Draft version June 5, 2019 Typeset using LATEX twocolumn style in AASTeX62

Clues on the Origin and Evolution of Massive Contact Binaries: Atmosphere Analysis of VFTS 352

Michael Abdul-Masih,1 Hugues Sana,1 Jon Sundqvist,1 Laurent Mahy,1 Athira Menon,2 Leonardo A. Almeida,3 Alex De Koter,1, 2 Selma E. de Mink,2 Stephen Justham,2, 4 Norbert Langer,5 Joachim Puls,6 Tomer Shenar,1 and Frank Tramper7

1Institute of Astrophysics, KULeuven, Celestijnenlaan 200 D, 3001 Leuven, Belgium 2Astronomical Institute Anton Pannekoek, Amsterdam University, Science Park 904, 1098 XH, Amsterdam, The Netherlands 3Departamento de F´ısicaTe´oricae Experimental, Universidade Federal do Rio Grande do Norte, CP 1641, Natal, RN, 59072-970, Brazil 4School of Astronomy & Space Science, University of the Chinese Academy of Sciences, Beijing 100012, China 5Argelander-Institut f¨urAstronomie, Universit¨atBonn, Auf dem H¨ugel 71, 53121 Bonn, Germany 6LMU M¨unchen, Universit¨atssternwarte, Scheinerstr. 1, 81679 M¨unchen, Germany 7Institute for Astronomy, Astrophysics, Space Applications & Remote Sensing, National Observatory of Athens, P. Penteli, 15236 Athens, Greece

(Received February 23, 2019; Revised -; Accepted May 25, 2019) Submitted to ApJ

ABSTRACT The massive O4.5 V + O5.5 V binary VFTS 352 in the Tarantula nebula is one of the shortest-period and most massive overcontact binaries known. Recent theoretical studies indicate that some of these systems could ultimately lead to the formation of gravitational waves via black hole binary mergers through the chemically homogeneous evolution pathway. By analyzing ultraviolet-optical phase-resolved spectroscopic data, we aim to constrain atmospheric and wind properties that could be later used to confront theoretical predictions from binary evolution. In particular, surface abundances are powerful diagnostics of the evolutionary status, mass transfer and the internal mixing processes. From a set of 32 VLT/FLAMES visual and 8 HST/COS ultraviolet spectra, we used spectral disentangling to separate the primary and secondary components. Using a genetic algorithm wrapped around the NLTE model atmosphere and spectral synthesis code fastwind, we perform an 11-parameter optimization to derive the atmospheric and wind parameters of both components, including the surface abundances of He, C, N, O and Si. We find that both components are hotter than expected compared to single-star evolutionary models indicating that additional mixing processes may be at play. However the derived chemical abundances do not show significant indications of mixing when adopting baseline values typical for the system environment.

Keywords: stars: massive – binaries: spectroscopic – binaries: close

1. INTRODUCTION interactions (about a quarter of all O-type stars) will lead to Massive stars are some of the most energetic cosmic en- an overcontact phase and subsequent coalescence. Despite gines driving the evolution of our universe. Because most of affecting such a large percentage of O-type stars, the over- these stars are found in relatively close multiple systems (see contact phase is one of the least understood phases of massive arXiv:1906.01066v1 [astro-ph.SR] 3 Jun 2019 e.g., Sana & Evans 2011, for a review), binary interactions star evolution. This is due to the interplay of several com- play an important role in their evolution. Based on galactic plex physical processes occurring simultaneously during this studies, about 40% of all stars born as O-type are expected to phase, including, but not limited to, mass exchange, internal interact with a companion before leaving the main sequence mixing, intense radiation fields, and potential internal struc- (Sana et al. 2012). Ignoring particular evolutionary pathways ture adjustments (Pols 1994; Wellstein et al. 2001; de Mink such as those involving chemically homogeneous evolution et al. 2007). In addition to the complex physics, our lim- or magnetic fields (though see below), more than half of these ited understanding also stems from a lack of observational constraints due to the short lived overcontact phase, which is expected to evolve on thermal timescales. Currently there Corresponding author: Michael Abdul-Masih are only eight O-type overcontact systems known (Almeida [email protected] 2 Abdul-Masih et al. et al. 2015; Popper 1978; Lorenzo et al. 2017; Howarth et al. et al. 2016), CHE was proposed to be a possible pathway to 2015; Hilditch et al. 2005; Penny et al. 2008) the formation of black hole binary systems close enough to Aside from binary interaction, stellar rotation can also have merge in a Hubble time (de Mink & Mandel 2016; Mandel a dramatic influence on the evolution of massive stars. As a & de Mink 2016; Marchant et al. 2016). Two massive bi- rapidly rotating massive star evolves, the core will shrink and nary systems to date, VFTS 352 (Almeida et al. 2015) and the envelope will expand, leading to differential rotation (von HD 5980 (Koenigsberger et al. 2014), show indications of Zeipel 1924; Eddington 1925, 1926; Vogt 1924). Differen- CHE. This paper focuses on VFTS 352 in the Tarantula Neb- tial rotation can in turn cause shear instabilities that produce ula (a.k.a. 30 Doradus or 30 Dor) in the Large Magellanic significant mixing (Zahn 1974). Additionally, rapidly rotat- Cloud (LMC). ing stars experience surface deformations which can lead to VFTS 352 is an eclipsing double-lined O-type spectro- Eddington-Sweet circulations due to the thermal imbalance scopic binary system discovered in the course of the VLT- between the poles and the equatorial regions. These large Flames Tarantula Survey (VFTS, Evans et al. 2011; Sana meridional currents and the shear instabilities allow fresh et al. 2013). With spectral types of O4.5 V(n)((fc))z + material to be mixed into the core, extending the lifetime O5.5 V(n)((fc))z) (Walborn et al. 2014), both stars are of the star. They also allow for nuclear burning products rather rapid rotators with projected rotation rates of approx. to be transported to the surface, leading to detectable abun- 290 km s−1 (Ram´ırez-Agudelo et al. 2015). Further spectro- dance anomalies (Maeder & Meynet 2000; Maeder 2000; scopic monitoring as part of the Tarantula Massive Binary Brott et al. 2011a). Additionally, evolutionary models that Monitoring (Almeida et al. 2017) allowed for a first charac- include rotation show that with additional mixing, the effec- terization of the orbit, yielding a short orbital period of 1.124 tive temperature of a star increases (Yoon & Langer 2005; days. Using a Wilson Devinney code to fit the light and ra- Yoon et al. 2006). dial velocity curves, Almeida et al.(2015) deduced stellar The efficiency of the rotational mixing depends on the masses of about 29M and showed that the system was in star’s rotation rate, mass and initial metallicity. If the mixing deep contact. With effective temperatures of 42540 ± 280 K is efficient enough, it can prevent the build up of a chemical and 41120 ± 290 K, Almeida et al.(2015) found that the gradient at the interface between the core and envelope, al- component stars were too hot for their dynamical masses, lowing the star material to be fully mixed. Such a chemically suggesting the presence of strong mixing and making VFTS homogeneous evolution (CHE) induced by rotational mixing 352 a good candidate for CHE. was first proposed by Maeder(1987). In the CHE regime, a In this paper, we investigate the evolutionary status of star will evolve up and to the left on an Hertzsprung-Russell VFTS 352 in greater detail by fitting synthetic spectra to opti- diagram (HRD), at first moving up along the zero-age main cal and UV data in order to constrain the physical and atmo- sequence (ZAMS), then to the left towards hotter tempera- spheric properties of the system components, including the tures and at roughly constant bolometric luminosities. If the surface abundances of helium, carbon, nitrogen and oxygen mixing is not efficient enough, a star can also undergo incom- that are powerful tracers of mixing. This paper is organized plete chemically homogeneous evolution (incomplete CHE) as follows. Section2 describes our data set and provides the where the star will initially evolve up and to the left but will journal of the spectroscopic observations. Section3 details eventually turn back and evolve more typically. Since CHE the disentangling methods including the removal of interstel- is dependent on the rotation rate, lower metallicities are fa- lar and nebular lines. Section4 describes the atmosphere vored for this pathway in the case of single stars (Yoon & analysis techniques and fitting methods, the results of which Langer 2005; de Mink et al. 2009; Brott et al. 2011b;K ohler¨ are discussed in Sect.5. Finally, Sect.6 addresses the evo- et al. 2015; Szecsi´ et al. 2015). Massive stars have stellar lutionary status of the system and Sect.7 summarizes our winds driven by ultraviolet (UV) metallic lines. Therefore, conclusions. low metallicity means weaker winds and thus less angular momentum lost from the winds. 2. OBSERVATIONS While initially introduced for fast rotating single stars, 2.1. Optical Spectroscopy CHE can also occur in massive binary systems. In very close The optical data consist of 32 well phase covered spectra binary systems, the component stars can be tidally locked collected over an 18-month period as part of the Tarantula and their surface rotation rates determined by the orbital pe- Massive Binary Monitoring (TMBM, PI: Sana H., ESO pro- riod and the stars radii. As first suggested by de Mink et al. grams: 090.D-0323 and 092.D-0136 Almeida et al. 2017), (2009), CHE could delay or prevent coalescence as the stars using the FLAMES-GIRAFFE multi-object spectrograph on remain compact as they evolve, and might thus stay within the ESO Very Large Telescope (VLT). The observations were their Roche lobes (see also Almeida et al. 2015). Just be- performed using the LR02 setup, which provides continu- fore the first direct detection of gravitational waves (Abbott ous wavelength coverage from 3950Å to 4550Å with a spec- Atmosphere Analysis of VFTS 352 3 tral resolving power of 6,400. Each of the 32 epochs con- Table 1. Journal of HST/COS UV Observations sists of three back-to-back exposures of 900 seconds. These 1 Visit Grating HJD at φ texp data were reduced using the ESO CPL GIRAFFE pipeline mid observation (s) v.2.12.1, which includes bias subtraction, flat-field correc- 1 G130M 2457158.08817 0.477 900 tion, spectral extraction and wavelength calibration. Sky cor- G160M 2457158.12413 0.509 1500 rections and normalization procedures were applied follow- 2 G130M 2457158.23676 0.609 900 ing the description in Evans et al.(2011) and Sana et al. (2013), respectively. The resulting spectra have signal-to- G160M 2457158.26459 0.634 1500 noise ratios within the same order of magnitude (∼ 150). The 3 G130M 2457158.38582 0.742 900 journal of the TMBM observations is given in Almeida et al. G160M 2457158.40381 0.758 1500 (2017). Figure1 (bottom panel) shows one epoch of the op- 4 G130M 2457165.26816 0.864 900 tical spectra at a phase of φ ≈ 0.75. G160M 2457165.28615 0.880 1500 5 G130M 2457156.40494 0.980 900 UV Spectroscopy 2.2. G160M 2457156.42294 0.996 1500 UV spectra were obtained with the Far-UV G130M and 6 G130M 2457155.41174 0.096 900 G160M gratings of the Cosmic Origins Spectrograph (COS) G160M 2457155.42974 0.112 1500 on the Hubble Space Telescope (HST) under the auspices of 7 G130M 2457160.05892 0.230 900 program GO 13806 (PI Sana). In total, eight spectra cover- G160M 2457160.08914 0.257 1500 ing the entire orbit by bins of 0.125 in phase were obtained 8 G130M 2457160.19075 0.347 900 over a 10-day period. The instrumental setup provides nearly G160M 2457160.22104 0.374 1500 continuous wavelength coverage from approximately 1130Å 1 to 1790Å with a central wavelength of 1291Å and resolving Computed using the ephemerides of Almeida et al.(2015) (see power of 18,000 for the G130M grating and a central wave- Table2) length of 1611Å and a resolving power of 19,000 for the G160M grating. The observations were completed in eight for this study, we use exclusively the I-band photometry as visits of one orbit each. Each visit consisted of 2 × 450 s ex- there are many more measurements available in the I-band posures with the G130M grating followed by 2 × 750 s expo- than V-band (760 versus 90 respectively). As discussed in sures with the G160M grating for a total exposure time (texp) Almeida et al.(2015), the light curve shows ellipsoidal vari- of 900 seconds and 1500 seconds, respectively. The obser- ations and the subsequent analysis performed shows that both vations were collected using the TIME-TAG mode with the components are filling their Roche lobes and the system is in Primary Science Aperture in lifetime position 3. For visits 1, an over-contact configuration. In this paper, we exclusively 3, 6 and 8, FP positions 1 and 3 were used while for visits use the photometry to estimate the dilution factor of spectral 2, 4, 5 and 7, FP positions 2 and 4 were used. These data lines as a function of the orbital phase to inform the spectral were uniformly processed in the standard fashion by CAL- disentangling described below. COS 3.0 (2014-10-30). Processing steps included correct- 3. SPECTRAL DISENTANGLING ing the photon-event table for dead-time and position effects caused by drifts in the detector electronics, geometric distor- An important difficulty that arises when attempting to fit tion, and the orbital Doppler shift of the observatory; bin- synthetic spectra to those observed from double lined spec- ning the time-tag data; wavelength calibration based on the troscopic binaries (SB2) systems is the fact that observations Pt-Ne spectra simultaneously acquired during each visit; ex- show a combination of the two component signals. With mul- traction and photometric calibration of the 1-D spectra; and tiple well phase covered observational epochs, it is possible shift and add combination of spectra obtained at different FP- to disentangle the signals from the two components and ob- POS positions for both grating settings. The resulting spectra tain separate spectra for each. This can be accomplished with all have similar signal-to-noise ratios on the order of ∼ 11.5. a variety of spectral disentangling methods (for a review, see An overview of the UV observations is given in Table1. Fig- Pavlovski & Hensberge 2010). While there are several codes ure1 (top four panels) shows one epoch of the UV spectra at well suited for this problem (see for example Simon & Sturm a phase of φ ≈ 0.75. 1994; Hadrava 1995, 2009; Skodaˇ et al. 2011), we choose the FDBinary code which uses Fourier techniques in combina- 2.3. Optical Photometry tion with the orbital parameters and the radial velocities of Over 10 years of OGLE I-band and V-band photometry the components to disentangle the spectra (Ilijic et al. 2004). have been obtained for VFTS 352 as part of the OGLE-III FDBinary allows for three component disentangling as well and OGLE-IV projects (Udalski et al. 2008). The full photo- as light ratio variations by phase, which, as we discuss below, metric data set is discussed in Almeida et al.(2015), however will be essential for our analysis. 4 Abdul-Masih et al.

