# Properties of Galactic B[e] Supergiants. X. Refined Orbit and Fundamental Parameters of the HD 327083 Binary System

A. S. Nodyarov, A. S. Miroshnichenko, S. A. Khokhlov, S. V. Zharikov, A. T. Agishev, I. A. Gabitova, N. L. Vaidman, N. Manset

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A. S. Nodyarov, A. S. Miroshnichenko, S. A. Khokhlov, S. V. Zharikov, A. T. Agishev, et al., Properties of Galactic B[e] Supergiants. X. Refined Orbit and Fundamental Parameters of the HD 327083 Binary System. The Astrophysical Journal, 2024, 968, 10.3847/1538-4357/ad4a63. insu-04863656

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# Properties of Galactic B[e] Supergiants. X. Refined Orbit and Fundamental Parameters of the HD 327083 Binary System

A. S. Nodyarov<fnref n="1" />, A. S. Miroshnichenko<fnref n="1" />,<fnref n="2" />,<fnref n="3" />, S. A. Khokhlov<fnref n="1" />, S. V. Zharikov<fnref n="4" />, A. T. Agishev<fnref n="1" />, I. A. Gabitova<fnref n="1" />, N. L. Vaidman<fnref n="1" />, and N. Manset<fnref n="5" />

Received 2024 March 5; revised 2024 May 8; accepted 2024 May 9; published 2024 June 11

## Abstract

HD 327083 is a binary system that consists of two supergiant components and exhibits the B[e] phenomenon. In this paper, we report the determination of a new set of the system's fundamental parameters using a combination of photometric and spectroscopic data as well as the Gaia EDR3 distance. We found that the orbital period of the system is $107.68 \pm 0.02$ days. The spectral line content implies the effective temperatures of $\approx 7000$ K and $25,400 \pm 1400$ K, while the photometric variations are consistent with the radii of $\approx 106 R_\odot$ and $\approx 10 R_\odot$ for the cool and hot components, respectively. The absorption lines of the cool component show a radial velocity semiamplitude of $48.3 \pm 1.7$ km s$^{-1}$, similar to that of the emission lines that originate around the hot component. The inclination of the system to the line of sight is $47_{-20}^{+17\circ}$. Modeling of the system's evolutionary history suggests that the components have masses of $\sim 12.5 M_\odot$ and currently undergo mass transfer between them. This configuration, which takes in heating of the surface of the cool component by the radiation from the hot one, can reproduce the photometric and spectroscopic data and is in agreement with previous infrared observations of the circumbinary disk. The results of this study further confirm the hypothesis that the reason for the presence of the B [e] phenomenon in most objects is a consequence of the evolution of various binary systems.

Unified Astronomy Thesaurus concepts: A stars (5); Binary stars (154); Emission line stars (460)

## 1. Introduction

The emission-line star HD 327083 (MWC 873) was discovered in the course of the Mount Wilson survey for stars with bright hydrogen lines (Merrill & Burwell 1949). Emission lines of hydrogen and helium with P Cyg-type profiles were reported by Henize (1952), who classified the star's spectral type as B5 based on the intensity ratio of the He I 4471 Å and Mg II 4482 Å absorption lines.

Over the next four decades, rare photometric and spectroscopic observations revealed some other properties of the object, such as a high reddening $E(B-V) \sim 1.9$ mag (Kozok 1985), near-IR excess, and CO emission features (Whitelock et al. 1983). Spectral classification of the star ranged from B8 (Carlson & Henize 1979) to B1.5 (The et al. 1994). A study of emission-line profiles in the object's optical spectrum led Lopes et al. (1992) to the following physical parameters: spectral type B6 I, $M_{bol} = -10.6$ mag (using a distance of 5 kpc from the strengths of the interstellar Na I lines), and $M \approx 68 M_\odot$. Machado et al. (2001) obtained intermediate-resolution spectra of HD 327083 around the H$\alpha$, H$\beta$, and several Fe II lines and modeled the Balmer line profiles with a spherical distribution of the circumstellar gas. They suggested two different sets of fundamental parameters for the star based on the line profile fits, although their fits did not closely reproduce the profile shapes. Both models implied a very high luminosity ($\ge 10^5 L_\odot$) and mass-loss rate ($\ge 10^{-5} M_\odot$ yr$^{-1}$). The radiation

source to power the emission-line spectrum was a star with an effective temperature ($T_{eff}$) of 9000 K and a mass of $60 M_\odot$ for the larger mass-loss rate model, while the other model was based on a $40 M_\odot$ star with $T_{eff} = 19,000$ K.

In a follow-up study, Machado & de Araújo (2003) presented an optical high-resolution ($R \approx 50,000$) spectrum of the object and derived the following object parameters: log (L/L$_\odot$) = 6.0, $T_{eff} = 11,500$ K, and $\dot{M} = 8 \times 10^{-5} M_\odot$ yr$^{-1}$. From these results, the authors concluded that HD 327083 is a superluminous evolved $M_{ZAMS} \sim 60 M_\odot$ star.

