mass transfer and intrinsic light variability in the...

Research ArticleMass Transfer and Intrinsic Light Variability in the ContactBinary MT Cas

Haifeng Dai Huiyu Yuan and Yuangui Yang

School of Physics and Electronic InformationInformation College Huaibei Normal University Huaibei 235000 China

Correspondence should be addressed to Yuangui Yang yygcn163com

Received 12 November 2018 Accepted 19 March 2019 Published 4 April 2019

Academic Editor Dean Hines

Copyright copy 2019 Haifeng Dai et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

First CCD photometry for the contact binary MT Cas is performed in 2013 in December The spectral type of F8V is determinedfrom the low-precision spectrum observed on 2018 Oct 22 With Wilson-Devinney code the photometric solutions are deducedfrom119881119877119888 light curves (LCs) andAAVSOrsquos andASAS-SNrsquos data respectivelyThe results imply thatMTCas is aW-typeweak-contactbinary with a mass ratio of 119902 = 2365(plusmn0005) and a fill-out factor of 119891 = 166(plusmn12) respectively The asymmetric LCs in 2013are modeled by a dark spot on the more massive component By analyzing the (119874minus119862) curve it is discovered that the orbital periodmay be undergoing a secular increase at a rate of 119889119875119889119905 = 112(plusmn009) times 10minus8d yrminus1 which may result from mass transfer from theless massive component to the more massive one With mass transferring MT Cas may evolve into a broken-contact configurationas predicted by TRO theory

1 Introduction

W Ursae Majoris binary contains two components whichare embedded in a common envelope [1 2] Models forcontact binary have been recently constructed by severalinvestigators (eg see [3ndash5]) However their evolutionarystatus still remains unclear because the spectra cannot beanalyzed for abundances due to the extreme broadening andblending of spectral lines Therefore it is crucially importantto observe contact binaries which may provide some specialphenomena and processes such as magnetic activity [6]third body [7] angular momentum evolution [3] flare [8]and stellar coalescence [9] It is helpful for us to understandtheir formation structure and evolution of contact binaries

MT Cas (=SVlowast SON 4671) was found by Gotz amp Wenzel[10] as a W UMa-type eclipsing binary Its visual magnitudeis 133mag and the depths of both eclipses are 083mag and072 mag respectively [11] Hoffmann [12] photoelectricallyobserved this binary Unfortunately the 119861119881 light curves didnot cover the complete period Pribulla et al [13] derived alinear ephemeris with a period of 031387775 days whichwas updated to be 03138789 days [14] Except for somephotometric data performed by several amateur observers of

AAVSO (httpswwwaavsoorgdata-download) and ASAS-SN database [15] (httpsasas-snosuedudatabaselightcurves335960) no additional observations for this binaryhave been presented up to now

In this paper the neglected binary MT Cas was studiedphotometrically and spectroscopically in Section 2 Theorbital period variation is analyzed in Section 3 and three setsof light curves (ie119881119877119888 LCs in 2013 AAVSOrsquos LC and ASAS-SN LC) are modeled in Section 4 In Section 5 we estimatedthe absolute parameters and discuss mass transfer betweentwo components and its evolutionary status

2 New Observations

21 Photometry CCD photometry for MT Cas was firstcarried out at six nights of 2013 with the 85-cm telescope[16] at the Xinglong station (XLs) of National AstronomicalObservatories of China (NAOC) The standard Johnson-Cousins UBVR119888I119888 systems were mounted onto this telescopeDuring the observation 119881119877119888 files are used in order to providethe enough high time resolution The image reductions aredone by using the Image Reduction (IMRED) and AperturePhotometry (APPHOT) packages in the Image Reduction

HindawiAdvances in AstronomyVolume 2019 Article ID 4593092 9 pageshttpsdoiorg10115520194593092

2 Advances in Astronomy

Table 1 CCD photometric observations in 119881 and 119877119888 bands119881 band 119877119888 band

HJD Δ119898 HJD Δ119898 HJD Δ119898 HJD Δ11989824566299265 +0066 24566329847 minus0273 24566299275 +0269 24566329895 minus007624566299285 +0106 24566329861 minus0280 24566299294 +0322 24566329962 minus009124566299304 +0133 24566329874 minus0273 24566299314 +0349 24566329976 minus011324566299323 +0176 24566329901 minus0289 24566299333 +0384 24566329989 minus009924566299343 +0225 24566329915 minus0300 24566299352 +0413 24566330003 minus011624566329766 minus0235 24566360355 minus0077 24566329814 minus005724566329780 minus0238 24566360373 minus0041 24566329827 minus006924566329793 minus0263 24566360391 minus0041 24566329841 minus006924566329807 minus0267 24566360409 +0007 24566329854 minus006324566329820 minus0270 24566360427 +0065 24566329868 minus008124566329834 minus0261 24566329881 minus0076NoteThe entire table is available only on the online journal

VRc-04mag

04

02

00

minus02

minus04

minus06

Δm

(mag

)

02 04 06 08 10 1200

Phase

Figure 1 119881119877119888 light curves of the contact binary MT Cas which areobserved in 2013 in December by using the 85-cm telescope Thedotted and solid lines are plotted by photometric solutions withoutor with a dark spot respectively

and Analysis Facility (IRAF) in a standard mode Differentialmagnitudes were then determined by aperture photometry

In the observing process we chose TYC 3657-1637-1(1205721198692000 = 00ℎ14119898591199044 and 1205751198692000 = +54∘39101584053101584010158401) andTYC 3657-1245-1 (1205721198692000 = 00ℎ14119898321199046 and 1205751198692000 =+54∘29101584016101584010158401) as the comparison and check stars respec-tively Typical exposure times are adopted to be 60s in119881 bandand 50s in119877119888 band respectively In total we obtained 383 and373 images in 119881 and 119877119888 bands The standard uncertaintiesare plusmn0005 mag in 119881 band and plusmn0004 mag in 119877119888 bandAll individual observations (ie HJD and Δ119898) are listed inTable 1 The differential magnitudes versus orbital phases aredisplayed in Figure 1 where phases are computed by a period

of 01198893138789 (Kreiner et al 2004) The 119881119877119888 LCs in 2013imply that MT Cas is an UMa-type eclipsing binary whoseamplitudes of variable light are 069 mag and 066 mag in119881 and 119877119888 bands respectively There exists an unequal heightbetween both maxima ie OrsquoConnell effect [17 18] MaxIIat phase 075 is brighter than MaxI at phase 025 up to 0025mag and 0029mag in119881 and 119877119888 bands respectivelyThis kindof stellar activity occurs on other WUMa-type binaries suchas VW Cep [19] DV CVn [20] V532 Mon [21] and BB Peg(Kalomeni et al 2007) and DZ Psc [22]

