GK Boo and AE For: Two low-mass eclipsing binaries with dwarf companions

0.5 MB·English

by  P. Zasche

Astronomy&Astrophysicsmanuscriptno.zasche (cid:13)c ESO2012
January25,2012
GK Boo and AE For: Two low-mass
⋆
eclipsing binaries with dwarf companions
P.Zasche1,P.Svoboda2,andR.Uhla´rˇ3
1 AstronomicalInstitute,FacultyofMathematicsandPhysics,CharlesUniversityPrague,CZ-18000Praha8,VHolesˇovicˇka´ch2,
CzechRepublic,e-mail:[email protected]
2 Privateobservatory,Vy´pustky5,Brno,CZ-61400CzechRepublic
3 PrivateObservatory,Pohoˇr´ı71,25401J´ılove´uPrahy,CzechRepublic
2 January25,2012
1
0 ABSTRACT
2
Context.Astudyoflate-typelow-masseclipsingbinariesprovidesuswithimportantinformationaboutthemostcommonstarsinthe
n
Universe.
a
J Aims.WeobtainthefirstlightcurvesandperformperiodanalysesoftwoneglectedeclipsingbinariesGKBooandAEFortoreveal
theirbasicphysicalproperties.
4
Methods.WeperformedbothaperiodanalysisofthetimesoftheminimaandaBVRlightcurveanalysis.Manynewtimesofminima
2
forboththesystemswerederivedandcollectedfromthedataobtainedbyautomaticandrobotictelescopes.Thisallowedustostudy

thelong-termperiodchangesinthesesystemsforthefirsttime.Fromthelightcurveanalysis,wederivedthefirstroughestimatesof
]
R thephysicalpropertiesofthesesystems.
Results.Wefindthattheanalyzedsystemsaresomewhatsimilartoeachother.Bothcontainlow-masscomponentsofsimilartypes,
S
bothareclosetotheSun,bothhaveshortorbitalperiod,andbothcontainanotherlow-masscompanionsonlongerorbitsofafew
.
h years.InthecaseofGKBoo,bothcomponentsareprobablyofK3spectraltype,whilethedistantcompanionisprobablyalateM
p star.ThelightcurveofGKBooisasymmetric,whichprobablycausestheshiftinthesecondaryminimaintheO−Cdiagram.System
- AEForcomprisestwoK7stars,andthethirdbodyisapossiblebrowndwarfwithaminimalmassofonlyabout47MJup.
o Conclusions.We succeed in completing period and light curve analyses of both systems, although a more detailed spectroscopic
r analysisisneededtoconfirmthephysicalparametersofthecomponentstoahigheraccuracy.
t
s
a Keywords.binaries:eclipsing–stars:fundamentalparameters–stars:individual:GKBoo,AEFor
[

1
1. Introduction 2. GKBoo
v
3
2.1.Introduction
7 Low-massstarsare the mostcommonstars in ourGalaxy (e.g.
9 Kroupa 2002). However, owing to their low luminosity, only
The system GK Boo (= BD+37 2556, V = 10.86 mag) is
4 these close to the Sun have been studied in detail and manyof max
an Algol-type eclipsing binary with an orbital period of about
1. themhaveneverbeenanalyzed.Hence,wefocusedontworather 0.48 day. It is also a primary component of a visual double
0 neglectedlow-masseclipsingbinarysystems:GK Boo and AE designated WDS J14384+3632in the Washington Double Star
2 For. Their light curves as well as their period modulation had
Catalog(WDS1,Masonetal.2001).Thesecondarycomponent
1 never been studied. Some studies indicate that most late-type
ofthisdoublestarisabout14′′ distant,andisprobablygravita-
: starsaresingle(e.g.Lada2006),butthenumberofpapersstudy-
v tionallyboundtoGKBooitself.Itisabout0.4magfainter,but
ingthemultiplicityofthelate-typesystemsisstillratherlimited.
i sinceitsdiscoveryin1933therehasbeennodetectablemutual
X Therefore,the incidenceof multiplesin late-typestars remains
motionofthepair,hencetheorbitalperiodisofaboutthousands
r unexplored.
ofyears(roughestimationfromtheKepler’slaw).
a
The study of eclipsing binaries provide us with important The star is too faint, thus was not observed by Hipparcos
informationaboutthe physicalpropertiesof bothoftheir com- satellite, and its distance is therefore rather uncertain.
ponents–theirradii,masses,andevolutionarystatus.However, Kharchenko(2001)introducedtheparallax30.29mas,whichis
whenconsideringonlywiththelightcurve,severalassumptions howeveronlyanestimate.Itsspectraltypeisalsounknown,but
have to be made. For the analysis presented in this paper we the B−V index derived from the Tycho catalogue (Høgetal.,
alsousedthephotometricdataobtainedbyautomaticandrobotic 2000), B−V = 0.89magindicatesaspectraltypeofaboutK1.
telescopes(suchas ASAS, Piofthe sky,andSWASP). Thanks Ontheotherhand,the2MASSinfraredphotometry(Cutrietal.,
tothesehugedatabasesofobservations,thelong-termevolution 2003)givesJ−H =0.527mag(thereforeaspectraltypeofK3).
ofthesesystemscanbestudiedforthefirsttime. Finally, Ammonsetal. (2006) introduced a temperature corre-
spondingtoaspectraltypeofaboutK2-3.Alltheseroughspec-
tralestimatesweretakenfromPopper(1980)andCox(2000).