At the same time, Miroshnichenko et al. (2003) reported the presence of photospheric lines of a cool secondary component and detected antiphased radial velocity (RV) variations of emission and absorption lines. They suggested that HD 327083 is a binary system and proposed two orbital solutions with periods of $\sim 55$ or $\sim 180$ days using eight spectra with a spectral resolving power of $R \sim 20,000$. The system components were classified as an early B-type and an early F-type star with the luminosities of log (L/L$_\odot$) = 5.0(4)$^6$ and 4.2(4), respectively.

The components' masses were found to be nearly equal from the close amplitudes of the RV variations of the emission and absorption lines. Also from photometric and spectroscopic data for projectionally close stars, Miroshnichenko et al. (2003) estimated a distance of 1.5(5) kpc to the system and suggested that HD 327083 represented an advanced evolutionary stage of a β Lyrae-type binary. The latest GAIA EDR3 parallax of HD 327083, $\pi = 0.41(2)$ mas, gives a distance of $d = 2.26_{-0.12}^{+0.17}$ kpc (Bailer-Jones et al. 2021).

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Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹Al-Farabi Kazakh National University, Al-Farabi Ave., 71, Almaty, 050040, Kazakhstan; aldiyar.agishev@gmail.com</footnote>

<footnote n="2">²Department of Physics and Astronomy, University of North Carolina at Greensboro, P.O. Box 26170, Greensboro, NC 27402-6170, USA</footnote>

<footnote n="3">³Fesenkov Astrophysical Institute, Observatory, 23, Almaty, 050020, Kazakhstan</footnote>

<footnote n="4">⁴Universidad Nacional Autónoma de México, Instituto de Astronomía, AP 106, Ensenada 22800, BC, México</footnote>

<footnote n="5">⁵Canada-France-Hawaii Telescope Corporation, 65-1238 Mamalahoa Hwy, Kamuela, HI 96743, USA</footnote>

<footnote>$^6$Hereafter, the number in brackets corresponds to a $1\sigma$ error.</footnote>
<table><caption>**Table 1**
Spectroscopic Observations and RVs of Spectral Lines of HD 327083</caption><thead><tr><th>Date<br>(1)</th><th>JD<br>(2)</th><th>Range (Å)<br>(3)</th><th>Obs.<br>(4)</th><th>Phase<br>(5)</th><th>RV<sub>abs</sub><br>(6)</th><th>RV<sub>FeII</sub><br>(7)</th></tr></thead><tbody><tr><td>2000/07/19</td><td>1744.630</td><td>3880–5845</td><td>Leon</td><td>0.589</td><td>−5(5)</td><td>...</td></tr><tr><td>2000/07/21</td><td>1746.580</td><td>5300–8450</td><td>Leon</td><td>0.607</td><td>−1(7)</td><td>−15(1)</td></tr><tr><td>2002/03/03</td><td>2336.830</td><td>5595–8740</td><td>Leon</td><td>0.089</td><td>−56(9)</td><td>25(6)</td></tr><tr><td>2002/05/23</td><td>2417.630</td><td>5710–8750</td><td>Leon</td><td>0.839</td><td>13(5)</td><td>−82(8)</td></tr><tr><td>2002/05/24</td><td>2418.710</td><td>5670–8740</td><td>Leon</td><td>0.849</td><td>13(4)</td><td>−79(6)</td></tr><tr><td>2002/06/23</td><td>2448.590</td><td>5800–9100</td><td>Leon</td><td>0.127</td><td>−62(5)</td><td>23(1)</td></tr><tr><td>2002/06/24</td><td>2449.740</td><td>5800–9050</td><td>Leon</td><td>0.138</td><td>−64(5)</td><td>21(5)</td></tr><tr><td>2002/06/25</td><td>2450.700</td><td>5800–9050</td><td>Leon</td><td>0.146</td><td>−67(5)</td><td>22(4)</td></tr><tr><td>2002/09/25</td><td>2543.580</td><td>5400–6720</td><td>McD</td><td>0.009</td><td>−36(5)</td><td>−27(2)</td></tr><tr><td>2006/08/05</td><td>3952.750</td><td>3960–10,000</td><td>CFHT</td><td>0.096</td><td>−57(3)</td><td>20(4)</td></tr><tr><td>2007/07/24</td><td>4285.907</td><td>3960–10,000</td><td>CFHT</td><td>0.190</td><td>−75(3)</td><td>19(4)</td></tr><tr><td>2008/07/19</td><td>4666.880</td><td>4300–10,000</td><td>CFHT</td><td>0.728</td><td>21(7)</td><td>−82(5)</td></tr><tr><td>2010/03/12</td><td>5267.847</td><td>3760–9460</td><td>ESO</td><td>0.309</td><td>−73(4)</td><td>20(3)</td></tr><tr><td>2010/03/13</td><td>5268.844</td><td>3760–9460</td><td>ESO</td><td>0.318</td><td>−72(3)</td><td>20(3)</td></tr><tr><td>2015/10/12</td><td>7307.522</td><td>3960–9200</td><td>ESO</td><td>0.251</td><td>−78(4)</td><td>23(4)</td></tr><tr><td>2015/10/15</td><td>7311.495</td><td>3960–9200</td><td>ESO</td><td>0.288</td><td>−75(2)</td><td>23(3)</td></tr><tr><td>2016/04/13</td><td>7491.670</td><td>3930–9200</td><td>ESO</td><td>0.961</td><td>−17(3)</td><td>30(5)</td></tr><tr><td>2016/07/28</td><td>7597.610</td><td>3880–9200</td><td>ESO</td><td>0.945</td><td>−13(3)</td><td>33(10)</td></tr><tr><td>2017/08/26</td><td>7991.608</td><td>3920–9200</td><td>ESO</td><td>0.604</td><td>−1(2)</td><td>−64(11)</td></tr><tr><td>2017/08/29</td><td>7994.610</td><td>3950–9200</td><td>ESO</td><td>0.632</td><td>7(3)</td><td>−64(10)</td></tr><tr><td>2017/09/02</td><td>7998.534</td><td>3820–9200</td><td>ESO</td><td>0.669</td><td>16(3)</td><td>−68(10)</td></tr></tbody></table>

