A&A 616, A75 (2018) Astronomy https://doi.org/10.1051/0004-6361/201832810 & © ESO 2018 Astrophysics

The triple system HD 150136: From periastron passage to actual masses ?,?? L. Mahy1,2,???, E. Gosset2,????, J. Manfroid2, C. Nitschelm3, A. Hervé4,5, T. Semaan2,6, H. Sana1, J.-B. Le Bouquin7, and S. Toonen8

1 Instituut voor Sterrenkunde, KU Leuven, Celestijnlaan 200D, Bus 2401, 3001 Leuven, Belgium e-mail: [email protected] 2 Space Sciences, Technologies, and Astrophysics Research () Institute, Université de Liège, Quartier Agora, Bât B5c, Allée du 6 août, 19c, 4000 Liège, Belgium 3 Unidad de Astronomía, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile 4 Astronomical Institute ASCR, Fricova˘ 298, 251 65 Ondrejov,˘ Czech Republic 5 Visitor Scientist at Gemini Observatory, Northern Operations Center, 670 North A’ohoku Place, Hilo, HI 96720, USA 6 Institute of Astronomy, University of Geneva, 51 chemin des Maillettes, 1290 Versoix, Switzerland 7 UJF-Grenoble 1/CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG), UMR 5274, Grenoble, France 8 Anton Pannekoek Institute for Astronomy, University of Amsterdam, 1090 GE Amsterdam, The Netherlands

Received 12 February 2018 / Accepted 30 April 2018

ABSTRACT

+ Context. The triple system HD 150136 is composed of an O3 V((f∗))–O3.5 V((f )) primary, of an O5.5–6 V((f)) secondary, and of a more distant O6.5–7 V((f)) tertiary. The latter component went through periastron in 2015–2016, an event that will not occur again within the next eight . Aims. We aim to analyse the tertiary periastron passage to determine the orbital properties of the outer system, to constrain its incli- nation and its eccentricity, and to determine the actual masses of the three components of the system. Methods. We conducted an intensive spectroscopic monitoring of the periastron passage of the tertiary component and combined the outcoming data with new interferometric measurements. This allows us to derive the orbital solution of the outer in three- dimensional space. We also obtained the light curve of the system to further constrain the inclination of the inner binary. Results. We determine an of 8.61 0.02 years, an eccentricity of 0.682 0.002, and an inclination of 106.18 0.14◦ ± ± +8.45 +4.96 ± for the outer orbit. The actual masses of the inner system and of the tertiary object are 72.32 8.49 M and 15.54 4.97 M , respectively. From the mass of the inner system and accounting for the known mass ratio between the primary− and the secondary,− we determine actual masses of 42.81 M and 29.51 M for the primary and the secondary components, respectively. We infer, from the different

mass ratios and the inclination of the outer orbit, an inclination of 62.4◦ for the inner system. This value is confirmed by photometry. Grazing eclipses and ellipsoidal variations are detected in the light curve of HD 150136. We also compute the distance of the system to 1.096 0.274 kpc. Conclusions.± By combining spectroscopy, interferometry, and photometry, HD 150136 offers us a unique chance to compare theory and observations. The masses estimated through our analysis are smaller than those constrained by evolutionary models. The formation of this triple system suggests similar ages for the three components within the errorbars. Finally, we show that Lidov–Kozai cycles have no effect on the evolution of the inner binary, which suggests that the latter will experience mass transfer leading to a merger of the two . Key words. stars: early-type – binaries: spectroscopic – stars: fundamental parameters – stars: individual: HD150136

1. Introduction massive star formation and evolution are still to be understood. Most of their fundamental parameters are poorly constrained, Massive stars are key objects in the . They influence both especially their masses. In this context, investigating the binary the chemical and the mechanical evolution of their surround- system population is the best way to derive these masses. The rel- ings through the creation of bubbles and of induced or inhibited atively small number of extremely massive galactic stars implies star formation. They are also the main sources of ultraviolet and that any system whose orbital parameters are accurately deter- ionizing radiations. Despite their importance, actual details of mined provides important new constraints to . Binarity, however, affects the way that stars evolve, making their ? Based on observations collected at the European Southern Observa- evolution more complex than that of single stars. This is espe- tory (Paranal and La Silla, Chile). cially relevant for massive stars, given their high fraction of ?? The journal of observations and the data are only available at the CDS via anonymous ftp to multiple systems (Duchêne & Kraus 2013; Sana et al. 2012, cdsarc.u-strasbg.fr (130.79.128.5) or via 2014). The situation is even more complex with gravitationally- http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/616/A75 bound hierarchical systems since the evolution of the stars in ??? F.R.S.-FNRS Postdoctoral Researcher. those systems can be ruled by the Lidov–Kozai cycles (Kozai ???? F.R.S.-FNRS Research Director. 1962; Lidov 1962). The latter can modulate the eccentricity