⋆ This paper uses observations made at the South African
AstronomicalObservatory(SAAO) 1 http://ad.usno.navy.mil/wds/
1
P.Zascheetal.:GKBooandAEFor:Twolow-masseclipsingbinarieswithdwarfcompanions
2.2.Lightcurve
1 B
ThestarwasobservedbytheSuperWASP(Pollaccoetal.,2006) 0.9 V
projectanditscompletelightcurve(hereafterLC) is available. R
However, we did not use these data for the LC analysis be- 0.8
causethesewerenotmeasuredinanystandardphotometricfil-
0.7
ter. These data were only used to derivethe minima times (see x
u
below). We observed the target at the Ondˇrejov observatory in Fl0.6
theCzechRepublicwiththe65-cmtelescopeequippedwiththe
0.5
CCD camera. For the light curve analysis, only the data from
two nights in May 2011 were used (see the electronic data ta- 0.4
bles). The remaining observations were used for the minima
0.3
timederivationandtoanalyzetheperiodchangesinthesystem
(seebelowsection2.3).Theobservationswereobtainedinstan- 0.05
dardB,V,andRfiltersaccordingtothespecificationofBessell 0 B
−0.05
(1990). 0.05
At first, the complete LC was analyzed using the program 0 V
−0.05
PHOEBE(Prsˇa&Zwitter,2005),whichisbasedontheWilson- 0.05
Devinney algorithm (WD, Wilson&Devinney 1971). The de- 0 R
−0.05
rived quantities are as follows: the secondary temperature T ,
2 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
the inclination i, the luminosities L, the gravity darkening co- Phase
i
efficients gi, the albedo coefficients Ai, and the synchronicity Fig.1. Light curves in BVR filters for GK Boo, the solid lines
parameters Fi. The limb darkening was approximated using representthefinalfit.Theresidualsafterthefitareplottedbelow.
a linear law, and the values of xi were interpolated from the Thecurvesareshiftedalongy-axisforreasonsofclarity.
vanHamme’stables,giveninvanHamme(1993).
Atthebeginningofthefittingprocess,wefixedthetempera-
tureoftheprimarycomponentatT1 =4700K(correspondingto rametersasdescribedabove.Atthebeginning,thevaluesof Ai
spectraltypeK3,Cox2000).Intheabsenceofspectroscopy,the and g were fixedto the appropriatevaluesof 0.5 and0.32,re-
i
massratiowasderivedviaa so-called”q-searchmethod”.This spectively.However,toachieveatighterfitbothA andg values
i i
meansthatwetrieddifferentvaluesofmassratiointherange1.5 werealsovariedacrosstherangefrom0to1instepsof0.05for
–0.5instepsof0.1andtriedtofindthebestLCfitaccordingto bothcomponents.ThesynchronicityparametersF convergedto
i
thelowestvalueofrms.Finally,wefoundthatthebest-fitsolu- much more reliable values. The value of mass ratio was fixed
tionwasreachedwiththevalueq= M2/M1 =0.9,whichagrees to q = 1.0 and then also fitted as a free parameter. This was
withbotheclipseshavingalmostequaldepths.Foragivenmass possiblebecausethereisacleardistortionoftheLCoutsidethe
ratio,thesemi-majoraxiswasfixedto anappropriatevaluefor minima(seee.g.Terrell&Wilson2005).Forthefittingprocess,
the primary mass to be equal to a typical mass of a particular thetwodifferentlimbdarkeninglawswerealsotried,namelya
spectral type (e.g. Popper 1980, Harmanec 1988, or Andersen linearandlogarithmic.Thelatteroneprovidesamuchtighterfit
1991).Withthisapproach,wewereabletoestimatethemasses, toourdata.AlloftheresultingLCparametersarealsogivenin
inadditiontotheradiiofbothcomponentsinabsoluteunits. Table1(togetherwithparametersoftwocoolerspotslocatedon
However, during the LC fitting process we found that the theprimarycomponent–longitude,latitude,radiusandtemper-
LC of GK Boo is asymmetric.In particular,the partof the LC aturefactor).Asonecansee,thetwosolutionsclearlydiffereven
nearthesecondaryminimumisdistortedinallBVRfilters.The outsidetheirrespectiveerrorbarsforsomeoftheparameters.
brightness just after the ascent from the secondary minimum Theindividualerrorsintheparameterswerenottakenfrom
(near the phase 0.6) is higher than the brightness just before theWDcode,butderivedinthefollowingway.Wecomputeda
the descent (phase 0.4). The difference is about 0.022 mag in rangeofsolutionsforGKBoo,whichwerethenusedforitserror
B,0.018maginV,and0.017maginRfilter,respectively. estimation.Allsolutionswithχ2 valueclosetotheminimalone
With the PHOEBE code, we tried to fix the values of A (5%fromourfinalsolution)weretakenandtheresultantvalues
i
and g to their appropriatevaluesof 0.5 and 0.32,respectively. ofparameterswereusedtocomputethedifferencesbetweenthe
i
However,afterthenwe alsoallowedtheseparameterstobefit- parameters. The errors in the individual parameters were then
ted, because the fit is tighter (rms). However, probably owing computedasamaximumdifferenceandtheirindividualWDer-
to the asymmetry of the LC these quantities converged to the rors,givenbymax(a −a )+δa +δa .
i min i min
ratherimprobablevaluesgiveninTable1,andtheshapeofthe ThissolutionobtainedwiththeROCHEprogramprovidesa
observedLCcouldnotbefittedproperly.Fortheasymmetryof muchcloserfittotheobserveddataandisthefitplottedinFig.
thecurve,we alsotriedtointroducea starspotoneitherofthe 1. Thevalueoftheeccentricitywasfixedat0(foradiscussion
components.However,no acceptable solutionwith spot(s) was aboutpossibleeccentricityseebelow).Ourresultantparameters
foundtodescribetheshapeofthelightcurvemoreaccuratelyin indicate that both the componentsare still located on the main
the PHOEBE program. The parameters of the LC fit are given sequence,(asrequiredbecausetheageoftheUniversedoesnot
inTable1,butthesecannotsufficientlydescribetheshapeofthe allowlow-massstarstohaveevolvedfromthemainsequence).