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Figure 1. Sample of normalized, pre-disentangled UV and optical spectra of VFTS 352 at a phase of approximately 0.75. Atmosphere Analysis of VFTS 352 5

The strong nebulosity in the Tarantula nebula causes neb- Table 2. Circular orbital solution from (Almeida et al. 2015) ular emission lines to be present in the observed spectra of Parameter Value VFTS 352. These cannot be properly subtracted because the P (day) 1.1241452 ± 0.0000004 FLAMES sky fibers do not sample their spatial variations orb T (HJD) 2455261.119 ± 0.003 with sufficient accuracy. The quality of the corrections fur- 0 K (km s−1) 327.8 ± 2.0 ther varies for one epoch to another as a result of small point- 1 K (km s−1) 324.5 ± 2.0 ing inaccuracies, variable seeing and atmospheric diffraction 2 (Evans et al. 2011). This presents a problem when disentan- gling as residuals from the nebular correction contaminate the profiles of lines of interest in the optical part of the spec- trum. If disentangling is performed on contaminated lines, the nebular lines will artificially narrow the final disentan- gled line profiles of the two component stars. This can affect the stellar parameters derived from the disentangled spectra, specifically temperature and surface gravity. For this reason, it is important to properly remove the contribution of the neb- ular emission lines before performing a two component dis- entangling. As mentioned above, the nebular contamination is not con- stant over the 32 spectra. The sky subtraction procedure de- scribed in Evans et al.(2011) removes a large portion of the nebular contamination but fails to remove all of it. The final spectra still contain nebular residuals that must be accounted for. To do so, our disentangling procedure consists of three Figure 2. The profile of the third light component following a three major steps: determination of average nebular line profiles, component disentangling is plotted in the upper part of the top of scaling and removal of the average nebular line profiles, and the plot, with the spline fit to the profile (after cutting the nebular finally a two component disentangling. We describe these line) overplotted. The spline-subtracted profile is shown in the mid- three steps below. dle. The bottom spectrum shows the final nebular line profile after continuum noise has been clipped. The spectra have been vertically In the following, we adopt the circular orbital solution of shifted for clarity. Almeida et al.(2015) for the disentangling (for convenience, the orbital elements are included here in Table2). This or- velocity. This assigns all signals without radial velocity vari- bital solution was obtained through a full Wilson Devinney ations to the third component. Since VFTS 352 is an over- fit of both the V and I band OGLE photometry as well as contact system, there are regions of the envelope which have the 32 radial velocity points obtained from the TMBM pro- radial velocity variations very close to zero, so some of this gram. More recently, Almeida et al.(2017) also derived an signal will be included in the disentangled third component orbital solution of this system based on 37 radial velocity spectra. Because we are only concerned with the shape of points, however this did not take the photometric informa- the nebular line profiles, we remove the signal from other tion into account, and for this reason, we choose to use the sources. As illustrated in Fig.2, this is done by selecting solution of Almeida et al.(2015). It is important to note that a small portion of the third light spectra around each of the in both Almeida et al.(2015, 2017) the radial velocities were nebular lines and then fitting a spline to the rest of the spec- determined by fitting Gaussian profiles to each component, tra. We then subtract the spline from the original data, which with the constraint that the Gaussians for each component yields the profiles of the nebular lines. Finally, we remove were identical for all phases. For an overcontact system, this the noise for the regions outside of the nebular line profiles method does not take into account the light ratio variations using the same cuts that were used before the spline was fit. throughout the orbit, which can lead to minor uncertainties This gives the final nebular line profiles. in the final radial velocities. 3.2. Removal of Nebular Lines 3.1. Nebular Line Profile Determination The second step of the disentangling procedure involves The first step of the disentangling procedure involves the the removal of the nebular lines. Using the radial velocity determination of the average nebular line profiles. This curve and the results of the three component disentangling can be accomplished using a three component disentangling from the previous step, we reconstruct each of the 32 origi- where the third component is given a constant, null Doppler nal spectra using the spectra of the primary component, sec- 6 Abdul-Masih et al.