Note. Column information: (1)—date of the observation (year/month/day); (2)—heliocentric Julian Date (JD−2450000+); (3)—informative range of each spectrum in Å; (4)—abbreviated name of the observatory; (5)—phase; (6)—RV of absorption lines in km s⁻¹; (7)—RV of several emission lines of Fe II in km s⁻¹. Uncertainties of both the emission and absorption line RVs are shown in brackets.

Later, Wheelwright et al. (2012a, 2012b) observed HD 327083 at the VLTI with the spectro-interferometric instrument AMBER and the spectrograph CRIRES in the K band at a medium (R~1500) and high (R~50,000) resolution, respectively. The ¹³CO bandhead emission was detected confirming that HD 327083 is a post-main-sequence object. They also found that the relative sizes of the continuum and the Brγ emitting regions were different from those of a single B[e] supergiant, where the standard dual outflow scenario was thought to apply. Using geometrical models, they found that the spatially unresolved binary system is surrounded by a circumbinary Keplerian disk with an inner radius ≈3.0(0.3) au that is viewed at an inclination angle of 48°5.

The above conclusions agree with the results of Maravelias et al. (2018), who studied eight Galactic B[e] supergiants with detected CO emission. These authors also searched for periodic photometric variations using the ASAS-3 survey data (Pojmanski 2002) and reported nine periods found through Fourier analysis of the light curve at a 99% confidence level, but have not explored them further.

The abovementioned studies indicate that HD 327083 is a complex object, whose properties have not been well defined. This prompted us to undertake a new study of the object based on a larger set of high-resolution spectra and optical photometric monitoring aimed at refining the fundamental parameters of the system's components as well as determining orbital parameters and evolutionary status.

## 2. Observations

This study is based on several different sets of spectra taken over a period of nearly 15 yr. The first eight of them were reported in Miroshnichenko et al. (2003) and include seven

spectra taken at the 2.1 m telescope of the Complejo Astronomico El Leoncito (Argentina, R~15,000) in 2000–2002 with the échelle-spectrograph REOSC mounted in the Nasmyth-2 focus and equipped with a 2K×2K CCD-chip and one spectrum taken at the 2.1 m Otto Struve telescope of the McDonald Observatory (Texas, USA, R = 60,000) in 2002 with the Sandiford spectrograph (McCarthy et al. 1993).

The rest of the collection includes three spectra taken at the 3.6 m Canada-France-Hawaii Telescope (CFHT; Maunakea, HI, USA, R = 65,000) with the ESPaDOnS spectropolarimeter (Manset & Donati 2003) in 2006–2008 and reduced with the Upena and Libre-ESPRIT software packages (Donati et al. 1997), as well as nine spectra taken at the 2.2 m telescope of the European Southern Observatory (ESO; Chile, R = 40,000–50,000) with the FEROS and UVES spectrographs in 2010–2017 and retrieved from the ESO data archive.<fnref n="7" /> Information about all the spectroscopic observations (16 spectra) from 2000 to 2017 is shown in Table 1.

Photometric observations of HD 327083 in the V- and g bands were taken from the ASAS-3 (2003–2010; Pojmanski 2002) and ASAS SN (2014–2022; Kochanek et al. 2017) surveys.

## 3. Data Analysis

### 3.1. Optical Spectrum

The optical spectrum of HD 327083 is dominated by absorption lines of mostly neutral metals, which were first reported by Miroshnichenko et al. (2003), who provided a list of 73 such lines between 4710 and 8085 Å. This feature unambiguously indicates the presence of a cool star in the

<footnote n="7">⁷ https://www.eso.org/UserPortal/</footnote>
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 1.** Comparison of the spectrum of HD 327083 taken at ESO on 2010 March 12 and that of α Per taken with the spectrograph NARVAL at the Observatoire Midi-Pyrénées on 2016 February 19. Both spectra are normalized to the local continuum. The left panel shows part of a shorter-wavelength region around 4560 Å, and the right panel shows a longer-wavelength region around the oxygen triplet at 7770–7775 Å. The spectra are shifted to the same wavelength scale, and the spectrum of HD 327083 is shifted up by 0.15 $I_c$ in both panels.</figcaption></figure>

object that was earlier classified as a B-type star (for the history of the spectral type assignments see Machado et al. 2001), which is responsible for the emission-line content.

