Accurate fundamental parameters and distance to a massive early-type eclipsing binary in the Danks 2 cluster
M. Kourniotis, A.Z. Bonanos, S.J. Williams, N. Castro, E. Koumpia, J.L. Prieto
aa r X i v : . [ a s t r o - ph . S R ] A ug Astronomy & Astrophysicsmanuscript no. Kourniotis2015 c (cid:13)
ESO 2018February 8, 2018
Accurate fundamental parameters and distance toa massive early-type eclipsing binaryin the Danks 2 cluster ⋆ M. Kourniotis , ,⋆⋆ , A.Z. Bonanos , S.J. Williams , N. Castro , E. Koumpia , and J.L. Prieto , IAASARS, National Observatory of Athens, GR-15236 Penteli, Greece Section of Astrophysics, Astronomy and Mechanics, Faculty of Physics, University of Athens, Panepistimiopolis, GR15784 Zo-grafos, Athens, Greece Argelander-Institut für Astronomie der Universität Bonn, Auf dem Hügel 71, 53121, Bonn, Germany SRON Netherlands Institute for Space Research, Landleven 12, 9747 AD Groningen, The Netherlands; Kapteyn Institute, Univer-sity of Groningen, The Netherlands Núcleo de Astronomía de la Facultad de Ingeniería, Universidad Diego Portales, Av. Ejército 441, Santiago, Chile Millennium Institute of Astrophysics, Santiago, Chile
ABSTRACT
We present a study of the properties of the O-type, massive eclipsing binary 2MASS J13130841-6239275 located in the outskirts ofthe Danks 2 cluster in the G305 star-forming complex, using near-infrared spectroscopy from VLT / ISAAC. We derive the massesand radii to be 24 . ± . ⊙ and 9 . ± . ⊙ for the primary and 21 . ± . ⊙ and 8 . ± . ⊙ for the secondary component. Inaddition, we evaluate the sensitivity of our parameters to the choice of the spectral features used to determine the radial velocities. Bothcomponents appear to be main-sequence O6.5 − O7 type stars at an age of ∼ A = . ± . BV I c JHK s photometry, wedetermine a distance to the system of 3 . ± .
08 kpc with a precision of 2%, which is the most well-determined distance to the Danks2 cluster and the host complex reported in the literature.
Key words. binaries: eclipsing – open clusters and associations: individual: Danks – stars: distances – stars: early-type – stars:massive
1. Introduction
The G305.4 + ii regions(Caswell & Haynes 1987), which are powered by the ionizingflux of hot stars and are spatially associated with maser emis-sion and at least five star clusters (Dutra et al. 2003) embeddedin the complex. Whereas the majority of these clusters are com-pact and thus unresolved, the Danks 1 & 2 clusters (Danks et al.1983, 1984), which reside in the center of the complex, are re-solved and thus allow for studies of their physical properties.Both clusters have been shown to be ≤ ⊙ were derived forDanks 1 and 2 respectively, with an uncertainty that reaches ∼
30% (Davies et al. 2012). Constraining the properties of theclusters relies on an accurate determination of the distance, ex-tinction and their associated uncertainties. To date, the most ro-bust method to provide accurate distance measurements to younggalactic clusters and nearby galaxies is with the use of eclipsingbinaries (EBs) (e.g. Pietrzy´nski et al. 2013). ⋆ Based on observations made with ESO Telescopes at the La SillaParanal Observatory under program ID 090.D-0065(A). ⋆⋆ [email protected] EBs exhibiting double-lined spectra provide a geometricalmethod to precisely measure the fundamental parameters of theircomponents (Andersen 1991; Torres et al. 2010). In particular,the light curve provides the orbital period, eccentricity, the fluxratio of the two stars, fractional radii and the inclination of thesystem with respect to the observer. From the double-lined spec-tra, we measure the velocities of the individual components. Thefit to these velocities yields the velocity semi-amplitudes, andtherefore, the ratio of the masses. E ff ective temperatures and thusluminosities can be estimated by fitting synthetic spectra to theobserved ones. Therefore, an accurate determination of the red-dening law and thereby distance, is feasible (e.g. Bonanos et al.2006, 2011). Selecting systems that host well-separated com-ponents (i.e. detached systems), avoids complexities that orig-inate from a common-envelope state. Such systems are of ma-jor importance for testing theoretical stellar evolutionary modelsof single stars. Light curves of detached systems that displayeclipses of similar depth ensure roughly equal contribution ofboth components to the total flux and such systems with orbitalperiods ≤
10 days are likely to provide double-lined and well-separated spectra.The majority of hot, massive stars are claimed to be in closebinary systems (Chini et al. 2012; Sana et al. 2012; Sota et al.2014), thus increasing the possibility of observing short-period,eclipsing configurations (e.g. Kourniotis et al. 2014). Such sys-tems not only constitute extragalactic anchors, ideal for the cal-
Article number, page 1 of 13 & Aproofs: manuscript no. Kourniotis2015 ibration of the cosmic distance scale (e.g. Guinan et al. 1998;Hilditch et al. 2005; Ribas et al. 2005; Bonanos et al. 2006,2011), but also, when found in young, Galactic clusters, canset tight constrains on the age, chemical composition and dis-tance (e.g. Southworth & Clausen 2006; Koumpia & Bonanos2012). In this work, we investigate the properties of 2MASSJ13130841-6239275 (hereafter, D2-EB), a massive EB located ∼ ′ from the center of the Danks 2 cluster that constitutes a lu-minous, double-lined spectroscopic system. A summary of theparameters of D2-EB derived in the present work along with theparameters of the Danks 2 cluster, are listed in Table 1.D2-EB was discovered to be a well-detached eclipsing sys-tem during the optical variability survey by Bonanos et al. (inprep.). Due to the heavy foreground visual extinction in the di-rection of the clusters (A v = − K -band spectroscopy to resolve doublelines in the system. The paper is organized as follows: in Sect. 2we describe the follow-up spectroscopy and the data reduction,in Sect. 3 we present the radial velocity analysis, in Sect. 4 wemodel the binary, in Sect. 5 we derive the distance, in Sect. 6 wediscuss our results and in Sect. 7 we finish with some concludingremarks.