22 Low-Precision Spectrum The low-precision spectrum forMT Cas was obtained by using the Yunnan Faint ObjectSpectrograph and Camera (YFOSC) which is attached to the24-m telescope at Lijiang station (LJs) of Yunnan Astro-nomical Observatory of China (YNAO) at UT 155013 of2018 October 22 During the observing process we chosea 140-mm-length slit and a Grism-3 with a wavelengthrange from 3200 A to 9200 A [23] The exposure time is10 minutes The phase of 098 almost corresponds to theobserved middle time HJD 2454141634 Reduction of thespectra was performed by using IRAF packages includ-ing bias subtraction flat-fielding and cosmic-ray removalFinally the one-dimensional spectrum was extracted Withthe winmk software (httpwwwappstateedusimgrayroMKwinmkhtm) we obtained a normalized spectrum which isdisplayed in Figure 2 By comparing the spectra of standardstars [24] the spectral type is determined to be F8V forthe primary (ie more massive component) of this binarybecause the secondary is eclipsed by the primary aroundphase 00 for the W-type contact binary (see Section 4)

3 Eclipse Times and Period Analysis

From our new observations and AAVSOrsquos data several timesof primary and secondary minima are generally determinedby using the method of Kwee amp van Woerden [25] FromASAS-SN database we downloaded 134 data types inV band

Advances in Astronomy 3

Table 2 New observed light minimum times

JD(Hel) Error Min Band TelescopeSource245662994355 plusmn000025 II 119881 85-cm (NAOC)245662994379 plusmn000022 II 119877119888 85-cm (NAOC)245663198406 plusmn000015 I 119881 85-cm (NAOC)245663198401 plusmn000014 I 119877119888 85-cm (NAOC)245663402521 plusmn000010 II 119881 85-cm (NAOC)245663402392 plusmn000027 II 119877119888 85-cm (NAOC)245656920623 plusmn000022 I 119881 AAVSO245656936322 plusmn000007 II 119881 AAVSO245657328617 plusmn000025 I 119881 AAVSO245657360003 plusmn000011 I 119881 AAVSO245657642499 plusmn000018 I 119881 AAVSO245657658236 plusmn000010 II 119881 AAVSO245657924973 plusmn000008 I 119881 AAVSO245657956341 plusmn000007 I 119881 AAVSO245701176746 II 119881 ASAS-SN

18

16

14

12

10

08

06

04

Rect

ified

Inte

nsity

3500 4000 4500 5000 5500 6000

Wavelength (angstroms)

MT Cas

NaHHH

Ca IIK amp H F8V

Figure 2 Spectroscopic observation for MT Cas observed by the24-m telescope at Lijiang station of YNAO on October 22 2018

for this binary With the Period04 package [26] we obtainedthe power spectrumwhich is shown inFigure 3The searchedfrequency is 1198911 = 637192dminus1 corresponding to 0156937days (ie half of an orbital period) The derived epoch HJD24570109922 (ie the secondary eclipse time) a bit differsfrom the given rough epoch HJD 245701176746 from theASAS-SN database The individual single-color minimumtimings with their errors are listed in Table 2

In order to construct the (119874 minus 119862) curve (ie ob-served values minus calculated ones) we collected allavailable light minimum times From the 119874 minus 119862 gateway(httpvar2astrocz) and TIDAK [14] (httpwwwasupkrakowplminicalcCASMTHTM) we accumulated 10 ldquopgrdquo(ie photographic) 21 ldquoperdquo (ie photoelectric) and 34 CCDmeasurements Table 3 lists all those eclipsing times whose

008

006

004

002

000

Pow

er

0 1 2 3 4 5 6 7 8 9 10

Frequency (day-1)

f1

Figure 3 The power spectrum for 134 ASAS-SN data types byFourier analysis

errors are not given for 10 pg 4 pe and 1 CCD from literatureThe standard derivations for all pe andCCDdata are averagedto be 000137 days For light minimum times without errorswe adopted the errors of 00137 for 10 pg data and 00014 daysfor 4 pe and 2 CCD onesTherefore the used weights dependon their errors while fitting the (119874 minus 119862) curve

By using the linear ephemeris [14]

MinI = HJD 2452500086 + 03138789 times 119864 (1)

we compute the initial residuals (119874 minus 119862)119894 which are listedin Table 3 and shown in Figure 4(a) From this figure thereexists a long gap between HJD 2430024400 [10] and HJD24515502943 [27] except for three data types [12] Howeverthe general trend of (119874minus119862)119894may be evidently described by an


Table 3 All light minimum times for MT Cas

JD(Hel) Error Epoch Method Min (119874 minus 119862)119894 (119874 minus 119862)119891 Ref(days) (days)