LC. If we follow the assumption of a K3V primary, then the sec-
We therefore tried a different code, called ROCHE, devel- ondary is also of K3V spectral type. These are consistent with
oped by Theo Pribulla (Pribulla, 2004), which is also based thephotometricindicespresentedabove,aswellaswiththein-
on the WD code but has for instance also some other comput- dividualmassesandradiiforthesetypesofstars(e.g.Harmanec
ingmethodsanddifferentcontrollingofthecalculationprocess. 1988).Anundetectablevalueofthethirdlightwasalsoresulted
Withthisprogram,weusedtwostarspotsandsimilarinputpa- derivedbythisanalysis.Thepresenceofphotosphericspotson
2
P.Zascheetal.:GKBooandAEFor:Twolow-masseclipsingbinarieswithdwarfcompanions
Table1.LightcurveparametersofGKBoo. Table2.FinalparametersofthelongorbitforGKBoo.
Parameter Value Parameter Value
PHOEBE ROCHE HJD 2454305.4570±0.0006
0
T [K] 4700∗ P[day] 0.47777174±0.00000022
1
T [K] 4540±50 4615±63 p [day] 1472.7±170.0
2 3
q(=M /M ) 0.9±0.1 0.95±0.12 p [yr] 4.032±0.450
2 1 3
e 0∗ A[day] 0.0126±0.0012
i[deg] 89.83±0.57 89.28±0.37 T 2454263.3±1108.3
0
g 0.00±0.04 0.35±0.05 ω [deg] 56.54±15.0
1 3
g 0.00±0.03 0.35±0.05 e 0.084±0.267
2 3
A 0.00±0.08 0.80±0.05 Q[·10−10] -1.071±0.206
1
A2 1.00±0.08 0.80±0.05 f(M3)[M⊙] 0.000633±0.000002
F1 1.892±0.107 1.131±0.096 M3,min[M⊙] 0.115±0.001
F2 1.866±0.116 1.295±0.108 M3,60[M⊙] 0.134±0.002
L1(B)[%] 54.8±1.9 52.4±1.1 M3,30[M⊙] 0.242±0.005
L2(B)[%] 45.2±1.8 47.6±1.0 a12sini[AU] 0.217±0.108
L1(V)[%] 53.5±1.5 51.6±1.2 a3[mas] 88.7±9.8
L (V)[%] 46.5±1.3 48.4±1.1
2
L (R)[%] 52.1±1.4 51.1±1.1
1
L (R)[%] 47.9±1.3 48.9±1.0
2 partofthelong-termperiodmodulation,althoughwehaveonly
Spots:
limiteddatacoverage.
l [deg] – 287.2±7.9
1
b [deg] – 60.5±3.2 Amoreinterestingfindingisthatofaperiodofabout4years.
1
r [deg] – 37.9±2.0 ApplyingtheLITEhypothesis,weobtainedafinalsetofparam-
1
k – 0.75±0.04 eters given in Table 2, namely the period of the third body p ,
1 3
l2[deg] – 63.3±7.4 the semi-amplitude of the effect A, the time of periastron pas-
b2[deg] – 47.4±12.8 sageT0,the argumentofperiastronω3, andthe eccentricitye3.
r2[deg] – 28.7±4.1 Despitethelowamplitude(aboutonly1.8minutes)oftheLITE,
k – 0.76±0.04
2 mostofthe observedminimatimes areof higherprecisionand
Derivedquantities:
themodulationisclearlyvisible.Table2alsoprovidesthemass
R [R ] 0.83±0.18 0.89±0.15
1 ⊙ functionofthethirdbody f(M ),whichhelpsustoestimateits
R [R ] 0.86±0.18 0.86±0.14 3
2 ⊙ predictedmass.
M [M ] 0.73±0.06 0.73±0.06
1 ⊙
M [M ] 0.66±0.06 0.70±0.06 Havingnoinformationabouttheinclinationbetweentheor-
1 ⊙
Note:∗-fixed. bits of the eclipsing pair and the hypothetical third body, we
plotted Fig. 3, where a plot mass versus inclination is shown.
Assuming the coplanar orbits (i.e. i = 90◦ → M = M ),
3 3 3,min
the resulted minimum mass of the third body is only about
bothcomponentsofsuchalatespectraltypestarisalsoforesee-
0.116 M , which places this body at the lower end of stellar
⊙
able.
masses,hencewecanruleoutthehypothesisofabrowndwarf
or even an exoplanet. Despite of there being no upper limit to
this mass (it goes to infinity with i → 0◦), we can estimate a
2.3.Periodanalysis 3
lower limit to the mass. Taking into accountthat no third light
To monitor the detailed long-term evolution of the sys- is detected in the LC solution, e.g. L /(L + L ) < 0.01 and
3 1 2
tem or its short-period modulation, we collected all avail- assuming a main-sequencestar, we can estimate its mass to be
able published minima observations. Photometry from the lower than 0.22 M , which is shown in Fig. 3 as a gray area.
⊙
SWASP (Pollaccoetal., 2006), ASAS (Pojmanski, 2002), and Furtherobservationsarestill neededto confirmthis hypothesis
PiOfTheSky (Burdetal., 2005) projects were used to derive withhigherconclusiveness.
many new minima times for GK Boo. All of these data are If we assume the parallax of GK Boo as given by
given in Table 10, which is available in electronic form only. Kharchenko(2001),π=30.29mas,wearealsoabletocompute
ThemethodofKwee&vanWoerden(1956)wasused.Someof theangulardistanceofahypotheticalbodytobeabout89mas.
thedatawereofpoorquality,butmostwereaccurateenoughto Thisseparationofcomponentsiswellabovethelimitformod-
perform a detailed period analysis of the system. The range of ernstellarinterferometers.However,thereisaproblemwiththe
thesedataisabout12years. brightnessofthethirdcomponent,whichwasfoundtobeabout
We used these data to analyze the period modulation and morethan fivemagnitudesfainterthan the eclipsingpair itself.
found some interesting results. Applying the hypothesis of a Withthebrightnessofabout11magforthesystem,thismakesa
thirdbodyinthesystem(theso-calledLIght-TimeEffect,here- detectionimpossible.Themagnitudedifferenceofthethirdbody
afterLITE,describede.g.byIrwin1959),wefoundaweakpe- withrespecttotheclosepairalsoclarifywhynothirdlightwas
riodmodulationwith a periodof aboutfouryears.The finalfit detectedintheLCsolution.
