp-7578-0.00024-0.00130WASP
3142.607480.00032CCDs-7574.50.00071-0.00035WASP
3143.403290.00021CCDp-7572-0.00014-0.00120WASP
3143.563650.00021CCDs-7571.50.00088-0.00018WASP
3146.431390.00022CCDs-7562.50.00063-0.00043WASP
3146.589310.00021CCDp-7562-0.00079-0.00184WASP
3828.536550.00085CCDp-54220.00077-0.00173WASP
3831.565310.00033CCDs-5412.50.00220-0.00031WASP
3832.521470.00035CCDs-5409.50.00236-0.00016WASP
3832.680370.00037CCDp-54090.00193-0.00059WASP
3833.476300.00024CCDs-5406.50.00119-0.00133WASP
3833.635820.00028CCDp-54060.00138-0.00114WASP
3837.459640.00031CCDp-53940.00121-0.00134WASP
3851.638930.00022CCDs-5349.5-0.00015-0.00276WASP
3852.435110.00027CCDp-5347-0.00064-0.00324WASP
3852.594990.0002CCDs-5346.5-0.00009-0.00270WASP
3854.507360.0001CCDs-5340.50.00028-0.00233WASP
3855.621820.00036CCDp-5337-0.00059-0.00321WASP
3856.577770.00013CCDp-5334-0.00064-0.00326WASP
4135.733910.00033CCDp-44580.003910.00007WASP
4140.673980.00024CCDs-4442.50.004650.00080WASP
4146.728750.00018CCDs-4423.50.004760.00089WASP
4147.684670.00025CCDs-4420.50.004680.00081WASP
4148.640600.0008pe Irs-4417.50.004610.00073[3]
4150.711030.00025CCDp-44110.00371-0.00016WASP
4157.722380.00015CCDp-43890.004410.00050WASP
4158.678070.00019CCDp-43860.004100.00018WASP
4160.589170.00021CCDp-43800.00320-0.00071WASP
4161.704440.00038CCDs-4376.50.00314-0.00078WASP
4162.662100.00029CCDs-4373.50.004800.00087WASP
4163.618360.00029CCDs-4370.50.005060.00113WASP
4165.688390.00022CCDp-43640.00376-0.00017WASP
4169.674420.0005CCDs-4351.50.006460.00251WASP
4171.584700.00028CCDs-4345.50.004750.00079WASP
4190.544840.00021CCDp-42860.004250.00022WASP
4191.500300.00022CCDp-42830.00371-0.00031WASP
4195.485200.00027CCDs-4270.50.005280.00124WASP
4202.494980.00029CCDs-4248.50.004400.00034WASP
4203.612890.00045CCDp-42450.006980.00292WASP
4204.566120.0002CCDp-42420.004210.00015WASP
4210.462620.00029CCDs-4223.50.005390.00130WASP
4210.620210.00026CCDp-42230.00365-0.00043WASP
4214.445190.00021CCDp-42110.004630.00053WASP
4214.605100.00025CCDs-4210.50.005210.00111WASP
4216.517000.00037CCDs-4204.50.005110.00101WASP
4216.675410.00018CCDp-42040.004190.00008WASP
4217.473210.00028CCDs-4201.50.005320.00121WASP
4218.429270.00032CCDs-4198.50.005380.00127WASP
4218.587030.00032CCDp-41980.00381-0.00029WASP
4219.543490.00037CCDp-41950.004270.00016WASP
4220.498550.00035CCDp-41920.00333-0.00077WASP
4221.454340.00039CCDp-41890.00313-0.00099WASP
4222.572300.00043CCDs-4185.50.005750.00163WASP
4223.529430.00028CCDs-4182.50.006880.00276WASP
4225.597970.00022CCDp-41760.00409-0.00003WASP
4226.395700.00018CCDs-4173.50.005160.00102WASP
4227.508770.0005CCDp-41700.00290-0.00123WASP
4230.539330.00056CCDs-4160.50.006130.00198WASP
4231.494530.00028CCDs-4157.50.005330.00118WASP
4232.450500.00026CCDs-4154.50.005300.00115WASP
4232.608340.00042CCDp-41540.00381-0.00034WASP
4233.406750.00019CCDs-4151.50.005550.00140WASP
4233.564340.0003CCDp-41510.00381-0.00034WASP
4234.520390.00056CCDp-41480.00386-0.00029WASP
4235.475730.00059CCDp-41450.00320-0.00095WASP
4236.432400.00033CCDp-41420.00387-0.00028WASP
4236.592750.00037CCDs-4141.50.004890.00072WASP
4247.586200.00022CCDp-41070.004360.00016WASP
4249.497160.00069CCDp-41010.00332-0.00087WASP
4250.452450.00079CCDp-40980.00261-0.00158WASP
4251.409600.00023CCDp-40950.00376-0.00044WASP
4252.527220.00036CCDs-4091.50.006050.00184WASP
4254.437990.00026CCDs-4085.50.004820.00061WASP
4256.507810.00031CCDp-40790.00331-0.00090WASP
4257.464640.00027CCDp-40760.00414-0.00007WASP
4260.493830.00047CCDs-4066.50.006000.00177WASP
4261.449160.0003CCDs-4063.50.005340.00110WASP
4265.431340.00027CCDp-40510.00419-0.00005WASP
4513.513600.0004pe Irs-3272.50.004810.00022[4]
4599.393520.0004CCD -Rp-30030.00418-0.00034[5]
4912.323300.0008pe Irp-20210.003750.00001[4]
4912.483500.0003pe Irs-2020.50.004610.00088[4]
4937.339200.0002pe Irs-1942.50.004350.00071[4]
4958.688700.0009pe s-1875.50.00321-0.00033[6]
4958.849000.003pe p-18750.004180.00063[6]
5243.892000.0002pe s-980.50.00026-0.00203[7]
5259.984800.0002CCDp-9300.00041-0.00180[8]
5322.442780.0001CCD p-734-0.00018-0.00214[9]