2429113517 minus745085 pg II +00160 minus00055 (1)2429129388 minus744580 pg I +00362 +00147 (1)2429144431 minus744100 pg I +00131 minus00083 (1)2429170336 minus743275 pg II +00231 +00017 (1)2429229342 minus741395 pg II +00200 minus00013 (1)2429249431 minus740755 pg II +00208 minus00004 (1)2429464441 minus733905 pg II +00243 +00035 (1)2429491425 minus733045 pg II +00148 minus00059 (1)2429498493 minus732820 pg I +00205 minus00002 (1)2430024400 minus716065 pg II +00247 +00050 (1)24449015705 minus242085 pe II minus00004 minus00015 (2)24449415925 minus240810 pe I +00021 +00010 (2)24449552420 minus240375 pe II minus00021 minus00032 (2)24515502943 plusmn00030 minus30260 CCD I minus00001 +00000 (2)24517803698 plusmn00021 minus22930 CCD I +00028 +00029 (3)24518073638 plusmn00002 minus22070 pe I +00032 +00033 (2)24519242811 plusmn00016 minus18345 CCD II +00009 +00010 (4)24520964442 plusmn00031 minus12860 CCD I +00019 +00019 (3)24521513705 plusmn00025 minus11110 CCD I minus00005 minus00004 (3)24521902867 plusmn00016 minus9870 CCD I minus00052 minus00052 (5)24522053590 plusmn00031 minus9390 CCD I +00010 +00010 (3)24522055152 plusmn00016 minus9385 CCD II +00002 +00002 (3)24522194813 plusmn00028 minus8940 CCD I minus00013 minus00013 (3)2452574321 plusmn0002 2365 CCD II minus00008 minus00008 (2)24526843376 plusmn00056 5870 CCD I +00015 +00014 (2)24528594828 11450 CCD I +00027 +00026 (3)24528795725 plusmn00033 12090 CCD I +00042 +00041 (2)24533026749 plusmn00004 25570 CCD I minus00011 minus00013 (2)24533296671 plusmn00002 26430 CCD I minus00024 minus00027 (2)24533533663 plusmn00007 27185 CCD II minus00010 minus00013 (2)24537386533 plusmn00001 39460 CCD I +00006 +00002 (2)24537593698 plusmn00022 40120 pe I +00011 +00007 (2)24537675305 plusmn00001 40380 CCD I +00010 +00006 (2)24542053900 plusmn00014 54330 pe I +00005 minus00001 (2)24544323199 plusmn00003 61560 pe I minus00035 minus00041 (2)24544324779 plusmn00002 61565 pe II minus00024 minus00030 (2)24547926557 plusmn00004 73040 CCD I +00002 minus00006 (2)24550674622 plusmn00014 81795 pe II +00064 +00055 (2)24550743675 plusmn00006 82015 pe II +00064 +00055 (2)24550745247 plusmn00004 82020 pe I +00067 +00058 (2)24554733027 plusmn00009 94725 pe II +00025 +00014 (2)24554734600 plusmn00056 94730 pe I +00029 +00018 (2)24554736167 plusmn00008 94735 pe II +00026 +00015 (2)24555177157 plusmn00003 96140 CCD I +00018 +00006 (2)24557975418 plusmn00087 105055 pe II +00055 +00042 (2)24562547090 plusmn00002 119620 CCD I +00092 +00076 (2)24565692062 plusmn00002 129640 CCD I +00006 minus00011 (6)24565693632 plusmn00001 129645 CCD II +00006 minus00011 (6)24565732862 plusmn00003 129770 CCD I +00001 minus00017 (6)24565736000 plusmn00001 129780 CCD I +00001 minus00017 (6)


Table 3 Continued


24565764250 plusmn00002 129870 CCD I +00001 minus00017 (6)24565765824 plusmn00001 129875 CCD II +00005 minus00013 (6)24565792497 plusmn00001 129960 CCD I +00000 minus00018 (6)24565795634 plusmn00001 129970 CCD I minus00002 minus00019 (6)24566299437 plusmn00002 131575 CCD II +00026 +00008 (6)24566319840 plusmn00001 131640 CCD I +00027 +00009 (6)24566340246 plusmn00002 131705 CCD II +00031 +00013 (6)24569502602 plusmn00013 141780 pe I +00065 +00045 (2)24569504193 plusmn00015 141785 pe II +00086 +00066 (2)24569505733 plusmn00005 141790 pe I +00057 +00037 (2)24570109918 143715 CCD II +00037 minus00017 (6)24572974095 152840 pe I +00066 +00044 (2)24573223625 plusmn00006 153635 pe II +00062 +00040 (2)24573642629 plusmn00004 154970 pe I +00039 +00016 (2)24573644204 plusmn00018 154975 pe II +00045 +00022 (2)Ref (1) Gotz ampWenzel 1956 (2) httpwwwkonkolyhuIBVSIBVShtml (3) [41] (4) [42] (5) [43] (6) present work

Year1935 1950 1965 1980 1995 2010 2025

+ 004+ 003+ 002+ 001000

minus001

+ 002+ 001000

minus001

minus002

(O-C

) i(d

ays)

(O-C

) f(d

ays)

minus80000 minus60000 minus40000 minus20000 0 20000

Epoch

pgpeCCD

(a)

(b)

Figure 4 The (119874 minus 119862) curve for MT Cas The crossing open andsolid circles represent photographic data andphotoelectric andCCDmeasurements respectively The continuous line is plotted by Eq(2)

upward parabolic curve A linear least-squares fitting methodwith weights leads to the following ephemeris

Min I = HJD 24525000896 (plusmn00011)+ 031387820 (plusmn000000002) times 119864+ 482 (plusmn004) times 10minus12 times 1198642

(2)

After being removed by Eq (2) we obtained the finalresiduals of (119874minus119862)119891 which are listed in Table 3 and shown inFigure 4(b) If we neglected low-precision photographic datawe could find no regularity such as sinusoidal variation only

from pe and CCD data which can be directly seen from theright part of Figure 4(b) except for a bit scatter

4 Modeling Light Curves

From the AAVSO and ASAS-SN databases two additionalV-band LCs for MT Cas are available and are displayed inFigure 5 Therefore three sets LCs are applied to derive thephotometric elements with the updated Wilson-Devinneybinary star modeling program [28 29] (W-D programcan be accessed from the site of ftpftpastroufledupubwilsonlcdc2015) Kuruczrsquos [30] stellar atmosphere modelwas applied Based on the spectral type of F8V with asubtype error we adopted a mean effective temperaturefor the more massive component (ie the primary) to be119879119901 = 5750(plusmn210) K (the subscripts ldquoprdquo and ldquosrdquo refer to theprimary component and the secondary one respectively)We fixed the gravity-darkening coefficients of 119892119901119904 = 032[31] and bolometric albedo coefficients of 119860119901119904 = 05 [32]which are appropriate for starswith convective envelopesThelogarithmic limb-darkening coefficients are interpolate fromvan Hammersquos [33] tables Other adjustable parameters are 119894119902 119879119904 Ω119901 = Ω119904 and 119871 119904