Using the Fourier analysis technique to derive the projected rotational velocity ($v \sin i$) from absorption line profiles in the highest-resolution spectra of HD 327083 taken at ESO and CFHT, we consistently got $v \sin i = 25(5)$ km s$^{-1}$. The presence of strong diffuse interstellar bands (DIBs) and a strong absorption associated with the oxygen triplet at 7770–7775 Å suggest a high luminosity of the cool component. We compared the absorption-line content with those of A- and F-type supergiants in a range of $T_{\text{eff}}$ from 6000 to 8000 K using data from the archive<fnref n="8" /> of spectra taken with the ESPaDoNS and NARVAL spectrographs ($R \sim 65,000$).

The best match was found with the spectrum of α Persei, whose fundamental parameters were recently determined by Kovtyukh (2007), Lyubimkov et al. (2010), and Luck (2014) and can be averaged as $T_{\text{eff}} = 6450(150)$ K and $\log g = 1.8(1)$. Also, $v \sin i = 17.1(1.0)$ km s$^{-1}$ of α Persei (De Medeiros et al. 2002) is close to that of the object (see Figure 1). Comparing the absorption-line strengths in the spectra of HD 327083 and α Persei, we estimated the contribution of the cool component to the total flux at ~60% near the $H\alpha$ line and at ~50% in the V band.

At the same time, it is clearly seen (especially in Figure 1) that the absorption-line strengths in the spectrum of HD 327083 decrease toward shorter wavelengths compared to those of α Persei indicating the presence of a blue continuum. Taking into account possible differences in the chemical compositions between the object and the comparison stars, we conservatively estimate the fundamental parameters of the cool component of HD 327083 as $T_{\text{c,eff}} = 6500–7000$ K and $\log g_c = 1.5(5)$.

The emission-line spectrum of HD 327083 contains lines of hydrogen (Balmer and Paschen series), He I, Fe II, and Ca II (see Figures 1–3 in Miroshnichenko et al. 2003). The He I lines are weak and indicate that the hot component has a $T_{\text{h,eff}}$ of ≥20,000 K (see Miroshnichenko 1996). The absorption-line spectrum of the hot component is strongly veiled by the spectrum of the cool component. We failed to identify any absorption line that can be attributed to the hot component even in the blue spectral region, where it is supposed to be comparable with the cool one. This suggests that the hot component has a high $v \sin i$. An upper limit for $T_{\text{h,eff}}$ can be estimated as ~28,000 K from the absence of high excitation species, such as He II and Fe III (Schmutz et al. 1991).

The interstellar features include DIBs, such as 5780, 5796, 6613, and 8620 Å as well as the lines of Na I at 5889 and 5895 Å. Using the relationships between the equivalent width (EW) of the DIB at 5780 Å and the color-excess $E(B-V)$ derived by Herbig (1993) and Kos & Zwitter (2013), we determined that $E(B-V) \approx 1.7(2)$ mag. Taking into account the GAIA distance, the object's apparent brightness, and the interstellar extinction we estimated the luminosity of the cool component to be $\log L_2/L_{\odot} \approx 4.1–4.8$.

We should note that the spectrum presented by Machado & de Araújo (2003) looks different from all our spectra. It does not clearly show any absorption lines of the cool component but contains some helium lines in pure absorption instead. We do not attempt to explain these discrepancies here, as this spectrum is unavailable to us. We can only add that according to Machado & de Araújo (2003) it has a relatively low signal-to-noise ratio of 34 at $\lambda \sim 5500$ Å, which is lower than in most of our spectra.

<footnote n="8">⁸ http://polarbase.irap.omp.eu/</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 2.** Variations of the spectral line positions of HD 327083 with the orbital phase. The phases are shown near each spectrum. The intensity is normalized to the local continuum, and the wavelength scale is heliocentric. The spectra are shifted by 0.2 $I_c$ with respect to each other. The dates of observations that correspond to the orbital phase are listed in Table 1.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 3.** Periodograms derived by the Fourier analysis of the absorption line RVs (upper panel) and ASAS SN V- and g-band photometry. The g-band data were shifted to match the V-band data in the overlapped time region. A linear trend was removed from the joint data set.</figcaption></figure>

### 3.2. RV Variations

Fourier analysis of the temporal variations of the absorption lines RVs (see Figure 2 and Table 1) showed the highest peak in the power spectrum at 107.7 days (Figure 3). A subsequent search for the orbital solution (Equation (1)) used this period as an initial approximation:

$$V_r = \gamma + K \cdot (\cos(v + \omega) + e \cdot \cos \omega), \quad (1)$$

where $V_r$ is the RV, $\gamma$ is the systemic RV, $K$ is the RV semiamplitude, $v$ is the true anomaly, $e$ is the orbital eccentricity, and $\omega$ is the argument of periastron.

The best fit was found for a circular orbit ($e=0$) with the following parameters: orbital period $P=107.68(2)$ days, RV semiamplitude of the cool component $K_c = 48.3(1.7)$ km s$^{-1}$, $\gamma = -28.8(1.2)$ km s$^{-1}$, and the epoch of a superior conjunction of the cool component JD$_0 = 2,451,681.2(7)$.

