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# Toward Understanding the B[e] Phenomenon. IX. Nature and Binarity of MWC645

A. S. Nodyarov¹, A. S. Miroshnichenko¹,²,³,⁴, S. A. Khokhlov¹, S. V. Zharikov¹,⁵,⁶, N. Manset⁷, V. G. Klochkova⁶, K. N. Grankin⁸, A. A. Arkharov³, N. Efimova³, S. Klimanov³, V. M. Larionov³,⁹, R. J. Rudy¹⁰, R. C. Puetter¹¹, R. B. Perry¹², I. V. Reva⁴, C. T. Omarov⁴, and R. I. Kokumbaeva⁴

¹Al-Farabi Kazakh National University, Al-Farabi Ave., 71, 050040, Almaty, Kazakhstan

²Department of Physics and Astronomy, University of North Carolina at Greensboro, P.O. Box 26170, Greensboro, NC 27402-6170, USA

³Central Astronomical Observatory of the Russian Academy of Sciences at Pulkovo, Pulkovskoye shosse 65-1, St. Petersburg, 196140, Russia

⁴Fesenkov Astrophysical Institute, Observatory, 23, Almaty, 050020, Kazakhstan

⁵Universidad Nacional Autónoma de México, Instituto de Astronomía, AP 106, Ensenada 22800, BC, MÉxico

⁶Special Astrophysical Observatory of the Russian Academy of Sciences, Nizhny Arkhyz, Zelenchukskiy region, Karachai-Cherkessian Republic, 369167, Russia

⁷Canada-France-Hawaii Telescope Corporation, 65-1238 Mamalahoa Hwy, Kamuela, HI 96743, USA

⁸Crimean Astrophysical Observatory, Scientific Research Institute, 298409, Nauchny, Russia

⁹V.V. Sobolev Astronomical Institute of the St.-Petersburg State University, St.-Petersburg, 198504, Russia

¹⁰Kookosint Scientific, 1530 Calle Portada, Camarillo, CA 93010, USA

¹¹Center for Astrophysics & Space Science University of California, San Diego, 9500 Gilman Dr La Jolla, CA 92093, USA

¹²Alabaster Scientific, P.O. Box 120, Irvington, VA 22480, USA

Received 2022 May 25; revised 2022 August 3; accepted 2022 August 4; published 2022 September 8

## Abstract

We present the results of optical and near-IR spectroscopy and multicolor photometry of the emission-line star MWC 645, which exhibits the B[e] phenomenon. The presence of positionally variable absorption lines of a cool star detected for the first time indicates that the object is a binary system. Using a combination of the photometric and spectroscopic data as well as the Gaia EDR3 distance ($D = 6.5 \pm 0.9$ kpc), we disentangled the components' contributions and estimated their surface temperatures and luminosities (18, 000 ± 2000 K and 4250 ± 250 K, log L/L$_{⊙}$ = 4.0 ± 0.5 and 3.1 ± 0.3 for the hot and cool components, respectively). Quasi-cyclic short-period (months) and long-period (~4 yr) photometric variations were detected in both optical and near-IR regions, and are most likely due to variable circumstellar extinction. Our analysis suggests that MWC 645 is a member of the FS CMa group. The object's properties can be described by an evolutionary model of a close binary system that currently undergoes a nonconservative mass transfer between intermediate-mass stars (e.g., 7 M$_{⊙}$ + 2.8 M$_{⊙}$).

Unified Astronomy Thesaurus concepts: A stars (5); Binary stars (154); Spectroscopic binary stars (1557); Be stars (142); Emission line stars (460)

Supporting material: machine-readable tables

## 1. Introduction

Among the first group of nearly 70 early-type stars with detected infrared (IR) excesses (Geisel 1970), there were six with very strong emission-line spectra (MWC 17, FS CMa, RY Sct, MWC 342, MWC 349, and MWC 645). A few years later, these objects were included in the group of peculiar Be stars or B[e] stars along with about 60 others (Allen & Swings 1976).

The class of B[e]-type stars is characterized by the presence of permitted and forbidden low-excitation emission lines, such as those of H I, Fe II, [Fe II], N II, O I, and others in the spectra of B-type stars combined with a strong near- and mid-IR excess due to radiation of circumstellar dust. The phenomenon is observed in stars with a wide range of masses and evolutionary states. The latter include pre-main-sequence Herbig Ae/Be stars, symbiotic binaries, protoplanetary nebulae, and a small group of supergiants (e.g., η Carinae), as was concluded by Lamers et al. (1998). Also, nearly 30 objects from the original list of B[e] stars remained unclassified due to a lack of observations and complex properties, which contained hints to more than one stellar group with known nature. Most of them became members of the new FS CMa-type group defined by

Miroshnichenko (2007), who suggested that these objects are most likely close binaries that are undergoing or have undergone a phase of mass transfer between the components.

