The orbital elements and physical properties of the eclipsing binary BD+36 3317, a probable member of $\delta$ Lyr cluster

0.46 MB·

by  E. Kıran

Astronomy&Astrophysicsmanuscriptno.evrim (cid:13)cESO2016
January27,2016
The orbital elements and physical properties of the eclipsing
◦ δ
binary BD+36 3317, a probable member of Lyr cluster
E.Kıran1,2,P.Harmanec1,Ö.L.Deg˘irmenci2,M.Wolf1,J.Nemravová1,M.Šlechta3,andP.Koubský3
1 AstronomicalInstituteoftheCharlesUniversity,FacultyofMathematicsandPhysics,
VHolešovicˇkách2,CZ-18000Praha8-Troja,CzechRepublic
2 UniversityofEge,DepartmentofAstronomy&SpaceSciences,35100Bornova-˙Izmir,Turkey
3 AstronomicalInstitute,AcademyofSciencesoftheCzechRepublic,25165Ondˇrejov,CzechRepublic
6
1
ReceivedJanuary27,2016
0
2
ABSTRACT
n
a
Context.Thefactthateclipsingbinariesbelongtoastellargroupisuseful,becausetheformercanbeusedtoestimatedistanceand
J
additionalpropertiesofthelatter,andviceversa.
6 Aims. Our goal is to analyse new spectroscopic observations of BD+36◦3317 along with the photometric observations from the
2
literatureand,forthefirsttime,toderiveallbasicphysicalpropertiesofthisbinary. Weaimtofindoutwhetherthebinaryisindeed

amemberoftheδLyropencluster.
]
Methods.ThespectrawerereducedusingtheIRAFprogramandtheradialvelocitiesweremeasuredwiththeprogramSPEFO.The
A
linespectraofbothcomponentsweredisentangledwiththeprogramKOREL andcomparedtoagridofsyntheticspectra. Thefinal
G combinedradial-velocityandphotometricsolutionwasobtainedwiththeprogramPHOEBE.
. Results.WeobtainedthefollowingphysicalelementsofBD+36◦3317: M1=2.24±0.07M⊙,M2=1.52±0.03M⊙,R1=1.76±0.01
h R ,R =1.46±0.01R ,logL =1.52±0.08L ,logL =0.81±0.07L .WederivedtheeffectivetemperaturesT =10450±420
⊙ 2 ⊙ 1 ⊙ 2 ⊙ eff,1
p K,T =7623±328K.BothcomponentsarelocatedclosetoZAMSintheHertzsprung-Russell(HR)diagramandtheirmasses
eff,2
-
o andradiiareconsistentwiththepredictionsofstellarevolutionarymodels. Ourresultsimplytheaveragedistancetothesystemd=
r 330±29pc.Were-investigatedthemembershipofBD+36◦3317intheδLyrclusterandconfirmedit.ThedistancetoBD+36◦3317,
t givenabove,thereforerepresentsanaccurateestimateofthetruedistanceforδLyrcluster.
s
a Conclusions.TherealityoftheδLyrclusterandtheclustermembershipofBD+36◦3317havebeenreinforced.
[
Keywords. Stars:binaries:eclipsingStars:fundamentalparametersStars:individual:BD+36◦3317

1
v
61. Introduction including δ Lyr cluster, belong to the Pleiades moving group.
8 For BD+36◦3317 he gave V = 8m.65, (B−V) = −0m.03, and
9 0 0
Eclipsingbinarieshaveplayedanimportantroleinastrophysics (U−B) = −0m.115 and a spectral class B9.5V. Later, Eggen
6 0
andinunderstandingthenatureandevolutionofbinarysystems (1983)obtaineduvbyphotometryofstarsfromtheδLyrcluster
0
by providing the most accurate values of stellar masses, radii, andmentionedthatBD+36◦3317isaspectroscopicbinarywith
.
1andluminosities.Especiallyusefulareeclipsingbinaries,which aradialvelocity(RV)rangefrom−90to+17kms−1. Hegives
0are members of some kind of cluster or association since they V =8m.79,(b−y)=0m.031,m =0m.150,andc =0m.885forthe
6 1 1
provide an excellent tool for accurately estimating the cluster system. Thesecanbecomparedtoindependentuvbyphotomet-
1
distanceandage,independentlyofphotometriccalibrations. ric results published by Anthony-Twarog(1984) as V = 8m.90,
:
v The eclipsing binary BD+36◦3317 (GSC 2651 802, SAO (b − y) = 0m.011, m1 = 0m.160, and c1 = 0m.904. She ob-
Xi67556, α2000 = 18h54m22s, δ2000 = 36◦51′.07′.′445, V = 8m.77) tained a large scatter in the distance moduliof individualclus-
islocatedin thefield ofδLyrcluster. Stephenson(1959), who ter members and again cast some doubt as to the existence of
r
aactually discovered the δ Lyr (Stephenson 1) cluster, gives a the cluster. She confirmed, however, that the observed colours
visual magnitude 8m.8 and spectral type A0 for BD+36◦3317. of BD+36◦3317 are indicative of an A-type spectroscopic bi-
nary. Interestingly, neither author noted that the range of pub-
Bronkalla(1963)obtainedphotoelectricUBV andphotographic
observations of many stars in the vicinity of δ Lyr and chal- lished valuesforthe V magnitudeof BD+36◦3317suggestsits
lenged the existence of the cluster. For BD+36◦3317 he ob- light variability. However, in 2008, Violat-Bordonau (2008)
tained V = 8m.800, (B−V) = +0m.041, and (U−B) = −0m.036. publish their 2007 V band observations of the system and an-
nouncethatBD+36◦3317isaneclipsingbinarywithaperiodof
However, Eggen (1968) made photoelectric(UBV) photometry
of77starsinthevicinityoftheδLyrclusterandpresentedsome 4d.30216. Theyalsogivethe epochoftheprimaryminimumas
HJD 2454437.25921. Özdarcanetal. (2012) obtained a set of
convincingevidencethattheclusterexists. Hederivedthemean
reddeningE(B−V) = 0m.05andadistancemodulusof7m.5. He completeUBV lightcurvesandimprovedtheephemeristo
arguedthattheδLyrclusterhasasimilarcolourmagnitudeand
propermotiontothePleiadesmovinggroup. ForBD+36◦3317 T =HJD2454437.2466(30)+4d.302162(27)×E. (1)
min.I
he obtainedV = 8m.80, (B−V) = +0m.02, and(U−B)= −0m.08.