Due to lack of radial velocity curves the ldquoq-searchrdquoprocess is carried out by obtaining a series of tried solutionsfrom119881119877119888 light curves Modeling calculations start to mode 2(ie detached configuration) and always converge to mode 3(ie contact one) For several fixed inclinations from 70∘ to90∘ with a step of 5∘ we first performed a series of solutionsFive computed curves for 119902 minus 119894 are shown in Figure 6(a)in which a minimum squared residual Σ(119900 minus 119888)2119894 occursaround 119902 = 24 and 119894 = 85∘ As a free parameter for theorbital inclination we obtained the relations of 119902 minus Σ and119902 minus 119891 (the fill-out factor for contact binary is defined by119891 = (Ω119894119899 minus Ω)(Ω119894119899 minus Ω119900119906119905) in which Ω119894119899 and Ω119900119906119905 are


134

132

130

128

126

124V

(mag

)

02 04 06 08 10 1200

Phase(a)

02 04 06 08 10 1200

Phase

134

132

130

128

126

124

V (m

ag)

(b)

Figure 5 AAVSOrsquos (a) and ASASrsquo (b) light curves The solid lines are the theoretical LCs which are computed by the photometric solutions

00 05 10 15 20 25 30 35 40

q

03

06

09

12

15

Σ(o

-c)2 i

i=90∘

i=85∘

i=80∘

i=75∘

i=70∘

(a)

00 05 10 15 20 25 30 35

q

060

055

050

045

04035

30

25

20

15

10

fill-o

ut (

)Σ

(o-c

)2 i

(b)

Figure 6 The relations of 119902 minus 119894 (a) 119902 minus Σ and 119902 minus 119891 (b) derived from 119881119877119888 light curves in 2013

inner and outer critical potentials respectively) which aredisplayed in Figure 6(b) The mass-ratio of 119902 = 24 with aminimum value of Σ(119900 minus 119888)2119894 indicates that MT Cas is a W-type contact binary (ie the less massive component eclipsedby the more massive component at the primary minima see[34]) After 119902 is considered to be a free parameter we deducedthe photometric solution which is listed in Table 4 Thecalculated light curves as dotted lines are shown in Figure 1Because119881119877119888 LCs in 2013 cause unequal heights between bothlight maxima up to MaxI-MaxIIsim 003 mag a dark spot isadded inmodeling the asymmetric LCs Assuming a cool spoton the equator of the more massive component (ie colati-tude 120601 = 90∘) we obtained the final photometric elements

which are given in Table 4 including other three parametersof spot (ie longitude 120579 angular radius 120574 and temperaturefactor119879119904119901119900119905119879119901)Themass ratio and fill-out factor forMTCasare 119902 = 2365(plusmn0005) and 119891 = 166(plusmn12) respectivelyThe corresponding theoretical light curves as solid lines areplotted in Figure 1 The OrsquoConnell effect for this binary canbe attributed the activity of stellar spot Its area is up to17 of the area of the more massive component Thereforethe spotted solution is accepted to be the final solution dueto its small value of Σ(119900 minus 119888)2119894 = 02223 Additionally weanalyzed AAVSOrsquos and ASASrsquo LCs respectively The derivedphotometric solutions are given in Table 4Themass ratio andfill-out factor almost agree with the previous result from our


Table 4 Photometric solutions for MT Cas

Parameters LCs in 2013 LC of AAVSO LC of ASASNo Spot With Spot (2878 data types) (134 data types)

119894(∘) 847 plusmn 03 852 plusmn 03 836 plusmn 01 803 plusmn 02119902 = 119872119901119872119904 2370 plusmn 0002 2365 plusmn 0005 2487 plusmn 0025 2415 plusmn 0013119879119901(119870) 5750 plusmn 210 5750 plusmn 210119883119901 119884119901 0650 0207 0650 0207119909119904119881 119910119904119881 0774 0232 0774 0232119909119904119877 119910119904119877 0694 0251 0694 0251119879119904(K)119886 6010+145minus238 6026+231minus249 5966+232minus232 6080+236minus137119883119904 119884119904 0649 0221 0649 0222 0649 0219 0648 0225119909119904119881 119910119904119881 0746 0260 0745 0261 0749 0256 0742 0265119909119904119877 119910119904119877 0675 0271 0674 0271 minusΩ119901 = Ω119904 5678 plusmn 0006 5660 plusmn 0007 5857 plusmn 0004 5767 plusmn 0031119871119904(119871119901 + 119871119904)119881 03602 plusmn 00006 03641 plusmn 00006 03422 plusmn 00002 03681 plusmn 00049119871119904(119871119901 + 119871119904)119877 03544 plusmn 00005 03559 plusmn 00005 minus119903119901(pole) 04342 plusmn 00013 04373 plusmn 00012 04375 plusmn 00005 04345 plusmn 00019119903119901(side) 04643 plusmn 00018 04683 plusmn 00016 04681 plusmn 00006 04644 plusmn 00025119903119901(back) 04937 plusmn 00024 04988 plusmn 00021 04868 plusmn 00008 04931 plusmn 00029119903119904(pole) 02932 plusmn 00016 02946 plusmn 00015 02884 plusmn 00005 02900 plusmn 00018119903119904(side) 03067 plusmn 00019 03083 plusmn 00018 03015 plusmn 00006 03030 plusmn 00022119903119904(back) 03438 plusmn 00032 03469 plusmn 00031 03380 plusmn 00009 03390 plusmn 00023120579(arc) minus 161 plusmn 007 minus120574(arc) minus 026 plusmn 004 minus119879119904119901119900119905119879119901 minus 085 plusmn 005 minusΣ(119900 minus 119888)2119894 03777 02223 02762 11616119891() 148 plusmn 11 166 plusmn 12 115 plusmn 06 102 plusmn 05Note aThe uncertainty of 119879119904 is determined from the input error for 119879119901

119881119877119888 light curvesThe calculated LCs are plotted as continuouslines in Figure 6 Their mass-ratios approximate to the resultof the photometric solution with a cool spot