The nature of almost all of the six objects mentioned above is not fully understood even now, although all of them have been suspected or found to be binary systems. In particular, MWC 17, FS CMa, MWC 342, and MWC 645 were included in the FS CMa group. MWC 645 can be considered one of the least studied objects among them, and is the main subject of our current paper.

Swings & Allen (1973) studied a blue spectral region of MWC 645 using coudé spectra with a spectral resolution of 20 Å mm$^{-1}$ taken in 1971. They found that all strong emission lines of Fe II and [Fe II] were double-peaked with an average radial velocity (RV) difference of 150 km s$^{-1}$ between the stronger red and the weaker blue peak, while the profiles of Hγ and Hδ exhibited three components. These authors found a strong resemblance between the spectrum of MWC 645 and that of η Car, except for the presence of higher-excitation emission lines in the spectrum of the latter.

Intermediate-resolution optical spectra of MWC 645 in a region from 3741 Å to 8790 Å with a gap between 5137 Å and 6332 Å taken in 1991–1995 were studied by Jaschek et al. (1996). Those authors identified 88 forbidden and permitted emission lines and measured an average heliocentric RV of −76 km s$^{-1}$ for those lines, but found no absorption lines

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formed in the stellar atmosphere. Comparing their results with those of other authors showed that the spectral lines were highly variable in the equivalent width (EW) up to a factor of 2, as well as that some lines were not detected in the spectra taken at different times.

The Hα profile of MWC 645 was reported to be very peculiar. It consists of a broad blueshifted peak and a much stronger narrow redshifted peak. This was noticed in low-resolution spectra taken by Swings & Andrillat (1981) in 1981 and later confirmed by Zickgraf (2003), who studied narrow spectral regions around several emission lines (e.g., Hα and [O I] 6300 & 6363 Å) in 1986–1988 and 2000–2002 and concluded that such a profile was found in no other object of a sample of 18 B[e] stars he observed at high resolution. This author also described the profiles of all permitted emission lines in the spectra of MWC 645 as exhibiting a characteristic asymmetry with a steep red flank and a wing on the blue side, while the forbidden lines were narrow and single-peaked.

Long-term brightness variations of the star were studied by Gottlieb & Liller (1978) and Kurochkin et al. (1979) using photographic plates taken between 1892 and 1985. These showed an average brightness of $m_{pg} = 14.1$ with an amplitude of 0.3 mag and a possible period of 23.6 yr. Craine & Tapia (1975) obtained several *UBVR* observations in 1974. Single infrared photometric observations at 5 and 10 µm were reported by Low (1970) and in the *JHKL* bands by Allen (1973). Marston & McCollum (2008) mentioned MWC 645 in a list of B[e] objects that show no extended circumstellar structure on a deep direct optical image.

Since all the studies of this object were carried out long ago and were inconclusive with respect to its nature, MWC 645 requires a more detailed study. In particular, properties of the circumstellar matter, fundamental parameters, spectral energy distribution (SED), and the light curve have not been closely studied. In this paper, we report the results of high- and low-resolution spectroscopy as well as multicolor optical and near-IR photometry of MWC 645 aimed at determining its fundamental parameters and evaluating its nature and evolutionary status.

## 2. Observations

We obtained optical high-resolution spectroscopic observations of MWC 645 with the 2.7 m Harlan J. Smith telescope of the McDonald Observatory (Texas, USA, R = 60,000) with the Tull coudé spectrograph TS2 (Tull et al. 1995), the 2.1 m telescope of the Observatorio Astronomico Nacional San Pedro Martir (OAN SPM, Baja California, Mexico, R = 18,000) with an REOSC spectrograph, the 6 m telescope of Special Astrophysical Observatory (SAO, Nizhni Arkhyz, Russia, R = 60,000) with the NES spectrograph (Panchuk et al. 2017), and the 3.6 m Canada-France-Hawaii Telescope (CFHT, Maunakea, HI, USA, R = 65,000) with the ESPaDOnS spectropolarimeter (Manset & Donati 2003). Observations obtained at CFHT were reduced with the Upena and Libre-ESpRIT software packages (Donati et al. 1997). Spectra from the other observatories were processed using the *echelle* package in IRAF. Table 1 presents the information about all our spectroscopic observations (14 spectra) from 2004 to 2021.