Eggen (1972) further developed the idea that several clusters, Theyderiveda simultaneoussolution of the lightcurves(LCs)
Articlenumber,page1of10
andnoticedthatthe system hasa totaleclipse in thesecondary Table 2. Orbital parameters and their uncertainties obtained with the
programSPEL.
minimum. Asaresult,theyderivedthemagnitudesandcolours
of the components separately. They give the intrinsic visual
magnitudes and colours of the components as V = 8m.883, Element Value
0
(U−B) = −0m.170, (B−V) = −0m.062 for the primary, and
0 0 P(d) 4.30216fixed
V = 10m.277, (U−B) = −0m.104, (B−V) = 0m.245 for the
0 0 0 T (HJD) 2454437.2359±0.0046
secondary. Theyestimatetheinterstellarreddeningandtotalvi- min.I
sual extinctionfor the system as E(B−V) = 0m.07, A = 0m.22. K1 (kms−1) 82.6±0.6
0 K (kms−1) 123.1±0.7
FromtheirLCanalysis,theyestimatetheabsolutephysicalpa- 2
q= K /K 0.67±0.01
rametersofthecomponentsandarriveatadistanceof353pcfor 1 2
thebinary. Theydonotgiveanerrorbarforthedistanceofthe V0(kms−1) −19.0±0.4
system. asini(R⊙) 17.5
2. Observationsanddatareductions
semi-amplitudesoftheradialvelocitycurvesofthecomponents,
Spectroscopic observations of BD+36◦3317 were made with andthesystemicvelocityofthebinaryinthiscase). Wekeptthe
the single order spectrograph attached to the 2 m reflector of orbital period from ephemeris (1) fixed and adopted a circular
the Ondˇrejov Observatory, Czech Republic. The spectra were orbit. There seems to be some weak evidence of a very small
recordedwith aCCD detector and cover the wavelength range eccentricityoftheorbitbutonlycontinuingobservationsofthe
of6260−6700Åwithatwo-pixelspectralresolutionof11700. timesofminimacould(dis)proveit. Inanycase,theuseofthe
Thetypicalexposuretimeswere90min,andtheratioofsignal circularorbithasanegligibleeffectonthe elementsthatdefine
tonoise(S/N)variesbetween80and200. Thesystem wasob- thebinarymasses. TheresultscanbefoundinTable2.
servedover20nightsfromMarchtoJuly2014. Eachnight,flat
fieldandbiasexposureswereobtainedandtheThorium-Argon
3.3.Improvedlinearephemeris
(ThAr)comparisonspectrawereobtainedbeforeandaftereach
stellar exposure. The initial reductions (bias subtraction, flat
HavingnowtwosetsofphotometricobservationsandnewRVs,
fielding, cosmicrayremoval,andwavelengthcalibration)were
whichspan a substantiallylongertime intervalthanbefore, we
carriedoutwiththe programIRAF byMŠ. Rectificationofthe decided to derive a new, more accurate linear ephemeris. To
spectraandtheRVmeasurementsofthestellarandselectedtel- thisend,wefirstusedtheprogramPHOEBE 1.0(Prša&Zwitter
luriclineswerecarriedoutwiththeprogramSPEFO,whichhas 2005, 2006), which is an extension of the widely used WD
written by Dr. J.Horn (Hornetal. 1996) and further developed program (Wilson&Devinney 1971). As mentioned above,
byŠkoda(1996)andMr. J.Krpata. Violat-Bordonau (2008) obtained the first V-band light curve
of the BD+36◦3317 and derived a linear ephemeris. Later,
Özdarcanetal. (2012) published a new ephemeris based on
3. Towardsbasicphysicalpropertiesofthebinary
their UBV light curves. We combined all four LCs with our
3.1.DirectRVmeasurements SPEFO RVstoobtainthefollowinglinearephemeris:
As already mentioned, the object had been classified as an A-
type star. This is corroborated by our red spectra, which con- Tmin.I =HJD2454437.2480(13)+4d.302152(1)×E. (2)
tain the Hα line with a sharp core and very broad wings, Siii
doubletat6347and6371Å, andseveralweakermetalliclines,
mainlyofFei,Feii,Cai,Nii,andMgii. FordirectRVmeasure-
ments, we used the three strongest lines (Hα core and the Siii
doublet), where both binary components were easily resolved. 3.4.Spectradisentanglingandanothertrialsolution
The measurements were carried out with the SPEFO program,
TochecktheresultsfromthedirectRVmeasurementsinSPEFO,
inwhichonecanslideanimageoftheflippedlineprofilewith
andto obtainline spectra of individualbinarycomponentsthat
respecttothedirectoneontothecomputerscreenuntilaperfect
were suitable for further analyses, we decided to disentangle
match of the desired parts of the profile is achieved (see, e.g.