to the data together with the theoretical curve is shown in Fig. Anotherinteresting resultwas a detection ofdisplaced sec-
2.Asonecansee,thereisalsosomelong-termperiodevolution ondaries. This can be clearly seen in more precise data points
oftheorbitalperiod(thebluedashedline),whichwasdescribed (SWASPandournewobservations).Thatsecondaryminimaoc-
as a quadratic term in ephemerides. It can be understood as a cur at a different phase of φ , 0.5 from the primary usually
2
slow period decrease caused by the mass loss from the system indicates that the system is on an eccentric orbit. GK Boo is a
ormassflowbetweenthecomponents(orevenmomentumloss, well-detachedsystem,sotheeccentricorbitcannotberuled-out
magneticbreaking,etc.).Anotherexplanationisthatthisisonly easily.Therefore,weassumedanapsidalmotionhypothesisfor
3
P.Zascheetal.:GKBooandAEFor:Twolow-masseclipsingbinarieswithdwarfcompanions
2452000 2453000 2454000 2455000 Table4.MethodsofminimafittingforGKBoo.
0.006 2000 2002 2004 2006 2008 2010 2012
0.01
0.004
Methodofminimafitting rms BIC
0.002 0.005
O−C (days)−−00..0000042 −−000..00105O−C (Period) LITLEITanEdaQqnuudaaLdldiirrnnaaeettaaiiccrreeeepppphhhheeeemmmmeeeerrrriiiissss:::: 0000....00000000001178154091 55226193....4025
−0.006
−0.015 LITE,quadraticephemerisandapsidalmotion: 0.00060 72.6
−0.008
−0.01 −0.02
0.005 0.01
2451000 2452000 2453000 2454000 2455000 2456000
0 0 0.004
2000 2002 2004 2006 2008 2010 2012
−0.005 −0.01
0.005
−6000 −5000 −4000 −3000 −2000 −1000 0 1000 2000 3000 0.002
Freipgr.e2s.ePnetsrioqduiacdrmatoidcuelpathieomneorfEisppo,echwriohdileGrKedBsoool.idBlluineedsatsahneddslifnoer O−C (days) 0 0 O−C (Period)
−0.002
the LITE hypothesis. Residuals are plotted in the bottom plot. −0.005
The largerthe symbol, the higherthe weight(higherthe preci- −0.004
sion). −7000−6000−5000−4000−3000−2000−1000 0 1000 2000 3000 4000
Epoch
Fig.4. O−C diagram of GK Boo with the apsidal motion hy-
1
pothesis,blackcolorisforprimaryminima,whileblueonefor
0.8 secondary.
M)Sun0.6
ass ( 0.4 sidalmotionanalysisbasedonlyontheminimatimesofapar-
M
ticularsystem.Somestudiesfoundthatthesecondaryminimum
0.2 is displaced because of the distortionof the LC, thusany stan-
dard routine for derivingthe time of minimum (e.g. Kwee-van
0
10 20 30 40 50 60 70 80 90 Woerden,bisectorchordmethodorpolynomialfitting)cannotbe
Inclination (deg)
used properly because these consider symmetric minima only.
Fig.3.GKBoo:MassofthethirdbodybasedonfromtheLITE Whenusingthesemethodstodetermineminimawherebothas-
hypothesiswithrespecttotheinclinationbetweentheorbits. cending and descending branches have different slopes, we re-
coveronlya”falseeccentricity”.
One can also ask about a significance of the fits presented
Table3.ApsidalmotionparametersforGKBoo.
inFigs. 2and4.Forthiscomparison,we summarizeddifferent
approachesinTable4.Inadditiontothermsvalues,wealsopro-
Parameter Value
videthevaluesofBIC(BayesianInformationCriterion,seee.g.
e 0.0944±0.0068
ω[deg] 268.9±2.5 Liddle2007),whichshowthesignificanceofthefit.According
ω˙ [deg/cycle] 0.00026±0.00001 to thismethod,the smaller thermsvalue,the tighterthe fit. To
U[yr] 1790±50 conclude,ourfinalfitprovidesthe smallest rms,butits signifi-
canceislowandstillhighlyspeculative.Thisisalsocausedby
thepoordatacoverage,andlargescatterintheminimaandtheir
low accuracy.Determinationsof new more precise minima are
ourdatasetofminimatimes.Wefollowedaproceduredescribed
thereforeneededtoconfirmorexcludethishypothesis.
bye.g.Gime´nez&Garc´ıa-Pelayo(1983)orGime´nez&Bastero
(1995)andobtainedasetofapsidalmotionparameters.Theplot
of residuals (after subtraction of the LITE fit) with the apsidal
3. AEFor
motionfitisshowninFig.4. Itisobviouslyveryslow because
the position of secondariesversusprimarieschangesonly very
3.1.Introduction
slowly. The resultant values of apsidal motion parameters are
giveninTable3. The Algol-type system AE For (= HIP 14568, V =
max
However,wehavetoruleoutthishypothesisbecauseitlead 10.22mag)isalsoapoorlystudiedbinary.Itspublishedspectral
tounacceptableresults.Withsomeinformationaboutthephysi- types range from K4 to M0, with the most probableone being
calparametersofbothcomponents,wecanusetheapsidalmo- K7V as derived by (Torresetal., 2006). The system was pre-
tion parametersto estimate the internal structure constant. The sentedasawide doublewith thestar HD19632basedontheir
theoretical log k value taken from Claret (2004) should similarparallaxesandpropermotions(seePovedaetal.1994).
2,theor
rangefrom-1.35to-1.65.However,themeanvalueoflogk of Neither the light curve nor the radial velocity curve of
2
both componentsthat can be derivedfrom our solution is very AE For have been studied. The star was observed by the
different, even when k < 0, which is unacceptable. Thus, the Hipparcos satellite and a few times also for the minima obser-
2
systemisveryprobablyonacircularorbit. vations.Itwasalsocontinuouslymonitoredwithautomaticpho-
Wemayaskwhythesecondaryminimadeviatefromthe0.5 tometricsystemssuchasPiOfTheSkyandASAS.However,the
phase.Wepublishedafindingthatthedisplacedsecondarymin- qualityofthesedatadonotallowustousethemforaLCanal-
ima can also be present in contact binaries where no eccentric ysis.ThedistancetothesystemwasderivedfromtheHipparcos
orbit is possible (Zasche, 2011), so one cannot perform an ap- datatobed=31.5pc.