2. Observations and data reduction
Bonanos et al. (in prep.) undertook an optical variability surveyof the Danks clusters in search of massive EBs over 25 nights inMarch, April and May 2011 with the 1-m Swope telescope at LasCampanas Observatory in Chile. The telescope is equipped witha 2048 × . ′′ / pixel and afield of view of 14 . ′ × . ′ . Observations were taken betweenHJD 2 455 648.5 and 2 455 687.83, in the broadband B , V , R , I c filters over approximately 50, 500, 950 and 530 epochs, respec-tively. The data were reduced, calibrated to the standard systemand the image subtraction package ISIS (Alard & Lupton 1998;Alard 2000) was used to extract the I c -band light curves of allsources. The light curves were searched for periodicity with theAnalysis of Variance (AoV) algorithm (Schwarzenberg-Czerny1989) yielding 21 EBs. Of these, 13 were found to display redcolors of R − I c ≥
0, likely corresponding to members of thehighly extincted clusters. The I c -band light curve of D2-EB wasfound to display a strong periodic signal of ∼ .
37 days andappeared to be an ideal target for follow up spectroscopy: a lu-minous, well-detached and nearly equal-depth eclipsing system.
We obtained K -band spectroscopy of the D2-EB with the In-frared Spectrometer and Array Camera (ISAAC) mounted at theNasmyth A focus of the 8.2m UT3 (Melipal) at the VLT facil-ity in Chile. The observations were taken under ESO programID 090.D-0065(A). The spectrograph is equipped with a 1024 x1024 Hawaii Rockwell array with a pixel scale of 0 . ′′ / pixel(Moorwood et al. 1998). A slit width 0 . ′′ was used, resulting ina resolving power of R ∼ ∼ .
88 Å) of an unblended telluric OH emis-sion feature at ∼ . µ m. To derive a precise measurementof the velocity semi-amplitudes, we requested eight visits, fourper quadrature. In total, eight observing blocks were executed inservice mode, six of which correspond to the first and two to thesecond quadrature of the system. For each observing block, nod- RA = = − ding 60 ′′ along the slit was applied in an AB pattern, resulting intwo spectra of total integration time 100 sec each.The spectra were reduced using basic IRAF routines and wavelength calibrated using telluric OH sky lines(Rousselot et al. 2000) that span the K -band wavelength range.Subsequently, the extracted pair of spectra of each observingblock were normalized and averaged, yielding a signal-to-noiseratio (S / N) ∼
150 as measured in the middle of the wavelengthcoverage ( ∼ . µ m). Cosmic rays were rejected using theL.A.Cosmic script (van Dokkum 2001). We employed the newlyreleased molecfit tool (Smette et al. 2015), which generates asynthetic model of atmospheric transmission based on the infor-mation provided by the FITS header of the science object, to re-move telluric features. Heliocentric corrections were calculatedusing IRAF’s rvcorr task and applied. Table 2 lists the Helio-centric Julian Dates (HJD) of the observations, exposure timesand the values of airmass. Of the eight spectra, we discarded theone obtained on HJD 2 456 378.808 74 from further analysis, asit was taken near an eclipse, at phase ∼ .
47, and contained onlyone set of spectral features.
3. Radial velocity analysis
The spectrum of the D2-EB clearly displays He ii (2.189 µ m) inabsorption, which is prominent for both components in phasesoutside of eclipse. As in the optical, He ii lines appear only inhotter stars and are the main indicator for identifying O-typestars. The observed He i (2.112 µ m) in absorption implies thatboth stars must be later than O5 (Hanson et al. 1996). Both com-ponents of the D2-EB are hence classified as intermediate / lateO-type stars. In addition, our spectra show Br γ (2.166 µ m) inabsorption, which provides evidence against a supergiant clas-sification. However, a precise luminosity classification stronglydepends on the resolution and requires a S / N > iv (2 . µ m) is evident only for the redshifted componentas the blueshifted feature is not within the observed wavelengthrange. Further analysis of the observed features that are used tomeasure the radial velocities and to assign a spectral type is pre-sented in Sec. 3.2. We used the stellar atmosphere code FASTWIND(Santolaya-Rey et al. 1997; Puls et al. 2005) to synthesizethe lines of H and He and measure the radial velocities. Thecode enables non-LTE calculations and assumes a sphericalsymmetry geometry. The wind velocity structure is included inthe model through a β -like law. We generated a grid of FAST-WIND templates at the metallicity of the Galaxy, spanning thetemperature range 35–40 kK with a step of 1 kK and fixed thesurface gravity at log g = . R ∼ χ minimization setting six free parameters, three foreach component; temperature, radial and projected rotationalvelocity. We built synthetic spectra and fit the regions aroundthe Br γ (2.166 µ m) / He i (2.162 µ m) blend and He ii (2.189 µ m)feature of the ISAAC spectrum taken on HJD 2 456 345.856 71 IRAF is distributed by the National Optical Astronomy Observato-ries, which are operated by the Association of Universities for Researchin Astronomy, Inc., under cooperative agreement with the National Sci-ence Foundation.Article number, page 2 of 13ourniotis et al.: Precise distance to the Danks 2 cluster that exhibits well-separated spectral features. Each compositespectrum consists of two FASTWIND templates weightedaccording to the light ratio provided by the light curve analysisand broadened at the projected rotational velocity range 50 − − . For the fit, we adopted a σ value of 0.006 7, whichcorresponds to the standard deviation of the noise in units ofnormalized flux, based on the mean S / N ratio ∼ χ ofthe fit with respect to the temperatures and projected rotationalvelocities of the components. For each set of parameters, radialvelocities were measured to optimize the fit. We found that theprojected rotational velocities that correspond to the best fit are150 ±