5384.424800.0042CCD -Irs-539.50.00126-0.00045[10]
5542.326500.006CCD DSLRp-440.003850.00261[11]
5556.343800.00017CCD p0-0.00016-0.00136The present paper
5556.343810.00017CCD p0-0.00015-0.00135The present paper
5556.344070.00023CCD p00.00011-0.00109The present paper
5556.344160.00021CCD p00.00020-0.00100The present paper
5561.284040.00131CCD s15.50.00075-0.00044The present paper
5561.284360.00084CCD s15.50.00107-0.00012The present paper
5561.284590.00118CCD s15.50.001300.00010The present paper
5561.284620.0002CCD s15.50.001330.00013The present paper
5602.550800.0006CCDp1450.00024-0.00087[12]
5609.403000.001CCDs166.50.001120.00001[12]
5637.445900.0006CCDs254.50.001390.00032[12]
5644.933600.0003pe p2780.00043-0.00061[9]
5645.412800.0002CCDs279.50.001630.00058[12]
5645.570800.0003CCDp2800.00030-0.00074[12]
5647.483000.0005CCDp2860.00050-0.00054[12]
5648.438600.0012CCDp2890.00011-0.00094[12]
5676.481200.0002CCD -Irp3770.00008-0.00093[13]
5678.392900.0002CCDp383-0.00022-0.00123[14]
5678.553800.0004CCDs383.50.001350.00033[14]
5680.785300.0002pe s390.50.002190.00117[9]
5682.378100.0004CCDs395.50.001650.00064[14]
5682.535600.0003CCDp396-0.00018-0.00119[14]
5686.367490.0008CCDp4080.007720.00670[15]
5716.476700.0003CCD s502.50.002970.00198[16]
5716.476800.0005CCD s502.50.003070.00208[16]
5716.476800.0002CCD s502.50.003070.00208[16]
5743.402600.0003CCD p5870.001580.00059[16]
5743.403200.0004CCD p5870.002180.00119[16]
5743.403800.0002CCD p5870.002780.00179[16]
5747.386300.0005CCD s599.50.001950.00096[16]
5747.387100.0003CCD s599.50.002750.00176[16]
5747.387400.0002CCD s599.50.003050.00206[16]
5751.369600.0003CCD p6120.001920.00093[16]
5751.370000.0003CCD p6120.002320.00133[16]
5751.370000.0003CCD p6120.002320.00133[16]
5751.370100.0002CCD p6120.002420.00143[16]
5751.370200.0003CCD p6120.002520.00153[16]
5751.370200.0004CCD p6120.002520.00153[16]
5918.350090.00022CCD p11360.001320.00019The present paper
6011.877800.0004CCD s1429.50.00050-0.00084[17]
6012.357000.0001CCD op14310.001700.00035[10]
6013.471980.0001CCDs1434.50.001340.00000[15]
6013.473500.0005CCD -Irs1434.50.002860.00152[10]
6013.629180.0001CCDp1435-0.00079-0.00213[15]
6013.632300.0011CCD -Irp14350.002330.00098[10]
6046.295700.0001CCD s1537.50.002450.00100[18]
6046.453700.0002CCD p15380.00111-0.00032[18]
6065.416600.0014CCD -Irs1597.50.003370.00187[19]
6076.726100.0004CCD p16330.00022-0.00131[17]
6091.385900.00006CCD p16790.00138-0.00020[20]
6092.342900.00008CCD p16820.002380.00079[20]
6092.502400.00015CCD s1682.50.002550.00095[20]
6308.398430.0001CCD p23600.00222-0.00023The present paper
6308.398430.00013CCD Np23600.00222-0.00023The present paper
6308.398620.00014CCD p23600.00241-0.00004The present paper
6348.231490.00016CCD p24850.00200-0.00063The present paper
6348.231630.00017CCD p24850.00214-0.00049The present paper
6348.231710.00014CCD Np24850.00222-0.00041The present paper
6690.958500.0002CCD Cs3560.50.00351-0.00054[21]
6735.408050.00016CCD p3700-0.00088-0.00506The present paper
6735.408410.00016CCD p3700-0.00052-0.00470The present paper
6764.412700.0017CCD -Ip37910.005150.00088[22]
6764.571700.0004CCD -Is3791.50.004810.00055[22]
6772.378600.0017CCD -Ip38160.004390.00010[22]
6772.538100.0031CCD -Is3816.50.004560.00027[22]
7068.418990.00017CCD p47450.00387-0.00067[22]
7068.419350.00015CCD p47450.00423-0.00031[22]
7075.430870.00019CCD p47670.005100.00055The present paper
7075.430870.00021CCD p47670.005100.00055The present paper
7079.253980.00013CCD p47790.00421-0.00033The present paper
7097.258170.00042CCD s4835.50.00376-0.00076The present paper
7097.258290.00032CCD s4835.50.00388-0.00064The present paper
7100.448600.0037CCD -Is4845.50.007530.00300[23]
7100.604400.0009CCD -Ip48460.00400-0.00052[23]
7408.435080.00035CCD p58120.00312-0.00059The present paper
7408.435440.00041CCD p58120.00348-0.00023The present paper
7496.385450.00021CCD Np60880.00162-0.00173The present paper
8232.184580.00019CCD p83970.00047-0.00051The present paper
8232.184670.00019CCD p83970.00056-0.00042The present paper
8232.184790.00016CCD p83970.00068-0.00030The present paper