Figure 3. UV and optical disentangled primary (top) and secondary (bottom) component spectra for VFTS 352 with prominent diagnostic lines labeled. The primary spectra have been vertically shifted for readability. Atmosphere Analysis of VFTS 352 7 ondary component, and the spline fit of the third component. Table 3. Summary of the diagnostic line list. The main identifier is Then, for each phase, we subtract the reconstructed spectra given in Col. 1. Since some lines contain blends, the components from the original spectra. Since the splines do not contain the contributing to each lines are listed in Col. 2 while the adopted fit- ting range is provided in Col. 3. nebular lines, the only signals seen in the residuals of the sub- traction should be from the nebular lines. Since the nebular Line Identifier Components λ Fitting Range contributions are not constant in strength across the 32 orig- (Å) inal spectra, the final nebular line profiles generated in the Hδ H i, He ii,N iii, Si iv 4088.3 – 4117.5 previous section need to be scaled for each spectra. Since the Hγ H i, He ii, Si iv 4325.4 – 4360.0 nebular lines are so sharp, each spans at most 3 or 4 pixels, He i 4026 He i, He ii 4022.8 – 4035.9 slight wavelength shifts can affect the line profile. Thus, we He i 4387 He i 4384.8 – 4399.0 perform a least squares minimization to fit the nebular line He i 4471 He i 4469.6 – 4481.1 profile to the residuals of the subtraction by leaving the scale He ii 4200 He ii,N iii 4194.9 – 4212.0 factor and wavelength shift as free parameters. Using the re- He ii 4541 He ii 4537.0 – 4553.9 sults of the minimization, we subtract the fitted nebular line C iii 1176 C iii 1174.3 – 1178.4 profiles from the original spectra. The results are the final C iii 1620 C iii 1619.5 – 1623.5 spectra that we use for the two component disentangling. C iv 1169 C iv 1167.7 – 1171.9 C iv 1548 C iv 1536.4 – 1565.6 3.3. Two Component Disentangling C iii 4069 C iii 4066.5 – 4078.5 The third and final step in the disentangling procedure is N iii 1750 N iii 1747.0 – 1757.0 the two component disentangling. The final spectra resulting N iv 1718 N iv 1715.4 – 1723.0 from the nebular line removal are used as the input spectra N iv 4058 N iv 4055.5 – 4067.5 for the two component disentangling. The orbital parameters O iv 1340 O iv 1337.4 – 1347.0 and Doppler velocities are set to those derived from Almeida O v 1371 O v 1369.0 – 1373.5 et al.(2015) and are held constant, and the light ratios are Si iv 1393 Si iv 1393.0 – 1397.0 calculated from the photometric data. To avoid numerical Si iv 1402 Si iv 1402.0 – 1405.9 issues, the spectra are disentangled in ∼20 Å-wide sections for the UV data and ∼100 Å-wide sections for the optical and the resulting spectra are stitched back together after dis- the primary component is hotter than the secondary. Addi- entangling. Due to the width of the Lyman alpha line, we tionally, the wings of the Hδ lines are asymmetric in the sec- remove it from our analysis, as it could not be disentangled ondary component while they appear symmetric in the pri- in sections as per our standard methodology. The final re- mary. sults of the disentangling procedure consist of two spectra, 4. ATMOSPHERIC ANALYSIS one for each component, which are displayed on Fig.3. Af- ter disentangling, the spectra have signal-to-noise ratios per In order to determine the atmospheric and wind parame- resolution element of ∼600 and ∼530, respectively, in opti- ters, as well as the surface abundances for each component cal. The UV signal-to-noise ratios are ∼23 and ∼21 for the star, we adjust the disentangled spectra with synthetic spec- primary and secondary stars respectively. tral line profiles generated by the stellar atmosphere code Reconstructing the phased spectra and comparing them to fastwind. fastwind is a 1D NLTE radiative transfer code for the observed spectra show minimal signal in the residuals single stars that accounts for the expanding atmosphere and above the level of the noise. No definite structure can be seen is suitable for the analysis of OBA stars (Puls et al. 2005). in the residuals aside from small imperfections in nebular Given a set of physical and atmospheric parameters, fastwind line removal indicating that the disentangling was successful. computes the model atmosphere and wind structure as well as Slight variations in spectral line residuals from one epoch to spectral line profiles from selected (so-called ”explicit”) ele- another can be seen in He i λ4471 and may be related to the ments, in our case H, He, C, N, O, Si and P (Puls et al. 2005; presence of the Struve-Sahade effect (Struve 1937; Sahade Rivero Gonzalez´ et al. 2012). fastwind, however, does not 1959; Linder et al. 2007). The amplitude of the effect is lim- have any fitting capabilities so a genetic algorithm is wrapped ited to about 1.5% of the continuum and does not seem to be around it (Charbonneau 1995). This technique, originally visible in other spectral lines. developed by Mokiem et al.(2005), allows for an e fficient The disentangled spectra of the two components are very exploration of the 11-dimension parameter space that is rele- similar at first sight. The primary component however dis- vant for our specific objects. plays weaker He i lines while the He ii lines for both com- 4.1. Genetic Algorithm ponents appear comparable. Qualitatively, this implies that 8 Abdul-Masih et al.

As the name suggests, genetic algorithms mimics how nat- • Microturbulence: We adopt a new depth-dependent ural selection works in nature. Given a population, only the microturbulence prescription in the formal solution, fittest individuals survive and reproduce. The offspring then which now uses a value that increases linearly with have a combination of the genes from the parents and again wind velocity from a fixed photospheric value: only the fittest members of the new generation will survive ph and reproduce. This cycle continues, eventually leading to a vturb = max(vturb, 0.1v) (2) population of individuals that are significantly fitter than the original population. This concept can be applied to create an ph where vturb is the photospheric microturbulent velocity algorithm that works in the same way. In a genetic algorithm, and v is the wind velocity. This prescription has been the parameters used to calculate the model are analogous to chosen to simulate the effects of the inhomogeneous the genes and the chi square of the fit is used to calculate a wind-structure on the P-Cygni line profiles, in particu- fitness metric. The fitness metric F is defined as lar the observed black troughs and the blueward exten-  −1 sion of such profiles beyond the terminal wind speed XN  F ≡  χ2  (1) (see, e.g., Hamann 1980; Lucy 1982; Prinja et al. 1990;  red,i i Puls et al. 1993) where N represents the total number of spectral lines being 2 th • Adjusted parameters: we expand our parameter set, fit over and χred,i represents the reduced chi square of the i spectral line (Mokiem et al. 2005). The reduced chi square is which now contains 11 fitting parameters. With the discussed in further detail in Section 4.2. addition of UV lines, we are able to directly constrain An initial population is created randomly across the param- wind parameters such as the terminal wind velocity eter space. The parameters from the models with the highest and the exponent of the wind acceleration law. Fur- fitness are combined to form the next generation. In addi- thermore, with the addition of more explicit elements tion, transcription errors and mutations are introduced (i.e. we can now attempt to constrain the abundances of car- switching two digits, deleting a digit, etc.) allowing the al- bon, nitrogen, oxygen and silicon. Our parameters and gorithm to efficiently explore the parameter space and find a the corresponding fit ranges can be found in Table4 best fit solution (Charbonneau 1995; Mokiem et al. 2005). and more details on each individual parameter and how This method has already been used to analyze the optical they qualitatively affect the final synthetic spectra can spectra of other O-type stars from various instruments (Mok- be found in AppendixA. AppendixA also discusses iem et al. 2006, 2007; Tramper et al. 2011, 2014; Ram´ırez- other parameters that affect the final synthetic spectral Agudelo et al. 2017), however this is the first time that it is profile, for which we do not fit. These parameters in- applied to UV and optical data simultaneously. clude microturbulence, macroturbulence, the inclusion We make several modifications and improvements to the of X-rays and clumping. genetic algorithm used in previous studies, however the fit- ting method and framework remain the same. • Luminosity anchor: Previous uses of this genetic al- gorithm approach used either the V- or Ks-band mag- • fastwind: The first major update is we use the most nitudes as luminosity anchors to compute the stellar recent available version of fastwind (version 10.3; radii. Here we adopt the radii of the components as Sundqvist & Puls 2018). With this update, we uti- derived from the light curve analysis of Almeida et al. lize a larger number of explicit elements than previ- (2015). ously, which includes hydrogen, helium, carbon, ni- trogen, oxygen, phosphorus and silicon (for nitrogen, • Population size: Most previous works used a popula- we use the model atom from Rivero Gonzalez´ et al. tion size of 78 individuals. Because of the larger set (2012), and for C, O, Si, and P, we use the database of parameters explored here, we increased our popu- from Pauldrach et al.(2001)). Additionally, fastwind lation size to 238 individuals. This values was chosen now supports treatment of UV lines. after several tests investigating the convergence of the • Line list: we modified the line list to include these new fitting process. With such a population size, most fits elements as well as the extended wavelength range. converged within 50 to 70 generations while we let the Some lines used in previous studies were removed as algorithm run for about 170 generations to ensure suf- they were either not present or outside of our wave- ficient mapping of the global optimum. This is indeed length coverage. Our full line list can be found in Ta- needed to derive proper confidence intervals on the fit- ble3 and include 24 spectral lines of H, He, C, N, O ted parameters as described in Sect. 4.2. and Si spread over 19 spectral regions. Atmosphere Analysis of VFTS 352 9