The corresponding mass function is

$$f(m) = \frac{M_h^3 \sin^3 i}{(M_h + M_c)^2} = \frac{P_{\text{orb}} K_c^3}{2\pi G} = 1.26(14) M_{\odot} \quad (2)$$

The emission line RVs were measured by averaging from those of several Fe II lines (e.g., 6416, 6432, and 6456 Å) and Paschen lines (e.g., P12, P14, P19, and P20) that are almost undistorted by lines of the cool component. When the emission lines were significantly contaminated by those of the cool component (near phases 0.0 and 0.5), we divided them by the spectrum of $\alpha$ Per scaled with the continuum contribution of the hot component.

They vary in antiphase to those of the absorption lines (see Figures 2 and 4, top panel). However, due to the weakness and broadness of most of the emission lines, their RVs are less accurate (5–7 km s$^{-1}$). Their profiles may also be affected by the wind/Envelope’s kinematics. This is why we consider the emission-line RVs shown in Figure 4 to have a lower statistical weight than those of the absorption lines. Nevertheless, the very similar RV amplitudes of the absorption and emission lines ($K_h \lesssim 55$ km s$^{-1}$) imply a components’ mass ratio close to $q \equiv M_c/M_h \equiv K_h/K_c \approx 1$ suggested by Miroshnichenko et al. (2003) and unchanged by nearly doubling the number of used spectra. Following the latter result, the mass function gives a direct relation between the components’ masses and the system inclination (see Figure 5) where $q = 0.96–1.16$ was selected.

### 3.3. Brightness Variations

The photometric data of HD 327083 retrieved from the ASAS-3 and ASAS SN surveys (see Section 2) were analyzed for periodicity using Fourier analysis. The dominant peaks in the power spectra of both data sets were found at the same orbital period as that detected in the RV data (see bottom panel of Figure 3).

The light curve folded with the orbital period is shown in the middle panel of Figure 4. The phase curve demonstrates sinusoidal variations with a full amplitude of 0.2 mag and a relatively large scatter (~0.1 mag) of individual data points. The minimum brightness corresponds to the orbital phase 0.5 when the cool component is located between the observer and the hot component.

## 4. System Components Evolution

Taking into account the information derived from the observational data, we tried to model the evolutionary history using single-star tracks. For this purpose, we used the 1D stellar evolutionary code MESA (version 23.05.1; Paxton et al. 2011, 2013, 2015, 2018, 2019; Jermyn et al. 2023). Calculations of the evolutionary tracks for the metallicity $Z=0.02$ show that stars only with masses of ~12–14 $M_{\odot}$ can evolve to the range of effective temperatures and luminosities derived for the cool component of the system in Section 3.1 (see Figure 6). Given the system’s orbital period, more massive stars would fill their Roche lobes at higher temperatures, while less massive stars achieve the expected luminosity range at lower effective temperatures. The radius of an evolved star with $M \lesssim 12 M_{\odot}$ at $T_{\text{eff}}=6750(250)$ K will be only about half of the cool component Roche lobe size. If such an evolved component has a mass lower than $12 M_{\odot}$, it would fill its Roche lobe at a lower temperature than 6750 K.
<figure><img src="image_9.png" /><figcaption>**Figure 4.** The RV curve (top panel), the light curve (middle panel), and *O-C* diagram for the light curve model of HD 327083 (bottom panel). The RVs of the absorption lines of the cool component and those of the emission lines of the hot component are shown by open and filled circles, respectively. The middle panel shows the observed (filled circles) and model (solid line) V-band light curves. The difference between observed and calculated magnitudes (*O-C*) values are expressed in units of a typical uncertainty of the photometric data (see error bars in the middle panel). The model shape of the secondary and primary and the brightness distribution over its surface as visible by an observer at phases 0.0, 0.25(-0.75), 0.5, and 0.75 are shown at the top of the plot. The color scale corresponds to the effective temperature as shown in Figure 8.</figcaption></figure>

Therefore, a combination of two stars with an initial orbital period of ~107 days and close but not equal masses can reproduce the system's current state. Using MESA, we searched for an evolutionary scenario for the binary system that satisfies the following conditions: the observed orbital period is 107 days; the current mass ratio of the system components is $q = M_c/M_b \approx 1$; and the cool component is close to filling its Roche lobe and has $T_{\text{eff}} \sim 6500$ K.

We calculated a set of models for a system of two massive stars initially at zero-age main sequence with solar metallicity. The more massive star has an initial mass of 12–14 $M_\odot$, while the mass ratio was considered within a range of $M_1/M_2 = 1.05–1.50$, where $M_1$ is the initially more massive component that will become the currently cool component. In our calculations, we chose a mass increment of 0.5 $M_\odot$ for the more massive and faster-evolving component and of 0.05 for the mass ratio. We

found solutions for a system with the more massive component masses $M_1 = 12.0–13.0 M_\odot$ and $q = M_1/M_2 = 1.05–1.20$, which can evolve to the properties that are close to the observed system parameters.