the spectra. For this we used the program KOREL, written
Harmanecetal.2015;Hornetal.1996,fordetails). Allspectra
and further developed by Hadrava (1995, 1997, 2004, 2009),
were independentlyreducedand measuredby EK andPH and,
and Škoda&Hadrava (2010), with the latest version available
afterverifyingthatbothsetsoftheseindependentmeasurements
throughthe VO-KORELweb service. Beforepreparingthein-
agreewellwitheachother,meanvaluesforeachspectrumwere
putdata for KOREL, we estimated the S/N of individualspectra
adopted,asrecordedinTable1.
in the line-free region 6625 – 6645 Å as the ratio of the mean
signalanditsrmserrorusingtheformula
3.2.AtrialRVsolutionwiththeprogramSPEL
To have some guidance for a more sophisticated analysis, we S S2−( S)2/m
firstderivedtheorbitalsolutionwiththeprogramSPEL,written S/N =Pm /r(cid:0)P m−P1 (cid:1), (3)
bthyetohrebliatateleDler.mJe.nHtso(ronr.b1itTahlepeprrioogdraamndreepqoucirhesofinmpuaxtivmaluumesRfVor,  
wheremisthenumberofpixelsusedinthewavelengthinterval.
1 The program has never been published but was We then weightedeachspectrumbythe weightproportionalto
carefully tested and used in several publications. (S/N)2 andnormalizedtothemeanS/Nofallspectrathatwere
http://astro.troja.mff.cuni.cz/ftp/hec/SPEL90/spel.pdf used. Therebinningoftheelectronicspectraandpreparationof
Articlenumber,page2of10
Kıranetal.:BasicphysicalelementsofBD+36◦3317
Table3.BesttrialorbitalsolutionwithKOREL (seethetextforthees-
103500
timationprocedureoftheerrorbars).
103000
102500 Element Value
s
al
u
sid 102000 P(d) 4.302152fixed
e
of r 101500 Tmin.I(HJD) 2454437.26469
uares 101000 KK1 ((kkmmss−−11)) 18204.8.1±±11.1.3
q 2
s
of 100500 q 0.650±0.015
m
su 100000 asini(R⊙) 17.4
99500
99000 SPEL solution in Table 2 as being quite representative of real
65 70 75 80 85 90 95
uncertainties.Secondly,wecanalsoestimateuncertaintiesofK
K1 (km/s) 1
and K from the RV measurementsgivenin Table 1. Accord-
104000 2
ingto the valuesin Table 1, ourRV measurementshave mean
103500 errorsof0.63and1.1kms−1fortheprimaryandsecondarycom-
103000 ponents,respectively. Thesevaluesare alsoin goodagreement
uals 102500 with the K errorsin Table 2. Thirdly,a close inspectionof the
of resid 102000 rσaqth=e0r.fl0a2tfmorinKim1aanidnqF,igre.s1pesuctgigveelsyts.Terhreorresfoofreσ,Kfi1n=a2llyk,mwse−a1daonpdt
es 101500 theaverageerrorsofσ =1.1kms−1,σ =1.3kms−1,andσ =
ar K1 K2 q
squ 101000 0.015forK1,K2andq,respectively.
of
m 100500
u
s 100000 3.5.Acomparisonofdisentangledandobservedspectra
withsyntheticones
99500
99000 To obtain the estimates of the effective temperatures, grav-
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ity accelerations, and projectedrotationalvelocitiesfromspec-
q
troscopy,weusedtwoindependentprocedures.
Fig. 1. Sum of squares of residuals for trial KOREL solutions with
First we used a program which compares synthetic spectra
fixedelementsasafunctionof(a)thesemi-amplitudeK (upperpanel),
1 withdisentangledorobservedspectraofmultiplesystemstoes-
and(b)themassratioK /K (lowerpanel).
1 2 timate radiativepropertiesof its components(see Nasserietal.
2014, for the details). The programuses severalpre-calculated
inputdataforKOREL wascarriedoutwiththeprogramHEC35D gridsof synthetic spectra. The primaryfalls within parameters
writtenbyPH.2 covered with grid POLLUX (Palaciosetal. 2010) and the sec-
ondaryfallswithingridAMBRE (deLavernyetal. 2012). The
Using the ephemeris (2) and the orbitalparametersderived
withSPEL,werunanumberoftests. First, wavelength band ∆λ ∈ {6330−6695}Å was fitted. The opti-
we kept all elements fixed and ran the program for several mized parameterswere the effective temperature, the projected
differentvaluesofthesemi-amplitudeK tofindoutwhichone rotationalvelocity,thesystemicradialvelocity,andtherelative
1
givesthelowestsumofsquaresoftheresiduals. Thisindicated luminosity3ofbothcomponents. TheresultispresentedinCol-
K ∼ 81 km s−1 as the optimal value (see the upper panel of umn2ofTable4.
1
Fig.1). Keepingthisvaluefixed,wecarriedoutasimilarmap- Uncertainties of fitted parameters were estimated with a
pingtoobtainthebestguessforthemassratioq = K /K . The Monte Carlo simulation, which was carried out as follows: 1)
1 2
resultisshowninthebottompanelofFig.1(q∼0.66). The continuum σc noise was estimated for each disentangled
Starting with these values, we then carried out a series of spectrum,usingthesame procedureastheprevioussection. 2)
KOREL solutions,butnowallowingthefreeconvergenceofthe AnartificialGaussiannoisewithσ=σcwasaddedtothedisen-
epochT ,semi-amplitudeK , andthemassratioq = K /K tangledprofile. 3)The adjusteddisentangledspectrumwas fit-
min.I 1 1 2
and variously kicking away the initial values from the adopted ted. Thisprocedurewasrepeated500timesandtheerrorswere
values. The solution that gives the lowest sum of squares of estimated from the distribution of results from all runs. These
residualsareshowninTable 3,andthecorrespondingdisentan- uncertaintiesdonotreflectthe needforthe re-normalizationof
gled spectra of the components are shown in Fig. 2. We note disentangled profiles. This step especially affects the width of
thatthe SPEL solutionbased on RVs measuredin SPEFO does Hαlineand,consequently,theobtainedparameters,particularly
notdiffersignificantlyfromtheoptimalKOREL solution. the gravitational acceleration and the projected velocity. The
TheKOREL programdoesnotprovideerrorestimatesofin- gravitationalaccelerationwasestimatedfromthelightcurveso-
lutionandfixedduringthefittingofdisentangledspectra,butthe
dividual parameters. However, certain error estimates can be
projectedrotationalvelocitywasfitted.