Article published by EDP Sciences A75, page 1 of7 A&A 616, A75 (2018) of the inner binary triggering modulations in their interactions spectroscopic monitoring covering both sides of the periastron (Toonen et al. 2016). In this context, HD 150136 is perfectly passage of the tertiary component. suited to better constrain this phenomenon. The present paper provides the analysis of the new spectro- This system is one of the two brightest stars hosted scopic data coupled with new interferometric and with unprece- in the center of the young NGC 6193 in the dented photometric observations of HD 150136. The paper OB1 association, for which the distance was first esti- is organized as follows. In Sect.2, we present the observa- mated by Herbst & Havlen(1977) to be 1.32 kpc. This object tional campaign and the different instruments used. Section3 is a triple hierarchical system formed of an inner binary with is devoted to the determination of the radial velocities of the + an O3 V((f∗))–O3.5 V((f )) primary and an O5.5–6 V((f)) sec- three components. Section4 presents the global orbital solution ondary1, orbiting around each other with a period of 2.67455 for the inner and the outer systems by combining spectroscopy days, and of an O6.5–7 V((f)) physically bound tertiary com- and interferometry. The light curve of the system is studied ponent located on a much longer orbit (Mahy et al. 2012). in Sect.5. Section6 discusses the evolutionary statuses of the This object is the nearest system harbouring an O3 star. It thus different components and, finally, we give our conclusions in constitutes a target of choice for investigating the fundamental Sect.7. parameters of such a star. HD 150136 is one of the X-ray-brightest massive stars known (log L = 33.39 (cgs), log(L /L ) = 6.4; Skinner et al. 2005), 2. Observations and data reduction X X bol − most likely as the result of a radiative colliding-wind interac- 2.1. Spectroscopic observations tion. Its X-ray light curve, however, presents variations whose origin remains unclear. The star was also reported as a non- We collected and retrieved 177 optical spectra of HD 150136 thermal radio emitter (Benaglia et al. 2006; De Becker 2007). obtained with the Fibre-fed Extended Range Optical Spec- This suggests that the system harbours a relativistic population trograph (FEROS) mounted successively on the ESO 1.52 m of electrons, probably accelerated through shocks in colliding- (for observations before 2002) and on the MPG/ESO 2.2 m wind regions. Mahy et al.(2012) showed that a non-thermal radio (for observations after 2002) telescopes at La Silla observa- emission originating in the inner system would hardly escape. tory (Chile). These data were partially presented and analysed The presence of the third object is thus required in order to in Mahy et al.(2012) and in Sana et al.(2013) but spectra that displace the emitting region in the outer system. were newly acquired around the periastron passage of the third Following the study of Mahy et al.(2012), the third com- component are introduced in the present paper. The monitoring ponent is expected to be sufficiently far from the inner system of HD 150136 on FEROS started in 1999, and went on every to be observable with long baseline interferometric facilities. until 2016, with breaks in 2007 and in 2010. FEROS provides The first detections of the outer pair were reported by Sana a resolving power of R = 48 000 and covers the entire optical et al.(2013) from the Precision Integrated-Optics Near-infrared range from 3800 to 9200 Å. The data were reduced following the Imaging ExpeRiment (PIONIER) and by Sanchez-Bermudez procedure described in Mahy et al.(2012). et al.(2013) from the Astrometrical Multi BEam combineR We also obtained Director’s Discretionary Time (DDT) (AMBER). Sana et al.(2013) combined the preliminary inter- with the UV-Visual Echelle Spectrograph (UVES; PI: Mahy ferometric observations with high-resolution spectroscopic data 297.D-5007, PI: Gosset 295.D-5025, and PI: Gosset 294.D-5041) to derive a first orbital solution of the outer companion in the mounted on the ESO-VLT to acquire eight additional spectra, three-dimensional space. These authors reported a period of which we have completed with two additional spectra pro- 3008 days, and an eccentricity of 0.73 for the outer orbit. Mean- vided by the EDIBLES team (see Cox et al. 2017; PI: Cox; while, interferometric and spectroscopic observations continue Large Programme: 194.C-0833(C)) taken in June and July 2015. to be obtained to constrain the full orbit. With the analysis of These data have a resolving power of R = 80 000. The eight these data, we realized that the expected periastron passage was DDT time spectra were acquired with the DIC 2 437+760 setup not yet observed and that the values provided by Sana et al. whilst the spectra taken in June and in July were obtained with (2013) needed to be revised. The parameters of the outer orbit the DIC 1 346+564 and the DIC 1 437+860 setups, respectively. were updated through the analysis of the interferometric data by The data reduction was performed with the standard reduction Le Bouquin et al.(2017). The latter changed the values of the pipeline. period and of the eccentricity to 3067 days and 0.68, and inferred Finally, we took three spectra of HD 150136 with the actual masses of 87 M for the inner system and of 27 M for the CORALIE spectrograph mounted on the Swiss 1.2 m Leonhard third component. However their lack of spectroscopic observa- Euler telescope at La Silla. CORALIE is an improved version tions close to the periastron passage prevented them from strictly of the ELODIE spectrograph (Baranne et al. 1996) covering the constraining the semi-amplitude of the outer orbit and therefore spectral range between 3850 and 6890 Å. Its resolving power is the minimum masses. R = 55 000. The data were reduced with the CORALIE pipeline. This emphasizes the uncertainties linked to the determina- The entire journal of observations is available at the CDS. tion of the dynamical masses of the three components. It indeed The heliocentric Julian date (HJD) is the time taken at mid- depends on the maxima of amplitudes of the radial velocity (RV) exposure and is given in the format HJD–2450000. curves for the outer orbit. In this context, we have undertaken a 2.2. Photometric observations 1 The ((f∗)) reports a spectrum with the N IV 4058 emission line stronger than the N III 4634–41 lines and a weak He II 4686 absorption The photometric observations of HD 150136 were carried out line, the ((f+)) refers to a spectrum with medium N III 4634–41 emission between April and August 2017 at Siding Spring Observatory lines, the weak He II 4686 line, and the Si IV 4089–4116 lines in emis- with the 0.43-m f/6.8 telescope (T17) of the iTelescope net- sion, and the ((f)) means that the emission N III 4634–41 lines are weak work2. The camera was equipped with a 1K*1K FLI ProLine and that the He II 4686 line is present in strong absorption (see Walborn 1971, for further details). 2 http://www.itelescope.net

A75, page 2 of7 L. Mahy et al.: The tripleL. Mahy system et HDal.: The 150136: triple From system periastron HD 150136 passage to actual masses

400 E2Vthe only CCD47-10-1-109 star in the field CCD with giving a suitable a 15 brightness.50 field at and a resolution it proved 1 ofto0 be.92 su00ffipixelciently− . A stable. narrow-band An aperture O III offilter 3.7 was arcsec used was in used order and to 300 avoida small saturation empirical of seeing the target correction star. The was observations applied because were ofmade the 200