In Figure 7, we show an example of the evolutionary track of such a system (left panel) and a part of it that is close to the current state of HD 327083 (right panel). The latter is marked by a yellow filled circle in the left panel of Figure 7. In this scenario, the system starts evolution with the following parameters: $M_1 = 13.0 M_\odot$, $M_2 = 12.0 M_\odot$, and $q = 1.08$. The more massive star size gets close to filling its Roche lobe after ~13.6 × 10⁶ years, while its $T_{\text{eff}}$ decreases to ~7000 K, and it starts transferring matter to the other component. The initially less-massive component gets hotter, while its radius keeps increasing. The components' masses become equal at the currently observed moment.
<figure><img src="image_10.png" /><figcaption>**Figure 5.** Relationship between the mass of the hot component $M_h$ and the system inclination angle $i$ for $0.96 \lesssim q \lesssim 1.16$. The colors show the relationship between the masses of the components and the mass ratio for different system inclinations. The area shown by the solid gray lines corresponds to systems that can reproduce the luminosity of the cool component in the range $4.1 \lesssim \log L_2/L_{\odot} < 4.8$. The thin light blue solid line corresponds to $q = 1.0$.</figcaption></figure>

It is a relatively short stage (tens of thousands of years) in the system's evolution. After that time ($+ \approx 10^6$ years) the mass transfer continues, the temperature of the cool component falls below 5000K, and the orbital period increases to $\sim 700$ days. The mass of the cool component drops to $\approx 4.2 M_{\odot}$, while that of the hot component increases to $\approx 21 M_{\odot}$. At the end of the system's evolution, the more massive component will become a supernova, and the less massive one will be converted into a red supergiant.

## 5. Light-curve Modeling

We analyzed the photometric data with a code developed by Zharikov et al. (2013) in which only the two stars contribute to the total brightness of the system. The limb-darkening (Claret et al. 2012) and the illumination of the cool component by the hot one are accounted for.

The following equation describes the temperatures at the opposite sides of the cool component of the system:

$$T_d = T_n \left[ 1 + \eta \times \cos(\alpha_{\text{norm}}) \frac{R_h^2 T_h^4}{a^2 T_n^4} \right]^{1/4}, \quad (3)$$

where $T_d$ and $T_n$ are, respectively, the effective temperatures of the surface elements of the cold component that face the hot star ("day-side") and the opposite side ("night-side"), $R_h$ is the radius of the hot component, $a$ is the components' orbital separation, $\alpha_{\text{norm}}$ is the angle between the incoming flux and the normal to the surface, and $\eta$ is the dimensionless heating efficiency. The phase-resolved light curves were calculated by integrating the flux from all visible elements of both components. More details of the model can be found in our recent papers (Subebekova et al. 2020; Kára et al. 2021).

The free parameters of the model are the system inclination angle $i$, the radius of the hot component $R_h$, the components' effective temperatures ($T_h$ and $T_c$), the interstellar extinction $A_V$, and the heating efficiency $\eta$. The cool component is nearly filling its Roche lobe. The components' masses and the inclination angle are constrained by the mass function

<figure><img src="image_11.png" /><figcaption>**Figure 6.** Evolutionary tracks calculated using the MESA code for single stars with indicated initial masses shown by the colored solid lines. The starting points of all the tracks are located at the zero-age main sequence. The top panel shows radius vs. effective temperature relationships, while the bottom panel shows the HR diagram. The lines of different colors show the tracks of the masses in solar units indicated in the top panel. The vertical dashed line corresponds to $T_{\text{eff}} = 6500$ K. The colored circles in the bottom panel mark the time, when the track of the same color reaches $T_{\text{eff}} = 7000$ K. The dashed lines in the top panel mark the radius of the Roche lobe for the corresponding mass, orbital period, and $q \approx 1$.</figcaption></figure>

(Equation (2)). The initial value of the cool component's effective temperature is assumed to be within 6500–7000 K. The range of parameters was limited by the area of the black zone crossed by the red line in Figure 5. In other words, the expected system's parameters are in agreement with the estimated object's luminosity, $\log g_c$, and the mass function.

We searched for the minimum of the $\chi^2$ function with the free parameters mentioned above using the gradient-descent method. The best fit and the observed-minus-calculated (O–C) residuals are shown in the middle and bottom panels of Figure 4, respectively. The best-fit model parameters are presented in Table 2. The errors of most of the fitted parameters, except for the components' masses and the system inclination angle, were calculated with a Gaussian approximation of the $\chi^2$ function, while the remaining parameters were fixed at the best-fit values. The errors of the masses and the inclination angle are estimated from the errors of the observed RVs.

From Figure 4 one can conclude that the observed light curve of HD 327083 can be reproduced by the model (see Figure 8) with the parameters that are very close to those expected from the evolutionary tracks. The contributions of the hot and cool components to the system brightness in the V band from our best-fit model are $\sim 20\%$ and $\sim 80\%$, respectively. They are different from those based on the comparison with the spectrum of $\alpha$ Persei (see Section 3.1) and imply the presence of an additional source of the continuum that is most likely due to free-free and bound-free radiation from the circumstellar material.