obtained as follows. First, since there is a good agreementbe-
tween the results fromRVs directlymeasuredwith SPEFO and To test the reliability of the estimated projected rotational
those from KOREL, one can adopt the K and q errors from the velocity, another fit that followed the same procedure was
computed, but the fitted wavelength range was only ∆λ ∈
2 The program and a manual to it can be downloaded from
http://astro.troja.mff.cuni.cz/ftp/hec/HEC35. 3 Thetotalluminositywasconstrainedasfollows: L +L =1.0.
1 2
Articlenumber,page3of10
1.1 1.05
1.0
1.00
0.9
x x
d flu 0.8 d flu 0.95
e e
z z
ali ali
m 0.7 m
or or 0.90
n n
0.6
0.85
0.5
0.4 0.80
6300 6350 6400 6450 6500 6550 6600 6650 6700 6750 6300 6350 6400 6450 6500 6550 6600 6650 6700 6750
l (Å) l (Å)
Fig.2. Disentangledspectraofprimary(leftpanel)andsecondary(rightpanel)componentsobtainedwithKOREL.
{6342−6350;6368−6374}Å.Thisregioncontainsapairofsil- Table4.PropertiesofthebinarycomponentsofBD+36◦3317estimated
icon lines Siii6347Å and Siii6371Å, which should be unaf- fromthecomparisonofthedisentangled(Column2)andobserved(Col-
umn3)spectrawithsyntheticones(seethetextfordetails).
fected by the re-normalization uncertainty. The optimal rota-
tionalvelocitiesarev sini=32.55±0.59kms−1,andv sini=
1 2
22.1±1.2km s−1. This shows that the true uncertainty of the Elements Disentangled Observed
rotationalvelocityofsecondaryis∼10kms−1.
T (K) 10500±340 10400±420
eff,1
Asanindependentapproachtodeterminetheeffectivetem- T (K) 7180±850 7600±880
eff,2
peraturesofthecomponentsweusedtheprogramCOMPO2writ- logg [cgs] 4.291 4.31±0.07
1
tenbyFrascaetal.(2006),whichcombinestworeferencespec- logg [cgs] 4.291 4.29±0.04
2
tra for both components for given effective temperatures, ra- L /L 0.74±0.012 0.80±0.022
1 tot
dial velocities (or systematic velocity), projected rotationalve- L /L 0.26±0.012 0.20±0.022
2 tot
locities, and gravitational accelerations and compare the com-
v sini(kms−1) 29.1±1.1 –
bined spectrum to the observed spectrum of a binary sys- 1
v sini(kms−1) 30.7±4 –
tem. To achieve this, we used the reference spectra taken 2
γ (kms−1) −18.1±0.2 –
from Valdesetal. (2004) and tried to reproduce our observed 1
γ (kms−1) −17.5±0.6 –
spectrum taken at maximum orbital elongations (0.75 phase). 2
COMPO2 tries to minimize the residuals between observed and
compositespectratofindoptimalparametervaluesforeffective Notes.1Thegravitationalaccelerationwasfixedavalueobtainedfrom
temperatureandfractionalfluxcontributions.Theresultsofthis thelightcurvesolution.2Thesevaluesrepresenttheluminosityratiofor
procedureare listed in Column3 of Table 4. As seen fromthe thestudiedspectralregion.
table,bothmethodsestimatealmostthesamevaluesforthepri-
mary’seffectivetemperature.Howevertherelativecontributions
ofthecomponentstothetotalluminosityinthespectralregions
effective temperature of the secondary component T , mass
underconsiderationdodiffersomewhatfromeachother. eff,2
ratioq,andrelativemonochromaticluminositiesoftheprimary
componentL inindividualphotometricpass-bands.
1
3.6.Simultaneoussolutionoflightandradialvelocitycurves
Torefinethetemperaturesoftheprimarycomponent,which
withPHOEBE
weobtainedinprevioussections,weappliedanT searchpro-
eff,1
cedure. WesubsequentlysolvedtheRVandLCcurvessimulta-
The final solution to obtain the binarymasses, radii, and lumi-
neouslyforanumberoffixedvaluesofT between10000K-
nosities was carried out with the program PHOEBE. The RVs eff,1
11250K.Therunoftheweightedsumofthesquareofresiduals
presented in Table 1 and all four LCs obtained from the litera-
(χ2=[ΣW(O−C)2])thusobtainedasafunctionoftheeffective
ture(JohnsonV observationsweretakenfromViolat-Bordonau
temperatureof the primaryis shown in Fig 3. As can be seen
(2008), and the Johnson U, B, and V observations from
from the figure, χ2 has its lowest value around T =10450 K
Özdarcanetal. (2012, and priv.com.)) are solved simultane- eff,1
whichagreeswithT =10750±450KgivenbyÖzdarcanetal.
ously. For the temperaturesof the components, the bolometric eff,1
(2012) withinthe uncertaintybars, andso forthefinalsolution
albedos A and gravitational darkening coefficients g were
1,2 1,2 weadoptedT =10450K.