4
P.Zascheetal.:GKBooandAEFor:Twolow-masseclipsingbinarieswithdwarfcompanions
Table5.LightcurveparametersofAEFor.
1 B
0.9 Parameter Value
V T [K] 4100∗
0.8 1
T [K] 4065±48
2
0.7 R q(=M2/M1) 1.0∗
ux e 0∗
Fl0.6 i[deg] 86.51±0.31
g =g 0.32∗
0.5 1 2
A =A 0.50∗
1 2
0.4 F1 =F2 1.000∗
L (B)[%] 63.2±1.3
1
0.3 L (B)[%] 36.8±1.0
2
L (V)[%] 63.1±1.2
1
0.05 L (V)[%] 36.9±1.0
0 B 2
−0.05 L1(R)[%] 62.6±1.4
0.05 L2(R)[%] 37.4±1.0
0 V Derivedquantities:
−0.05
0.05 R1[R⊙] 0.66±0.10
0 R R [R ] 0.52±0.08
2 ⊙
−0.05 M [M ] 0.50±0.05
−0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 M1[M⊙] 0.50±0.05
Phase 1 ⊙
Note:∗-fixed.
Fig.5.Lightcurvein BVRfiltersforAEFor,thesolidlinerep-

resents the final fit. The curves are shifted along the y-axis for
2448000 2450000 2452000 2454000 2456000
greaterclarity.
0.004 1990 1995 2000 2005 2010 20150.004
0.003 0.003
0.002 0.002
3W.2e.oLbigshertvceudrvtehe star from the South African Astronomical O−C (days)−−000...0000000121 −−00.000..00010021O−C (Period)
Observatory (SAAO) in 2010, using the classical one-channel −0.003 −0.003
−0.004
−0.004
photoelectricphotometer mountedon the 50-cm telescope. All
−6000 −5000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000 5000
measurements were carefully reduced to the Cousins E-region Epoch
standardsystem (Menziesetal., 1989) andcorrectedfordiffer-
entialextinction.
0.002
Thanks to its orbital period close to one day, its complete
lightcurvewasobservedonceinstandardBVRfilters,withsome 0.001
overlappingpoints(about170datapointsineachfilterwereob- ays)
tained).Unfortunately,the qualityof the data acquiredforsev- −C (d 0.0
O
eralnightswas notverygood,hence the scatter in the curveis 0.001
affected by these conditions. Two secondary and one primary
−0.002
minimawereobserved(seebelow).
0 0.25 0.5 0.75 1 1.25 1.5
We analyzedourdata using the same computationalproce- Phase
dureas for GK Boo. The primarytemperaturewas fixed to the Fig.6. O −C diagram of AE For. Up: With linear ephemeris.
appropriatevalueof4100K(spK7V),theeccentricitywasfixed Bottom:Withrespecttothephase.Thedatapointsarefittedwith
to 0, the values of gravity darkening coefficients were fixed at thecurverepresentingthethirdbodyhypothesis(seethetextfor
0.32, and the albedo coefficients to 0.5 (as recommended for details).
stars with convectiveenvelopes), while the limb darkeningco-
efficients were interpolated from values given in vanHamme
(1993).Thecomputationalapproachwas differentforthemass
3.3.Periodanalysis
ratioq,whichwasfixedtoq=1.0becauseoftheweakoutside-
eclipse ellipsoidal variations and its detached configuration.In SimilarlytoGKBoo,wetriedtoperformtheperiodanalysisof
addition, the synchronicityparameters Fi were set to values of allavailableminima.Thecollectionofminimaismuchsmaller,
1.0 for both components. The program ROCHE was used and butthankstothefirstobservationbyHipparcos(Perrymanetal.,
theresultingLCparametersaregiveninTable5,whilethefinal 1997)thesecoveralongertimespanthanforGKBoo.Several
solutionispresentedinFig.5. new minimawerederivedbased onournew observationsfrom
OnecanseethatthesecondarytemperatureT isclosetothe SAAOaswellasthosefromtheASASandPiOfTheSkysurveys.
2
valueofT ,indicatingthatthecomponentsaresimilar.Thus,the ThesamehypothesisasforGKBoowasappliedtothedata
1
estimatedspectraltypesofbothstarsareprobablyK7V+K7V. points here. All of the minima times used for the analysis are
Bothcomponentsarestilllocatedonthemainsequenceandtheir summarized in Table 11, which is available in electronic form
propertiesareinagreementwiththetypicalvaluesofK7Vstars only.AsonecanseefromFig.6,thereisaclearvariationinthe
(aspresentedbye.g.Harmanec1988).Thethirdlightwas also minimatimes.We usedthesamethird-bodyhypothesis(LITE)
notdetectedhereinanyfilter.IncontrasttoGKBoo,theLCof as for GK Boo, derivinga final fit to the data givenby the pa-
AEForseemstobesymmetric. rametersinTable6.TheLITEhypothesisresultedinaratherec-
5
P.Zascheetal.:GKBooandAEFor:Twolow-masseclipsingbinarieswithdwarfcompanions
Table6.FinalparametersofthelongorbitforAEFor. metricandspectroscopicobservationsareneededtoconfirmor
refutethishypothesis.
Parameter Value The system GK Boo has an asymmetric light curve, which
HJD 2452605.97070±0.00035 istheprobablyaccountsfortheshiftinthesecondaryminimum
0
P[day] 0.91820943±0.00000012 in phase with the primary one. The apsidal motion hypothesis
p3[day] 2524.6±149.6 cannotexplainthisdiscrepancy.
p3[yr] 6.912±0.409 In general, if the third body hypothesis as proposed based
A[day] 0.00083±0.00032
on the period analysis is found to be the correct one, here we
T 2453548.8±413.1
0 haveconsideredquitecuriousexamplesofhierarchicalquadru-
ω [deg] 146.2±57.8
3 ple systems of low masses. As far as we know, there are only
e 0.601±0.414
3 a few similar multiple late-type systems for which one of the
f(M )[M ] 0.000098±0.000001
3 ⊙
M [M ] 0.047±0.001 componentsisaneclipsingbinary(e.g.BBSclorMRDel).