innearness sequences of the lasting stars. about The best 20 minutesdata of each of short sequence exposures. were ave Ther- ] 1 − reductionsaged in order were to build done the with final the data IRAF set. daophot packages. The 100 nearby HD 150135 was used as a comparison. It is the only star in the field with a suitable brightness and it proved to be suffi- 0 2.3. Interferometric observations ciently stable. An aperture of 3.7 arcsec was used and a small 100 − empiricalIn complement seeing to correction the spectroscopic was applied and because photometric of the nearness data, we Radial velocities [km s 200 ofalso the used stars. the The astrometric best data observations of each sequence compiled were by averagedLe Bouqu inin − order to build the final data set. et al. (2017)to better constrain the orbital parameters of the outer 300 orbit. Two additional points were obtained in May and August − 400 2.3. Interferometric observations − 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 2017 (PI: Sana, 596.D-0495(J))with the PIONIER combiner (Le − Phase [Φ] InBouquin complement et al. 2011). to the We spectroscopic refer to Le Bouquin and photometric et al. (2017) data, for we a alsodescription used the of astrometric the data reduction observations procedure. compiled by Le Bouquin Fig. 1. RV curves of the inner system corrected for the presence of ththee et al.(2017) to better constrain the orbital parameters of the outer tertiary component. component. Red dots give the RVs of the primary whilwhilstst the orbit.3. Radial Two additional velocity pointsmeasurements were obtained in May and August black ones indicate the secondary component. 2017 (PI: Sana, 596.D-0495(J)) with the PIONIER combiner In order to attain a good accuracy on the radial velocity (RV) (Le Bouquin et al. 2011). We refer to Le Bouquin et al.(2017) We applycompare the the Heck-Manfroid-Mersch different sets of RVs method in Fig. (HeckA.1 and et we al. formeasurements, a description we of the proceed data reduction in different procedure. steps to measure them conclude to a global agreement. In the following, we use the for the three components. In the first step, we fit the line pro- 1985), revised by Gosset et al. (2001), on the difference between theset ofRVs RVs of the obtained primary by and cross-correlation, the secondary givento determine that they the rep- or- files with Gaussian profiles. Given the spectral classification of resent average values on several main spectral lines. The RVs 3. Radial velocity+ measurements bital period of the inner (primary/secondary) system and on the O3V((f∗))-O3.5V((f )) attributed to the primary component, its are given with the journal of observations that is available at the spectrum presents lines of N v 4604–19that only this component RVs of the tertiary component for the orbital period of the outer In order to attain a good accuracy on the radial velocity (RV) CDS. exhibits. We also focus on the N iv 4058, He ii 4542, O iii 5592, (primary + secondary/tertiary) system. For the inner system, an measurements, we proceed in different steps to measure them We apply the Heck–Manfroid–Mersch1 method (Heck et al. and He i 5876 lines. The lines formed by elements in higher ion- outstanding peak at 0.373895d− , corresponding to a period of for the three components. In the first step, we fit the line pro- 1985), revised by Gosset et al.(2001), on the difference between ization stages are expected to be created closer to the stellar pho- 2.674548 0.000007 days is detected. This value confirms that files with Gaussian profiles. Given the spectral classification of the RVs of± the primary and the secondary to determine the tospheres, which infers a better estimation of the amplitudes of obtained by Mahy et al. (2012). For the outer system, the pe- O3 V((f ))–O3.5 V((f+)) attributed to the primary component, orbital period of the inner (primary/secondary) system1 and the RVs.∗ These sets of lines, however, have their disadvantages: riodogram provides an outstanding peak at 0.000318d− , corre- its spectrum presents lines of N V 4604–19 that only this com- spondingon the RVs to a of period the tertiary of 3144.7 component days, which for isthe slightly orbital larger periodthan of ponent– the Nexhibits.iv 4058 We line also is present focus in on emission the N IV in4058, the primary He II 4542, spec- the period outer (primary of 3067 days+ secondary/tertiary) provided by Le Bouquin system. et For al. (2017).the inner 1 O IIItrum.5592, This and line He I shows5876 anlines. asymmetry The lines that formed can be by due elements to the system, an outstanding peak at 0.373895 d− , corresponding in higherwind-wind ionization interaction stages zone are expectedbetween the to beprimary created and closer the sec- to to a period of 2.674548 0.000007 days is detected. This ± the stellarondary photospheres, (see Mahy et which al. 2012) infers or a to better tidal estimation interactions of thebe- 4.value Orbital confirms parameters that obtained for the by Mahy global et system al.(2012). For the amplitudestween these of the two RVs. components. These sets Furthermore, of lines, however, this line have is their con- outer system, the periodogram provides an outstanding peak at We combine1 the RV measurements of the three components ob- iii 0.000318 d− , corresponding to a period of 3144.7 days, which disadvantages:taminated by the C 4070 line, especially at the maximum tained through spectroscopy with the interferometric datapoints is slightly larger than the period of 3067 days provided by – theof separation, N IV 4058 which line is can present make the in assessmentemission in of the asymmetry primary to perform a global fit of the inner and outer . The orbital Le Bouquin et al.(2017). spectrum.uncertain. This line shows an asymmetry that can be due parameters of the inner system confirm those given by Mahy the spectral widths of the He ii 4542 lines are different for the – to the wind-wind interaction zone between the primary and et al. (2012) and Sana et al. (2013). Figure.1 shows the RV three components, given their spectral classifications. There- the secondary (see Mahy et al. 2012) or to tidal interac- curves of the inner system corrected for the presence of the ter- fore, the primary’s line is the most prominent feature, in 4. Orbital parameters for the global system tions between these two components. Furthermore, this line tiary. comparison with that of the secondary or the tertiary com- is contaminated by the C III 4070 line, especially at the WeWith combine the two the new RV interferometric measurements datapoints, of the three the components outer orbit ponents, making the latter barely detectable outside epochs maximum of separation, which can make the assessment of isobtained now well through constrained, spectroscopy and confirms with the the values interferometric provided by data- Le close to the maxima of separation. asymmetry uncertain; Bouquinpoints to et perform al. (2017). a global The fit global of the fit inner depends and on outer 14 parametersorbits. The – the spectralO iii 5592 widths line is of not the included He II 4542 in thelines UVES are different setting, for which the orbital parameters of the inner system confirm those given by prevents us from obtaining the related RVs close to the peri- because we keep fixed the eccentricity and the argument of the three components, given their spectral classifications. There- periastronMahy et al. for(2012 the) inner and Sana system. et al.Besides(2013). the Figure orbital1 shows parame theters, fore,astron the passage. primary’s line is the most prominent feature, in RV curves of the inner system corrected for the presence of the – the He i 5876 line is formed further away from the photo- the combination of the astrometric data with the spectroscopic comparison with that of the secondary or the tertiary com- onestertiary. from the intensive monitoring during the periastron pas- ponents,sphere and making can give the latterlarger barely errors detectable on the actual outside RVs epochs of the With the two new interferometric datapoints, the outer orbit components. sage of the tertiary component allows us to obtain more accurate close to the maxima of separation; minimumis now well masses constrained, than those and reported confirms in the Sana values et al. provided (2013) and by To– determinethe O III 5592 the RVs line for is not the includedthree components, in the UVES we used setting, the inLe Le Bouquin Bouquin et al. et( al.2017 (2017).). The globalThe RV fit curves depends computed on 14 parameters from the restwhich wavelengths prevents provided us from by obtaining Conti et the al. (1977) related and RVs Underhi close toll systemicbecause we velocities keep fixed of the the inner eccentricity system and at di thefferent argument epochs of and the (1995)the forperiastron wavelengths passage; shorter and longer than 5000Å, respec- fromperiastron the RVs for of the the inner tertiary system. are shown Besides in the the orbital left panel parameters, of Fig. 2 tively.– the He I 5876 line is formed further away from the photo- whilstthe combination the best fit of of the the astrometric relative motion data on with the the sky spectroscopic plane of the sphereIn the second and can step give we larger disentangled errors on the the spectra actual RVsand refined of the tertiaryones from around the theintensive inner system monitoring is displayed during in the the periastron right panel pas- of by cross-correlationcomponents. the RVs of each component. This method Fig.2.sage of The the tertiary global orbital component parameters allows for us to the obtain inner more and the accurate outer Towas determine already described the RVs for in Mahythe three et al. components, (2012), and we we used refer the to rest this systemsminimum are masses listed inthan Table those 1. reported in Sana et al.(2013) and wavelengthspaper for any provided additional by details.Conti et This al.(1977 method) and allows Underhill us to(1995 obtain) in LeBy Bouquin combining et al. the(2017 SB3). Theradial RV velocity curvesamplitudes computed from with the the forRVs, wavelengths constituting shorter average and values longer on than all the 5000 line Å, profiles. respectively. sizesystemic and inclination velocities of the the relative inner system orbital at motion different on the epochs sky, itand is InWe the compare second the step, diff weerentsets disentangled of RVs the in Fig.A.1 spectra and and we refined con- possiblefrom the to RVs determine of the tertiary the individual are shown masses in the of left each panel compone of Fig.nt2 byclude cross-correlation to a global agreement. the RVs In of the each following, component. we useThis the method set of andwhilst the the distance best fit to of the the system.relativemotion We use on the the same sky approachplane of the as wasRVs already obtained described by cross-correlation, in Mahy et al. given(2012 that), and they we represe refer tont this av- thattertiary given around by Le the Bouquin inner system et al. is (2017) displayed to estimate in the right the distanc panel ofe papererage for values any onadditional several details. main spectral This method lines. Theallows RVs us areto obtain given andFig.2 the. The individual global orbital masses parameters of the inner forsystem the inner and and the the tertiar outery RVs,with theconstituting journal of average observations values that on all is theavailable line profiles. electronically. componentsystems are (see listed their in Table Equations1. 1, 2 and 3).