## 6. Discussion

The addition of the new collection of high-resolution spectra and the long-term photometric monitoring data resulted in
<figure><img src="image_12.png" /><figcaption>**Figure 7.** Left: evolutionary tracks of a binary system with the components' masses of 13.0 $M_\odot$ and 12.0 $M_\odot$ and an initial orbital period of 107 days. The yellow filled circles indicate the current properties of the system components. The gray area corresponds to the evolutionary tracks within ±0.1 $M_\odot$ of the components' masses. Right: changes of the components' luminosity (top), radius (middle), and mass (bottom) near the current state of the system (marked by the vertical dashed line). Components' effective temperatures are indicated by colors.</figcaption></figure>

<table><caption>**Table 2**
Parameters of Eclipse Light-curves Fit</caption><thead><tr><th>Parameters</th><th>Values</th></tr></thead><tbody><tr><td><strong>Fixed:</strong></td><td></td></tr><tr><td>P<sub>orb</sub> (days)]</td><td>107.68(2)</td></tr><tr><td>Distance (kpc)</td><td>2.26(6)</td></tr><tr><td>q ≡ M<sub>c</sub>/M<sub>h</sub></td><td>1.01(6)</td></tr><tr><td>E(B − V) (mag)</td><td>1.70(4)</td></tr><tr><td>i (deg)</td><td>47<sup>+15</sup><sub>−20</sub></td></tr><tr><td>M<sub>h</sub> (M<sub>☉</sub>)</td><td>12.8(1.0)</td></tr><tr><td>R<sub>h</sub> (R<sub>☉</sub>)</td><td>9.7(8)</td></tr><tr><td>T<sub>h</sub> (K)</td><td>25400(1400)</td></tr><tr><td>M<sub>c</sub> (M<sub>☉</sub>)</td><td>12.8(8)</td></tr><tr><td>η</td><td>3.3(1.5)</td></tr><tr><td><strong>Calculated:</strong></td><td></td></tr><tr><td>a (R<sub>☉</sub>)</td><td>278</td></tr><tr><td>R<sub>c,Y</sub> (R<sub>☉</sub>)</td><td>106</td></tr><tr><td>R<sub>c,X</sub> (R<sub>☉</sub>)</td><td>139</td></tr><tr><td>T<sub>c</sub><sup>n</sup> (K)</td><td>7100</td></tr><tr><td>T<sub>c</sub><sup>d</sup> (K)</td><td>8600</td></tr><tr><td>log L<sub>c</sub>/L<sub>☉</sub></td><td>4.41</td></tr><tr><td>log L<sub>h</sub>/L<sub>☉</sub></td><td>4.55</td></tr></tbody></table>

**Note.** Numbers in brackets for the variables are uncertainties defined as $1\sigma$ of the Gaussian function approximation used to describe the one-dimensional $\chi^2$ function. $R_{c,Y}$ is the radius of the cool component in the Y-direction (see Figure 8), and $R_{c,X}$ is the corresponding maximum radius in the X-direction.).

constraining the orbital period of this previously recognized binary system (Miroshnichenko et al. 2003) as well as in deriving a model that consistently explains the observed spectral and photometric variations. This model involves the evolution of a binary system with relatively massive (~12–13 $M_\odot$) components that were formed with an orbital period close to the currently observed one.

Currently, the system has reached a stage when the more massive component is close to filling its Roche lobe and has begun transferring matter to the less massive component. The estimated age of the system is ~13.7 million yr.

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 8.** Geometry of HD 327083. The color bar corresponds to the effective temperature of the emitting regions of the stars.</figcaption></figure>

Also, we checked whether the system rotated synchronously using the approach developed by Gies & Bolton (1986; their Equation (2)), which connects the ratio of the projected rotational velocity of the Roche lobe filling star and the semiamplitude of its RV curve to the ratio of the star's spin angular velocity to the orbital angular velocity and the system's mass ratio. Using our results for $q$, $K_c$, and $v \sin i$ and assuming that the cool component is close to filling its Roche lobe, we found that the ratio of the mentioned angular velocities, $v_c \sin i/v_{c,sync} \sin i = 25(5)/36.5 = 0.68(14)$, is below unity. Therefore, the system is probably not fully synchronized yet.

Another factor that may slightly result in a systematic error of the cool component's RV amplitude determination is the shifting of the center of light toward the hot component around quadrature phases due to the illumination discussed above. It is most likely very mild, as the illuminated fraction of the cool
<figure><img src="image_15.png" /></figure>

**Figure 9.** Spectral energy distribution of HD 327083. UV spectrum was obtained from the IUE database (Valenti et al. 2003). The photometric data were taken from several sources, including ASAS SN, Wide-field Infrared Survey Explorer, AKARI, Midcourse Space Experiment, the Hipparcos and Tycho Catalogues, the Guide Star Catalog, AAVSO DR9, Gaia DR1, SkyMapper DR1, and Gaia EDR3 (Kochanek et al. 2017; Cutri et al. 2013; Ishihara et al. 2010; Egan et al. 2003; Lasker et al. 2008; Henden et al. 2016; Gaia Collaboration et al. 2016; Wolf et al. 2018; Maíz Apellániz et al. 2023). The data were corrected for the corresponding interstellar extinction (see Section 3.1). The theoretical spectral energy distributions for the system's components (blue line—hot; green line—cool) are represented by the model atmospheres from Castelli & Kurucz (2003). The sum of them scaled according to the contributions derived from the light-curve modeling is shown by the black line.

component's surface and the surface temperature variation caused by this effect (see Table 2 and Equation (3)) are both small.