Photometric observations in the optical range were obtained at the Maidanak Observatory (Uzbekistan) on 50 nights in 2004–2005 and at the Crimean Astrophysical Observatory (CrAO) on one night in 2008 with a single-element photometer with a set of broadband *UBVR* Johnson filters. Photometric

<table><caption>**Table 1**
Spectroscopic Observations</caption><thead><tr><th>Date</th><th>HJD</th><th>Exp., s</th><th>Range, Å</th><th>Obs.</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th></tr></thead><tbody><tr><td>10/07/2004</td><td>3286.424</td><td>18000</td><td>5200–6800</td><td>SAO</td></tr><tr><td>10/12/2005</td><td>3655.633</td><td>900</td><td>4300–6800</td><td>SPM</td></tr><tr><td>12/21/2005</td><td>3725.595</td><td>1200</td><td>4050–10100</td><td>McD</td></tr><tr><td>11/17/2007</td><td>4421.634</td><td>6000</td><td>3900–6800</td><td>SPM</td></tr><tr><td>10/04/2008</td><td>4744.632</td><td>4800</td><td>4100–6900</td><td>SPM</td></tr><tr><td>10/08/2008</td><td>4748.635</td><td>6000</td><td>4000–6900</td><td>SPM</td></tr><tr><td>12/10/2008</td><td>4810.699</td><td>2400</td><td>4000–10000</td><td>CFHT</td></tr><tr><td>12/11/2008</td><td>4811.699</td><td>2400</td><td>4000–10000</td><td>CFHT</td></tr><tr><td>11/03/2009</td><td>5139.665</td><td>4800</td><td>4100–7100</td><td>SPM</td></tr><tr><td>10/18/2010</td><td>5487.748</td><td>6000</td><td>4100–7350</td><td>SPM</td></tr><tr><td>11/18/2012</td><td>6250.611</td><td>4800</td><td>3800–7350</td><td>SPM</td></tr><tr><td>10/18/2013</td><td>6583.705</td><td>3600</td><td>4550–8100</td><td>SPM</td></tr><tr><td>10/18/2016</td><td>7679.242</td><td>4686</td><td>3800–10450</td><td>CFHT</td></tr><tr><td>11/26/2021</td><td>9544.500<sup>a</sup></td><td>10200</td><td>4000–10000</td><td>CFHT</td></tr></tbody></table>

**Note.** Column information: (1) Date of the observation (Month/Day/Year). (2) Heliocentric Julian Date (JD=2450000+). (3) Total exposure time in seconds. (4) Informative range of each spectrum in Å. (5) Abbreviated name of the observatory.

<sup>a</sup> The CFHT observation of 2021 consists of 10 combined individual exposures taken on three consecutive nights (2021 November 24–26).

*BVR* data in the Johnson–Cousins system of a 10' × 10' field around MWC 645 were obtained on 4 nights at a 1 m telescope of the Tien-Shan Observatory (TShAO) of the Fesenkov Astrophysical Institute (near Almaty, Kazakhstan) in 2022 April–June. A 3056 × 3056 Apogee F9000 D9 CCD camera with 12 µm pixels and a three-step cooling system was used with a set of *BVR*<sub>c</sub> filters. The TShAO data were reduced using the Maxim-DL software.<sup>13</sup> All our optical photometric data are shown in Table 2.

Near-IR *JHK* photometric observations were obtained at the 1.1 m optical telescope AZT–24 of the Observatory Campo Imperatore (Italy) between 2008 September and 2017 May with the imager/spectrometer SWIRCAM (D’Alessio et al. 2000). The data set contains 62 observations. One *JHK* observation was carried out at the 0.84 m telescope of OAN SPM in 2009 November. The IR camera CAMILA with a NICMOS 3 HgCdTe detector (Cruz-Gonzales et al. 1994) was used at this observing site. The *JHK* data are presented in Table 3.

Two low-resolution near-IR spectra of MWC 645 were taken at the 3 m Shane reflector of the Lick Observatory (USA, California, 0.46–2.5 µm, R~700) in July 2005 and November 2009 with the Aerospace near-infrared imaging spectrograph VNIRIS (Rudy et al. 1999). The spectral range covered was 0.46–2.5 µm in 2005 and 0.8–2.5 µm in 2009.

## 3. Data Analysis

### 3.1. Emission Lines

The optical spectrum of MWC 645 exhibits numerous emission lines in agreement with the previous studies. The strong permitted and forbidden emission lines are represented by hydrogen (Balmer and Paschen series), Fe II, Cr II, Ti II, Ca II, O I, N I, N I, Ca II, [Fe II], [Ni II], [Ca II], [O I], and a few lines of other elements. The RVs of the emission lines were

<footnote n="13"><sup>13</sup> http://diffractionlimited.com/product/maxim-dl/</footnote>
<table><caption>**Table 2**
Optical Photometry of MWC 645</caption><thead><tr><th>JD</th><th>V</th><th>U - B</th><th>B - V</th><th>V - R</th><th>JD</th><th>V</th><th>U - B</th><th>B - V</th><th>V - R</th></tr></thead><tbody><tr><td>53228.3921</td><td>13.00</td><td>-0.05</td><td>0.88</td><td>2.24</td><td>53580.4124</td><td>13.05</td><td>...</td><td>0.86</td><td>2.12</td></tr><tr><td>53229.3847</td><td>13.07</td><td>-0.08</td><td>0.89</td><td>2.26</td><td>53581.3039</td><td>13.02</td><td>...</td><td>0.89</td><td>2.05</td></tr><tr><td>53230.3417</td><td>13.06</td><td>-0.02</td><td>0.86</td><td>2.24</td><td>53584.3708</td><td>13.04</td><td>...</td><td>0.91</td><td>2.09</td></tr><tr><td>53231.3557</td><td>13.00</td><td>-0.08</td><td>0.86</td><td>2.22</td><td>53585.3626</td><td>13.03</td><td>...</td><td>0.87</td><td>2.09</td></tr><tr><td>53232.2836</td><td>13.00</td><td>-0.20</td><td>0.86</td><td>2.23</td><td>53586.3608</td><td>13.03</td><td>...</td><td>0.86</td><td>2.08</td></tr></tbody></table>