Table 4. Summary of the GA parameter set used for fitting.

Parameter Symbol Fitting Range unclumped 2.0 Effective temperature (K) T 39000 – 47000 clumped h i eff porosity Surface gravity cm s−2 log g 3.5 – 4.5   Projected rotational velocity km s−1 v sin i 200 – 400 1.5 h −1i Mass loss rate M yr log M˙ −8.0 – −6.0

Velocity field exponent β 0.5 – 4.0 1.0  −1

Terminal wind speed km s v∞ 500 – 4000 Normalize Flux

He surface abundance εHe 0.05 – 0.3 0.5 C surface abundance εC 6.0 – 9.0

N surface abundance εN 6.0 – 9.0 0.0 O surface abundance εO 6.0 – 9.0 1540 1545 1550 1555 1560 Si surface abundance εSi 6.0 – 9.0 Wavelength (Å)

Figure 4. Two fastwind synthetic spectra with identical parameters 4.2. Error Calculation except for the clumping factor, one with fcl = 1 (black) and one with f = 10 (red) are plotted to demonstrate the indirect effect of clump- We use the same error calculation techniques described cl ing (due to increased recombination) on the C iv λ1548 resonance in Tramper et al.(2011, 2014) and Ram ´ırez-Agudelo et al. line. Another synthetic spectrum (green) with the same parameters 2 (2017). The first step is to normalizing the overall χ val- as the clumped model as well as porosity in velocity space included 2 2 ues such that the lowest χ satisfies χred = 1. This implicitly is plotted for comparison (using a velocity filling factor fvel = 0.3) assumes that the best model provides a satisfactory fit to the to show that the inclusion here of velocity-porosity counteracts the data. This is done to ensure that the final error bars are not effects of optically thin clumping. The parameters used for these computations can be found in the primary model with χ2 column influenced by over- or under-estimation of the errors in the min in Table5. flux values. The next step is to calculate the probability (P) that the observed re-normalized χ2 is not due to statistical red that the bridge of overcontact systems should be significantly fluctuation. This probability is given by P = 1−Γ(χ2/2, ν/2), cooler than the poles (von Zeipel 1924), meaning that the where Γ is the incomplete gamma function and ν is the de- spectral contribution from this region is probably very dif- grees of freedom. Models with P ≥ 0.05 are considered ac- ferent from that of the poles. Thus, we would expect to see ceptable models and the range of parameters of the accepted slight temperature and surface gravity variations as a function family of solutions are adopted as the 95%-confidence in- of phase as possibly suggested by residual variation in, e.g., terval. As for all χ2-fitting methods, all models that satisfy the He i λ4471 line as discussed above. From a PHOEBE P ≥ 0.05 represent the data in a statistically indistinguishable model (Prsaˇ et al. 2016) corresponding to the light curve so- way and are thus considered statistically equivalent. lution of Almeida et al.(2015), we estimate temperature dif- 4.3. Framework and Assumptions ferences of the order of 5% between the pole and the equator and 30% between the pole and the bridge, however, the sur- In this section, we acknowledge two main assumptions that face area subtended by these regions account for a very small form the framework of the present work and we discuss the portion of the total surface area and therefore these regions associated uncertainties and potential impacts on the derived do not strongly affect the results of the disentangling. These parameters. spectral differences are washed out by the disentangling pro- cedure, so that the resulting disentangled spectra are effec- 4.3.1. Non-spherical geometry tively time- and space-averaged profiles across the surface of One of the most prominent assumption probably concerns each star. It should also be noted that the disentangling pro- the geometry of the system. As stated previously, VFTS 352 cedure does not distinguish between photospheric and wind is an overcontact system so that the surface has roughly the lines, and applies the same radial velocity shifts and light ra- shape of a peanut (see Figure 3 in Almeida et al.(2015)). tios to both. This non-spherical geometry is not properly accounted for The non-spherical nature of the system also presents a in the disentangling and the atmosphere fitting. Specifically, problem when performing the atmosphere fitting. fastwind is when disentangling, FDBinary assumes that the stars are well a one dimensional code, that implicitly assumes that the stars separated point sources and that the individual spectral sig- are spherical. Furthermore, fastwind is designed for single natures do not vary with phase, aside from the scaling due stars, with the assumption that there is no incident intensity to light ratio variations. The von Zeipel theorem suggests 10 Abdul-Masih et al.

1.5

1.0

0.5 C IV C III O IV O IV O V Si IV Si IV C IV C IV C III N IV N III Normalized Flux

1170 1175 1180 1340 1345 1540 1545 1550 1555 1560 1715 1720 17251750 1755 1370.01372.51392.51395.01397.51402.51405.0Wavelength (Å) 1620.01622.5

1.2

1.0

0.8 C IV C III O IV O IV O V Si IV Si IV C IV C IV C III N IV N III H He I+II N IV H He II H He I DIB He I He II

Normalized Flux 0.6

4000 4100 4200 4300 4400 4500 Wavelength (Å)

Figure 5. fastwind synthetic spectra (plotted in red) for each model in the family of statistically equivalent solutions are overplotted on the disentangled UV and optical data for the primary (blue) and secondary (black). from outside sources at the outer boundary. Neither of these rameters. The results are given in Table5 and displayed in conditions are met in this case, however it should be noted Fig.5. Figures A.1 and A.2 in the Appendix, show the χ2 that there are no three-dimensional NLTE radiative transfer distribution projected on the individual parameter axis. Here codes currently available. we first briefly discuss the results. The evolutionary status of VFTS 352 will be discussed in Sect.6. 4.3.2. Clumping The effective temperatures for both the primary and the Another important source of uncertainty comes from the secondary are in the ranges of 43000 – 45500 K and 40500 – effect of clumping on the ionization balance. Given the pa- 41500 K, respectively. The derived values for the projected rameters of this system, the increased density in the clumps rotational velocities (in the range of 240 to 310 km s−1, de- is enough to cause a noticeable shift in the ionization balance pending on the object) are in good agreement with expecta- −1 of carbon, specifically, C v recombines to form C iv. Fig- tion from tidal locking (veq sin i ∼ 270 km s ). The derived ure4 illustrates the e ffect of optically thin clumping on the surface gravity of log g ≈ 3.8 to 4.2 for both components C iv λ1548 resonance doublet. It shows how the C iv lines are normal for main sequence O-type dwarfs. The mass loss −1 become stronger, implying a lower carbon abundance for the rates of log M˙ ≈ −7.0 (in units of M yr ) is however lower same observed line strength. A similar effect on the C iv line than predicted from Vink et al.(2001) by a factor of about would also result from increasing the mass-loss rate, but in 6 for the primary and 2 for the secondary. This can be re- this case other lines in the UV (especially the N iv λ1720) lated to the fact that, with bolometric luminosities of about become too strong. On the other hand, the C iv doublet is log Lbol/L ≈ 5.2, the VFTS 352 components are at the limit expected to weaken in strength if light-leakage effects as- of delivering enough UV flux to drive a strong stellar wind sociated with porosity in velocity space are considered, as (Martins et al. 2005; Muijres et al. 2011). The low mass loss compared to the optically thin clumping model. Figure4 rate is reinforced by the fact that the C iv λ1548 wind line illustrates this, showing the C iv doublet for a comparison is not saturated, as it would be with a higher mass loss rate. model including velocity-porosity using a velocity filling fac- The β is higher than expected with values in the ranges of tor fvel = 0.3 (see Sundqvist & Puls 2018, for details). Con- 2.5 to 4 for the primary and 1.5 to 3 for the secondary. The sidering the quite large effect found on the C iv lines, these helium abundances for both components are approximately clumping-effects certainly need to be investigated in more de- 0.1, while the nitrogen and silicon abundances are smaller tail in future work. than 7.5, the carbon abundance between 7 and 8 and the oxy- gen abundance between 7.5 and 9. 5. ATMOSPHERIC ANALYSIS RESULTS The photometric analysis of VFTS 352 by Almeida et al. After disentangling, we separately ran the genetic fitting (2015) concluded that the temperature of the primary and algorithm to adjust fastwind profiles to the primary and sec- secondary are too hot for their dynamical masses when con- ondary components and determine their stellar and wind pa- Atmosphere Analysis of VFTS 352 11

Table 5. Results of the 11-parameter genetic algorithm fit of fastwind models to the primary and secondary components assuming an unclumped wind. The model corresponding to the lowest χ2 as well as the 95%-confidence intervals are given.