5 Results and Discussions

Up to now no spectroscopic elements have been publishedand the absolute parameters of this binary cannot be directlydetermined Assuming the spectral type of F8V with asubtype uncertainty the mass of the primary was roughlyestimated to be119872119901 = 119(plusmn007) M⊙ [35] Using the massratio and orbital period the separation between componentsand the mass of the secondary are estimated to be 119886 =232(plusmn005) R⊙ and 119872119904 = 050(plusmn003) M⊙ respectivelyOther absolute parameters for MT Cas are as follows 119877119901 =108(plusmn005) R⊙ 119877119904 = 073(plusmn004) R⊙ 119871119901 = 115(plusmn011) R⊙and 119871 119904 = 063(plusmn007) R⊙

The mass-luminosity diagram is displayed in Figure 7in which the zero-age main sequence (ZAMS) and theterminal-age main sequence (TAMS) are constructed by thebinary-star evolution code [36]TheW-type low-temperaturecontact binaries (LTCBs see [3]) are plotted as black open andfilled circles From this figure the primary component of MTCas is close to the TAMS line implying that it is a normalmain-sequence star Meanwhile the secondary component

lies above the TAMS line indicating that it may be a smallhelium star in an advanced evolutionary stage [4]

From Eq (2) the orbital period ofMTCasmay be under-going a secular increase at a rate of 119889119875119889119905 = +104(plusmn009) times10minus8 d yrminus1 This case occurs in other weak-contact binarieswhich are listed in Table 5Therefore the period increase ratefor MT Cas may be a small value for this kind of binariesThe long-term period increases can be generally interpretedbymass transfer from the lessmassive component to themoremassive one Under conserved mass transfer assumption themass transfer rate can be computed by the following formula[37]

119875 = 3 (

119872119901119872119904 minus 1)

119901119872119901 (3)

Inserting the values of 119875 119872119901 and 119872119904 into Eq (3) themass transfer rate is estimated to be 119901 = +104(plusmn009) times10minus8M⊙ yrminus1 With the period increasing the separationbetween two components will increase Meanwhile masstransfer from the secondary one to the primary one alsocauses the mass ratio to decreaseThis may result in the innerand outer Roche lobes shrinking which will cause the fill-out factor to decrease Finally theweak-contact configuration


Table 5 Several weak-contact binaries with secular period increasing

Star Spectral Period q 119889119875119889119905 f Reftype (day) (times10minus7d yrminus1) ()

44i Boo K2V 026782 0487 +149 50 (1)(2)CWCas G8V 031886 0448 minus034 65 (3)BE Cep minus 042439 0427 minus048 69 (4)DD Com minus 026921 0271 +34 88 (5)AD Cnc K0V 028274 0770 +494 83 (6)XY Leo K2V 028410 0610 +027 67 (7)MT Cas F8V 031388 0423119886 +011 166 (8)Note aThe mass ratio is flipping ie 12365References (1) [44] (2) [45] (3) [46] (4) [47] (5) [48] (6) [49] (7) [50] (8) present paper

15

10

05

00

minus05

minus10

minus15

Log(

LL ⊙

)

08 04 00 minus04 minus08 minus12

Log(MM⊙)

PrimarySecondary

ZAMS TAMS

Figure 7The mass-luminosity diagram for MT Cas The filled andopen circles represent the primary and secondary components forthe W-type LTCBs [3]

may be broken ThereforeMTCas may evolve into a broken-contact configuration as predicted by TRO theory [3 38ndash40] In the future it necessitates to obtain high-precisionphotometry and spectroscopy to identify the orbital periodvariations and to determine its absolute parameters

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This research is partly supported by the National Natural Sci-ence Foundation of China (grants Nos 11873003amp 11473009)

Natural Science Research Project of the Educational Depart-ment of Anhui Province (grant No KJ2017A850) and theOutstanding Young Talents Program (grant No gxyq2018161)of the Educational Department of Anhui Province Newobservations of MT Cas were obtained by using the 6085-cm telescopes at the Xinglong Station of NAOC and 24-mtelescope at the Lijiang Station of YNAO

Supplementary Materials

Table 1 CCD photometric observations in V and Rc bands(Supplementary Materials)

References

[1] L B Lucy ldquoThe structure of contact binariesrdquo AstrophysicalJournal vol 151 p 1123 1968

[2] L B Lucy ldquoThe Light Curves of W Ursae Majoris StarsrdquoAstrophysical Journal vol 153 p 877 1968

[3] K Yakut and P P Eggleton ldquoEvolution of close binary systemsrdquoThe Astrophysical Journal vol 629 no 2 pp 1055ndash1074 2005

[4] K stępien ldquoEvolutionary status of late-type contact binariesrdquoActa Astronomica vol 56 p 199 2006

[5] L-F Li F-H Zhang Z Han and D-K Jang ldquoFormation andevolution of w ursaemajoris contact binariesrdquoTheAstrophysicalJournal vol 662 no 1 p 596 2007

[6] J H Applegate ldquoAmechanism for orbital period modulation inclose binariesrdquoAstrophysical Journal vol 385 pp 621ndash629 1992

[7] J B Irwin ldquoThe determination of a light-time orbitrdquo TheAstrophysical Journal vol 116 p 211 1952

[8] S-B Qian J-J Wang L-Y Zhu et al ldquoOptical flares and along-lived dark spot on a cool shallow contact binaryrdquo TheAstrophysical Journal Supplement Series vol 212 no 1 p 4 2014

[9] R Tylenda M Hajduk T Kaminski et al ldquoV1309 Scorpiimerger of a contact binaryrdquoAstronomy amp Astrophysics vol 528Article ID A114 p 10 2011

[10] W Gotz and W Wenzel ldquoDie veraenderlichen Sterne dernordlichenMilstrasse Teil VIIIrdquo Veroeff Sternwarte Sonnebergvol 2 pp 279ndash366 1956

[11] O Y Malkov E Oblak E A Snegireva and J Torra ldquoAcatalogue of eclipsing variablesrdquoAstronomy ampAstrophysics vol446 no 2 pp 785ndash789 2006