Article number,A75, page 3 of7 8 A&A proofs:A&Amanuscript 616, A75 no.(2018) hd150136_le

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Fig. 2. 2.LeftLeft: panel RV: curves RV curves of the of outer the outer system. system. Black Black dots dots represent represent the thesystemic systemic velocities velocities of of the the inner inner (P (P++S)S) system system whilst whilst the the red red ones ones represent thethe tertiary tertiary component. component.Right Right: panel Relative: relative astrometric astrometric orbit orbitof the of tertiary the tertiary component component in the in outerthe outer system; system; the the inner inner syst systemem is considered is considered as fixedas fixed at at(0,0). (0,0). The The periastron periastron of of the the tertiary tertiary is is represented represented by by an an op openen pentagon pentagon symbol. symbol. The The observations observations are are indicated indicated in in red red an andd are are accompanied accompanied with theirtheir error error ellipses. ellipses.

Orbital solution of the inner and outer systems. Errors represent 1-σ. Table 1. Orbital solution of the inner and outer systems. Innersystem Outersystem PInner system S P+S Outer system T P [day] 2.674548PSP0.000007+ ST 3144.7 7.4 e 0.0(fixed)± 0.682 ±0.002 P [day] 2.674548 0.000007 3144.7± 7.4 ω[e◦]0.0 (fixed)± – 0.682 248.47±0.0020.24 ± ± T0ω[HJD[◦] 2450000] 1327.1554–0.0003 248.471025.82 0.2416.55 q M /M − ± ±± (T01[HJD2)2450000] 1327.1554 1.451 0.0170.0003 1025.82 4.654 16.550.494 γ 1 − ±± ± q[km(M1 s/−M]2) 22.40 1.4511.31 0.01720.30 1.76 – 4.654 0.49419.43 1.12 1 1 − ± ± − ± ± − ± Kγ[km[km s− s−]] 230.8322.40 1.531.31 334.9120.30 1.762.42 14.99 – 3.5319.43 69.75 1.122.01 1 − ± − ±± ± − ±± a sinK [kmi [R s]− ] 230.83 12.21 0.111.53 334.91 17.71 2.420.12 681.83 14.99 3.5326.43 3172.97 69.75 2.0121.61 3 ⊙ ± ± ± ± Masinsin i [RM ]] 12.2129.77 ±0.110.42 17.7120.52 ±0.120.31 681.83 64.06± 26.437.64 3172.97 13.77± 21.614.43 3 ⊙ ±± +1.3 ±± ±± ±± i[◦M]sin i [M ] 29.77 0.42 62.4 2 20.52.4 0.31 64.06 7.64106.18 13.770.14 4.43 ± − ± ± ± ± a [mas] –+1.3 17.03 0.10 i[◦] 62.4 106.18 ±0.14 Ω[◦] –2.4 293.73 0.19 a [mas] –− 17.03 ±±0.10 M [M ] 42.81+3.64 29.51+2.70 72.32+8.45 ± 15.54+4.96 Ω[ ]⊙ 2.05 –2.35 293.738.49 0.19 4.97 ◦ − − − ± − +3.64 +2.70 +8.45 +4.96 M [M ] 42.81 2.05 29.51 2.35 72.32 8.49 15.54 4.97 − − +0.304 − − We estimate the total mass of the system to 87.86 13.71 M , ̟ = 0.912 0.182 mas. This parallax is then compared to the re- ± +8.45 ⊙ − Notes.givenErrors dynamical represent masses 1σ. for the inner system of 72.32 8.49 M cent parallax ̟ = 0.944 0.120mas provided by Gaia Data Re- +4.96 − ⊙ lease 2 (Gaia Collaboration± et al. 2016, 2018) for HD150136, and of 15.54 4.97 M for the third object. From the minimum masses of the− primary⊙ and secondary components derived from showing a very good agreement between both values. By combining the SB3 radial velocity amplitudes with the by interferometry.While the inner The system distance is orbiting of HD in 150136 the framework is left as ofa free the sizespectroscopy and inclination and the of dynamical the relative mass orbital of motion the inner on system the sky, com- it is parameter in our global fitting process. The idea is to compare puted from interferometry,we infer for the inner system an incli- outer system, its distance to the observer changes with the outer possible to determine the individual masses of each component the values of the semi-major axis provided by spectroscopy and nation of 62.4◦, and provide dynamical masses of 42.81 M for system periodicity. To this distance change, a time-delay effect is and the distance to the system. We use the same approach as⊙ that associated.by interferometry The semi-amplitude by constraining of thisthe distancetime delay of is the rather systemsmall to giventhe primary by Le Bouquin and of 29.51 et al.(M2017for) to the estimate secondary. the distance The inclination and the is slightly larger than that of⊙ 49 estimated in Mahy et al. (2012) (avoid< 0.02 any days). correlation We correct between the the observation two values times of this of the parameter. spectra individual masses of the inner system◦ and the tertiary component We estimate that HD 150136 is at a distance of 1.096 0.274 kpc. and in Sana et al. (2013). This yields masses lower than those for the time delay and we re-analyse the inner system± data. We (see their Eq. (1)–(3)). recoverThis value the validates same value the for distance parameters of 1.15 indicating kpc for NGC the robust 6193ness pro- from the standard values provided by Martins et. al. (2005). for We estimate the total mass of the system to 87 86 13 71 M , ofvided our by solution. Kharchenko et al.(2005) even though it does not allow givenstars with dynamical these spectral masses classifications. for the inner system of 72±.32+8.45 M 8.49 us to reject the distance of 1.32 kpc reported by Herbst & Havlen To estimate+4.96 the distance of HD150136, we compare− the and of 15.54 4.97 M for the third object. From the minimum (1977), which remains within 1σ. If we convert our distance into two values of− the semi-major axis provided by spectroscopy $ = . +0.304 masses of the primary and secondary components derived from 5.a parallax Photometry value, we obtain 0 912 0.182 mas. This parallax is spectroscopyand by interferometry. and the dynamical The distance mass of the HD150136 inner system is left com- as then compared to the recent parallax $−= 0.944 0.120 mas pro- puteda free from parameter interferometry, in our global we inferfitting for process. the inner The system idea is an to Wevided model by Gaia the light Data curve Release of the 2 ( innerGaia system Collaboration by± using 2016 PHOEBE, 2018) inclinationcompare the of values62.4◦, and of the provide semi-major dynamical axis masses provided of 42.81 by spec-M (PHysicsfor HD 150136, Of Eclipsing showing BinariEs, a very good v0.31a, agreement Prša & Zwitter between 2005 both) fortroscopy the primary and by and interferometry of 29.51 M byfor constraining the secondary. the The distanc inclina-e of software.values. The orbital period of the outer orbit being too long, tionthe system is slightly to avoid larger any than correlation that of 49 between◦ estimated the in two Mahy values et al. of weWhile are not the able inner to see system any is variations orbiting fromin the the framework tertiary in of our the (this2012 parameter.) and in Sana We etestimate al.(2013 that). This HD150136 yields masses is at a lower distance than of lightouter curve. system, We its therefore distance to focus the observer on the parameters changes with of the the inneouterr those1.096 from0.274 the standard kpc. This values value provided validates by theMartins distance et al. of(2005 1.15) system.system periodicity. We thus keep To fixedthis distance the parameters change, of a time-delay the inner orbit effect de is- ± forkpc stars forNGC6193 with these spectral provided classifications. by Kharchenko et al. (2005) even terminedassociated. through The semi-amplitude the spectroscopic of this analysis. time delay PHOEBE is rather allow smalls thoughTo estimate it does thenot distance allow us of to HD reject 150136, the distance we compare of 1.32 the two kpc one(<0. to02 modeldays). the We light correct curve the and observation the RV curves times of of the the object spectra at valuesreported of by the Herbst semi-major & Havlen axis (1977), provided which by remainsspectroscopy within and 1- thefor samethe time time. delay This and software we re-analyse is based onthe Wilson inner system and Devinney’ data. Wes σ. If we convert our distance into a parallax value, we obtain code (Wilson & Devinney 1971) and uses Nelder and Mead’s