20 km s − and 130 ±
20 km s − for the primary and theless luminous secondary component, respectively. These valuesare in good agreement with those of a tidally locked systemwhose orbital period is identical to the rotational period for bothcomponents (Sect. 4).To construct the radial velocity curve, we fixed the afore-mentioned projected rotational velocities and ran the fitting algo-rithm for the seven ISAAC spectra. Given that the best-fit tem-peratures are found to range from 36 kK to 38 kK with a 1 kKdi ff erence between the temperature of the components, we even-tually examined two cases: a set with 37 kK and 38 kK modelsand a set with 36 kK and 37 kK models. While the former re-sulted in a best fit for the He ii line, the latter appeared to opti-mally fit the Br γ / He i feature. We adopted the first case for pro-viding reliable velocity measurements as He ii is a more accuratetracer of the stellar photosphere for stars at these temperatures.Contours of χ values for the He ii fit were plotted in two di-mensional radial velocity diagrams and the center of the contourcorresponding to the lowest χ was adopted to generate the bestfit. Fig. 2 presents the best-fit composite spectra overplotted ontothe observed ones, which were smoothed for clarity. The inferredvelocities are listed in Table 3. The uncertainties correspond tothe standard deviation of the residuals of the observed velocitiescompared to the best-fit model described in Sect. 4. We also explored a di ff erent method of analysis by comparingour observations against near-IR spectra of early-type stars ofsimilar resolution and S / N. The work by Hanson et al. (2005)(hereafter, H05) provides a near-infrared atlas of Galactic hotstars that comprises of 37 well known, OB-type stars observedwith VLT / ISAAC and Subaru / IRCS with a resolution of R ∼ −
12 000 and a mean S / N ∼ − iv at 2 . µ m and the blend of the CNO complex at 2 . µ m with He i at 2 . µ m. As mentioned in H05, the atlas should not be usedfor an accurate spectral classification but rather, to obtain a firstestimate for the temperatures.Given that the H05 spectra are calibrated to air wavelengths(M. Hanson, private communication), we first applied an air-to-vacuum unit conversion. The resolution of the spectra was re-duced to match that of our data and the light ratio was fixed inaccordance with the light curve analysis. We found that a com-posite spectrum of two identical O6.5 III spectra yielded an opti-mal fit to our observed spectra. However, there is no O6.5 main-sequence counterpart in the atlas, hence luminosity class at thattemperature is not well-determined. The resulting spectral typeis in agreement with the e ff ective temperature of 38 kK adoptedusing FASTWIND models; the recent temperature-spectral type calibration for O-type stars by Simón-Díaz et al. (2014) assignsan e ff ective temperature of 38.7 kK to an O6.5 Milky Way dwarfof surface gravity 3.8 dex, with typical uncertainties of up to 1.5kK and 0.15 dex, respectively.The O6.5 III spectrum from H05 displays helium and hydro-gen features in both the H and K -band. While the centroid of theHe i lines appear within 0.5 Å from their theoretical wavelengths(in air, 1 .
700 25 µ m and 2 .
112 01 µ m), the He ii line (2 .
188 52 µ m) clearly displays a ∼ . ff set redward. Comparing to theadopted FASTWIND template, the blue wing of He ii appearsweaker with respect to the red wing. It is unlikely that this isdue to ine ffi cient telluric correction, as the H -band He ii feature(1 .
691 84 µ m) also su ff ers a similar, although smaller ( ∼ ff set. In addition, a phase-dependent velocity discrepancy be-tween the CNO / He i blend and the He ii line is prominent in theISAAC spectra, as can be seen in Fig. 3. The He ii line is mainlyformed in the transition region from the stellar photosphere tothe wind (Lenorzer et al. 2004), hence it is dominated by the un-certainty in the wind density structure. We therefore concludethat contamination by stellar winds is the most plausible expla-nation for this He ii o ff set (A. Herrero, private communication)as stellar winds are prominent in early-type stars. To avoid a def-inite bias of this e ff ect to our study, we proceeded to measurevelocities with the H05 spectra in two ways; first, fitting all fea-tures except for the Br γ / He i blend and second, fitting only the2 . µ m He i line along with the CNO complex. While the firstmethod relies on the contribution of four independent features,it is hindered by the uncertainty of the aforementioned He ii ef-fect and of a possible, ine ffi cient correction in our observationsfor the strong, telluric CO absorption band near 2 . µ m, inthe region of C iv . Furthermore, both C iv and He ii are found atthe edges of the observed regime where the S / N is expected tobe lower and in addition, the blueshifted component of C iv isat most phases beyond the edge of our observed spectrum. Oursecond method employs fewer features, which, however, have abetter S / N and do not su ff er from telluric contamination. The de-rived velocities following both methods are listed in Table 4 asin Table 3, whereas the best-fit composite spectra are shown inthe two panels of Fig. 3. For brevity, the method that excludesthe Br γ / He i feature is labeled in the figures and tables as "-Br γ / He i ", whereas the method that employs only the CNO / He i blend feature is labeled as "CNO / He i ".