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 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 Grol 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 = 6.58(11) yr and an amplitude of = 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.

4. Photometric Solutions

Photometric solutions of HH Boo were obtained by Dal & Sipahi [16] and Grol 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 [3841]. During the solution process, the effective temperature of star 1 was chosen as = 5680 K according to our result G2V and Grol 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., = = 0.32 [42] and = = 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 (); the mean temperature of star 2 (); the monochromatic luminosity of star 1 (, , , ); and the dimensionless potential of star 1 ( = , mode 3 for overcontact configuration). We chose the initial value of as 1.70 obtained by Grol 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 = 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.


Parameters Photometric elements

orbital inclination i 69.084(95)
mass ratio 1.703(31)
primary temperature 5680K
temperature ratio / 0.9368(15)
Luminosity ratio /( + ) in band 0.4886(14)
Luminosity ratio /( + ) in band 0.5114(14)
Luminosity ratio /( + ) in band 0.4625(11)
Luminosity ratio /( + ) in band 0.5375(11)
Luminosity ratio /( + ) in band 0.44920(93)
Luminosity ratio /( + ) in band 0.55080(93)
Luminosity ratio /( + ) in band 0.43946(81)
Luminosity ratio /( + ) in band 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) : 0.34436(33)
Equal-volume radius of star 2 (relative to semimajor axis) : 0.43735(32)
Radius ratio /: 1.2700(15)

5. 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 = 359 K higher than that of the more massive one. The fill-out factor is about 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 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 Grol 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 Grol 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 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 the eclipsing pair of HH Boo is about 6.58 years. With the semiamplitude of the oscillation, the value is calculated to be 0.31(3) AU. Then, by using the following equation,a small mass function of = 0.00065(22) is determined. Combined with the masses of the two components = 0.627 , = 1.068 obtained by Grol 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 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.

Data Availability

All our data is already shown in the paper.

Disclosure

This paper makes use of data from the DR1 of the WASP data [60] as provided by the WASP consortium, and the computing and storage facilities at the CERIT Scientific Cloud, reg. no. CZ.1.05/3.2.00/08.0144 which is operated by Masaryk University, Czech Republic.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This project was supported by the Joint Research Fund in Astronomy (no. U1831109) under cooperative agreement between the National Natural Science Foundation of China (NSFC) and CAS and the Key Laboratory for the Structure and Evolution of Celestial Objects, CAS (no. OP201708). The low-resolution spectrograms were observed by Dr. Yuangui Yang using Xinglong 2.16 m telescope, and we would like to thank him. CCD photometric observations of HH Boo were obtained with Xinglong 85 cm telescope, the 1 m and the 60 cm R-C reflect telescope, Yunnan Astronomical Observatory of CAS.

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Copyright © 2019 Jia-jia He and Jing-jing Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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