A75,Article page number, 4 of7 page 4 of 8 L. Mahy et al.: The triple system HD 150136

Table 2. Top: Observed stellar parameters of the three components; bottom: Stellar parameters derived by BONNSAI.

Primary Secondary Tertiary L log L 5.65 0.09 5.17 0.08 4.86 0.10 ± ± ± T [K] 46500 1000 40000 1000 36000 1000 eff ± ± ± log g [cgs] 4.0 0.1 4.0 0.1 3.5 0.25 1 ± ± ± v sin i [km s− ] 171 20 136 20 72 10 ±+0.4 ±+0.3 ±+1.1 Rmean [R ] 10.3 8.5 6.9 0.3 0.2 1.0 −+3.64 −+2.70 −+4.96 M [M ] 42.81 2.05 29.51 2.35 15.54 4.97 − − − +1.1 +0.7 +1.0 Rtheo [R ] 10.8 0.7 8.5 0.8 7.0 0.8 − − − 0 +5.0 +2.4 +2.0 Mini [M ] 56.4 4.6 31.2 2.3 22.4 1.9 − − − 0 +4.6 +2.5 +1.9 Mact [M ] 55.4 4.4 30.6 2.1 22.4 2.1 − − − 0 1 +22.9 +21.5 +11.2 vini [km s− ] 203.3 22.6 157.8 21.3 75.8 11.2 0 1 +−21.2 +−20.9 +−11.2 vrot [km s− ] 193.3 21.0 152.8 20.0 75.8 11.2 − − − 0 Age [Myrs] 0.6 0.3 1.7 0.7 2.3 1.6 00 ± ± ± 00 0 0 0 0 0 Notes. Errors are 1σ. L. Mahy et al.: The triple system HD 150136: From periastron passage to actual masses

00 curve5.8 obtained by PHOEBE with an inclination of 62.4◦. The dispersion around the theoretical light curve seems50M to be phase 000 ⊙ dependent (compare both sides of phase 0.25). Additional pho- 00 tometric5.6 data are necessary to confirm the last remark40 asM well as ⊙ 00 the existence and shape of the eclipses.