taken from Claret (2001) and Claret (1998), respectively. The eff,1
limb-darkening coefficients x were computed automatically The final results are shown in Table 5. The values of the
1,2
by PHOEBE from internaltables of the programmewhich were parameters P, i, a, and q given in Table 5 correspond to K =
1
generated according to the models given by Castelli&Kurucz 82.23±0.82kms−1andK =121.29±0.85kms−1,whichmatch
2
(2004).Convergencewasallowedfortheepochofprimarymin- the results of SPEL and KOREL in previous subsections. The
imumT ,theorbitalperiodP,thesemi-majoraxisoftherel- modellightandRV curvesare comparedwith the observations
min.I
ative orbita, systemic velocityV , orbitalinclinationi, dimen- inFig.4.TheyshowasmallRossiter(rotational)effect(Rossiter
γ
sionless surface potentials of the components Ω and Ω , the 1924)intheRVcurvesnearthephasesofbinaryeclipses.
1 2
Articlenumber,page4of10
Kıranetal.:BasicphysicalelementsofBD+36◦3317
Table5.FinalsolutionforthephysicalpropertiesofBD+36◦3317.TheuncertaintiesarederivedlocallybyPHOEBE fromthecovariancematrix.
Element Primary System Secondary
T (HJD) 2456803.4598±0.0001
min.I
P(d) 4.302152±0.000001
e 0.0(fixed)
a(R ) 17.3±0.1
⊙
V (kms−1) −17.8±0.5
γ
x -0.02 0.14
bol
A 1.00 0.92
g 1.00 0.90
i(◦) 89.27±0.02
T (K) 10450(fixed) 7623±8.1
eff
Ω 10.49±0.02 9.19±0.02
q 0.678±0.002
logg[cgs] 4.29 4.29
(l/l )1U band 0.84±0.01 0.16
tot
(l/l )1 Bband 0.83±0.01 0.17
tot
(l/l )1V band 0.79±0.01 0.21
tot
(l/l )2V band 0.79±0.01 0.21
tot
r 0.1019±0.0002 0.0844±0.0002
pole
r 0.1021±0.0002 0.0846±0.0002
point
r 0.1020±0.0002 0.0845±0.0002
side
r 0.1021±0.0002 0.0846±0.0002
back
(N)3 6847
χ2 11987
Notes.1Özdarcanetal.(2012),2Violat-Bordonau(2008),3thetotalnumberoftheobserved(LCandRV)points.
(2005),wecalculatedthede-reddenedmagnitudes,colours,dis-
12400
tance moduli and the distances of the components. These are
also given in Table 6. Considering that the primary is much
12300 brighter than the secondary, we weighted the individually de-
rived distances to the components with their luminosities and
estimatedthemeandistancetothesystemasd =330±29pc.
12200 In Fig. 5 we show the positions of the components in the
2 Hertzsprung-Russell(HR) diagram, with the ZAMS line taken
c fromClaret&Giménez(1989)forthesolarcomposition. Both
12100
componentsareclearlylocatedveryclosetoZAMS.Inthesame
figure, the evolutionary tracks by Bertellietal. (2009) for the
compositionofz=0.017,y=0.3arealsoshown.Theseagreewell
12000
withthemassesofthecomponentsthatwederived.
11900 9800 10000 10200 10400 10600 10800 11000 11200 11400 4. IsBD+36◦3317amemberoftheδLyrcluster?
T
eff,1 Although there were some doubts about the very exis-
tence of the δ Lyr (Stephenson 1) cluster, Kharchenkoetal.
Fig.3. Searchforthebestvalueoftheeffectivetemperature(T )
eff,1 (2005),Kharchenkoetal.(2013)andDiasetal.(2014)havein-
forprimarycomponentwithPHOEBE solutions.
cluded δ Lyr cluster in their open clusters (OCs) catalogues.
Kharchenkoetal.(2004)andKharchenkoetal.(2013)usethree
differentcriteria forthe membershipof individualstarsin each
3.7.Physicalpropertiesofthesystem
consideredcluster: propermotionsP ,photometricproperties
kin
Using the results of the final solution from Table 5, we calcu- P , and spatial properties P of the stars, respectively. For
ph sp
lated the basic physical properties of the components. These δ Lyr cluster, Kharchenkoetal. (2013) give E(B−V)= 0m.031,
aresummarisedinTable6. Themassesoftheprimaryandsec- RV=−27.5kms−1,anddistanced =373pc.
ondary components are consistent with the spectral types A3 Foranindependentdeterminationofthereddeninganddis-
V and F2 V, respectively. Using the observed V-band magni- tancemodulusoftheopenclusterδLyr,wedecidedtouseonly
tude outside the eclipses and (U−B) and (B−V) colours given thestars thathavemembershipprobabilitiesover50 %in each
by Özdarcanetal. (2012), the relative luminosities from the of the three criteria used by Kharchenkoetal. (2004). They
PHOEBE solution, and the bolometric corrections from Gray are listed in Table 7. To fit the theoretical main sequence of
Articlenumber,page5of10
2.2
8.0
2.0
U Ozdarcan et al. (2012)
1.8
9.0
2.5 M
sun
1.6
B Ozdarcan et al. (2012) + 1m.0
)un 1.4 2.2 Msun
10.0 Ls
L/
mag V Ozdarcan et al. (2012) + 2m.0 log ( 1.2
1.0
11.0
1.6 M
sun
0.8
V Violat-Bordonau (2008) + 3m.0 1.5 Msun
0.6
12.0
0.4
4.3 4.2 4.1 4.0 3.9 3.8 3.7 3.6
log T
eff
13.0
0.4 0.6 0.8 1.0 1.2
Fig. 5. Positions of the primary (black filled dot) and secondary
phase
(bluefilledtriangle)componentsintheHRdiagram. Theredsolidline
200 representstheZAMSfromtheClaret&Giménez(1989)models. The
evolutionarytrackslabelledwiththecorresponding model massesare
150 takenfromBertellietal.(2009).
