Advances in Astronomy
Volume 2019 (2019), Article ID 5641518, 18 pages
https://doi.org/10.1155/2019/5641518

Research Article

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

Jia-jia He1,2,3 and Jing-jing Wang2,4

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

Correspondence should be addressed to Jia-jia He; hjj@ynao.ac.cn

Received 17 September 2018; Accepted 12 December 2018; Published 6 February 2019

Academic Editor: Yue Wang

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.

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 as

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 = 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].

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 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.

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

Stars

(mag)
(mag)

HH Boo

11.80
11.021

GSC03472-00043 (C)

13.57
12.87

GSC03472-01201 (K)

14.38
13.66

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

The CCD photometric data obtained on December 25, 27, and 30, 2010, in , , , and bands are listed in Tables 2–5 and shown in Figure 3, respectively. The complete CCD light curves in the four bands with respect to the linear ephemeris,

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].

Table 2: The observations in band for HH Boo (Hel. JD 2,455,500+).

Hel. JD

Hel. JD

Hel. JD

Hel. 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

Table 3: The observations in band for HH Boo (Hel. JD 2,455,500+).

Hel. JD

Hel. JD

Hel. JD

Hel. JD

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
-1.834

Table 4: The observations in band for HH Boo (Hel. JD 2,455,500+).

Hel. JD

Hel. JD

Hel. JD

Hel. 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

Table 5: The observations in band for HH Boo (Hel. JD 2,455,500+).

Hel. JD

Hel. JD

Hel. JD

Hel. 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

Figure 3: CCD photometric observations for HH Boo in the , , , and 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 the , , , and bands obtained using the Xinglong 85 cm telescope in 2012. The magnitude differences between the comparison and the check stars are shown in the low pane.

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.

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-60cm

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

2450000+
Error
Method
Ecl. type

Residual
Reference

1274.74700
-
CCD
p
-13436
0.00221
-0.00002
ROSTE

2749.53280
0.0007
CCD
p
-8808
0.00080
-0.00150
[1]

2764.50965
0.0003
CCD
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
pe
s
-1875.5
0.00321
-0.00033
[6]

4958.84900
0.003
pe
p
-1875
0.00418
0.00063
[6]

5243.89200
0.0002
pe
s
-980.5
0.00026
-0.00203
[7]

5259.98480
0.0002
CCD
p
-930
0.00041
-0.00180
[8]

5322.44278
0.0001
CCD
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
CCD
p
0
-0.00016
-0.00136
The present paper

5556.34381
0.00017
CCD
p
0
-0.00015
-0.00135
The present paper

5556.34407
0.00023
CCD
p
0
0.00011
-0.00109
The present paper

5556.34416
0.00021
CCD
p
0
0.00020
-0.00100
The present paper

5561.28404
0.00131
CCD
s
15.5
0.00075
-0.00044
The present paper

5561.28436
0.00084
CCD
s
15.5
0.00107
-0.00012
The present paper

5561.28459
0.00118
CCD
s
15.5
0.00130
0.00010
The present paper

5561.28462
0.0002
CCD
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
pe
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
pe
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
CCD
s
502.5
0.00297
0.00198
[16]

5716.47680
0.0005
CCD
s
502.5
0.00307
0.00208
[16]

5716.47680
0.0002
CCD
s
502.5
0.00307
0.00208
[16]

5743.40260
0.0003
CCD
p
587
0.00158
0.00059
[16]

5743.40320
0.0004
CCD
p
587
0.00218
0.00119
[16]

5743.40380
0.0002
CCD
p
587
0.00278
0.00179
[16]

5747.38630
0.0005
CCD
s
599.5
0.00195
0.00096
[16]

5747.38710
0.0003
CCD
s
599.5
0.00275
0.00176
[16]

5747.38740
0.0002
CCD
s
599.5
0.00305
0.00206
[16]

5751.36960
0.0003
CCD
p
612
0.00192
0.00093
[16]

5751.37000
0.0003
CCD
p
612
0.00232
0.00133
[16]

5751.37000
0.0003
CCD
p
612
0.00232
0.00133
[16]

5751.37010
0.0002
CCD
p
612
0.00242
0.00143
[16]

5751.37020
0.0003
CCD
p
612
0.00252
0.00153
[16]

5751.37020
0.0004
CCD
p
612
0.00252
0.00153
[16]

5918.35009
0.00022
CCD
p
1136
0.00132
0.00019
The present paper

6011.87780
0.0004
CCD
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
CCD
s
1537.5
0.00245
0.00100
[18]

6046.45370
0.0002
CCD
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
CCD
p
1633
0.00022
-0.00131
[17]

6091.38590
0.00006
CCD
p
1679
0.00138
-0.00020
[20]

6092.34290
0.00008
CCD
p
1682
0.00238
0.00079
[20]

6092.50240
0.00015
CCD
s
1682.5
0.00255
0.00095
[20]

6308.39843
0.0001
CCD
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
CCD
p
2360
0.00241
-0.00004
The present paper

6348.23149
0.00016
CCD
p
2485
0.00200
-0.00063
The present paper

6348.23163
0.00017
CCD
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
CCD
p
3700
-0.00088
-0.00506
The present paper

6735.40841
0.00016
CCD
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
CCD
p
4745
0.00387
-0.00067
[22]

7068.41935
0.00015
CCD
p
4745
0.00423
-0.00031
[22]

7075.43087
0.00019
CCD
p
4767
0.00510
0.00055
The present paper

7075.43087
0.00021
CCD
p
4767
0.00510
0.00055
The present paper

7079.25398
0.00013
CCD
p
4779
0.00421
-0.00033
The present paper

7097.25817
0.00042
CCD
s
4835.5
0.00376
-0.00076
The present paper

7097.25829
0.00032
CCD
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
CCD
p
5812
0.00312
-0.00059
The present paper

7408.43544
0.00041
CCD
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
CCD
p
8397
0.00047
-0.00051
The present paper

8232.18467
0.00019
CCD
p
8397
0.00056
-0.00042
The present paper

8232.18479
0.00016
CCD
p
8397
0.00068
-0.00030
The 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.

Figure 5: diagram of the short-period close binary HH Boo based on all the primary and secondary available photoelectric and CCD times of light minimum. The black solid line showed a cyclic period variation with a period of 6.58 yr. Residuals after the cyclic change was removed are shown in the lower panel. The black solid dots refer to the data collected by Grol et al. [31], the blue solid dots refer to the data by WASP database, the red solid dots refer to the data obtained by Nelson [21], Hubscher Lehmann [22] or Hubscher [23], and green solid dots refer to the data obtained by us.

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 [38–41]. 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.

Table 8: Photometric solutions analyzed using the W-D code.

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)

Figure 6: Observed light curves of HH Boo in , , , and 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 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.

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.

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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