4. Binary modeling
We proceeded to a simultaneous fit of both the I c -band lightcurve and radial velocity curves with a detached, binary model.We used PHOEBE Subversion (release date, 2012 − − ff erential Corrections (DC) poweredby a Levenberg-Marquardt fitting scheme. We employed radialvelocities measured using FASTWIND templates and the spectrafrom H05 following both methods discussed in Sec. 3.2.The primary component is defined to be the star eclipsed atphase zero. The period determined from the AoV analysis of thephotometric curve was assigned as an initial guess to the periodin PHOEBE. We then fit the light curve with the following freeparameters: time of primary eclipse HJD , period P (days), in-clination i (deg), e ff ective temperature of the secondary compo-nent T e f f (K) and surface potentials Ω , . We fixed the e ff ectivetemperature of the primary component at 38 kK. The light curvedoes not provide evidence for eccentricity, hence we fixed e = Article number, page 3 of 13 & Aproofs: manuscript no. Kourniotis2015
Both components were assumed to be tidally sychronized andsurface albedos and gravity brightening exponents were fixed tounity, as for stars with radiative envelopes. Limb darkening co-e ffi cients were taken from van Hamme (1993) using the square-root law. The well-determined period and HJD were fixed totheir converged values and we fit the radial velocity curve forthe semi-major axis α (R ⊙ ), systemic velocity γ (km s − ) and theratio q of the mass of the secondary component over that of theprimary component. In addition, the Rossiter–McLaughlin e ff ect(Rossiter 1924) was taken into account to correct for velocityshifts near the conjuction that occur when part of the approach-ing / receding surface of the occulted star is blocked. The root-mean-square (RMS) value of the fit of each velocity curve wasassigned to the "sigma" parameter in PHOEBE, to weight thedata in the overall cost function of the analysis. As a next step,both light and radial velocity curves were fit simultaneously, set-ting free all nine mentioned parameters.To prevent convergence to a local minimum of the solutionspace, we used the method of parameter-kicking. We first de-fined convergence as three consecutive iterations where adjustedparameters are less than or equal to their returned uncertainties.When the criterion is satisfied, all parameters are o ff set by arelative sigma ("kick"), defined as σ kick = . (cid:16) χ / N tot (cid:17) N tot is the total number of pointsfrom the fitted photometric and velocity data-sets. Of the 1 000sets of parameters, we chose the set that yields the lowest sumof χ values resulting from the fit of both the light and radial ve-locity curves. We then imported the particular set as input to anew run of 1 000 iterations, having the parameter-kicking optiondisabled. The mean and standard deviation of the values for eachparameter were derived to provide the solution and the 1- σ un-certainties, respectively. The above procedure was repeated threetimes, for each radial velocity set obtained with FASTWIND andthe two methods for the O6.5 III spectrum from H05. The finalvalues are presented in Table 5. It appears that the fit using He ii contributes to a separation of the components that is larger by 1R ⊙ , compared to the method fitting only on the CNO / He i fea-ture. In addition, complementing the He ii fit with that of C iv ,yields components of almost equal mass. The systemic velocitymodeled with the fit of the synthetic He ii from FASTWIND, islarger by ∼
20 km s − than that modeled with the H05 spectra.The residuals of the three di ff erent fits are shown in Tables 3 and4. We found that the velocity measurements based exclusivelyon the fit of the CNO / He i blend, yield the best-fit model as canbe seen from the resulting RMS values of 11 and 8 km s − forthe radial velocity curves of the primary and the secondary com-ponent, respectively. This best-fit model is displayed in Fig. 4.The physical parameters of D2-EB are presented in Table 6.All methods resulted in a surface gravity value for both com-ponents of log g ∼ .
9, which is typical for Galactic O-typedwarfs, whereas e ff ective temperatures of 38 kK and 37 kK in-dicate spectral types of O6.5 and O7 respectively, with a typi-cal uncertainty of half a spectral type (Martins et al. 2005). Weadopted a conservative uncertainty of 1kK for the temperatures,equal to the step of the FASTWIND templates used. The inferredlight ratio for each method was used to calculate the contribu-tion of the component spectra to the total composite spectrum,as mentioned in Section 3. In addition, we derived a negative fill-ing factor F ∼ − . ∼
140 and ∼
130 km s − , which are in good agreement with those inferredfrom the fitting process (Section 3.1).Both methods that employ velocities measured from the He ii line, yield a total mass which is ∼
10% greater than the methodwhich discards He ii , owing to the larger separation of the com-ponents in the observed spectra. The latter best-fit method pro-vides measurements of the mass and radius of 24 . ± .
15 M ⊙ and 9 . ± .
07 R ⊙ for the primary and 22 . ± .
68 M ⊙ and8 . ± .
10 R ⊙ for the secondary component. The radii measure-ments correspond to radii of spheres with equal volume to thosedefined by the WD surface potentials. Compared to the latestupdated catalogue of well-studied, detached EBs by Southworth(2014), the primary component of D2-EB is the third most mas-sive star to be studied with an precision better than ∼
2% and themost well-determined star with mass ≥ . ⊙ . Nevertheless,we caution that our 0.6% precision for the mass of the primary isderived as the uncertainty of the solution that optimizes the fit toour observations. Confirming this precision requires more veloc-ity diagnostics and a larger number of observations taken at bothquadratures. We hence conclude that the 0.6% precision shouldbe taken with caution. For this reason, a di ff erent code than WDwas also applied to evaluate the current solution and revise theuncertainties.We employed the genetic optimizer of ELC(Orosz & Hauschildt 2000) to fit the orbit based on eightinput parameters. Specifically, the fit parameters in ELC wereHJD , P , i , the Roche lobe filling factor for each star, f ,which is the ratio of the radius of the star toward the innerLagrangian point L to the distance to L from the centerof the star, f ≡ x point / x L , T e f f , the primary star’s velocitysemi-amplitude, K , and q . In fitting the orbit for D2-EB, ELCcomputed ∼ × orbits where the values of the eight inputparameters varied between fixed ranges judged to be applicablebased on the WD fit of the CNO / He i radial velocity set. Thesubsequent χ space was then projected as a function of eachorbital and astrophysical parameter of interest in the same wayas was done in Williams (2009). From the global χ min , weestimate 1- σ uncertainties for derived and fitted parametersfrom the region where χ ≤ χ min +
1. These values are listed inTable 6. The inferred masses and radii are 24 . ± . ⊙ and9 . ± . ⊙ for the primary and 21 . ± . ⊙ and 8 . ± . ⊙ for the secondary component. The best-fit model with ELC isdisplayed in Fig. 5.The masses derived from the best ELC fit are found to beconsistent within uncertainties with those derived by PHOEBEand the WD code. The revised uncertainties of the masses of theprimary (3 . . −
5% than those derived by the WD code and precise to 1%. Thisis not surprising, as the radii rely on the well-constrained lightcurve, while the masses rely more on the sparse radial velocitydata set. We adopt the values from the ELC analysis as theiruncertainties are more conservative.