Primary Secondary 2 2 Parameter Model with χmin Confidence interval Model with χmin Confidence interval

T (K) 44200 42850 – 45550 40750 40600 – 41550 eff h i log g cm s−2 4.14 4.09 – 4.24 3.90 3.80 – 4.00   v sin i km s−1 268.0 240.0 – 284.0 296.0 278.0 – 310.0 h −1i log M˙ M yr −7.1 −7.25 – −6.95 −7.05 −7.50 – −7.00 β 3.30 2.30 – 4.00 1.55 1.45 – 2.95  −1 v∞ km s 2300 2000 – 2900 2600 2200 – 4000

εHe 0.10 0.085 – 0.13 0.08 0.07 – 0.10

εC 7.70 7.40 – 8.00 7.25 7.05 – 7.55

εN 6.40 6.10 – 7.55 6.20 6.00 – 7.35

εO 8.35 7.45 – 8.65 8.00 7.45 – 9.00

εSi 6.95 6.00 – 7.45 6.50 6.00 – 7.15 sidering mixing from rotation alone (42540 K ± 280 and wind. There are five X-Ray parameters needed for 41120 K ± 290 for the primary and secondary respectively). the fastwind calculations and they are described in Our results also showed increased temperatures, qualitatively Carneiro et al.(2016). For this run, we adopt the fol- agreeing with the conclusions of Almeida et al.(2015). The lowing parameter values: fX = 0.06, u∞ = 400, γx = input primary temperature that we derived is slightly higher than 0.75, mx = 20, Rmin = 1.5, which corresponds to an −8 what was found in Almeida et al.(2015). The temperature X-ray luminosity of Lx/Lbol = 2 × 10 . An X-ray −7 of the secondary is however consistent with their photomet- luminosity of Lx/Lbol = 1 × 10 is a typical value ric analysis. The only other parameter in our data set that for a main sequence star in this mass range, how- was constrained by Almeida et al.(2015) is the surface grav- ever one might expect a lower X-ray luminosity for a ity, with values of 4.18 cm s−2 ± 0.01 both the primary and system with weaker winds for a given luminosity (as secondary. The surface gravity that we derived for the pri- is the case in this system) since the X-ray luminosity mary (log g = 4.09 – 4.24) is consistent with the photometric scales directly with the star’s mass loss rate (Owocki & analysis, however the one derived for the secondary (log g Cohen 1999). The addition of X-rays caused the tem- = 3.80 – 4.00) is smaller by about 0.2 dex. It is known that perature for both the primary and secondary to drop fastwind tends to provide lower surface gravities than cmf- by around 1000 K but they still agree within error. gen (Hillier & Miller 1998), by typically 0.1 dex (Massey The surface gravity and the mass loss also decrease et al. 2013). Accounting for this difference would resolve the slightly for both but remain within error. Addition- apparent discrepancy. ally, the overall confidence intervals for β and for the oxygen abundance increase by around 0.5, both for 5.1. Robustness of the results the primary and secondary however they still largely Several tests were conducted to assess the robustness of the overlap with the confidence intervals given in Table5. resulting parameters. Since our parameter set did not include The nitrogen and carbon abundance are left unaffected. clumping or X-rays, we conduct two separate fitting runs for The resulting best-fit line profiles are left unchanged, each component where we include these parameters. Addi- but with very small variations in the C iv λ1548 line. tionally, we compute several other GA runs where we hold We thus concluded that X-ray production in the stellar certain parameters constant or remove certain lines to deter- winds do not critically affect our results, except maybe mine whether and how these affect the final solution. The of a ∼1000 K shift in Teff. obtained results are detailed below. Each fitting run uses the same base setup, parameters and line list as detailed in Sec- tion4 with the exception of the changes explicitly stated in • Inclusion of clumping - As discussed earlier, clump- the following. ing can affect both the shapes and strengths of the wind lines and can further alter the ionization balance in the • Inclusion of X-rays - As discussed in AppendixA, wind. We conduct a fitting run with a fixed clumping X-rays affect the ionization balance. We conducted a factor fcl = 10 and assuming optically thin clumps. fitting run with the X-rays option turned on in fast- The addition of such clumping lowers the temperature 12 Abdul-Masih et al.

by about 500 K but remains within error in the pri- follow the relations described in Vink et al.(2001), mary star. It raises the temperature of the secondary specifically, we set the β to 0.9, the mass loss rate to by about 500 K, though again this value is well within −6.46 and −6.77 for the primary and secondary re- error. Moreover, there is an increase in the β param- spectively and the terminal wind velocity to 2986 and eter to well above 3.5 for both the primary and the 2991 km s−1, respectively. It leads to a significantly secondary. Additionally, the carbon abundance drops worse fit of the C iv λ1548, lower Teff (by 1500 K), to around 6.8 for both the primary and the secondary, higher gravity (by 0.1 dex) as well as lower abun- i.e., significantly smaller than the confidence interval dances of N, C and O (by ∼1.0 dex) for the primary listed in Table5. The reduction in carbon abundance is star. The situation is less dramatic for the secondary, driven by the need to have an unsaturated C iv λ1548 with similar fit quality for all lines, a higher Teff (by line. All other parameters, including the mass-loss 900 K) and similarly lower N, C and O abundances. rate, are left unchanged. Fixing the stellar wind properties to the prescription of Vink et al.(2001) actually bring the largest di fferences in our entire analysis. This strengthens the hypothesis • Fixed β - The β values that we determined for both that the components of VFTS 352 have weak winds the primary and secondary determined are higher than (e.g. Martins et al. 2005; Muijres et al. 2011), for predicted. For O-type main sequence stars, β values which the Vink et al.(2001) prescription is known to between 0.8 and 1.0 are usually expected (e.g., Puls break down. Implications for the evolutionary state of et al. 1996; Muijres et al. 2011). We conducted fitting the object are discussed in the next section. This test runs with β = 0.9 to see if the high beta found here has demonstrates the importance of adjusting the abun- any significant effects on the final parameters. For both dances and wind parameters simultaneously. Without the primary and the secondary, the range of accept- including the wind parameters in the fit, large system- able temperatures narrows and drops by around 500 - atic errors in the abundances are introduced. 1000 K but remains within error. Additionally, the sur- face gravity drops by 0.1 for the primary – still within error – and by 0.2 for the secondary, which is no longer • Non-depth-dependent Microturbulence - We also within error. The mass loss rate decreases by approx- compare our prescription for the depth-dependent mi- imately 0.2 dex for the primary but remains the same croturbulent velocity with the radially fixed microtur- for the secondary. The oxygen abundance increases for bulence prescription used in previous studies (Mok- both the primary and the secondary by about 0.5 but iem et al. 2007; Tramper et al. 2011, 2014; Ram´ırez- these values are still consistent within error. The range Agudelo et al. 2017). In these studies, the microturbu- for the carbon abundance narrows slightly but not sig- lence is not depth-dependent and two separate micro- nificantly. One significant difference however is that turbulent velocities are used, one for the computation the projected rotation rates increase by about 50 km s−1 of the NLTE occupation numbers and the atmosphere and are no longer in agreement with values listed in and wind structure, and a second one for the formal Table5, nor with the projected rate of 270 km s −1 that solution used to compute the synthetic spectra. As a is expected from tidal locking. A visual inspection test, we set the microturbulence in the NLTE calcula- −1 indeed reveal that the optical lines suffer too heavily tions to 15 km s and we leave the one used in the from rotational broadening, so that this lead to a signif- formal solution as a free parameter. The resulting vturb +5 −1 icantly worse fit. As a final check, we also conducted is 50−10 km s . While most parameters remain the two additional GA runs using β = 0.9, however now same, some do change when the non-depth-dependent also (i) removing the O iv λ1340, as we have found it vturb prescription is used. For example, the temperature to be particularly sensitive to β, and (ii) removing both of the primary is lower by 1500 and 500 K for the pri- O iv λ1340 and C iv λ1548, to see whether this would mary and secondary. Moreover, β for both the primary affect the derived abundances for carbon and oxygen. and secondary now become even higher, with values However, these two runs turn out to be almost identical between 3 and 4. Additionally, while there is some to the ones where these lines are included. overlap in the confidence intervals, the carbon abun- dance for the primary is lowered by approximately 0.4 dex, suggesting some degeneracy between microturbu- • Fixed stellar wind properties - Our analysis finds lence and abundances. Qualitatively, the line profiles mass loss rates that are almost an order of magnitude from the non-depth-dependent microturbulence ac- lower than predicted by Vink et al.(2001). We thus run tually gave a closer match to the observed spectra as the fit fixing all of the wind parameters such that they compared to the line profiles from the depth-dependent Atmosphere Analysis of VFTS 352 13