Note. Column information: JD (2400000+) – Julian Date, V-band brightness in the Johnson photometric system, and color indices (U - B, B - V, V - R). Average uncertainties of individual measurements are ~0.01–0.02 mag. Full table is available in the electronic version of the paper.
(This table is available in its entirety in machine-readable form.)

<table><caption>**Table 3**
Near-IR Photometry of MWC 645</caption><thead><tr><th>JD</th><th>J</th><th>σJ</th><th>H</th><th>σH</th><th>K</th><th>σK</th><th>JD</th><th>J</th><th>σJ</th><th>H</th><th>σH</th><th>K</th><th>σK</th></tr></thead><tbody><tr><td>54757.2845</td><td>9.33</td><td>0.01</td><td>7.98</td><td>0.01</td><td>6.48</td><td>0.01</td><td>56057.6038</td><td>9.70</td><td>0.01</td><td>8.34</td><td>0.03</td><td>6.63</td><td>0.01</td></tr><tr><td>54773.3028</td><td>9.24</td><td>0.01</td><td>7.90</td><td>0.01</td><td>6.46</td><td>0.01</td><td>56520.5480</td><td>9.58</td><td>0.01</td><td>8.25</td><td>0.02</td><td>6.67</td><td>0.01</td></tr><tr><td>54780.3520</td><td>9.19</td><td>0.02</td><td>7.88</td><td>0.01</td><td>6.42</td><td>0.01</td><td>56539.5120</td><td>9.64</td><td>0.02</td><td>8.27</td><td>0.04</td><td>6.72</td><td>0.01</td></tr><tr><td>55139.5000<sup>a</sup></td><td>9.65</td><td>0.02</td><td>8.08</td><td>0.02</td><td>6.77</td><td>0.04</td><td>56540.5127</td><td>9.70</td><td>0.01</td><td>8.35</td><td>0.02</td><td>6.77</td><td>0.01</td></tr><tr><td>55307.5931</td><td>...</td><td>...</td><td>8.20</td><td>0.03</td><td>6.56</td><td>0.04</td><td>56558.5672</td><td>9.66</td><td>0.01</td><td>8.31</td><td>0.02</td><td>6.72</td><td>0.01</td></tr></tbody></table>

Note. Column information: JD (2400000+)—average heliocentric Julian Date of the observation; J-, H-, and K-band brightness; σJ, σH, and σK – brightness uncertainties in the JHK-bands.

<sup>a</sup> The observation was taken at OAN SPM. Full table is available in the electronic version of the paper.

(This table is available in its entirety in machine-readable form.)

<table><caption>**Table 4**
List of Emission Lines Identified in the 2008 CFHT Spectrum of MWC 645</caption><thead><tr><th>Line</th><th>Mult</th><th>λ<sub>lab</sub></th><th>RV</th><th>Line</th><th>Mult</th><th>λ<sub>lab</sub></th><th>RV</th><th>Line</th><th>Mult</th><th>λ<sub>lab</sub></th><th>RV</th><th>Line</th><th>Mult</th><th>λ<sub>lab</sub></th><th>RV</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>1</th><th>2</th><th>3</th><th>4</th><th>1</th><th>2</th><th>3</th><th>4</th><th>1</th><th>2</th><th>3</th><th>4</th></tr></thead><tbody><tr><td>Fe II</td><td>3</td><td>3966.43</td><td>-61.3</td><td>Fe II</td><td>37</td><td>4472.92</td><td>-54.4</td><td>[Fe II]</td><td>19</td><td>5220.06</td><td>-62.6</td><td>Fe II</td><td>199</td><td>6482.21</td><td>-86.8</td></tr><tr><td>Hα</td><td>1</td><td>3970.07</td><td>-54.0</td><td>[Fe II]</td><td>7</td><td>4474.91</td><td>-62.3</td><td>Ti II</td><td>70</td><td>5226.53</td><td>-51.9</td><td>Fe II:</td><td>...</td><td>6491.28</td><td>-107.7</td></tr><tr><td>Fe II</td><td>29</td><td>3974.16</td><td>-82.3</td><td>Fe II</td><td>37</td><td>4489.19</td><td>-75.8</td><td>Fe II</td><td>49</td><td>5234.62</td><td>-79.1</td><td>Fe II</td><td>40</td><td>6516.05</td><td>-62.8</td></tr><tr><td>[Fe II]</td><td>9</td><td>3979.71</td><td>-74.6</td><td>Fe II</td><td>37</td><td>4491.40</td><td>-65.5</td><td>Cr II</td><td>43</td><td>5237.34</td><td>-64.7</td><td>Fe II</td><td>210</td><td>6627.28</td><td>-74.2</td></tr><tr><td>[Cr II]</td><td>4</td><td>3993.29</td><td>-83.4</td><td>Ti II</td><td>31</td><td>4501.27</td><td>-57.3</td><td>[V II]</td><td>8</td><td>5254.49</td><td>-38.3</td><td>[Ni II]</td><td>...</td><td>6666.80</td><td>-62.1</td></tr></tbody></table>