5. Distance
A prerequisite to precisely determining independent distancesto a double-lined eclipsing system is to fit a spectral energydistribution (SED) to accurate, multi-band photometry takenat a known phase. Baume et al. (2009) conducted wide field
U BVI c observations of the complex that hosts the Danks clustersand their surrounding field and obtained point spread function Article number, page 4 of 13ourniotis et al.: Precise distance to the Danks 2 cluster (PSF) photometry of ∼
35 000 sources including our D2-EB .The U − band photometry was not available for D2-EB likely dueto the high extinction. Using the ephemerides derived by our fourmethods, we converted the Julian dates of the six per-filter expo-sures from the Baume et al. (2009) data (G. Carraro, priv. com-munication) to units of phase. We supplemented the optical pho-tometry with 2MASS measurements (Cutri et al. 2003) in the J,H, K s -band obtained on JD 2 451 594.871 3 . All observationsare consistent within their uncertainties, to out-of-eclipse phasesof equal brightness (Figs. 4, 5). To convert the magnitudes tofluxes, we used zeropoints from Bessell et al. (1998) for the op-tical photometry and from Cohen et al. (2003) for 2MASS.SEDs in accordance with the physical parameters of the best-fit spectra were generated with FASTWIND, to provide the fluxdensity per surface unit through our studied bands. The compos-ite flux measured at Earth from a binary at a distance d , at awavelength λ , reddened to extinction A ( λ ), is given by f λ = d ( R F ,λ + R F ,λ ) × − . A ( λ ) where R , and F , are the radii and the surface fluxes of thecomponents, respectively. The composite SED was reddened ac-cording to the new family of optical and near-infrared extinctionlaws for O-type stars provided by Maíz Apellániz et al. (2014),which constitute an improvement of the widely used extinctionlaws by Cardelli et al. (1989). We ran a fitting algorithm over awide range of distances with a step of 0.05 kpc, setting free themonochromatic parameters R and E (4405 − χ . Toestimate the uncertainty of our measurements, we used a MonteCarlo approach. In particular, we ran the fitting procedure 1 000times using sets of randomly selected parameters (photometryand radii) within their uncertainties assuming they are Gaussian-distributed. The corresponding values of distance are shown inTable 6 for every set of radii and temperatures determined fromthe four di ff erent fit models. Our adopted radii measured withELC yielded d = . ± .
08 kpc, E (4405 − = . ± . R = . ± .
04 and A = . ± . e f f ∼
36 kK. Assuming a spectroscopicT e f f =
37 kK, the distance changed slightly to d = . ± . χ of our re-sulting fits was measured to be χ ∼ E (4405 − E ( B − V ) (and so increasing the degrees of freedom byone). Specifically, we calculated ( B − V ) = − .
27 mag from thesynthetic unreddened model at the isophotal wavelengths, whichis in agreement with the intrinsic color of O6-9 giants / dwarfsprovided by Martins & Plez (2006), thus yielding E ( B − V ) = . ± .
16 mag. Our best-fit model then yielded d = . ± . χ ∼
23) than thatachieved when setting E (4405 − E (4405 − = .
66 mag,the residuals indicate a better fit to the
JHK s -band photome-try and a reasonable fit to the I c -band photometry. The B -bandphotometry clearly deviates from our adopted model causingthe discrepancy of ∼ . B -band photometric data ( >
22 mag).However, it may also leave room for a further improvement of B = . ± .
16 mag, V = . ± .
02 mag, I c = . ± .
03 mag J = . ± .
03 mag, H = . ± .
03 mag, K s = . ± .
03 mag the extinction laws. Indeed, having the B -band photometry ex-cluded from the fit, our procedure yielded d = . ± .
08 and χ ∼
14 (with two degrees of freedom), which still deviatesfrom χ =
1. We caution that in the optical, both families of ex-tinction laws by Maíz Apellániz et al. (2014) and Cardelli et al.(1989) have been tested on a sample of low / intermediate red-dened stars ( E (4405 − < . ff er-ent value of the power law exponent for the near-infrared range,could result in a better fit.The measured distance to the D2-EB is in good agree-ment with reported values of distance to the Danks 2 clusterin the literature: 3 . ± . . ± . . ± . ∼ ff ers from substantial reddening with E ( B − V ) = . A V = . ff erential across their studied region. D2-EB residesoutside their adopted boundary of Danks 2 and likely coincideswith molecular gas that contaminates the north-east of the clus-ter (Fig. 7), which appears to be the reason for our higher valueof A = . Spitzer / GLIMPSEmap at 5.8 µ m and found emission in the region of the gas.