3,min ⊙
M [M ] 0.055±0.001
3,60 ⊙
M [M ] 0.098±0.003 Acknowledgements. Wethankthe”ASAS”,”SWASP”and”Piofthesky”teams
3,30 ⊙ formakingalloftheobservationseasilypublicavailable.PZwishtothankthe
a sini[AU] 0.167±0.064
12 staffatSAAOfortheirwarmhospitalityandhelpwiththeequipment.Authors
a [mas] 117.2±8.3
3 arealsogratefultoTheoPribullaforhishelpfulcommentsabouttheROCHE
code.Ananonymousrefereeisalsoacknowledgedforhis/herhelpfulandcrit-
ical suggestions. This work was supported by the Czech Science Foundation
Table7.MethodsofminimafittingforAEFor.
grantno.P209/10/0715andalsobytheResearchProgrammeMSM0021620860
oftheCzechMinistryofEducation.ThisresearchhasmadeuseoftheSIMBAD
Methodofminimafitting rms BIC database, operated at CDS, Strasbourg, France, and of NASA’s Astrophysics
Linearephemeris: 0.000255 24.4 DataSystemBibliographicServices.
LITEandlinearephemeris: 0.000163 44.8
References
centricorbit,althoughtheresultisaffectedbyarelativelylarge Ammons,S.M.,Robinson,S.E.,Strader,J.,Laughlin,G.,Fischer,D.,&Wolf,
A.2006,ApJ,638,1004
error,hencemaybethee valueshouldbelower.Onlyadditional
3 Andersen,J.1991,A&ARev.,3,91
observationswouldhelpusconfirmorrefutethishypothesis,re-
Bessell,M.S.1990,PASP,102,1181
finetheperiod,andpossiblydetectsomelong-termevolutionof Burd,A.,etal.2005,NewA,10,409
the period similar to that in GK Boo, because the first obser- Claret,A.2004,A&A,424,919
vation from Hipparcosdeviates significantly from the fit. With Cox,A.N.2000,Allen’sAstrophysicalQuantities,
Cutri,R.M.,etal.2003,VizieROnlineDataCatalog,2246,0
the same procedure as for GK Boo, we computed the signifi-
Gime´nez,A.,&Garc´ıa-Pelayo,J.M.1983,Ap&SS,92,203
cance of the fits according to the BIC criterion (see Table 7). Gime´nez,A.,&Bastero,M.1995,Ap&SS,226,99
Asonecansee,thefitisstill verypoorandhighlyspeculative. vanHamme,W.1993,AJ,106,2096
However,usingonlythelinearephemeris,thereremainsaclear Harmanec,P.1988,BAICz,39,329
Høg,E.,etal.2000,A&A,355,L27
quasi-sinusoidalvariation,whichneedssomephysicalexplana-
Irwin,J.B.1959,AJ,64,149
tion.
Kharchenko,N.V.2001,KinematikaiFizikaNebesnykhTel,17,409
From the LITE parameters, we were able to calculate the Kroupa,P.2002,Science,295,82
minimal mass of the third body (i.e. coplanar orbits), which Kwee,K.K.,vanWoerden,H.1956,BAN,12,327
we found to be only about 47 M , which is even lower than Lada,C.J.2006,ApJ,640,L63
Jup Liddle,A.R.2007,MNRAS,377,L74
the limit of stellar masses. Therefore, if the orbits were copla-
Mason,B.D.,Wycoff,G.L.,Hartkopf,W.I.,Douglass,G.G.,&Worley,C.E.
nar (which only would be our assumption, because the pro- 2001,AJ,122,3466
cessoftidalcoplanarizationisveryslow),thethirdbodywould Menzies,J.W.,Cousins,A.W.J.,Banfield,R.M.,Laing,J.D.1989,SAAOC13,
veryprobablybeabrowndwarf(exoplanetshavemassesabout 1
Perryman,M.A.C.,Lindegren,L.,Kovalevsky,J.,etal.1997,A&A,323,L49
one half of this value). With such a body, we reach minimal
Pojmanski,G.2002,AcA,52,397
massesthatcanbedetectedbythismethod,becausetheampli-
Pollacco,D.L.,etal.2006,PASP,118,1407
tudeofLITEiscomparabletothetypicalprecisionofindividual Popper,D.M.1980,ARA&A,18,115
minima-timemeasurements.Whateverappliestothepossiblein- Poveda, A., Herrera, M. A., Allen, C., Cordero, G., & Lavalley, C. 1994,
terferometricdetectionofGKBoocompanionalsoapplieshere, RMxAA,28,43
Pribulla,T.2004,SpectroscopicallyandSpatiallyResolvingtheComponentsof
becauseitsluminosityistoolow.
theCloseBinaryStars,318,117
Prsˇa,A.,&Zwitter,T.2005,ApJ,628,426
Terrell,D.,&Wilson,R.E.2005,Ap&SS,296,221
4. Discussionandconclusions Torres,C.A.O.,Quast,G.R.,daSilva,L.,deLaReza,R.,Melo,C.H.F.,&
Sterzik,M.2006,A&A,460,695
We have derived preliminary light-curve solutions and period Wilson,R.E.,&Devinney,E.J.1971,ApJ,166,605
Zasche,P.2011,IBVS,5991,1
analyses of the poorly studied Algol-type eclipsing binaries
GK Boo and AE For, which we have foundto have severalin-
terestingandsimilarfeatures.Sincebothofthemarelow-mass
starsofverysimilartypes(K3+K3forGKBoo,andK7+K7for
AEFor),bothofthemhaveshortorbitalperiods.Moreover,both
are relatively close to the Sun and also appear to contain third
bodies in their systems, which cause a periodic modulation of
theorbitalperiodsofbothsystems. Assuminga coplanarorbit,
forAEForthisthirdbodyappearsto bea browndwarf,which
makesthissystemevenmoreinteresting.However,morephoto-
6
P.Zascheetal.:GKBooandAEFor:Twolow-masseclipsingbinarieswithdwarfcompanions
Table8.HeliocentricminimaofGKBoousedfortheanalysis. Table9.MinimaofGKBoo,cont.