Note. Column information: (1) Element and ionization state. (2) Multiplet number. (3) Line laboratory wavelength in Å. (4) RV in km s⁻¹. Full table is available in the electronic version of the paper.

(This table is available in its entirety in machine-readable form.)

determined by fitting the line peaks to a Gaussian. The lines were identified using a list of lines in stellar spectra by Coluzzi (1999), and the EW were measured by integration in the continuum-normalized spectra.

A list of 226 emission lines and their RVs in a wavelength region of 3966–10,407 Å identified in the CFHT 2008 spectrum is presented in Table 4, where the RVs of double-peaked lines are related to the most intense (redshifted) peak, as the RVs of the blueshifted peaks are difficult to measure, due to their weakness in most lines except for the strongest Balmer lines. A spectral atlas with marked positions of most emission lines is presented in Figures 11–18 in the Appendix. Parameters of the Hα and Hβ emission lines are shown in Table 5.

The average RV of the emission lines determined in all our highest-resolution spectra taken at the SAO (2004), McD (2005) and CFHT (2008, 2016, 2021) is −61.0 ± 4.3 km s⁻¹. Comparing high-resolution and high signal-to-noise ratio spectra, we did not find disappearance of any of the spectral

lines mentioned by Jaschek et al. (1996). Although the line intensities are different in the spectra obtained in different years, we found no strong variability in the emission-line RVs in individual spectra.

Figure 1 shows an example of the variations of the Hα line profile. Its very intense and wide blueshifted peak has an average RV of −252 ± 9 km s⁻¹ and an FWHM of 224 ± 10 km s⁻¹, while the narrow redshifted peak has an average RV of −30 ± 2 km s⁻¹ and an FWHM of 60 ± 15 km s⁻¹. We used all our highest-resolution spectra taken at SAO and CFHT to derive these average data.