6. Discussion
To measure the age of D2-EB and therefore the Danks 2 clus-ter, we used the evolutionary models of Ekström et al. (2012)for single stars, at Z = . −
220 km s − , which aresuitable for our case. All methods followed to derive massesagree with an age of ∼ . ii for measuring velocities, the obtainedmasses found are ∼
15% lower than those predicted, for bothcomponents. When excluding He ii from the velocity analysis,this mass discrepancy increases to ∼ ∼
11% massdiscrepancy observed in two detached systems in the Large Mag-ellanic Cloud. A recent study by Markova & Puls (2015) showedthat a mass discrepancy for Galactic O stars with initial mass <
35 M ⊙ is evident, with the spectroscopically derived masses be-ing systematically lower than the evolutionary masses inferredfrom the theoretical models. Stars with spectroscopically mea-sured masses of ∼
25 M ⊙ and ∼
22 M ⊙ , equal to our adoptedvalues for the components of D2-EB, were shown to display evo-lutionary masses of ∼
30 M ⊙ and ∼
27 M ⊙ respectively, which Article number, page 5 of 13 & Aproofs: manuscript no. Kourniotis2015 are in a good agreement with our predictions from the theoreticalmodels.Davies et al. (2012) suggested an age for the cluster of 2 − − ii are both con-sistent with an age of 4.5 Myr. Our adopted, best-fit model yieldsan age of ∼ ′ . ± ′ . − ± − ) is not in agreementwith the radial velocity of Danks 2 ( − ± − , Chené et al.2012) nor the host G305 complex ( − ± − , Davies et al.2012). This suggests that D2-EB may have been ejected from thecluster as a runaway binary. The radial velocity of D2-EB rela-tive to the cluster is 37 ± − . This can be taken as a lowerlimit for the space velocity at which the system is escaping fromthe cluster. The angular distance 2 ′ . . ± . ∼ − .Blaauw (1961) hypothesized that runaway stars are createdwhen a massive component within a binary system explodes asa Type II supernova. The secondary is then ejected with a ve-locity comparable to the orbital velocity at the time of the su-pernova event. The explosion may not disrupt the system (Hills1983), which will be observed as a OB-neutron star / black-holesystem and eventually become a high-mass X-ray binary. Giventhat D2-EB is a double-lined O-type binary, it is unlikely thatsuch a mechanism took place. Alternatively, D2-EB could havebeen part of a triple system including a very massive component( ≥
85 M ⊙ ) with a lifetime of less than 4 . / or longperiod. Observations of D2-EB over a longer time span than thedata presented here are required to investigate the possibility ofa third body in the system. Poveda et al. (1967) suggested thatrunaway stars are dynamically ejected due to encounters of col-lapsing protostars in / near the core of young clusters. Interactionsin clusters that contain initial "hard" binaries increase the num-ber of escapees via binary-binary interactions (Mikkola 1983).The less massive binary system reaches peculiar space velocitiesup to ∼
200 km s − , while the more massive system travels ata speed less than ∼
100 km s − (Leonard & Duncan 1988). Thebinary frequency for runaways with V ∞ >
30 km s − is predictedto be 10% and it is striking that systems hosting components of M ∼
20 M ⊙ as the most massive members are not predictedto escape with more than 50 km s − (Leonard & Duncan 1990).This does not conflict with the observed lower limit for the spacevelocity of D2-EB. A young, dense cluster core increases thepossibility of dynamical ejection, with the consequence that thekinematic age of the runaways is similar to the age of the clus-ter (Gualandris et al. 2004). In this case, the unreasonably lowestimated value for the tangential velocity of D2-EB renders thepossibility of the dynamical ejection through binary-binary in-teraction to be unlikely.
7. Conclusions
We present an analysis of new K -band spectra from VLT / ISAACwith which we determined accurate fundamental parameters ofD2-EB, a massive, early-type eclipsing binary in the young clus-ter Danks 2, which is embedded in the G305 Galactic, star-forming region. The best-fit model to the binary was obtained byusing the He i line (2 . µ m) and the CNO complex for mea-suring radial velocities. The system was found to contain twoco-evolutionary O6.5-7 main-sequence components with an ageof ∼ . ± . ⊙ and 9 . ± . ⊙ for the primary and 21 . ± . ⊙ and 8 . ± . ⊙ for the secondary component with a precision ∼ .
8% for themasses and ∼
1% for the radii. Models utilising a fit of He ii formeasuring velocities, were found to yield a ∼
10% higher totalmass and ∼ . d = . ± .
08 kpc froma fit to the SED of the system. Up to now, this is the most well-constrained distance measurement to the Danks clusters and thusto the host complex, with a precision of ∼ A = . ± . , whichwill be complete down to 20th mag in the visual, should con-strain the motion of both the cluster and the system, and providewell-determined values of the space velocity and the kinematicage of D2-EB. Acknowledgements.
MK and AZB acknowledge funding by the European Union(European Social Fund), National Resources under the "ARISTEIA" action ofthe Operational Programme "Education and Lifelong Learning" in Greece. MK,AZB and EK acknowledge research and travel support from the European Com-mission Framework Program Seven under the Marie Curie International Reinte-gration Grant PIRG04-GA-2008-239335. Support for JLP is in part by FONDE-CYT through the grant 1151445 and by the Ministry of Economy, Development,and Tourisms Millennium Science Initiative through grant IC120009, awardedto The Millennium Institute of Astrophysics, MAS. This publication makes useof data products from the Two Micron All Sky Survey, which is a joint project ofthe University of Massachusetts and the Infrared Processing and Analysis Cen-ter / California Institute of Technology, funded by the National Aeronautics andSpace Administration and the National Science Foundation. The Digitized SkySurveys were produced at the Space Telescope Science Institute under U.S. Gov-ernment grant NAG W-2166. The images of these surveys are based on photo-graphic data obtained using the Oschin Schmidt Telescope on Palomar Mountainand the UK Schmidt Telescope. The plates were processed into the present com-pressed digital form with the permission of these institutions. This research hasmade use of the VizieR catalogue access tool, CDS, Strasbourg, France.
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Teff (K) T e ff ( K ) Fig. 1.