HJD-2400000 Error Type Filter Reference HJD-2400000 Error Type Filter Reference
51260.8547 0.0007 sec - IBVS5060 54163.55942 0.00065 prim - SWASP
51273.9890 prim - A.Paschke-Rotse 54165.70909 0.00037 sec - SWASP
51311.7377 0.0004 prim - IBVS5060 54166.66462 0.00022 sec - SWASP
53128.46588 0.00024 sec - SWASP 54167.62053 0.00034 sec - SWASP
53128.70498 0.00041 prim - SWASP 54170.72638 0.00023 prim - SWASP
53129.66141 0.00056 prim - SWASP 54171.68178 0.00043 prim - SWASP
53130.61697 0.00047 prim - SWASP 54189.59755 0.00032 sec - SWASP
53132.52777 0.00021 prim - SWASP 54190.55322 0.00019 sec - SWASP
53135.39435 0.00010 prim - SWASP 54191.50702 0.00053 sec - SWASP
53137.54360 0.00024 sec - SWASP 54194.61418 0.00029 prim - SWASP
53138.49891 0.00028 sec - SWASP 54195.57050 0.00029 prim - SWASP
53139.45491 0.00021 sec - SWASP 54202.49743 0.00046 sec - SWASP
53141.60560 0.00027 prim - SWASP 54206.55909 0.00039 prim - SWASP
53152.59424 0.00025 prim - SWASP 54208.46922 0.00027 prim - SWASP
53153.54982 0.00020 prim - SWASP 54208.70823 0.00143 sec - SWASP
53154.50553 0.00017 prim - SWASP 54210.61908 0.00030 sec - SWASP
53155.46071 0.00015 prim - SWASP 54212.53056 0.00050 sec - SWASP
53156.41642 0.00014 prim - SWASP 54213.48698 0.00049 sec - SWASP
53158.56492 0.00048 sec - SWASP 54214.44267 0.00029 sec - SWASP
53159.52074 0.00022 sec - SWASP 54214.68147 0.00039 prim - SWASP
53160.47640 0.00021 sec - SWASP 54215.63620 0.00057 prim - SWASP
53161.43169 0.00026 sec - SWASP 54216.59233 0.00019 prim - SWASP
53163.58313 0.00031 prim - SWASP 54217.54805 0.00038 prim - SWASP
53164.53862 0.00031 prim - SWASP 54218.50359 0.00021 prim - SWASP
53165.49392 0.00015 prim - SWASP 54219.45928 0.00030 prim - SWASP
53166.44965 0.00020 prim - SWASP 54220.41494 0.00069 prim BVR PS
53169.55361 0.00034 sec - SWASP 54220.41498 0.00029 prim - SWASP
53170.50939 0.00024 sec - SWASP 54222.56423 0.00066 sec BVR PS
53171.46489 0.00034 sec - SWASP 54222.56444 0.00028 sec - SWASP
53172.42077 0.00031 sec - SWASP 54223.51949 0.00169 sec BVR PS
53175.52707 0.00024 prim - SWASP 54223.51994 0.00108 sec - SWASP
53176.48289 0.00047 prim - SWASP 54224.47565 0.00035 sec - SWASP
53180.54262 0.00022 sec - SWASP 54225.43110 0.00022 sec - SWASP
53181.49835 0.00017 sec - SWASP 54225.67010 0.00026 prim - SWASP
53182.45376 0.00018 sec - SWASP 54226.38671 0.00034 sec - SWASP
53183.41009 0.00076 sec - SWASP 54226.62544 0.00036 prim - SWASP
53191.53267 0.00080 sec - SWASP 54227.58111 0.00026 prim - SWASP
53192.48678 0.00031 sec - SWASP 54228.53676 0.00031 prim - SWASP
53193.44381 0.00026 sec - SWASP 54230.44800 0.00019 prim - SWASP
53194.39850 0.00045 sec - SWASP 54231.40365 0.00019 prim - SWASP
53197.50383 0.00080 prim - SWASP 54231.64168 0.00048 sec - SWASP
53198.46046 0.00023 prim - SWASP 54232.59790 0.00032 sec - SWASP
53199.41623 0.00026 prim - SWASP 54233.55304 0.00025 sec - SWASP
53203.47632 0.00029 sec - SWASP 54234.50899 0.00034 sec - SWASP
53209.44918 0.00047 prim - SWASP 54235.46550 0.00054 sec - SWASP
53215.42110 0.00040 sec - SWASP 54236.42047 0.00028 sec - SWASP
53220.43588 0.00083 prim - SWASP 54236.65842 0.00085 prim - SWASP
53221.39317 0.00039 prim - SWASP 54237.37517 0.00137 sec BVR PS
53226.40796 0.00058 sec - SWASP 54239.52553 0.00091 prim BVR PS
53231.42630 0.00045 prim - SWASP 54249.55879 0.00027 prim - SWASP
53232.38275 0.00032 prim - SWASP 54250.51471 0.00031 prim - SWASP
53237.39732 0.00033 sec - SWASP 54251.47023 0.00057 prim - SWASP
53243.37030 0.00082 prim - SWASP 54252.42644 0.00028 prim - SWASP
53248.38731 0.00078 sec - SWASP 54254.57647 0.00059 sec - SWASP
53259.85637 0.00078 sec - SWASP 54256.48657 0.00172 sec BVR PS
53827.68574 0.00085 prim - SWASP 54256.48655 0.00039 sec - SWASP
53829.59740 0.00088 prim - SWASP 54257.44222 0.00025 sec - SWASP
53830.55201 0.00069 prim - SWASP 54261.50367 0.00031 prim - SWASP