These values are similar to those reported by Zickgraf (2003): RVs of −218 km s⁻¹ and −30 km s⁻¹ and FWHMs of 229 km s⁻¹ and 59 km s⁻¹, respectively. Therefore, the Hα profile peaks show no drastic changes over the last four decades, reflecting a relative stability of the circumstellar environments. We present the parameters of the Hα and Hβ lines in Table 3. Most permitted emission lines show similar
<table><caption>**Table 5**
Parameters of the Hα and Hβ Lines in the Spectra of MWC 645</caption><thead><tr><th>Date</th><th>Obs.</th><th>RV<sub>blue</sub></th><th>RV<sub>red</sub></th><th>I<sub>blue</sub></th><th>I<sub>red</sub></th><th>Hα<br>EW</th><th>RV<sub>blue</sub></th><th>Hβ<br>RV<sub>red</sub></th><th>I<sub>blue</sub></th><th>I<sub>red</sub></th><th>EW</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>8</th><th>9</th><th>10</th><th>11</th><th>12</th></tr></thead><tbody><tr><td>10/07/2004</td><td>SAO</td><td>-250.4</td><td>-33.7</td><td>85.5</td><td>95.2</td><td>-561.9</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>10/12/2005</td><td>SPM</td><td>-222.5</td><td>-18.6</td><td>135.8</td><td>448.2</td><td>-1603.5</td><td>...</td><td>-25.4</td><td>...</td><td>15.9</td><td>-31.2</td></tr><tr><td>12/21/2005</td><td>McD</td><td>-195.1</td><td>2.9</td><td>...</td><td>...</td><td>...</td><td>...</td><td>-1.4</td><td>...</td><td>20.9</td><td>-44.6</td></tr><tr><td>11/17/2007</td><td>SPM</td><td>-221.6</td><td>-5.3</td><td>197.2</td><td>347.2</td><td>-1557.5</td><td>-230.9</td><td>2.3</td><td>32.1</td><td>56.8</td><td>-93.7</td></tr><tr><td>10/04/2008</td><td>SPM</td><td>-240.8</td><td>-21.8</td><td>207.6</td><td>292.4</td><td>-1833.9</td><td>-252.5</td><td>-24.2</td><td>23.8</td><td>47.8</td><td>-66.4</td></tr><tr><td>10/08/2008</td><td>SPM</td><td>-241.2</td><td>-21.8</td><td>207.2</td><td>294.7</td><td>-1345.5</td><td>-254.4</td><td>-25.4</td><td>23.7</td><td>46.8</td><td>-81.2</td></tr><tr><td>12/10/2008</td><td>CFHT</td><td>-261.3</td><td>-30.9</td><td>194.5</td><td>280.1</td><td>-1609.0</td><td>-280.3</td><td>-35.3</td><td>37.8</td><td>50.1</td><td>-75.1</td></tr><tr><td>12/11/2008</td><td>CFHT</td><td>-260.9</td><td>-30.9</td><td>192.9</td><td>273.4</td><td>-1595.7</td><td>-280.9</td><td>-34.7</td><td>38.5</td><td>50.9</td><td>-75.6</td></tr><tr><td>11/03/2009</td><td>SPM</td><td>-213.8</td><td>-7.6</td><td>180.3</td><td>483.4</td><td>-1765.9</td><td>-278.4</td><td>-2.6</td><td>7.5</td><td>29.8</td><td>-30.6</td></tr><tr><td>10/18/2010</td><td>SPM</td><td>-222.5</td><td>-8.5</td><td>156.2</td><td>492.2</td><td>-1771.7</td><td>-195.7</td><td>-11.8</td><td>18.1</td><td>45.6</td><td>-67.8</td></tr><tr><td>11/18/2012</td><td>SPM</td><td>-236.2</td><td>-8.5</td><td>298.8</td><td>359.6</td><td>-1951.4</td><td>-243.3</td><td>-10.0</td><td>37.1</td><td>48.6</td><td>-83.8</td></tr><tr><td>10/18/2013</td><td>SPM</td><td>-215.2</td><td>-17.2</td><td>213.0</td><td>633.9</td><td>-1998.8</td><td>...</td><td>-13.7</td><td>...</td><td>40.5</td><td>-61.8</td></tr><tr><td>10/18/2016</td><td>CFHT</td><td>-241.7</td><td>-29.1</td><td>237.1</td><td>350.2</td><td>-1631.8</td><td>-241.4</td><td>-29.7</td><td>33.8</td><td>45.2</td><td>-100.3</td></tr><tr><td>11/26/2021</td><td>CFHT</td><td>-244.9</td><td>-27.3</td><td>111.7</td><td>356.1</td><td>-1192.5</td><td>-282.1</td><td>-30.4</td><td>4.3</td><td>19.8</td><td>-70.7</td></tr></tbody></table>

**Note.** Column information: (1) Date of the observation (Month/Day/Year). (2) Abbreviated name of the observatory. (3), (4), (8), and (9) The heliocentric RVs or the blueshifted (RV<sub>blue</sub>) and redshifted (RV<sub>red</sub>) emission peaks. (5), (6), (10), and (11) Peak intensities in continuum units. (7) and (12) The EWs of the emission line in Å. It should be noted that the Hα line was close to an edge of the spectral order in the 2005 spectrum taken at the McDonald Observatory to determine a reasonable continuum level.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Comparison of the Hα line profiles taken in 2008 (red line) and 2021 (blue line) CFHT. The arrows show the RVs of the peaks. The intensity is normalized to the continuum, and RVs are heliocentric.</figcaption></figure>

profiles, while a split in the peaks of forbidden line profiles is not obvious.

The emission line of He I λ6678 Å reported by Jaschek et al. (1996) in their 1995 spectrum was absent in the 1987 spectrum from Zickgraf (2003). We do not see any obvious signs of the presence of this line in our spectra, and we discuss this result in Section 4.

Also, identification of the emission line near λ6665 Å was thought to be uncertain by Zickgraf (2003), who suggested that it could be a blend of Fe I lines around λ6667 Å. However, the spectrum of MWC 645 contains emission lines of Fe II, not those of Fe I. We identified this line as a line of [Ni II] λ6666.80 Å, which is observed in the spectra of some other FS CMa-type objects, such as MWC 17 (Klochkova & Chentsov 2016).

The emission lines identified in the near-IR spectra taken at the Lick observatory using previously published data taken with the same equipment (e.g., Venturini et al. 2002; Miroshnichenko et al. 2004) are shown in Figure 2. The main spectral content in the 0.8–2.5 µm range includes lines of the

Paschen and Brackett series of hydrogen, as well as lines of Fe II, N I, and O I. Two emission lines of He I at 1.083 µm and 2.058 µm with moderate intensities are present in both near-IR spectra taken in 2005 and 2009.