[12] M Hoffmann ldquoMT Cassiopeiae Another Contact Binary withComplete Eclipsesrdquo Information Bulltin onVariable Stars 20631 1982


[13] T Pribulla J M Kreiner and J Tremko ldquoCatalogue of thefield contact binary starsrdquo Contributions of the AstronomicalObservatory Skalnate Pleso vol 33 no 1 pp 38ndash70 2003

[14] J M Kreiner ldquoUp-to-date linear elements of eclipsing binariesrdquoActa Astronomica vol 54 pp 207ndash210 2004

[15] T Jayasinghe K Z Stanek C S Kochanek et al ldquoThe ASAS-SN Catalog of Variable Stars II Uniform Classification of412000 KnownVariablesrdquo 2018 httpadsabsharvardeduabs2018arXiv180907329J

[16] A-Y Zhou X-J Jiang Y-P Zhang and J-Y Wei ldquoMiCPhota prime-focus multicolor CCD photometer on the 85-cmtelescoperdquo Research in Astronomy and Astrophysics vol 9 no3 p 349 2009

[17] E F Milone ldquoThe peculiar binary RT Lacertaerdquo AstronomicalJournal vol 73 pp 708ndash711 1968

[18] T J Davidge and E F Milone ldquoA study of the OrsquoConnell effectin the light curves of eclipsing binariesrdquo Astrophysical Journalvol 55 pp 571ndash584 1984

[19] G Kaszas J Vinko K Szatmary et al ldquoPeriod variation andsurface activity of the contact binary VW Cepheirdquo Astronomyamp Astrophysics vol 331 no 1 pp 231ndash243 1998

[20] H-F Dai Y-G Yang and X-G Yin ldquoA photometric study oftheWUMa-type binary DF CanumVenaticorumrdquoNewAstronvol 16 no 3 pp 173ndash176 2011

[21] Y-G Yang H-F Dai H-Y Yuan and X-L Zhang ldquoPhotomet-ric studies for two contact binaries V532 monocerotis and GUorionisrdquo Publications of the Astronomical Society of Japan vol69 no 4 Article ID 69 2017

[22] Y-G Yang S-B Qian L-Y Zhang et al ldquoDeep low mass ratioovercontact binary systems XIII DZ piscium with intrinsiclight variabilityrdquoThe Astronomical Journal vol 146 no 2 p 352013

[23] Y-F Fan J-M Bai J-J Zhang et al ldquoRapid instrumentexchanging system for the Cassegrain focus of the Lijiang 24-m Telescoperdquo Astronomy and Astrophysics vol 15 no 6 p 9182015

[24] A J Pickles ldquoA stellar spectral flux library 1150ndash25000 ArdquoPublications of the Astronomical Society of the Pacific vol 110no 749 p 863 1998

[25] K K Kwee and H van Woerden ldquoA method for computingaccurately the epoch of minimum of an eclipsing variablerdquoBulletin of the Astronomical Institutes of the Netherlands vol 12p 327 1956

[26] P Lenz and M Breger ldquoPeriod04 user guiderdquo Communicationsin Asteroseismology vol 146 pp 53ndash136 2005

[27] M Zejda ldquoCCDTimes ofMinima of Faint Eclipsing Binaries in2000rdquo Information Bulltin on Variable Stars 5287 1 2002

[28] R EWilson and E J Devinney ldquoRealization of AccurateClose-Binary Light Curves Application to MR Cygnirdquo AstrophysicalJournal vol 166 p 605 1971

[29] R E Wilson ldquoAccuracy and efficiency in the binary starreflection effectrdquo The Astrophysical Journal vol 356 pp 613ndash622 1990

[30] R L Kurucz ldquoPeculiar versus normal phenomena in a-type andrelated starsrdquo in Proceedings of the International AstronomicalUnion Colloquium No 138 vol 44 p 87 Astronomical Societyof the Pacific San Francisco Calif USA 1993

[31] L B Lucy ldquoGravity-darkening for stars with convectiveenvelopesrdquo Zeitschrift fur Astrophysik vol 65 p 89 1967

[32] S M Rucinski ldquoThe W UMa-type systems as contact binariesI Twomethods of geometrical elements determination Degreeof contactrdquo Acta Astronomica vol 23 p 79 1973

[33] W vanHamme ldquoNew limb-darkening coefficients formodelingbinary star light curvesrdquo Astronomical Journal vol 106 no 5pp 2096ndash2117 1993

[34] L Binnendijk ldquoThe orbital elements of W Ursae Majorissystemsrdquo Vistas in Astronomy vol 12 pp 217ndash256 1970

[35] A N Cox Allenrsquos Astrophysical Quantities Springer New YorkNY USA 4th edition 2000

[36] J RHurley C A Tout andO R Plos ldquoEvolution of binary starsand the effect of tides on binary populationsrdquo Monthly Noticesof the Royal Astronomical Society vol 329 no 4 pp 897ndash9282002

[37] M Singh and U S Chaubey ldquoMass loss from wolf-rayet starsrdquoAstrophysics and Space Science vol 124 no 2 pp 389ndash396 1986

[38] L B Lucy ldquoW Ursae Majoris systems with marginal contactrdquoThe Astrophysical Journal vol 205 pp 208ndash216 1976

[39] B P Flannery ldquoA cyclic thermal instability in contact binarystarsrdquoThe Astrophysical Journal vol 205 pp 217ndash225 1976

[40] J A Robertson and P P Eggleton ldquoThe evolution of W UrsaeMajoris systemsrdquo Monthly Notices of the Royal AstronomicalSociety vol 179 no 3 pp 359ndash375 1977

[41] L Brat M Zejda and P Svoboda ldquoBRNO Contributions34rdquo Open European Journal on Variable Stars vol 74 no 1 p1 2007

[42] R Diethelm ldquo157 List of minima of eclipsing binariesrdquo TechRep The group of eclipsing binary observers of the SwissAstronomical Society (BBSAG) Bulletins BBSAG Bull 124 12001

[43] E Blattler ldquo159 List of minima of eclipsing binariesrdquo TechRep The group of eclipsing binary observers of the SwissAstronomical Society (BBSAG) Bulletins BBSAG Bull 126 12001