Reduced- χ panel of the fit of composite FASTWIND spectra to the ISAAC spectrum of HJD 2 456 345.856 71. Axes denote the e ff ectivetemperature of the components and are split into six, equal intervals with 16 subdivisions of 10 km s − each, to represent the projected rotationalvelocity range 50 −
200 km s − . We find that the best fit corresponds to a pair of templates with T ef f =
38 kK, T ef f =
37 kK and v sin i values of150 ±
20 and 130 ±
20 km s − , respectively. Wavelength (µm) N o r m a li z e d F l u x + c o n s t . φ=0.13φ=0.14φ=0.14φ=0.19φ=0.43φ=0.69φ=0.92 Fig. 2.
Normalized ISAAC spectra (blue) sorted by the orbital phase ( φ ) of D2-EB, including the Br γ (2.166 µ m) / He i (2.162 µ m) blend and theHe ii (2.189 µ m) line. The composite spectra (red) of two FASTWIND templates of 38kK and 37kK, weighted, summed and shifted to our derivedvelocities, are overplotted. The best-fit velocites are obtained from the fit of He ii . For clarity, a smoothing window is applied to the observedspectra and a constant is added to the relative fluxes. Absorption features in the wavelength range 2 . − . µ m are due to poor telluriccorrection.Article number, page 8 of 13ourniotis et al.: Precise distance to the Danks 2 cluster Wavelength (µm) N o r m a li z e d F l u x + c o n s t . φ=0.14φ=0.15φ=0.15φ=0.2φ=0.44φ=0.71φ=0.93 φ=0.14φ=0.15φ=0.15φ=0.2φ=0.44φ=0.71φ=0.93 Fig. 3.
Same as in Fig. 2, but the composite spectrum is comprised of two O6.5 III spectra taken from Hanson et al. (2005). In the left panel , weshow the entire wavelength range of the ISAAC spectra, which includes lines of C iv (2.08 µ m), He i (2.113, 2.162 µ m), the CNO complex (2.115 µ m), Br γ (2.166 µ m) and He ii (2.189 µ m). The best-fit velocities are measured by fitting all features except for the Br γ / He i blend. In the rightpanel , we show the result of the separate fit to the CNO / He i blend, which was employed to derive velocities. I - b a n d ( m a g ) −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Phase −0.03−0.02−0.010.000.010.020.03 O - C −300−200−1000100200300 R a d i a l V e l o c i t y ( k m s − ) −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Phase −30−20−1001020 O - C Fig. 4.
The left panel shows the I c -band light curve of D2-EB, phased to the best-fit parameters derived with PHOEBE using spectra from the H05atlas. Radial velocities were inferred from the fit of the CNO / He i blend. The right panel shows the radial velocity measurements overplotted bythe modeled curve. The solid line denotes the primary and the dashed line the secondary component. Uncertainties correspond to the rms of thebest-fit, i.e. 11 km s − for the primary and 8 km s − for the secondary. Green, solid lines represent the two observation dates of the BV I c photometryby Baume et al. (2009) (six per filter), while the black dashed line indicates the date of the 2MASS measurements. Residuals of the fits are shownin the lower panels. Article number, page 9 of 13 & Aproofs: manuscript no. Kourniotis2015 I - b a n d ( m a g ) Phase −0.03−0.02−0.010.000.010.020.03 O - C −300−200−1000100200300 R a d i a l V e l o c i t y ( k m s − ) Phase −30−20−1001020 O - C Fig. 5.
Same as Fig. 4, but for the best-fit parameters inferred using ELC. Uncertainties for the radial velocity measurements correspond to 14km s − for the primary and 10 km s − for the secondary component. −18.0−17.5−17.0−16.5−16.0−15.5−15.0−14.5−14.0 l o g F λ ( e r g s c m − s − Å − ) SED a 3.52 kpc, R = 3.26, E(4405−5495) free = 3.66 mag, χ ∼11SED a 3.34 kpc, R = 3.67, E(4405−5495) fixed = 3.28 mag, χ ∼233.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 logλ (Å) −0.10−0.050.000.050.100.15 l o g ( F o b s / F c a l c ) Fig. 6.
Fit of the reddened, composite SEDs using FASTWIND models to the
BV I c JHK s photometry, setting the amount of extinction E (4405 − E ( B − V ) (blue). The former method providedthe best-fit model yielding d = . ± .
08 kpc, E (4405 − = . ± .
06 mag, R = . ± .
04 and A = . ± . Table 1.
Summary of the parameters of the Danks 2 cluster and D2-EB.
Parameter Danks 2 D2-EB (this work)Total Mass (M ⊙ ) 3 000 ± . ± . − ∼ . ± . . ± . References: Davies et al. (2012), Chené et al. (2012), Bica et al. (2004), Baume et al. (2009)
Article number, page 10 of 13ourniotis et al.: Precise distance to the Danks 2 cluster
1’ NE
Fig. 7.
Digitized Sky Survey (DSS-2) map of Danks 2 in the red filter. D2-EB (blue arrow) is located outside the 1 ′ . ± ′ . log (T eff / K) l o g ( L / L ⊙ )
20 M ⊙
20 M ⊙
25 M ⊙
25 M ⊙
32 M ⊙
32 M ⊙ FASTWINDH05 (-Brγ/HeI)H05 (CNO/HeI)H05 (CNO/HeI) / ELC
Fig. 8.
H-R diagram showing the comparison of the parameters of D2-EB modeled with the WD code and our three, di ff erent sets of radialvelocities obtained with: the fit of He ii of FASTWIND templates (red circles), the fit of all K − band features of H05 spectra except for the Br γ / He i blend (black triangles), the fit of the CNO / He i blend of the H05 spectra (green squares). The last set is also modeled with ELC and parametersare shown with blue asterisks. Evolutionary tracks and isochrones for single stars (Ekström et al. 2012) at Z = .