The spectral energy distribution of the object (Miroshnichenko et al. 2003) shows an infrared excess caused by the presence of a circumbinary disk (Wheelwright et al. 2012a, 2012b). From the fit of the CO-emitting circumbinary Keplerian disk model based on CRIRES spectra, Wheelwright et al. (2012b) estimated the system total mass and inclination angle are ~25 $M_\odot$ and $i = 45^\circ$8, respectively. These values are very close to our result (see Table 2), which follows from the period determination, analysis of the RV curves, and the best fit to the photometric data.

In Figure 9 we present the object's spectral energy distribution composed from the photometric data from UV to far-IR. It is clearly seen that the model spectra reproduce the observed optical data and show a strong deviation from observed points in the infrared and UV regions. While the infrared excess is caused by the circumbinary disk (Wheelwright et al. 2012a, 2012b), the origin of the UV excess is not clear. It can be related to the presence of additional radiation from the wind of the hot component, a complicated accretion flow from the Roche lobe filling cool component, or caused by a calibration problem of the International Ultraviolet Explorer (IUE) spectrum.

The physical mechanism of forming the complex circumstellar environments of supergiant B[e] stars is yet unclear. Wheelwright et al. (2012b) mentioned that the lack of IR variability suggests a relatively stable structure of the circumbinary disk, which is most probably formed as a result of the mass-loss from the stellar components by their radiatively driven wind that occurs through the L2 Lagrangian point of the system

(Plets et al. 1995). It is possible that the same mechanism is responsible for the excess of the UV radiation.

## 7. Summary

Our study of the spectroscopic and photometric data of the southern emission-line object HD 327083 resulted in the following findings:

1. The amplitude of the RV variations (48.3(1.7) km s⁻¹) of absorption lines in the spectrum of the cool component is nearly the same as that of the emission lines, which represent the motion of the hot component.

2. The V-band light curve shows nearly sinusoidal variability with a full amplitude of ≈0.2 mag.

3. From analysis of the spectroscopic and photometric observations, we determined a system orbital period of $P_{\text{orb}} = 107.68(2)$ days.

4. Analysis of the evolutionary state of the system suggests that the system was formed by two massive stars, which are currently undergoing a stage of mass transfer. The more massive component nearly fills its Roche lobe and begins transferring matter to the less massive one. The current components' masses are ~12.5 $M_\odot$, the cool component has a $T_{\text{eff}} \approx 7000$ K, and its radius is ~106 $R_\odot$. It evolved from a star with a mass ≈13.0 $M_\odot$. The hot component initially had a mass of ≈12.0 $M_\odot$. It accumulated some mass from the cool component and evolved to a star with a $T_{\text{eff}} \sim 25,400$ K and a radius of 9.7 $R_\odot$. This configuration with accounting for heating of the surface of the cool component that faces the hot one can reproduce the observed photometric and spectroscopic data and is in agreement with previous infrared observations of the circumbinary disk reported by Wheelwright et al. (2012a, 2012b).

5. The presence of the circumbinary disk is responsible for the infrared excess, while accretion and wind structures around the hot component are responsible for the emission lines and probably for the UV excess.

Despite the large progress in understanding the nature of HD 327083, a number of issues related to binarity and circumbinary disk formation still need to be clarified by follow-up observations and more detailed modeling.

## Acknowledgments

This research was funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (grant No. AP19578879). This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France; SAO/NASA ADS, ASAS, and Gaia data products. This paper is partly based on observations obtained at the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique de France, and the University of Hawaii as well as on observations obtained at the 2.1 m Otto Struve telescope of the McDonald Observatory (Texas, USA), the 2.1 m telescope of Complejo Astronomico El Leoncito (Argentina), and the 2.2 m telescope of the European Southern Observatory (ESO). The observations at the Canada-France-Hawaii Telescope were performed with care and respect from the summit of Maunakea, which is a significant cultural and historic site. S.V.Z. acknowledges PAPIIT grant IN119323.
Facilities: Max Planck:2.2m, CFHT, CASLEO:JST

Software: This work has used MESA (version 23.05.1; Paxton et al. 2011, 2013, 2015, 2018, 2019; Jermyn et al. 2023), CVlab (Zharikov et al. 2013), and the Python module: matplotlib (Hunter 2007).

## Data Availability

The data underlying this paper will be shared on reasonable request to the corresponding author.

The MESA inlists for our models may be found on Zenodo at doi:10.5281/zenodo.11044827 with further explanations.

## ORCID iDs

A. S. Nodyarov https://orcid.org/0000-0002-0045-5457

A. S. Miroshnichenko https://orcid.org/0000-0002-3833-1038

S. A. Khokhlov https://orcid.org/0000-0001-5163-508X

S. V. Zharikov https://orcid.org/0000-0003-2526-2683

A. T. Agishev https://orcid.org/0000-0001-9788-7485

I. A. Gabitova https://orcid.org/0000-0002-5328-8568

N. L. Vaidman https://orcid.org/0000-0002-7449-0108

N. Manset https://orcid.org/0000-0001-7548-0190

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