[44] W Lu S M Rucinski and W Ogłoza ldquoRadial Velocity Studiesof Close Binary Stars IVrdquo The Astronomical Journal vol 122no 1 p 402 2001

[45] G Hill W A Fisher and D Holmgren ldquoStudies of late-type binaries I The physical parameters of 44i Bootis ABCrdquoAstronomy and Astrophysics vol 211 pp 81ndash98 1989

[46] T-Y Jiang L-F Li Z-W Han and D-K Jiang ldquoPhotometricinvestigation and possible light-time effect in the orbital periodof a marginal contact system CW cassiopeiaerdquo Publications ofthe Astronomical Society of Japan vol 62 no 2 pp 457ndash4652010

[47] H-F Dai and Y-G Yang ldquoA comprehensive photometric studyof the marginal-contact binary BE CepheirdquoNew Astron vol 17no 3 pp 347ndash352 2012

[48] L Zhu S-BQian ZMikulasek et al ldquoPhotometric study of thevery short period shallow contact binary DD comae berenicesrdquoThe Astronomical Journal vol 140 no 1 Article ID 215 2010

[49] S-B Qian J-Z Yuan B Soonthornthum et al ldquoAD cancria shallow contact solar-type eclipsing binary and evidence fora dwarf third component and a 16 year magnetic cyclerdquo TheAstrophysical Journal vol 671 no 1 p 811 2007

[50] K Yakut C Ibanoglu B Kalomeni and O L DegirmencildquoNew light curve analysis and period changes of the overcontactbinary XY Leonisrdquo Astronomy and Astrophysics vol 401 pp1095ndash1100 2003

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components


Shock and Vibration


High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Acoustics and VibrationAdvances in



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

Antennas andPropagation

International Journal of




Geophysics

Advances inOpticalTechnologies

Hindawiwwwhindawicom

Volume 2018

Applied Bionics and BiomechanicsHindawiwwwhindawicom Volume 2018

Advances inOptoElectronics


Volume 2018


Mathematical PhysicsAdvances in


ChemistryAdvances in


Journal of

Chemistry


Advances inPhysical Chemistry


RotatingMachinery



Journal ofEngineeringVolume 2018

Submit your manuscripts atwwwhindawicom


Table 1 CCD photometric observations in 119881 and 119877119888 bands119881 band 119877119888 band

HJD Δ119898 HJD Δ119898 HJD Δ119898 HJD Δ11989824566299265 +0066 24566329847 minus0273 24566299275 +0269 24566329895 minus007624566299285 +0106 24566329861 minus0280 24566299294 +0322 24566329962 minus009124566299304 +0133 24566329874 minus0273 24566299314 +0349 24566329976 minus011324566299323 +0176 24566329901 minus0289 24566299333 +0384 24566329989 minus009924566299343 +0225 24566329915 minus0300 24566299352 +0413 24566330003 minus011624566329766 minus0235 24566360355 minus0077 24566329814 minus005724566329780 minus0238 24566360373 minus0041 24566329827 minus006924566329793 minus0263 24566360391 minus0041 24566329841 minus006924566329807 minus0267 24566360409 +0007 24566329854 minus006324566329820 minus0270 24566360427 +0065 24566329868 minus008124566329834 minus0261 24566329881 minus0076NoteThe entire table is available only on the online journal

VRc-04mag

04

02

00

minus02

minus04

minus06

Δm

(mag

)

02 04 06 08 10 1200

Phase

Figure 1 119881119877119888 light curves of the contact binary MT Cas which areobserved in 2013 in December by using the 85-cm telescope Thedotted and solid lines are plotted by photometric solutions withoutor with a dark spot respectively

and Analysis Facility (IRAF) in a standard mode Differentialmagnitudes were then determined by aperture photometry

In the observing process we chose TYC 3657-1637-1(1205721198692000 = 00ℎ14119898591199044 and 1205751198692000 = +54∘39101584053101584010158401) andTYC 3657-1245-1 (1205721198692000 = 00ℎ14119898321199046 and 1205751198692000 =+54∘29101584016101584010158401) as the comparison and check stars respec-tively Typical exposure times are adopted to be 60s in119881 bandand 50s in119877119888 band respectively In total we obtained 383 and373 images in 119881 and 119877119888 bands The standard uncertaintiesare plusmn0005 mag in 119881 band and plusmn0004 mag in 119877119888 bandAll individual observations (ie HJD and Δ119898) are listed inTable 1 The differential magnitudes versus orbital phases aredisplayed in Figure 1 where phases are computed by a period

of 01198893138789 (Kreiner et al 2004) The 119881119877119888 LCs in 2013imply that MT Cas is an UMa-type eclipsing binary whoseamplitudes of variable light are 069 mag and 066 mag in119881 and 119877119888 bands respectively There exists an unequal heightbetween both maxima ie OrsquoConnell effect [17 18] MaxIIat phase 075 is brighter than MaxI at phase 025 up to 0025mag and 0029mag in119881 and 119877119888 bands respectivelyThis kindof stellar activity occurs on other WUMa-type binaries suchas VW Cep [19] DV CVn [20] V532 Mon [21] and BB Peg(Kalomeni et al 2007) and DZ Psc [22]

22 Low-Precision Spectrum The low-precision spectrum forMT Cas was obtained by using the Yunnan Faint ObjectSpectrograph and Camera (YFOSC) which is attached to the24-m telescope at Lijiang station (LJs) of Yunnan Astro-nomical Observatory of China (YNAO) at UT 155013 of2018 October 22 During the observing process we chosea 140-mm-length slit and a Grism-3 with a wavelengthrange from 3200 A to 9200 A [23] The exposure time is10 minutes The phase of 098 almost corresponds to theobserved middle time HJD 2454141634 Reduction of thespectra was performed by using IRAF packages includ-ing bias subtraction flat-fielding and cosmic-ray removalFinally the one-dimensional spectrum was extracted Withthe winmk software (httpwwwappstateedusimgrayroMKwinmkhtm) we obtained a normalized spectrum which isdisplayed in Figure 2 By comparing the spectra of standardstars [24] the spectral type is determined to be F8V forthe primary (ie more massive component) of this binarybecause the secondary is eclipsed by the primary aroundphase 00 for the W-type contact binary (see Section 4)