microturbulence. Specifically, for the latter several of nance line that is too strong in both the emission and absorp- the UV lines that are sensitive to the wind start turning tion components. In addition to the line shown, the expected into P-Cygni profiles, making the absorption lines ap- mass loss rate also forces other wind lines in the UV to turn pear slightly blue-shifted. P-Cygni shaped. As pointed out above, a likely explanation for this is that the two stars lack the luminosity to develop a strong wind (Puls et al. 2008, e.g.). For galactic stars, Muijres • Other NLTE atmosphere codes – We also compute et al.(2011) predicted that wind driving becomes strongly cmfgen and PoWR (Grafener¨ et al. 2002; Hamann & decreased at log Lbol/L ≈ 5.2 (see also Lucy 2012). As a Grafener¨ 2003; Sander et al. 2015) models with the result of their chosen physical treatment of wind driving, this parameters adopted from the best fit solution listed in is not accounted for (self-consistently) by Vink et al.(2001). Table5 as a final test to see whether the parameters Winds in this low-luminosity regime are referred to as weak derived from fastwind are reasonable and consistent. winds. For LMC stars the boundary between strong and weak Figure6 shows the comparison between the line pro- winds will be at a somewhat higher luminosity, i.e. above the files computed with these three codes. Overall, the luminosities of VFTS 352 (of log Lbol/L ≈ 5.2). Conse- three codes are in quite good agreement. There are quently it is expected that the components of VFTS 352 have some slight deviations in some of the line profiles of weak winds. the more complex wind lines such as C iv 1548. The The expected β drastically changes the shape of the He i λ4471 to He ii λ4541 ratio computed by cmfgen C iv λ1548 line, causing it to disagree strongly with obser- and fastwind are in very good agreement while a fit vations. For the helium abundance predicted by Brott et al. with PoWR would have likely yielded a slightly lower (2011a) the lines of this species are too deep, i.e. the actual temperature to increase He i λ4471. Both the cmfgen He abundance must be lower. The expected carbon abun- and the PoWR models provide an actual better fit to the dance does not fit the C iii λ1176 and C iv λ1169 doublet. line profiles affected by the adopted depth-dependent The expected nitrogen abundance causes the N iv λ1720 line microturbulence prescription (see above), suggesting to turn P-Cygni, which clearly does not fit with the obser- that the abundances that we derived are indeed opti- vations. The expected oxygen abundance is within the error mum despite uncertainties linked to the latter prescrip- range for the secondary but too low for the primary. We con- tion. clude that these tests show that the components of VFTS 352 do not comply with evolution predictions of single massive We also perform additional tests to ensure that the errors stars. obtained are reasonable and that the values expected for cer- tain parameters can be rejected with reasonable confidence. 6. 2 EVOLUTIONARY STATUS To do this, we take the fastwind model with χmin for the primary and secondary and determine which rotation rate is Currently no appropriate grid of evolutionary models has needed to recover the current positions of the components been published to which we can compare our observations, on the HRD. For single star evolution as described by Brott however computing such a grid is beyond the scope of the present paper. Here we compare our observational con- et al.(2011a), very rapidly rotating initially 30 M stars re- cover the Hertzsprung-Russell diagram positions of the two straints to single star evolutionary tracks as well as a set of components with a rotation rate of 512 km s−1. From these MESA binary evolution models for qualitative comparison. evolution models, we extracted the abundances of helium, According to mixing theory, higher rotation rates corre- nitrogen, carbon and oxygen that correspond with the HRD spond to more mixing. Therefore, the rotation rate can be position and computed a series of additional fastwind models used as a proxy for measuring the expected efficiency of the where we change each of these abundance values to the pre- mixing processes in a star. By comparing our results with dicted one to see how the spectrum changes. We do a similar evolutionary models at different rotation rates, we can dis- exercise with β and the mass-loss rate, where we set β to 0.8 cuss whether more or less mixing (higher or lower rotation (Muijres et al. 2011) and the mass-loss rate to that expected rate) is required to reproduce the abundances and tempera- from the Vink et al.(2001) recipe. Figures 9 and 10 show tures observed. a comparison between the best fit family of solutions gener- ated from the genetic fitting and the expected values detailed 6.1. Location in the HRD above for both the primary and secondary. We first compare the effective temperatures that we derived These plots reveal that many of the theoretically predicted to models from Brott et al.(2011a) which account for rota- values result in spectral lines that are clearly incompatible tionally induced mixing through shear and Eddington Sweet with the observed profiles. The expected mass loss rate for circulations. Figure9 shows the location of VFTS 352 pri- both the primary and secondary produce a C iv λ1548 reso- mary and secondary components in the Hertzsprung-Russell C IV C III O IV O IV O V Si IV Si IV C IV C IV C III N IV N III H He I+II N IV H He II H He I DIB He I He II C IV C III O IV O IV O V Si IV Si IV C IV C IV C III N IV N III

14 Abdul-Masih et al.

1.5

1.0

0.5 Normalized Flux C IV C III O IV O IV O V Si IV Si IV C IV C IV C III N IV N III

0.5 0.0 Residuals

1170 1175 1180 1340 1345 1540 1545 1550 1555 1560 1715 1720 17251750 1755 1370.01372.51392.51395.01397.51402.51405.0 1620.01622.5 Wavelength (Å)

1.1 1.0 0.9 0.8

Normalized Flux 0.7 C IV C III O IV O IV O V Si IV Si IV C IV C IV C III N IV N III H He I+II N IV H He II H He I DIB He I He II

0.1 4000 4100 4200 4300 4400 4500 0.0 Residuals

4000 4100 4200 4300 4400 4500

Wavelength (Å)

Figure 6. fastwind, cmfgen and PoWR synthetic spectra with the same input parameters (plotted in red, green and orange respectively) for the 2 models with χmin are overplotted on the disentangled UV and optical data for the primary (top) and secondary (bottom) components. Residual plots showing observed minus model are included with the same color scheme. For convenience zero-point residual lines are plotted in gray.

diagram. For a 30 M star at LMC metallicity with initial 1.2 days) and masses (q = M2/M1 = 0.6 − 1 and M2 + M1 = abundances of 7.75, 6.90, 8.35 and 7.20 for carbon, nitro- 56.4 M , the currently-inferred total mass of the system), gen, oxygen and silicon respectively (Kurt & Dufour 1998; and assuming a rotational mixing factor of fc=0.033, which Hunter et al. 2007), rotating at 332 km s−1, the expected is a commonly adopted value (Heger & Langer 2000). At zero age main sequence (ZAMS) temperature is ∼ 40 000 K the start of the calculation the stars begin with a uniform (Brott et al. 2011a). As already discussed by Almeida et al. initial composition appropriate for young stars in the LMC (2015), both stars lay to the left of their single-star evolution- (Brott et al. 2011a). For these calculations we used the stel- ary track given their masses and rotation rates. The effect is lar evolution package MESA (version 10398, Paxton et al. most prominent for the primary star and is even stronger in 2011, 2013, 2015, 2018), with the physical assumptions from the current analysis compared to Almeida et al.(2015), with Marchant et al.(2016) for modeling the over-contact phase. differences of at least 3000 K for the primary star. Significant Mass transfer is treated as conservative. The parameters used additional mixing, e.g., more efficient rotational mixing than to compute our models are available as MESA inlist files 1. implemented in the models, is required for single star evolu- We find the binary model from our grid that most closely tionary models to reproduce the location of VFTS 352’s two matches the data is an equal-mass binary, with initial masses components in the HRD. Using enhanced rotation rates as a of 28.74 + 28.74 M and an orbital period of 1.07 days. This proxy for enhanced mixing, an initial rotation rate as high as system is initially in an over-contact configuration (i.e., both 500 km s−1 would be required for VFTS 352a (Fig.9). This stars are larger than their Roche lobes), and it soon detaches is an indication that the primary star could be evolving chem- and then once again reaches overcontact as the stars expand ically homogeneously. on the main sequence. There is no net mass transfer in this Since there is no suitable grid of binary models avail- able (see however Marchant et al. 2016), we computed a 1 set of binary-star models by varying initial periods (P=1.0- https://github.com/orlox/mesa input data/tree/master/2016 double bh Atmosphere Analysis of VFTS 352 15

logM He

2.00 logM = -6.32 = 0.8 1.04 He = 0.193 [-7.25,-6.95] 1.4 [2.3,4.0] [0.085,0.13] 1.75 1.02