100 Table6.BasicpropertiesofBD+36◦3317.
50
s) Element Primary Secondary
m/
k 0
V ( M (M⊙) 2.24±0.07 1.52±0.03
R R (R ) 1.76±0.01 1.46±0.01
-50 ⊙
T (K) 10450±420 7623±328
eff
-100 logL (L⊙) 1.52±0.08 0.81±0.07
M (mag) 0.9±0.2 2.7±0.2
bol
-150 logg [cgs] 4.29±0.01 4.29±0.01
(b) V0 (mag) 9.02±0.01 10.44±0.01
-200 (B−V) (mag) 0.017±0.014 0.316±0.014
0.4 0.6 0.8 1 1.2
BC (mag) -0.310 0.028
phase
(B−V) (mag) −0.037±0.014 0.243±0.014
0
Fig.4. (a)Observed(dots)andtheoretical(solidlines)lightcurvesof E(B−V) (mag) 0.054 0.073
BD+36◦3317. Thetheoreticalcurvesarecalculatedusingtheparame- M (mag) 1.25±0.17 2.69±0.19
tersgiveninTable5. (b)AphaseplotofRVsofBD+36◦3317. Black v
(m−M) (mag) 7.77±0.18 7.75±0.19
dotsandopencirclesdenotetheRVsoftheprimaryandsecondary,re- v
A (mag) 0.17±0.04 0.23±0.04
spectively. SolidlinesshowthetheoreticalRVcurvesderivedwiththe v
PHOEBE program (see Section 3.6). We note the presence of a small d (pc) 332 320
Rossiter(rotational)effect.
of the distance modulus by hand, to find the smallest standard
the cluster in both colour-colour diagram (hereafter CCD) and deviationσ(m− M) for the differencesbetween the theoretical
colour-magnitude diagram (hereafter CMD), we consider only andobservedmainsequences.Consequently,theresultingvalue
thesehighlyprobableclustermembers.Thetheoreticalmainse- ofthedistancemoduluscorrespondstothesmallesterrorofdis-
quencesin CCD and CMD are shifted along the axes to fit the tance d for the value of the corresponding E(B−V), too. The
observedmainsequences. procedure was then repeated with a new value for the redden-
We used the theoretical main sequence given by Johnson ing. We show the variation of the smallest standard deviation
(1966) and Schmidt-Kaler (1982) and represented it by a sixth σ(m− M), which was obtained for the cluster’s distance mod-
order polynomial. Then we fitted this polynomial to the most ulus as a function of the reddening in Fig. 6. This shows that
probable members of δ Lyr cluster. After this, we carried out anerrorof0.01magfor E(B−V)isacceptableandweadopted
asearchingprocedureforthecolourexcessE(B−V). Todoso, E(B−V)=0m.06±0.01forthecluster. Thisvalueoftheredden-
we first shifted the theoreticalmain sequence along the (B−V) ing corresponds to an apparent distance modulus (m − M) =
v
axisforagivenvalueofE(B−V),andthendeterminedthevalue 7m.98±0.13. Adoptingthe visualextinction A = 3.1E(B−V),
v
Articlenumber,page6of10
Kıranetal.:BasicphysicalelementsofBD+36◦3317
Table7. MostprobablemembersoftheδLyrcluster.
0.1320
WEBDANo TYCNo Pkin Pph Psp 0.1315
11 26501250 0.82 0.56 1.00
0.1310
528 26501237 0.69 1.00 1.00
529 26502146 0.93 1.00 1.00
533 26511056 0.98 0.81 1.00 M) 0.1305
−
m
542* 2651802 0.67 0.91 1.00 ( 0.1300
s
545 2651882 0.94 0.73 1.00
96 2651772 0.76 1.00 1.00 0.1295
552 2651189 0.99 1.00 1.00
(*)BD+36◦3317. 0.1290
0.1285
Table8. RVmeasurementsofstarsinδLyrcluster. 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
E(B−V)
Name RV References Notes Fig.6. IterativedeterminationoftheoptimalE(B−V)–seetextfor
details.
HD174959 −12.4±2.4 1 –
HD175081 −26.0±7.4 2 –
δ Lyr −17.2±4.3 1 spectroscopicbinary 0
1
δ Lyr −25.5±0.5 1 pulsatingstar
2
BD+36◦3317 −17.8±0.5 thisstudy EB
References.(1)Gontcharov(2006);(2)Kharchenkoetal.(2007). 5
we obtain A = 0.19 mag and the distance of δ Lyr cluster of
v
362±22pc,lowerthanthatfoundbyKharchenkoetal.(2013).
10
In addition, we estimate a reddening of about 0m.04 in (U−B)
V
from the CCD, as shown in Fig. 7. In Fig. 7 the photometric
UBVdata were taken from Eggen (1968) and Bronkalla (1963)
and the stars in the vicinity of the δ Lyr cluster are shown, as
15
wellasthemostprobableclustermembersandtheprimaryand
secondarycomponentsofBD+36◦3317.
Kharchenkoetal. (2005) givethe cluster radiusas 0.87de-
grees and RV= −21.6 km s−1 (compared with -27.5 km s−1 in
Kharchenkoetal.2013). OnlyfourstarshavetheRV measure- 20
mentsintheδLyrclusterfield. ThesestarsandtheRVmeasure-
ments are given in Table 8. Low membership probabilitiesare
-0.5 0.0 0.5 1.0 1.5 2.0
given for δ Lyr and HD 174959 in (Kharchenkoetal. 2013).