014 with rotation, are shown.Isochrones from left to right, correspond to 3.2, 4 and 5 Myr. All methods yield co-evolutionary components with an age of ∼ . & Aproofs: manuscript no. Kourniotis2015
20 22 24 26 28
M (M ⊙ ) R ( R ⊙ )
20 M ⊙
20 M ⊙
25 M ⊙
25 M ⊙
32 M ⊙
32 M ⊙ FASTWINDH05 (-Brγ/HeI)H05 (CNO/HeI)H05 (CNO/HeI) / ELC
Fig. 9.
Mass-Radius (M-R) diagram showing the comparison of the parameters of D2-EB with evolutionary tracks and isochrones for single stars(Ekström et al. 2012) at Z = .
014 with rotation. The symbols denoting each method are the same as in Fig. 8. Isochrones from the bottom up,correspond to 3.2, 4, 5 and 6.3 Myr. We find that both methods based on a He ii fit for measuring velocities yield co-evolutionary components ofage 4.5 Myr. The best-fit model based on the CNO / He i blend fit yields an age of ∼ Table 2.
Log of spectroscopic observations of D2-EB with VLT / ISAAC.
HJD Total integration time (s) Airmass2 456 340.782 01 2x100 1.312 456 345.856 71 2x100 1.282 456 360.828 68 2x100 1.302 456 360.840 70 2x100 1.312 456 360.859 82 2x100 1.352 456 378.695 33 2x100 1.292 456 378.808 74* 2x100 1.342 456 383.715 90 2x100 1.27(*) Discarded from our analysis.
Table 3.
Radial velocity measurements of D2-EB using FASTWIND models.
FASTWINDHJD Orbital RV (O − C) RV (O − C) phase (km s − ) (km s − ) (km s − ) (km s − )2 456 340.782 01 0.19 − ±
19 24 279 ±
30 322 456 345.856 71 0.69 229 ± − − ±
30 552 456 360.828 68 0.13 − ± −
12 207 ±
30 82 456 360.840 70 0.14 − ± −
19 182 ± −
212 456 360.859 82 0.14 − ± −
23 217 ±
30 82 456 378.695 33 0.43 − ± −
27 88 ± −
342 456 383.715 90 0.92 142 ±
19 13 − ±
30 18
Article number, page 12 of 13ourniotis et al.: Precise distance to the Danks 2 cluster
Table 4.
Radial velocity measurements of D2-EB using spectra from H05.
H05 (-Br γ / He i ) H05 (CNO / He i )HJD Orbital RV (O − C) RV (O − C) Orbital RV (O − C) RV (O − C) phase (km s − ) (km s − ) (km s − ) (km s − ) phase (km s − ) (km s − ) (km s − ) (km s − )2 456 340.782 01 0.20 − ±
14 1 209 ± −
12 0.21 − ± −
17 229 ± −
42 456 345.856 71 0.70 189 ± − − ±
11 8 0.71 194 ± − − ± − ± −
11 197 ±
11 17 0.15 − ± −
13 207 ± − ± −
18 197 ±
11 13 0.15 − ±
11 5 207 ± − ± − ± − − ± − ± −
72 456 378.695 33 0.44 − ± −
14 83 ±
11 3 0.45 − ± − ± −
22 456 383.715 90 0.93 107 ±
14 14 − ±
11 8 0.94 92 ±
11 10 − ± Table 5.
Results from the analysis of the light and radial velocity curves with PHOEBE.
Parameter FASTWIND H05 (-Br γ / He i ) H05 (CNO / He i )Period, P (days) 3 .
373 652 ± .
000 002 3 .
373 474 ± .
000 003 3 .
373 335 ± .
000 003Time of primary eclipse, HJD .
653 33 ± .
000 1 2 455 685 .
652 73 ± .
000 1 2 455 685 .
652 45 ± .
000 1Inclination, i (deg) 68 . ± . . ± . . ± . Ω . ± .
02 4 . ± .
05 4 . ± . Ω . ± .
04 4 . ± .
05 4 . ± . L / L . ± .
01 0 . ± .
05 0 . ± . q . ± .
01 0 . ± .
02 0 . ± . γ (km s − ) 11 ± − ± − ± α (R ⊙ ) 34 . ± .
04 35 . ± .
17 34 . ± . K (km s − ) 233 ± ± ± K (km s − ) 254 ± ± ± , pole . ± .
002 0 . ± .
002 0 . ± . , side . ± .
002 0 . ± .
002 0 . ± . , point . ± .
003 0 . ± .
003 0 . ± . , back . ± .
003 0 . ± .
002 0 . ± . , pole . ± .
002 0 . ± .
002 0 . ± . , side . ± .
003 0 . ± .
002 0 . ± . , point . ± .
003 0 . ± .
003 0 . ± . , back . ± .
003 0 . ± .
003 0 . ± . Table 6.
Physical parameters of D2-EB.
Parameter FASTWIND H05 (-Br γ / He i ) H05 (CNO / He i ) H05 (CNO / He i ) (ELC) M ( M ⊙ ) 26 . ± .
20 25 . ± .
09 24 . ± .
15 24 . ± . M ( M ⊙ ) 24 . ± .
16 25 . ± .
66 22 . ± .
68 21 . ± . R ( R ⊙ ) 9 . ± .
05 9 . ± .
07 9 . ± .
07 9 . ± . R ( R ⊙ ) 9 . ± .
06 9 . ± .
19 8 . ± .
10 8 . ± . g . ± .
01 3 . ± .
01 3 . ± .
01 3 . ± . g . ± .
01 3 . ± .
01 3 . ± .
01 3 . ± . T e f f (K) 38000 (fixed)T e f f (K) 36833 ± ± ± ± L / L ⊙ . ± .
05 5 . ± .
05 5 . ± .
05 5 . ± . L / L ⊙ . ± .
05 5 . ± .
05 5 . ± .
05 5 . ± . . ± .
08 3 . ± .
09 3 . ± .
08 3 . ± .08