3 Eclipse Times and Period Analysis

From our new observations and AAVSOrsquos data several timesof primary and secondary minima are generally determinedby using the method of Kwee amp van Woerden [25] FromASAS-SN database we downloaded 134 data types inV band




18

16

14

12

10

08

06

04

Rect

ified

Inte

nsity

3500 4000 4500 5000 5500 6000


MT Cas

NaHHH

Ca IIK amp H F8V




008

006

004

002

000

Pow

er

0 1 2 3 4 5 6 7 8 9 10

Frequency (day-1)

f1




MinI = HJD 2452500086 + 03138789 times 119864 (1)







Table 3 Continued



Year1935 1950 1965 1980 1995 2010 2025

+ 004+ 003+ 002+ 001000

minus001

+ 002+ 001000

minus001

minus002

(O-C

) i(d

ays)

(O-C

) f(d

ays)


Epoch

pgpeCCD

(a)

(b)




(2)







134

132

130

128

126

124V

(mag

)

02 04 06 08 10 1200

Phase(a)

02 04 06 08 10 1200

Phase

134

132

130

128

126

124

V (m

ag)

(b)


00 05 10 15 20 25 30 35 40

q

03

06

09

12

15

Σ(o

-c)2 i

i=90∘

i=85∘

i=80∘

i=75∘

i=70∘

(a)

00 05 10 15 20 25 30 35

q

060

055

050

045

04035

30

25

20

15

10

fill-o

ut (

)Σ

(o-c

)2 i

(b)














119875 = 3 (

119872119901119872119904 minus 1)

119901119872119901 (3)






15

10

05

00

minus05

minus10

minus15

Log(

LL ⊙

)


Log(MM⊙)

PrimarySecondary

ZAMS TAMS



Data Availability




Acknowledgments





References























































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery








18

16

14

12

10

08

06

04

Rect

ified

Inte

nsity

3500 4000 4500 5000 5500 6000


MT Cas

NaHHH

Ca IIK amp H F8V




008

006

004

002

000

Pow

er

0 1 2 3 4 5 6 7 8 9 10

Frequency (day-1)

f1




MinI = HJD 2452500086 + 03138789 times 119864 (1)







Table 3 Continued



Year1935 1950 1965 1980 1995 2010 2025

+ 004+ 003+ 002+ 001000

minus001

+ 002+ 001000

minus001

minus002

(O-C

) i(d

ays)

(O-C

) f(d

ays)


Epoch

pgpeCCD

(a)

(b)




(2)







134

132

130

128

126

124V

(mag

)

02 04 06 08 10 1200

Phase(a)

02 04 06 08 10 1200

Phase

134

132

130

128

126

124

V (m

ag)

(b)


00 05 10 15 20 25 30 35 40

q

03

06

09

12

15

Σ(o

-c)2 i

i=90∘

i=85∘

i=80∘

i=75∘

i=70∘

(a)

00 05 10 15 20 25 30 35

q

060

055

050

045

04035

30

25

20

15

10

fill-o

ut (

)Σ

(o-c

)2 i

(b)














119875 = 3 (

119872119901119872119904 minus 1)

119901119872119901 (3)






15

10

05

00

minus05

minus10

minus15

Log(

LL ⊙

)


Log(MM⊙)

PrimarySecondary

ZAMS TAMS



Data Availability




Acknowledgments





References























































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery










Table 3 Continued



Year1935 1950 1965 1980 1995 2010 2025

+ 004+ 003+ 002+ 001000

minus001

+ 002+ 001000

minus001

minus002

(O-C

) i(d

ays)

(O-C

) f(d

ays)


Epoch

pgpeCCD

(a)

(b)




(2)







134

132

130

128

126

124V

(mag

)

02 04 06 08 10 1200

Phase(a)

02 04 06 08 10 1200

Phase

134

132

130

128

126

124

V (m

ag)

(b)


00 05 10 15 20 25 30 35 40

q

03

06

09

12

15

Σ(o

-c)2 i

i=90∘

i=85∘

i=80∘

i=75∘

i=70∘

(a)

00 05 10 15 20 25 30 35

q

060

055

050

045

04035

30

25

20

15

10

fill-o

ut (

)Σ

(o-c

)2 i

(b)














119875 = 3 (

119872119901119872119904 minus 1)

119901119872119901 (3)






15

10

05

00

minus05

minus10

minus15

Log(

LL ⊙

)


Log(MM⊙)

PrimarySecondary

ZAMS TAMS



Data Availability




Acknowledgments





References























































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery






134

132

130

128

126

124V

(mag

)

02 04 06 08 10 1200

Phase(a)

02 04 06 08 10 1200

Phase

134

132

130

128

126

124

V (m

ag)

(b)


00 05 10 15 20 25 30 35 40

q

03

06

09

12

15

Σ(o

-c)2 i

i=90∘

i=85∘

i=80∘

i=75∘

i=70∘

(a)

00 05 10 15 20 25 30 35

q

060

055

050

045

04035

30

25

20

15

10

fill-o

ut (

)Σ

(o-c

)2 i

(b)














119875 = 3 (

119872119901119872119904 minus 1)

119901119872119901 (3)






15

10

05

00

minus05

minus10

minus15

Log(

LL ⊙

)


Log(MM⊙)

PrimarySecondary

ZAMS TAMS



Data Availability




Acknowledgments





References























































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery















119875 = 3 (

119872119901119872119904 minus 1)

119901119872119901 (3)






15

10

05

00

minus05

minus10

minus15

Log(

LL ⊙

)


Log(MM⊙)

PrimarySecondary

ZAMS TAMS



Data Availability




Acknowledgments





References























































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery









15

10

05

00

minus05

minus10

minus15

Log(

LL ⊙

)


Log(MM⊙)

PrimarySecondary

ZAMS TAMS



Data Availability




Acknowledgments





References























































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery















































Shock and Vibration





Volume 2018














Geophysics



Volume 2018




Volume 2018






Journal of

Chemistry




RotatingMachinery





mass transfer and intrinsic light variability in the...

Documents