1.50 1.2 1.00

1.25 0.98 1.0 1.00 0.96

0.8 0.75 0.94 Normalized Flux Normalized Flux Normalized Flux

0.50 0.6 0.92

0.25 0.90 0.4 0.00 0.88 1540 1545 1550 1555 1560 1540 1545 1550 1555 1560 4190 4195 4200 4205 4210 4215 Wavelength (Å) Wavelength (Å) Wavelength (Å) C N O 1.4 1.3 C = 6.8 N = 8.55 O = 7.16 1.4 [7.4,8.0] [6.1,7.55] 1.2 [7.45,8.65] 1.2 1.1 1.2

1.0 1.0

1.0 0.9 0.8

0.8

Normalized Flux Normalized Flux 0.8 Normalized Flux

0.6 0.7 0.6 0.6 0.4

0.4 0.5 1166 1168 1170 1172 1174 1176 1178 1180 1714 1716 1718 1720 1722 1724 1726 1338 1340 1342 1344 1346 Wavelength (Å) Wavelength (Å) Wavelength (Å)

Figure 7. fastwind synthetic spectra representing the confidence intervals for 6 parameters (plotted as red shaded areas) are overplotted on specific lines sensitive to each parameter in the disentangled UV and optical data for VFTS 352’s primary component. An extra fastwind synthetic spectra is computed for each parameter using (i) the (Vink et al. 2001) mass loss rate, (ii) β of 0.8, and (iii-vi) the expected He, C, N, and O abundances corresponding to the derived effective temperature of the star (see text). system since the stars begin with equal masses. The stars Given the high rotation rates and higher than expected ef- are in an over-contact configuration on the main sequence at fective temperatures, significant surface enrichment is ex- ≈ 1.8 Myr, at which stage this model has stellar masses, radii, pected. However, we detect no sign of strong He or N en- rotational velocities, a mass ratio, and an orbital period that richment while our data would allow us to do so (see e.g., are roughly consistent with the observationally-inferred pa- Figs.7 and8). The derived abundances of C and O are pos- rameters. It does not, however, reproduce the observed lumi- sibly subject to uncertainties related to stellar wind physics. nosities or effective temperatures. This calculation continues Due to the absence of strong optical diagnostics lines, our until the stars overflow their outer Lagrangian points, after abundance diagnostics rely on the UV-portion of the spec- which a merger can be expected to take place. trum. The derived Helium and Nitrogen abundances, how- We also tested an enhanced-mixing version of this model, ever, should be more robust. keeping all other initial parameters the same and only chang- The same comparison with single-star evolutionary mod- ing the rotational mixing factor to fc = 0.2. This model els as the one we did above for Teff can be done with sur- again predicts luminosities and temperatures lower than the face abundances. Figure 10 compares the confidence inter- observationally-inferred values for VFTS 352. This may in- vals that we obtained with the Brott et al.(2011a) 30 M - dicate more efficient mixing of helium in this system than in evolutionary models with varying rotation rates showing the our models. The evolutionary tracks associated with the best abundances of CNO elements as a function of age and range fit binary model and the enhanced-mixing binary model can of rotation rates. It also displays our two binary evolutionary be found in Fig.9. models discussed above. With the CNO abundances in agree- ment with baseline, the primary is either very young (0.5 Myr 6.2. Surface abundances at most) or does not follow the N-enrichment/C-depletion 16 Abdul-Masih et al.

logM He 1.8 1.6 logM = -6.7 = 0.8 1.04 He = 0.1129 1.6 [-7.5,-7.0] [1.45,2.95] [0.07,0.1] 1.4 1.02 1.4 1.00 1.2 1.2 0.98

1.0 1.0 0.96

0.8 0.8 0.94 Normalized Flux Normalized Flux Normalized Flux

0.6 0.92 0.6

0.4 0.90 0.4 0.2 0.88 1540 1545 1550 1555 1560 1540 1545 1550 1555 1560 4190 4195 4200 4205 4210 4215 Wavelength (Å) Wavelength (Å) Wavelength (Å) C N O 1.4 1.3 C = 7.05 N = 8.36 O = 7.89 1.4 [7.55,8.0] [6.0,7.35] 1.2 [7.45,9.0] 1.2 1.1 1.2

1.0 1.0

1.0 0.9 0.8

0.8

Normalized Flux Normalized Flux 0.8 Normalized Flux

0.6 0.7 0.6 0.6 0.4

0.4 0.5 1166 1168 1170 1172 1174 1176 1178 1180 1714 1716 1718 1720 1722 1724 1726 1338 1340 1342 1344 1346 Wavelength (Å) Wavelength (Å) Wavelength (Å)

Figure 8. Same as Fig.7 for the secondary component. scheme expected from the rotation rate and high effective temperature. While not shown in Fig. 12, the high effective temperature that we derived would suggest a He enrichment of the order of He ∼ 0.19 i.e., well above our detection limit +0.02 and in contradiction with our estimates of He ∼ 0.11−0.03. For the secondary however, neither the single stars nor the binary models can simultaneously match all the inferred sur- face abundances. The secondary shows no N-enrichment but still seems slightly C-depleted. The oxygen abundance that we derive are compatible with all single and binary evolu- tionary tracks, and hence provide no discriminatory power. The Si-abundance is not as sensitive to mixing, and given the derived error bars, we cannot constrain the evolutionary status with Si. The derived nitrogen and helium abundances are compatible with each other for the both the primary and secondary The enhanced-mixing binary model comes closer to matching the surface carbon abundance for the secondary, Figure 9. Location of VFTS 352 in the HR diagram. Single star but predicts a higher nitrogen surface abundance, which is LMC evolutionary tracks from Brott et al.(2011a) for 15, 20, 30, not seen. The binary model with a standard mixing param- and 50 M and three different initial rotation rates are indicated. The best fit binary model and the enhanced-mixing binary models eter has roughly the opposite problem in reproducing the are plotted in purple and red respectively. observations. The surface nitrogen abundances are in better agreement while the carbon abundance is more discrepant. Atmosphere Analysis of VFTS 352 17

We conclude that even chemically homogeneously evolv- mixing and that either the system is too young for mixing to ing models can not provide a good fit to the VFTS 352 sys- have significantly affected the derived surface abundances or tem. They reproduce the HRD position of the stars, but also that the mixing behaves in a different way from what theory predict a higher N and He enrichment than currently ob- predicts and suggests. served. The anomalous abundances raise many questions. Despite The fundamental limits imposed by the nuclear physics double-checking our results with both the cmfgen and PoWR of the CNO cycle mean that reproducing the inferred car- NLTE atmospheric models, complementary optical data are bon depletion at the surface of the secondary, whilst avoid- highly desirable. The inclusion of He ii λ4686 and H α would ing helium and nitrogen surface enhancement seems chal- help to lift some of the possible degeneracies with wind pa- lenging, impossible even. A possible explanation is that the rameters. Additionally, a broader optical wavelength cov- CNO abundances that we derive are somehow biased, pos- erage including several additional carbon and nitrogen lines sibly as the results of degeneracies with several wind pa- would help to confirm the derived abundances for this sys- rameters as discussed above (β, clumping, etc). As shown tem. in Sect.5, including clumping or a stronger mass loss rate Putting these findings in the context of chemically homo- would only worsen the disagreement. Data covering a wider geneous evolution, VFTS 352 still appears to be a good can- optical range would be useful to access diagnostics lines that didate for future CHE. The low metallicity, high masses and should be less affected by the wind properties. Further in- rotation rates indeed place this object in the regime where vestigation of the abundances of this system could lift the CHE is expected to occur (de Mink et al. 2008, 2009). We aforementioned degeneracy between the abundances and the cannot definitively rule out CHE based on our analysis. The wind parameters. system can be young and may not have had enough time to sufficiently mix, however its location in the outskirts of the 7. CONCLUSIONS Tarantula nebula would raise further questions. Alternatively, We performed a full atmospheric analysis of the two com- if the system is older, then the implication is that our un- ponents of VFTS 352, a massive LMC overcontact binary derstanding of the mixing processes in massive stars may be with an orbital period as short as 1.1 day. Using new phase- flawed and may need to be revisited. Either way, our pre- resolved HST observations and existing optical spectroscopy, liminary binary modeling of this system paves the way for a we disentangled UV-optical spectra of both components and more extensive investigation in a dedicated paper. adjusted fastwind NLTE atmosphere models to constrain 11 atmospheric parameters for either stars, including their effec- tive temperature and surface abundances. The two stars of their respective masses appear hotter than This work is based on data obtained at the European South- the ZAMS temperature and more luminous than expected for ern Observatory under program IDs. 182.D-0222, 090.D- single stars at LMC metallicity. The binary models we com- 0323, and 092.D-0136. Support for Program number GO puted can reproduce some of the observed orbital and stellar 13806 was provided by NASA through a grant from the parameters, however they do not reproduce the position of the Space Telescope Science Institute, which is operated by the stars on the HR diagram. Furthermore, we detect no sign of Association of Universities for Research in Astronomy, In- strong He enrichment as expected for stars of such high tem- corporated, under NASA contract NAS5-26555. We ac- peratures. Although the more strongly mixed binary model knowledge support from the FWO-Odysseus program under can roughly reproduce the observed C value in the secondary, project G0F8H6N This project has received funding from the they indicate a higher value of N and He than observed in the European Research Council under European Union’s Hori- stars. zon 2020 research programme (grant agreement No 772225) One possible explanation for the observed discrepancies is LAA thanks to Aperfeic¸oamento de Pessoal de N´ıvel Supe- binary interactions. If the system formed with two unequal rior (CAPES) and Fundac¸ao˜ de Amparo a` Pesquisa do Es- mass stars that then underwent a mass transfer event prior to tado de Sao˜ Paulo (FAPESP – 2011/51680-6, 2012/09716-6, the contact phase, we would expect a measured age discrep- 2013/18245-0) for financial support. The authors are grate- ancy between the two stars. This could cause the temperature ful to Dr. Alex Fullerton, Dr. Elena Sabbi, and Dr. Andrew difference observed between the primary and secondary and Tkachenko for useful discussion. The authors would also like may also explain the lack of abundance enhancements. This to thank the referee for their helpful comments and useful would imply that the increased temperature is not due only to discussion.