2
B-V
However the probabilities of the membership for δ Lyr and
1
HD175081arehigher. ThesystemicRVofBD+36◦3317from Fig.8. HRdiagramofδLyrcluster.Thetrianglesandsquaresdenote
oursolutionagreeswithδ1Lyr,butnotwithHD175081.Never- theprimaryandsecondarycomponents,respectively. Blackdotsrepre-
theless,thelocationsofthecomponentsofBD+36◦3317inboth sentthestarsinthefieldoftheclusterandthebigbluedots,thestars
CCDandCMD(seeFig.7),areingoodagreementwiththeother having high membership probability. Padova isochrones taken from
highlyprobablemembersofthecluster. Also,Kharchenkoetal. Bertellietal.(2009)areshown for thereddening of 0m.06andtheap-
(2004, 2013) classify the system as a highlyprobablemember. parent distance modulus of 7m.98. The isochrones shown are for 25
(red line) and 32 (blue line) Myrs and for the chemical composition
Theadopteddistance,whichistheluminosity-weightedaverage
(y,z)=(0.3,0.017).
of the distances obtained for the components from Table 6, is
330±29pc,consistentwiththecluster’sdistance(362±22pc)
withinthequotederrors. So, we concludethatBD+36◦3317is 3×107yrsforthecluster. Thisvalueisalsoingoodaccordance
oneofthemostprobablemembersoftheδLyrcluster,although with the evolutionarystatus of BD+36◦3317, as pointed out in
obtainingmoreobservations,inparticularRVs,formorecluster
Sec. 3.7.
membercandidatesisstillverydesirable.
At this point we decided to estimate the age of the cluster.
Sowetriedtoobtainbestisochronefittingfortheclusterbyus-
5. Conclusion
ing only the most probable members given in Table 7. To do
so, we considered both the turn-off point and the slope of the Obtaining and studying the first series of electronic spectra of
main sequencetogether. We comparedourCMD with the YZ- BD+36◦3317andsolvingtheRVcurvesofbothbinarycompo-
VARPadovaIsochronesproducedbyBertellietal. (2009). We nentstogetherwithalreadypublishedlightcurves,weobtained
obtainedthebestfitfortheisochroneof(y,z) = (0.3,0.017)for thefirstcompletesetofbasicphysicalpropertiesforthiseclips-
the cluster. Finally, as seen in Fig. 8, the age of the cluster is ing binary, which is a probable member of δ Lyr cluster. The
between logt = 7.4 and 7.5. So we accepted an age of about resultscanbesummarisedasfollows.
Articlenumber,page7of10
-1.5 0
-1.0
5
-0.5
0.0
10
B
U- V
0.5
15
1.0
1.5
20
2.0
-0.5 0.0 0.5 1.0 1.5 2.0 -0.5 0.0 0.5 1.0 1.5 2.0
B-V B-V
Fig.7. CCD(leftpanel)andCMD(rightpanel)diagramsforδLyrcluster. ThesolidlinesrepresentthetheoreticalZAMSshiftedinbothaxes
byappropriate amounts(seethetext).Thetriangleandsquaresymbols denotetheprimaryandsecondary component, respectively. Blackdots
representthestarsinthefieldoftheclusterwhilethebigbluedotsrepresentthestarshavinghighmembershipprobability.
1. Themasses,radii,effectivetemperatures,andabsolutelumi- References
nositiessummarisedinTable6showthatbothcomponentsof
Anthony-Twarog,B.J.1984,AJ,89,655
BD+36◦3317arelittleevolvedfromtheZAMSandcompat-
Bertelli,G.,Nasi,E.,Girardi,L.,&Marigo,P.2009,A&A,508,355
iblewiththepublishedevolutionarymodelsofBertellietal. Bronkalla,W.1963,AstronomischeNachrichten,287,249
(2009). Castelli,F.&Kurucz,R.L.2004,ArXivAstrophysicse-prints,0405087
Claret,A.1998,A&AS,131,395
2. Thespin-orbitsynchronisationforoursolutionwouldpredict
Claret,A.2001,MNRAS,327,989
theprojectedrotationalvelocitiesof20.7and17.2kms−1for Claret,A.&Giménez,A.1989,A&AS,81,1
theprimaryandsecondary,respectively. Thisdoesnotcon- deLaverny,P.,Recio-Blanco, A.,Worley,C.C.,&Plez,B.2012,A&A,544,
tradictthevaluesweestimatedfromthelineprofiles,taking A126
Dias,W.S.,Monteiro,H.,Caetano,T.C.,etal.2014,A&A,564,A79
theirassociatederrorsintoconsideration.
Eggen,O.J.1968,ApJ,152,77
3. WereinforcetheconclusionthatBD+36◦3317isaprobable Eggen,O.J.1972,ApJ,173,63
memberoftheδLyrcluster. Bothbinarycomponentsseem Eggen,O.J.1983,MNRAS,204,391
Frasca,A.,Guillout,P.,Marilli,E.,etal.2006,A&A,454,301
toagreewiththeothermembersofδLyrclusteronthemain
Gontcharov,G.A.2006,AstronomyLetters,32,759
sequenceinCMD. Gray, D.F.2005, TheObservation andAnalysis ofStellar Photospheres, 3rd
4. Using the de-reddened magnitudes from our solution in- Edition,UK:CambridgeUniversityPress,533pp
dividually for both components, we derived the weighted Hadrava,P.1995,A&AS,114,393
Hadrava,P.1997,A&AS,122,581
mean distance of BD+36◦3317 of 330 ± 29 pc. This dis- Hadrava,P.2004,PublicationsoftheAstronomicalInstituteoftheCzechoslovak
tance is within the boundaries of the cluster distance esti- AcademyofSciences,92,15
matedfromCMDofδLyrclusterand,ifthemembershipof Hadrava,P.2009,ArXive-prints,#0909.0172
BD+36◦3317intheclustercanbeconfirmeddefinitively,it Harmanec,P.,Koubský,P.,Nemravová,J.A.,etal.2015,A&A,573,A107
Horn,J.,Kubát,J.,Harmanec,P.,etal.1996,A&A,309,521
wouldrepresentthe mostaccurateestimate forthe distance Johnson,H.L.1966,ARA&A,4,193
oftheδLyrcluster. Kharchenko,N.V.,Piskunov,A.E.,Röser,S.,Schilbach,E.,&Scholz,R.-D.