53831.50729 0.00051 prim - SWASP 54262.45860 0.00020 prim - SWASP
53832.46270 0.00015 prim - SWASP 54263.41487 0.00037 prim - SWASP
53832.70138 0.00024 sec - SWASP 54265.56380 0.00079 sec - SWASP
53833.65681 0.00047 sec - SWASP 54266.51892 0.00042 sec - SWASP
53837.47803 0.00029 sec - SWASP 54267.47491 0.00020 sec - SWASP
53851.57305 0.00105 prim - SWASP 54268.43084 0.00017 sec - SWASP
53852.52690 0.00049 prim - SWASP 54271.53663 0.00070 prim - SWASP
53853.48213 0.00027 prim - SWASP 54272.49225 0.00033 prim - SWASP
53854.43799 0.00032 prim - SWASP 54273.44808 0.00026 prim - SWASP
53855.39312 0.00090 prim - SWASP 54276.55314 0.00095 sec - SWASP
53855.63171 0.00037 sec - SWASP 54277.50813 0.00065 sec - SWASP
53856.58695 0.00051 sec - SWASP 54278.46353 0.00031 sec - SWASP
53887.40789 0.00024 prim - SWASP 54279.41942 0.00021 sec - SWASP
53901.50285 0.00080 sec - SWASP 54305.45758 0.00157 prim BVR PS
54140.62657 0.00022 prim - SWASP 54307.37045 0.00141 prim BVR PS
54149.70458 0.00021 prim - SWASP 54568.70649 0.00072 prim - Piofthesky
54150.65998 0.00028 prim - SWASP 54568.94557 0.00097 sec - Piofthesky
54153.76487 0.00119 sec - SWASP 54925.36514 0.0001 sec R OEJV107
54154.71989 0.00026 sec - SWASP 54937.3112 0.0020 sec Ir IBVS5918
54155.67581 0.00061 sec - SWASP 54937.5462 0.0005 prim Ir IBVS5918
54156.63161 0.00053 sec - SWASP 54947.34260 0.0014 sec R OEJV107
54157.58667 0.00065 sec - SWASP 54958.8085 0.0007 sec V IBVS5894
54159.73799 0.00019 prim - SWASP 54959.52489 0.0001 prim R OEJV107
54160.69347 0.00018 prim - SWASP 55354.40380 0.00148 sec BVR PS
54161.64928 0.00022 prim - SWASP 55364.4367 0.0001 sec BVRI IBVS5965
54162.60325 0.00019 prim - SWASP 55385.45891 0.00131 sec BVR PS
7
P.Zascheetal.:GKBooandAEFor:Twolow-masseclipsingbinarieswithdwarfcompanions
Table10.MinimaofGKBoo,cont.
HJD-2400000 Error Type Filter Reference
55386.41381 0.00104 sec BVR PS
55391.43075 0.00097 prim BVR PS
55392.38658 0.00113 prim BVR PS
55590.66335 0.00036 prim - RU
55599.50146 0.00018 sec - RU
55616.46275 0.00005 prim B PZ
55616.46266 0.00012 prim R RU
55619.56796 0.00010 sec R RU
55634.61898 0.00016 prim R RU
55640.58947 0.00019 sec R RU
55644.41169 0.00005 sec B PZ
55650.62303 0.00014 sec R RU
55651.34031 0.00113 prim B PZ
55662.56706 0.00013 sec R RU
55671.40664 0.00007 prim VR PZ
55685.50021 0.00012 sec R RU
55687.41150 0.00011 sec BVR PZ
55692.42853 0.00004 prim BVR PZ
55700.55071 0.00004 prim BVR PZ
55707.47805 0.00008 sec BVR PZ
Table11.HeliocentricminimaofAEForusedfortheanalysis.
HJD-2400000 Error Type Filter Reference
48500.6581 0.001 prim Hp Hipparcos
51180.9089 prim R VSOLJ37
51180.9090 0.0002 prim R VSOLJ47
51191.0099 prim R VSOLJ37
51191.0100 0.0002 prim R VSOLJ47
51191.9279 prim V VSOLJ37
51191.9280 0.0001 prim V VSOLJ47
51196.9770 0.0001 sec R VSOLJ47
51196.9774 sec R VSOLJ37
51504.11886 prim I VSOLJ37
51504.1190 0.0002 prim I VSOLJ47
52065.14178 0.00121 prim V ASAS
52065.60355 0.0025 sec V ASAS
52235.0140 prim I VSOLJ39
52240.9825 sec I VSOLJ39
52258.8860 0.0002 prim R VSOLJ39
52605.9710 prim I VSOLJ40
52818.07823 0.00077 prim V ASAS
52818.53514 0.00165 sec V ASAS
52901.1754 sec I VSOLJ42
52929.1801 prim I VSOLJ42
52936.0674 sec I VSOLJ42
52957.1865 sec V VSOLJ42
52970.0410 sec I VSOLJ42
52976.0097 prim I VSOLJ42
52987.0267 prim V VSOLJ42
52987.9466 prim I VSOLJ42
53300.1379 prim V VSOLJ43
53335.0300 prim V VSOLJ43
53340.0796 sec V VSOLJ43
53705.0677 0.0002 prim V VSOLJ44
53728.02219 0.00093 prim V ASAS
53728.48316 0.00194 sec V ASAS
54039.75501 0.00027 sec - PiOfTheSky
54040.67301 0.00045 sec - PiOfTheSky
54047.1000 0.0001 sec V VSOLJ45
54052.60840 0.00149 sec - PiOfTheSky
54448.81542 0.00039 prim - PiOfTheSky
54726.11607 0.00187 prim V ASAS
54726.57421 0.00131 sec V ASAS
54862.9297 0.0002 prim V VSOLJ50
55558.0139 prim V VSOLJ51
55570.41065 0.00072 sec BVR PZ-SAAO
55571.32812 0.00105 sec BVR PZ-SAAO
55576.37847 0.00065 prim BVR PZ-SAAO
8