## 3.2. Absorption Lines

The spectrum of MWC 645 contains a number of absorption lines created in the interstellar medium, including strong diffuse interstellar bands (DIBs), such as 5780, 5796, 6613 Å. The Na I at 5889 and 5895 Å line profiles show a complex structure (Figure 3) that consists of several components. The two shorter-wavelength components (a narrow one at an RV of −70 km s⁻¹ and a broad one at RVs from −52 to −32 km s⁻¹) seem to form in the interstellar medium, while the longer-wavelength one (between RVs of −22 to −12 km s⁻¹), whose position is close to that of the redshifted peak of the Hα line, varies in shape and may contain some contribution from the circumstellar material.

No absorption lines typical of a B-type star atmosphere have been found in any of our spectra. This may be due to a combination of a fast rotation rate of the hot star, veiling by the circumstellar continuum, and a relatively low signal-to-noise ratio in the blue spectral region, where the veiling effects are smaller. However, for the first time, we detected a number of weak absorption lines of neutral metals that are typical of cool star spectra in our highest signal-to-noise ratio spectra taken at CFHT in 2008 and 2021. These lines are lost in the noise in all other spectra from our collection. The absorption lines identified using the catalog by Coluzzi (1999) along with RVs are shown in Table 6.

To ensure reliable identification, we also compared our highest signal-to-noise CFHT spectra of MWC 645 with those of MWC 623, a binary system with a B-type and a K-type component (Zickgraf 2001). MWC 623 was listed by Allen & Swings (1976) in the original list of B[e] stars and recognized as a member of the FS CMa group (Miroshnichenko 2007).
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Parts of the low-resolution near-IR spectrum of MWC 645 taken at the Lick Observatory on 2005 July 3. Wavelengths are given in microns, and fluxes are given in units of $10^{-12}$ W m$^{-2}$ µm$^{-1}$.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Portion of the optical high-resolution spectra of MWC 645 obtained at CFHT in 2008 (top panel) and 2021 (bottom panel), which shows the structure of the Na I D2-line. RVs are shown with respect to the lab wavelength of the line (5889.92 Å). The intensity is normalized to the continuum. The red arrow shows the average RV of the redshifted peak of the Hα line.</figcaption></figure>

The average RV of the absorption lines in the 2008 spectrum is $-23.8 \pm 3.6$ km s$^{-1}$, while it is $-50.2 \pm 3.7$ km s$^{-1}$ in the 2021 spectrum (see Figure 4). This result may be a sign of the orbital motion of the cool component. No absorption lines have been found in our near-IR spectra, most likely due to their veiling by the circumstellar dust radiation.

In order to disentangle the contributions of the hot and cool component, we calculated synthetic spectra in several narrow wavelength regions and searched for the best agreement between the observed and synthetic spectra, which contain various fractions of an additional continuum. The latter represents the contribution from the hot component with no absorption lines, which are undetected in our spectra. Such an approach is justified by a negligible change of the components' contributions in the wavelength ranges used in this analysis.

For the synthetic spectra, we downloaded model atmospheres provided by F. Castelli$^{14}$ and calculated the spectra with the code SPECTRUM by Gray & Corbally (1994; see Figure 5) for $T_{\text{eff}}$ between 3500 K and 5000 K, $\log g = 1.5$ and 2.0, and projected rotational velocities of $v \sin i$ between 10 km s$^{-1}$ and 20 km s$^{-1}$. These spectra were compared with the observed spectra obtained at the CFHT in 2008 and 2021. Comparing the absorption line intensities and widths in the synthetic and observed spectra by dividing them and searching for the smallest difference between the two, we derived the most likely contributions of the components. The relative contributions of the hot and the cool components turned out to be 85%/15% in the 5540–5580 Å region, 75%/25% in the 6100–6175 Å region, and 70%/30% in the 6700–6775 Å region, respectively.

The contributions were found to be the same in both the CFHT spectra, while the best-fit accuracy was ~5%. The best fits were found for the following parameters of the cool component: $T_{\text{eff}} = 4250$ K and $v \sin i = 10$ km s$^{-1}$. The parameters of the hot component are derived in Section 3.4 from the SED fitting and the relative contribution of the cool component.

### 3.3. Brightness Variations

The brightness in both visual and near-IR photometric bands varies within ~0.5–0.6 mag and contains short-term and long-term changes. The K-band minimum near JD 2456900 was about the same deepness as the V-band minimum near JD 2458400. Judging from the overlapped V- and K-band data, the brightness changes were nearly synchronous in these bands. Analysis of the color indices' behavior shows that, as the object grows fainter, J–H and H–K become larger while B–V becomes smaller. This conclusion regarding the B–V variations comes from comparison of its values at three different V-band brightness levels. The Maidanak data of 2004–2005 show an average $V = 13.02 \pm 0.05$ mag and $B–V = 0.86 \pm 0.04$ mag.