2004,AstronomischeNachrichten,325,740
Kharchenko,N.V.,Piskunov,A.E.,Röser,S.,Schilbach,E.,&Scholz,R.-D.
Acknowledgements. WethanktoDr. O.Özdarcanforsharinghisphotometric
dataofBD+36◦3317withus,andtoDr.Ö.Çakırlıforhissupportconcerningthe 2005,A&A,438,1163
programCOMPO2fortemperaturesearchingprocesswiththecompositespectra Kharchenko,N.V.,Piskunov,A.E.,Schilbach,E.,Röser,S.,&Scholz,R.-D.
2013,A&A,558,A53
method.ThevisitofEKinPrahaandOndˇrejovwassupportedbyTheScientific
andTechnological ResearchCouncilofTurkey(TÜB˙ITAK)bythefellowship Kharchenko,N.V.,Scholz,R.-D.,Piskunov,A.E.,Röser,S.,&Schilbach,E.
ofB˙IDEP-2214International Doctoral Research Fellowship Programme. She 2007,AstronomischeNachrichten,328,889
Nasseri,A.,Chini,R.,Harmanec,P.,etal.2014,A&A,568,A94
thanks colleagues in theAstronomical Institute ofthe Charles University and
Özdarcan,O.,Sipahi,E.,&Dal,H.A.2012,NewA,17,483
AstronomicalInstitute oftheAcademyofSciences oftheCzechRepublic for
Palacios,A.,Gebran,M.,Josselin,E.,etal.2010,A&A,516,A13
theirhospitalityandhelpduringherstay.ResearchofPH,MW,andJNwassup- Prša,A.&Zwitter,T.2005,ApJ,628,426
portedbygrantsP209/10/0715andGA15-02112SoftheCzechScienceFoun- Prša,A.&Zwitter,T.2006,Ap&SS,36
dationandtheresearchofJNwasadditionallysupportedwithgrantno.250015 Rossiter,R.A.1924,ApJ,60,15
ofGrantAgencyoftheCharlesUniversityinPrague.Webenefitedfromtheuse Schmidt-Kaler,T.,ed.1982,Landolt-Börnstein:NumericalDataandFunctional
oftheSIMBADdatabaseandtheVizieRserviceoperatedatCDS,Strasbourg, Relationships in Science and Technology - New Series ” Gruppe/Group 6
FranceandtheNASA’sAstrophysicsDataSystemBibliographic Servicesand Astronomyand Astrophysics ”Volume 2Schaifers/Voigt: Astronomy and
theWEBDAopenclusterdatabase. Astrophysics/AstronomieundAstrophysik”StarsandStarClusters/Sterne
undSternhaufen
Articlenumber,page8of10
Kıranetal.:BasicphysicalelementsofBD+36◦3317
Škoda,P.1996,inAstronomicalSocietyofthePacificConferenceSeries,Vol.
101,AstronomicalDataAnalysisSoftwareandSystemsV,ed.G.H.Jacoby
&J.Barnes,187
Stephenson,C.B.1959,PASP,71,145
Škoda,P.&Hadrava,P.2010,inAstronomicalSocietyofthePacificConference
Series,Vol.435,Binaries-KeytoComprehensionoftheUniverse,ed.A.Prša
&M.Zejda,71
Valdes,F.,Gupta,R.,Rose,J.A.,Singh,H.P.,&Bell,D.J.2004,ApJS,152,
251
Violat-Bordonau,T.,F..-H.2008,InformationBulletinonVariableStars,5900,
7
Wilson,R.E.&Devinney,E.J.1971,ApJ,166,605
Articlenumber,page9of10
A&A–evrim,OnlineMaterialp10
Table1.HeliocentricRVsofBD+36◦3317measuredinSPEFO (mean
ofthreespectrallines).
HJD−2400000 RV RV
1 2
(kms−1) (kms−1)
56744.5862 -91.3±1.2 91.7±1.2
56746.4816 63.5±0.7 -143.6±0.2
56764.4510 11.3±0.2 -63.8±2.0
56765.4209 -89.4±0.3 90.5±1.3
56778.4182 -93.4±0.3 94.3±0.4
56782.5511 -86.4±1.3 76.4±3.3
56799.5499 -67.4±0.2 56.9±1.5
56815.5215 59.5±0.6 -135.4±0.0
56816.3854 -24.5±1.3 –
56817.4476 -100.2±0.3 100.7±0.6
56819.3930 61.3±0.8 -138.0±0.2
56822.4202 -61.3±0.3 44.0±0.2
56826.4377 -88.0±0.1 78.7±1.4
56827.5433 31.1±0.6 –
56852.4845 -63.2±1.5 51.9±1.0
56852.5226 -61.6±0.2 47.9±4.6
56861.5258 -14.6±0.5 –
56862.4931 62.4±0.9 -139.8±0.0
56865.4533 58.2±0.3 41.0±0.6
56866.5585 52.1±0.9 -115.5±0.9