0 0 00 0 0 0 0 0 6.) Evolutionary5.4 status 30M ⊙ Φ ⊙ From the individual parameters determined from photometry, Fig. 3. Light curve of HD 150136 (black dots) and the PHOEBE best fit we5 compute.2 the of the three components. Based Fig. 3. Light curve of HD 150136 (black dots) and the PHOEBE best log (L/L fit(red). (red). The The magnitude magnitude outside outside the the eclipses eclipses has has been been set set to to 0 0 and lower on the determination of the effective temperatures made by L luminosities correspond to negative values. Mahy et al.(2012), we compute a of log L = 20M 5.0 L ⊙ 5.65 0.09 for the primary and log L = 5.17 0.08 for ± ± recover the same value for parameters indicating the robustness the secondary. We also use the new distance that we have Simplexof our solution. fitting method to adjust all the input parameters to find the best fit to the light curve. We take into account the effec- determined and the brightness factors between the different components4.8 given by Mahy et al.(2012) to derive from a tive temperatures of the inner components determined by Mahy different50000 method45000 the40000 luminosities35000 30000 of the25000 three20000 components.15000 et5. al. Photometry (2012), meaning 46500K and 40000K for the primary and We obtain log L = 5Effective.70, 5.16 temperature, and 4.86 [K] for the primary,15M the secondary, respectively (see Table 2 in the present paper). We L ⊙ We model the light curve of the inner system by using PHysics . Fig.secondary 4. Positions and in tertiary the Hertzsprung-Russell components, respectively, diagram of thewhich three agrees com- alsoOf Eclipsing add a third BinariEs light for (PHOEBE, the modelling v0.31a; with Prša a value & Zwitter of 0 156 2005 as) estimated from Mahy et al. (2012). ponentswell with of theHD other150136. above-mentioned Tracks are from valuesBrott et we al. determined. (2011) computed software. The orbital period of the outer orbit being too long, 1 The light curve clearly displays ellipsoidal variations and withThese an initial new rotational estimations velocity infer of about new 300 positions km s− . for the three we are not able to see any variations from the tertiary in our objects in the Hertzsprung–Russell diagram (Fig.4) compared seeminglylight curve. grazing We therefore eclipses. focus We on confirm the parameters the inclination of the inner of 62.4 +1.3 but given the errors on the photometric data, we can- to those given in Mahy et al.(2012). These new parameters are ◦ 2.4 + . 3 system.− We thus keep fixed the parameters of the inner orbit used1 as9 input for BONNSAI (Schneider et al. 2014), a publicly not be more accurate on these values. This result validates our 22.4 2.1 M , respectively. Compared to the errors on the masses determined through the spectroscopic analysis. PHOEBE allows andavailable to− the tool, age⊙ of which the components,the allows one to derive amountof stellar parameters mass lost by (e.g., the massone to estimations model the light for the curve two and components the RV curves in the of inner the object system, at as described in Section4. Figure.3 displays the fit of the light threemass, components radius, age) during from their the comparison present lifetime of a is set not of yet observa- signif- the same time. This software is based on Wilson and Devinney’s tional parameters (e.g., , , curve obtained by PHOEBE with an inclination of 62.4◦. The icant. Whilst the radii and the rotational velocities of the com- code (Wilson & Devinney 1971) and uses Nelder and Mead’s ponentsrotational agree velocity) with the with observational the evolutionary measurements, tracks of theBrott mas etses al. dispersionSimplex fitting around method the theoretical to adjust all light the curve input seems parameters to be to ph findase dependent (compare both sides of phase 0.25). Additional pho- are(2011 larger). We than use what as we input found.A the effective general temperatures, agreement gives gravities, an age the best fit to the light curve. We take into account the effective betweenluminosities, 0 and and2 Myrs projected for the global rotational system. velocities From their of the radii three and tometrictemperatures data of are the necessary inner components to confirm determined the last remark by Mahy as well et al.as the existence and shape of the eclipses. theircomponents. rotational The velocities, Bayesian the two approach stars of provides the inner initial system masses are in (2012), meaning 46 500 and 40 000 K for the primary and the +5.0 +2.4 +2.0 co-rotationof 56.4 4.6 with, 31. their2 2.3, orbit. and 22.4 1.9 M , for the primary, sec- secondary, respectively (see Table2). We also add a third light − − − ondary,To predict and tertiary the evolution components, of HD150136, respectively, we whilst have the used actual the for the modelling with a value of 0.156 as estimated from Mahy . +4.6 . +2.5 6. Evolutionary status triple-starmasses are evolution estimated code byTRES BONNSAI(Toonen to 55 et4 al.4. 2016).4, 30 6 We2.1, find and et al.(2012). +1.9 − − that22.4 the2.1 outerM , respectively. star does not Compared affect the to evolution the errors of on the the inner masses two FromThe the light individual curve parameters clearly displays determined ellipsoidal from photometry variations,we and and− to the age of the components, the amount of mass lost computeseemingly the grazing luminosities eclipses. of the We three confirm components. the inclination Based on the of stars. As the outer period is three orders of magnitude longer +1.3 thanby the that three of the components compact inner during orbit, their the present outer and lifetime inner orbiis notts determination62.4◦ 2.4 but given of the the effective errors temperatures on the photometric made by data, Mahy we et can- al. − L areyet practically significant. kinematically Whilst the radii discoupled. and the rotational velocities of (2012),not be more we compute accurate a on luminosity these values. of log ThisL result= 5.65 validates0.09 our for ⊙ ± mass estimations forL the two components in the inner system, 3 TheA notorious BONNSAI manifestation web-service is of available the three-body at http://www.astro. dynamics are the primary and log L = 5.17 0.08 for the secondary. We also as described in Sect.⊙4. Figure±3 displays the fit of the light theuni-bonn.de/stars/bonnsai Lidov-Kozai cycles. During. these cycles the mutual inclina- use the new distance that we have determined and the bright- tion and eccentricity of the inner binary vary periodically. The ff ness factors between the di erent components given by Mahy timescale of these cycles in HD150136 is about 57A75, kyrs page (based 5 of7 et al. (2012) to derive from a different method the luminosities L on Kinoshita & Nakai 1999). A higher order level of interaction of the three components. We obtain log L = 5.70, 5.16, and ⊙ (i.e. the octupole level) is not strongly relevant for HD150136 4.86 for the primary, secondary and tertiary components, respec- as estimated by the octupole parameter epsilon ǫ = 0.0019 < tively, which agrees well with the other above-mentioned values ǫcritical 0.01 (see e.g. Naoz et al. 2011). we determined. ≈ Regarding the Lidov-Kozai timescale in HD150136, it is These new estimations infer new positions for the three ob- short compared to the stellar lifetimes (>several Myrs), which in jects in the Hertzsprung-Russell diagram (Fig.4) compared to principle allows the inner binary to undergo many Lidov-Kozai those given in Mahy et al. (2012). These new parameters are cycles in its lifetime. However, the cycles are repressed due to used as input for BONNSAI2 (Schneider et al. 2014), a pub- strong tidal effects in the inner binary. For this reason, the orbit licly available tool, which allows one to derive stellar param- of the inner binary does not reach significant eccentricities, not eters (e.g., mass, radius, age) from the comparison of a set even for mutual inclinations of 90 degrees at which the ampli- of observational parameters (e.g., effective temperature, sur- tude of the eccentricity cycles is maximized. The evolution of face gravity, rotational velocity) with the evolutionary tracks the inner binary is similar to that of an isolated binary. of Brott et al. (2011). We use as input the effective tempera- tures, gravities, luminosities, and projected rotational velocities After a few Myrs (going from 2.6Myrs to 5.5Myrs, depend- of the three components. The Bayesian approach provides initial ing on the binary population synthesis code that we use), when +5.0 +2.4 +2.0 both stars will still be on the , the inner binary will masses of 56.4 4.6, 31.2 2.3, and 22.4 1.9 M , for the primary, secondary, and− tertiary components,− respectively,− ⊙ whilst the ac- experience mass transfer, leading to a merger of the two stars. +4.6 +2.5 According to our simulations, a single main-sequence-like star tual masses are estimated by BONNSAI to 55.4 4.4,30.6 2.1, and − − of 65 M will be created, orbited by the previous tertiary star ∼ ⊙ 2 The BONNSAI web-service is available at http://www.astro.uni- (see e.g. Glebbeek et al. 2013, for simulations about high-mass bonn.de/stars/bonnsai stellar mergers).