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8.25 8.25 8.25

8.00 8.00 8.00

7.75 7.75 7.75 C N 7.50 7.50 O 7.50

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APPENDIX A. PARAMETER SET DESCRIPTIONS A brief description of each of our parameters and the lines sensitive to them are listed below.

• Effective temperature (Teff) - The effective temperature affects the profiles of many lines. In the temperature regime of VFTS 352 (& 40 000K) the lines most affected in the observed optical wavelength range are the helium and hydrogen lines. In this temperature regime, slight changes in temperature have strong effects on the ionization balance of helium. Thus, the ratio of He i to He ii (e.g. He i λ4471 : He ii λ4541) is a strong temperature diagnostic; higher temperatures cause stronger He ii lines and weaker He i lines. The ratio of N iv and N v is also a valid temperature diagnostic in this temperature regime, however the nitrogen lines in the optical portion of our data set are too weak for accurate estimates. The cores of the Balmer lines are also sensitive to temperature.

• Surface gravity (log g) - The surface gravity affects the wings of the Balmer lines. A higher surface gravity will make the wings broader while a lower gravity will make the wings narrower.

• Projected equatorial rotational velocity (veq sin i) - The rotational velocity affects all of the lines in the sample. Higher rotational velocities will broaden lines while low rotational velocities will cause the lines to be narrower.

• Mass loss rate (log M˙ ) - The mass-loss rate is a wind parameter representing the mass lost in a radially supersonic wind outflow. Mass lost from Roche lobe overflow or other mechanisms are not considered. The mass loss rate most strongly affects the shape of C iv λ1548, O iv λ1340 and N v λ1243 in the UV, and of Hα and He ii λ4686 in the optical. Both Hα and He ii λ4686 are outside the TMBM wavelength range while N v λ1243 is deeply embed in the wing of Lyman alpha and is thus unusable for VFTS 352. Aside from the dominant UV-diagnostic lines, Balmer and helium lines in the TMBM wavelength range are also affected by the mass loss rate. As the mass loss rate increases, the emission from the winds fills in the absorption profiles, eventually turning them into emission lines.

• Beta (β) - Beta is a wind parameter that describes the shape of the wind velocity profile. The velocity of the wind as a function of radial distance from the surface of the star is given by a beta law, the exponent of which is our parameter:

!β bR v(r) = v 1 − ∗ , (A1) ∞ r

where b is obtained from the assumed velocity at the wind-photosphere boundary. All wind lines are affected by beta but some more than others. In our data set, the lines that are affected by beta most strongly are C iv λ1548 and O iv λ1340.

• Terminal wind speed (v∞) - The terminal wind speed defines the maximum speed of the wind. The terminal wind sets the wavelength of the blue absorption edge of saturated P-Cygni lines and affects the shape of the blue edge of unsaturated P-Cygni lines. Higher terminal wind speeds in unsaturated lines will cause the slope to be shallower while lower speeds will cause the slope to be sharper. In our sample, the only P-Cygni line is C iv λ1548 and it is unsaturated.

• Surface abundances (Helium, Carbon, Nitrogen, Oxygen, Silicon) - The five abundance parameters behave in the same manner: to strengthen the lines with higher abundances or weaken the lines with lower abundances. In practice, the abundance of each element only affects lines of that element, with the exception of He that is anti-correlated with that of H. In the main text, the abundance of helium is given by:

NHe εHe = , (A2) NH

where NHe and NH are the number densities of helium and hydrogen respectively. The abundance of the other elements is given by:

NX εX = log + 12, (A3) NH where NX and NH are the number densities of the given element and hydrogen respectively. 22 Abdul-Masih et al.

There are several other parameters that can affect the lines in our sample, however we do not fit over these. The most important of these parameters and their effects on the shapes of the lines are described below. To explore how some of these parameters affect our computations, we conducted additional fitting runs where we keep these parameters fixed, however we change the fixed value from that of the original GA run. These are indicated in the descriptions below.

• Microturbulent velocity (vturb) - A microturbulent velocity is considered in the calculation of the atmosphere and wind structure as well as in the formal solution in fastwind. The microturbulence is set to 15 km s−1 for the calculation of the atmosphere and wind structure but a depth-dependent prescription is used for the calculation of the formal solution as ph −1 described in Eq.2 (in this case vturb = 15 km s ). The microturbulence affects the shape of all lines and especially the wind lines. It primarily affects the cores of the lines, changing the line depth, but has a minor impact on the line wings. For optically thick lines, microturbulence can change the equivalent width, hence affecting the derived abundances.

• Macroturbulent velocity - Macroturbulence in principle, may affect both the line cores and wings but leaves the equivalent widths unaffected. The stellar components of VFTS 352 are however both rapidly rotating, so that the line broadening is dominated by rotation broadening. In consequence, we neglect the macroturbulence as its contribution is negligible.

• Clumping - In fastwind, optically thin clumping is parameterized via a clumping factor

< ρ2 > f = ≥ 1, (A4) cl < ρ >2 which essentially is the multiplication factor that describes how much higher the density within the clump is compared to the mean density. Thus, fcl = 1 implies a smooth uniform wind while fcl > 1 implies a non-uniform wind with localized regions of high density. Wind clumping affects different spectral diagnostics differently. As long as clumps are optically thin, diagnostics depending on the square of the density, such as Hα in hot stars, become stronger in a clumped wind than in a smooth one of the same mass-loss rate. On the other hand, diagnostics depending only linearly on density (e.g., UV wind resonance lines) are not directly affected by such optically thin clumping (though indirectly they can be affected through a modified wind ionization balance). Finally, if clumps start to become optically thick, this then leads to an additional leakage of light through porous channels (in physical and/or velocity space) in the wind. For a detailed discussion on the effect of clumping on the adopted diagnostics, see Sundqvist & Puls(2018). For our calculations, the clumping factor is set to 1.0, which corresponds to a homogeneous outflow. We conducted an additional fitting run with the clumping factor set to 10, assuming optically thin clumping.

• X-rays - The inclusion of X-rays in the fastwind calculations (Carneiro et al. 2016) affects the ionization balance, driving species to higher ionization states. This then affects the ratios between lines of different ionization states for the same element. For our calculations, we currently do not include X-Rays, however we conduct an additional GA run including an X-Ray radiation field to explore this effect further.

B. GA RESULTS Atmosphere Analysis of VFTS 352 23 models are included. The family fastwind 40 000 computed ∼ is indicated by a vertical (black) line within the shaded areas. It is also given on bottom of each 2 χ merit surface projected along the individual parameter axis. All the 2 χ 11 dimension Primary component: Figure A.1. of acceptable solutions is indicated with shaded areas while the model with the best panel. 24 Abdul-Masih et al. Same as Fig. A.1 but for VFTS 352b. Secondary component: Figure A.2.