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00 00 0 0 0 0 0 L. Mahy et al.: The triple system HD 150136: From periastron passage to actual masses A&A 616, A75 (2018)

00 5.8 the third object composing HD 150136. We have combined them 50M 000 ⊙ with data from older campaigns and with the astrometric obser- vations either new or previously reported by Le Bouquin et al. 00 5.6 40M (2017), to determine the three-dimensional orbit for the outer ⊙ 00 system. In addition to the inclination of the inner and the outer orbits, 0 0 00 0 0 0 0 0 ) 5.4 30M this study allowed us to constrain with accuracy the dynam- ⊙ Φ ⊙ +3.64 +2.70 ical masses of the three objects to 42.81 2.05, 29.51 2.35, and 15.54+4.96 M for the O3, O5.5, and O6− components,− respec- 5.2 4.97 Fig. 3. Light curve of HD 150136 (black dots) and the PHOEBE best log (L/L tively.− This constitutes the first estimation of the actual mass of fit (red). The magnitude outside the eclipses has been set to 0 and lower a galactic O3 star on the main sequence. luminosities correspond to negative values. 20M 5.0 ⊙ Acknowledgements. We are very grateful to our anonymous referee for his or her remarks and comments with the goal of improving our manuscript. This Simplex fitting method to adjust all the input parameters to find research was supported by the Fonds National de la Recherche Scientifique the best fit to the light curve. We take into account the effec- 4.8 (F.R.S.-F.N.R.S.), by the PRODEX XMM contract (Belspo), and through the tive temperatures of the inner components determined by Mahy 50000 45000 40000 35000 30000 25000 20000 15000 ARC grant for Concerted Research Actions, financed by the French Commu- nity of Belgium (Wallonia-Brussels Federation). We kindly thank Nick Cox et al. (2012), meaning 46500K and 40000K for the primary and Effective temperature [K] 15M and the EDIBLES team for providing advance access to their UVES data the secondary, respectively (see Table 2 in the present paper). We ⊙ Positions in the Hertzsprung-Russell diagram of the three com- for extracting the stellar RV values. AH is supported by the grant 14-02385S also add a third light for the modelling with a value of 0.156 as Fig. 4. Positions in the Hertzsprung–Russell diagram of the three com- from GA CR.ˇ Some of the observations obtained with the MPG 2.2 m tele- ponents of HD 150136. Tracks are from Brott et al. (2011) computed estimated from Mahy et al. (2012). ponents of HD 150136. Tracks are from Brott et al.1(2011) computed scope were supported by the Ministry of Education, Youth and Sports project– with an initial rotational velocity of about 300 km s−1 . The light curve clearly displays ellipsoidal variations and with an initial rotational velocity of about 300 km s− . LG14013 (Tycho Brahe: Supporting Ground-based Astronomical Observations). seemingly grazing eclipses. We confirm the inclination of We would like to thank the observers S. Vennes and L. Zychova for obtaining the data. Computational resources were supplied by the Ministry of Education, 62.4 +1.3 but given the errors on the photometric data, we can- ◦ 2.4 the components+ . agree with the observational measurements, the Youth and Sports of the Czech Republic under the Projects CESNET (Project − 1 9 not be more accurate on these values. This result validates our 22.4 2.1 M , respectively. Compared to the errors on the masses No. LM2015042) and CERIT-Scientific Cloud (Project No. LM2015085) pro- massesand to− the are age⊙ larger of the than components,the what we found. amountofA general agreement mass lost by gives the mass estimations for the two components in the inner system, an age between 0 and 2 Myrs for the global system. From their vided within the programme Projects of Large Research, Development, and three components during their present lifetime is not yet signif- Innovations Infrastructures. We are grateful to the staff of La Silla ESO as described in Section4. Figure.3 displays the fit of the light radii and their rotational velocities, the two stars of the inner icant. Whilst the radii and the rotational velocities of the com- Observatory for their technical support. curve obtained by PHOEBE with an inclination of 62.4◦. The system are in co-rotation with their orbit. dispersion around the theoretical light curve seems to be phase ponents agree with the observational measurements, the masses are largerTo predict than what the evolution we found.A of HDgeneral 150136, agreement we have gives used an ag thee dependent (compare both sides of phase 0.25). Additional pho- triple-star evolution code TRES (Toonen et al. 2016). We find tometric data are necessary to confirm the last remark as well as between 0 and 2 Myrs for the global system. From their radii and References thattheir the rotational outer star velocities, does not the affect two starsthe evolution of the inner of the syst innerem are two in the existence and shape of the eclipses. stars. As the outer period is three orders of magnitude longer co-rotation with their orbit. Baranne, A., Queloz, D., Mayor, M., et al. 1996, A&AS, 119, 373 than that of the compact inner orbit, the outer and inner orbits Benaglia, P., Koribalski, B., & Albacete Colombo J. F. 2006, PASA, 23, 50 are practicallyTo predict kinematically the evolution discoupled. of HD150136, we have used the Brott, I., de Mink, S. E., Cantiello, M., et al. 2011, A&A, 530, A115 6. Evolutionary status triple-starA notorious evolution manifestation code TRES of(Toonen the three-body et al. 2016). dynamics We find are Conti, P. S., Leep, E. M., & Lorre, J. J. 1977, ApJ, 214, 759 From the individual parameters determined from photometry,we thethat Lidov–Kozai the outer star cycles. does not During affect these the evolution cycles, the ofthe mutual inner incli- two Cox, N. L. J., Cami, J., Farhang, A., et al. 2017, A&A, 606, A76 stars. As the outer period is three orders of magnitude longer De Becker M. 2007, A&ARv, 14, 171 compute the luminosities of the three components. Based on the nation and eccentricity of the inner binary vary periodically. Duchêne, G., & Kraus, A. 2013, ARA&A, 51, 269 determination of the effective temperatures made by Mahy et al. Thethan timescale that of the of compact these cycles inner inorbit, HD the 150136 outer is and about inner 57 orbi kyrsts Gaia Collaboration, (Prusti, T., et al.) 2016, A&A, 595, A1 L are practically kinematically discoupled. Gaia Collaboration, (Brown, A. G. A., et al.) 2018, A&A, 616, A1 (2012), we compute a luminosity of log L = 5.65 0.09 for (based on Kinoshita & Nakai 1999). A higher order level of L ⊙ ± interactionA notorious (i.e. the manifestation octupole level) of the is three-body not strongly dynamics relevantare for Glebbeek, E., Gaburov, E., Portegies Zwart, S., & Pols, O. R. 2013, MNRAS, the primary and log L = 5.17 0.08 for the secondary. We also 434, 3497 ⊙ ± HDthe Lidov-Kozai150136 as estimated cycles. During by the these octupole cycles the parameter mutual incl epsilonina- use the new distance that we have determined and the bright- Gosset, E., Royer, P., Rauw, G., Manfroid, J., & Vreux, J.-M. 2001, MNRAS, tion= 0 and.0019 eccentricity<  of0. the01 (see inner e.g. binary Naoz vary et al. periodically 2011). . The ness factors between the different components given by Mahy critical 327, 435 timescaleRegarding of these the cycles Lidov–Kozai≈ in HD150136 timescale is about in HD 57 150136, kyrs (based it is Heck, A., Manfroid, J., & Mersch, G. 1985, A&AS, 59, 63 et al. (2012) to derive from a different method the luminosities shorton Kinoshita compared & toNakai the stellar 1999). lifetimes A higher (>several order level Myrs), of interacti whichon in Herbst, W., & Havlen, R. J. 1977, A&AS, 30, 279 of the three components. We obtain log L = 5.70, 5.16, and L principle(i.e. the octupole allows the level) inner is binary not strongly to undergo relevant many for Lidov–Kozai HD150136 Kharchenko, N. V., Piskunov, A. E., Röser, S., Schilbach, E., & Scholz, R.-D. ⊙ 2005, A&A, 438, 1163 4.86 for the primary, secondary and tertiary components, respec- cyclesas estimated in its lifetime. by the octupole However, parameter the cycles epsilon are repressedǫ = 0.0019 due to< tively, which agrees well with the other above-mentioned values Kinoshita, H., & Nakai, H. 1999, Celest. Mech. Dyn. Astron., 75, 125 strongǫcritical tidal0.01 effects (see e.g. in the Naoz inner et al. binary. 2011). For this reason, the orbit Kozai, Y. 1962, AJ, 67, 579 we determined. ≈ of theRegarding inner binary the Lidov-Kozai does not reach timescale significant in eccentricities, HD150136, it not is Le Bouquin, J.-B., Berger, J.-P., Lazareff, B., et al. 2011, A&A, 535, A67 These new estimations infer new positions for the three ob- Le Bouquin, J.-B., Sana, H., Gosset, E., et al. 2017, A&A, 601, A34 evenshort for compared mutual to inclinations the stellar lifetimes of 90 degrees (>several at which Myrs), the which ampli- in jects in the Hertzsprung-Russell diagram (Fig.4) compared to Lidov, M. L. 1962, Planet. Space Sci., 9, 719 tudeprinciple of the allows eccentricity the inner cycles binary is to maximized. undergo many The Lidov-Koz evolution ofai those given in Mahy et al. (2012). These new parameters are Mahy, L., Gosset, E., Sana, H., et al. 2012, A&A, 540, A97 thecycles inner in binary its lifetime. is similar However, to that the of an cycles isolated are binary.repressed due to Martins, F., Schaerer, D., & Hillier, D. J. 2005, A&A, 436, 1049 used as input for BONNSAI2 (Schneider et al. 2014), a pub- strongAfter tidal afew effects Myrs in the (going inner from binary. 2.6 For to 5.5 this Myrs, reason, depending the orbit Naoz, S., Farr, W. M., Lithwick, Y., Rasio, F. A., & Teyssandier, J. 2011, Nature, licly available tool, which allows one to derive stellar param- onof the innerbinary binary population does notsynthesis reach codesignificant that we eccentricitie use), whens, both not 473, 187 eters (e.g., mass, radius, age) from the comparison of a set Prša, A., & Zwitter, T. 2005, ApJ, 628, 426 starseven forwill mutual still be inclinations on the main of sequence, 90 degrees the at innerwhich binary the ampli will- of observational parameters (e.g., effective temperature, sur- Sana, H., de Mink, S. E., de Koter, A., et al. 2012, Science, 337, 444 experiencetude of the mass eccentricity transfer, cycles leading is maximized. to a merger The of the evolution two stars.of face gravity, rotational velocity) with the evolutionary tracks Sana, H., Le Bouquin, J.-B., Mahy, L., et al. 2013, A&A, 553, A131 Accordingthe inner binary to our is simulations, similar to that a singleof an isolated main-sequence-like binary. star Sana, H., Le Bouquin, J.-B., Lacour, S., et al. 2014, ApJS, 215, 15 of Brott et al. (2011). We use as input the effective tempera- of 65 M will be created, orbited by the previous tertiary star Sanchez-Bermudez, J., Schödel, R., Alberdi, A., et al. 2013, A&A, 554, tures, gravities, luminosities, and projected rotational velocities ∼After a few Myrs (going from 2.6Myrs to 5.5Myrs, depend- L4 (seeing on e.g. the Glebbeek binary population et al. 2013 synthesis, for simulations code that about we use), high-mass when of the three components. The Bayesian approach provides initial stellar mergers). Schneider, F. R. N., Langer, N., de Koter, A., et al. 2014, A&A, 570, A66 +5.0 +2.4 +2.0 both stars will still be on the main sequence, the inner binary will Skinner, S. L., Zhekov, S. A., Palla, F., & Barbosa, C. L. D. R. 2005, MNRAS, masses of 56.4 4.6, 31.2 2.3, and 22.4 1.9 M , for the primary, − − − ⊙ experience mass transfer, leading to a merger of the two stars. 361, 191 secondary, and tertiary components, respectively, whilst the ac- Toonen, S., Hamers, A., & Portegies Zwart S. 2016, Comput. Astrophys. +4.6 +2.5 According to our simulations, a single main-sequence-like star tual masses are estimated by BONNSAI to 55.4 4.4,30.6 2.1, and 7. Conclusion Cosmol., 3, 6 − − of 65 M will be created, orbited by the previous tertiary star Underhill, A. B. 1995, ApJS, 100, 433 ∼ ⊙ 2 The BONNSAI web-service is available at http://www.astro.uni- In(see the e.g. present Glebbeek analysis, et al. 2013, we have for simulations described the about observations high-mass Walborn, N. R. 1971, ApJS, 23, 257 bonn.de/stars/bonnsai obtainedstellar mergers). in spectroscopy during the last periastron passage of Wilson, R. E., & Devinney, E. J. 1971, ApJ, 166, 605

A75, page 6 of7 Article number, page 5 of 8 L. Mahy et al.: The triple system HD 150136

Appendix A: Comparison between the radial velocities

Fig. A.1. Comparison between the RVs measured on several lines for the primary (top panel), secondary (middle panel), and tertiary (bottom panel) components, respectively.

A75, page 7 of7