<footnote n="14">14 https://wwwuser.oats.inaf.it/castelli/grids/gridp00k2odfnew/ap00k2tab.html</footnote>
<table><caption>**Table 6**
List of Absorption Lines Identified in the Spectrum of MWC 645</caption><thead><tr><th>Line</th><th>Mult</th><th>λ<sub>lab</sub></th><th>RV</th><th>EW</th><th>RV</th><th>EW</th><th>Line</th><th>Mult</th><th>λ<sub>lab</sub></th><th>RV</th><th>EW</th><th>RV</th><th>EW</th></tr><tr><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th><th>7</th></tr></thead><tbody><tr><td>FeI</td><td>319</td><td>4611.19</td><td>-20.2</td><td>0.09</td><td>...</td><td>...</td><td>FeI</td><td>205</td><td>6677.96</td><td>-19.3</td><td>0.06</td><td>...</td><td>...</td></tr><tr><td>FeI</td><td>383</td><td>5139.47</td><td>-26.7</td><td>0.07</td><td>...</td><td>...</td><td>All</td><td>5</td><td>6695.97</td><td>-22.8</td><td>...</td><td>-44.8</td><td>0.04</td></tr><tr><td>TiI</td><td>4</td><td>5173.74</td><td>-22.7</td><td>0.06</td><td>...</td><td>...</td><td>All</td><td>5</td><td>6698.63</td><td>-21.5</td><td>...</td><td>-49.2</td><td>...</td></tr><tr><td>FeI</td><td>37</td><td>5446.87</td><td>-27.5</td><td>0.20</td><td>-50.6</td><td>0.14</td><td>FeI</td><td>268</td><td>6703.57</td><td>-24.3</td><td>...</td><td>-49.8</td><td>0.04</td></tr><tr><td>FeI</td><td>15</td><td>5497.51</td><td>-19.6</td><td>0.06</td><td>-47.9</td><td>0.12</td><td>FeI</td><td>1197</td><td>6705.12</td><td>-25.8</td><td>...</td><td>-59.3</td><td>...</td></tr><tr><td>FeI</td><td>686</td><td>5615.65</td><td>-27.4</td><td>0.09</td><td>-60.4</td><td>0.10</td><td>LiI</td><td>1</td><td>6707.74</td><td>-21.5</td><td>...</td><td>-47.4</td><td>0.04</td></tr><tr><td>CaI</td><td>47</td><td>5857.45</td><td>-19.2</td><td>0.08</td><td>...</td><td>...</td><td>FeI</td><td>34</td><td>6710.31</td><td>-24.6</td><td>...</td><td>-50.5</td><td>...</td></tr></tbody></table>

Note. Column information: (1) Element and ionization state. (2) Multiplet number. (3) Lab wavelength in Å. (4) RV in km s⁻¹ measured in the 2008 CFHT spectrum. (5) EW in Å measured in the 2008 CFHT spectrum. (6) RV in km s⁻¹ measured in the 2021 CFHT spectrum. (7) EW in Å measured in the 2021 CFHT spectrum. “-” EW was not measured, due to line weakness, contamination with noise, or blending. Full table is available in the electronic version of the paper.

(This table is available in its entirety in machine-readable form.)

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Comparison of a part of the spectra with absorption lines taken in 2008 and 2021 CFHT. Vertical lines show positions of some lines in the 2008 spectrum, to outline the shift from those in the 2021 spectrum.</figcaption></figure>

mag; the ASAS SN data of 2018 show $V = 13.37 \pm 0.05$ mag and $V - g = 0.32 \pm 0.02$ mag, which corresponds to $B - V = 0.72 \pm 0.03$ mag according to a set of conversions between the Johnson and SDSS photometric systems from Smith et al. (2002); and the TShAO data of 2022 show $V = 13.26 \pm 0.03$ mag and $B - V = 0.76 \pm 0.02$ mag. These results allowed us to establish an approximate relationship between the V- and g-band brightness as $V = 1.25 \times g - 3.74$.

There are just a few historical photometric observations reported for MWC 645. A similar average color index $B - V = 0.86 \pm 0.02$ mag and $V = 13.30 \pm 0.02$ mag were measured by Craine & Tapia (1975), who took six separate

observations in August 1974. However, Swings (1981) derived $B - V = 1.25$ mag from optical spectrophotometry. This result might not have taken into account the filter's response curve, and should be considered with caution.

The object's light curves in the V- and K-band shown in Figure 6 are composed from the ASAS SN data (Kochanek et al. 2017) in the V-band (from December 2014 to November 2018) and the SDSS g-band (from April 2018 to July 2022) as well as from our observations presented in Tables 2 and 3. The ASAS SN g-band magnitudes were converted into V-band magnitudes using the aforementioned relationship. Additionally, two K-band data points were derived from the absolutely calibrated near-IR low-resolution spectra taken at the Lick Observatory (see Section 2).

The light curves contain two deep minima in October/ November 2014 (K-band, near JD 2456961) and in August/ September 2018 (V/g-band, near JD 2458364). More recent data suggest a hint for a new minimum, which may occur in the second half of 2022, especially if these minima are regular. Similarly to the short-term minima, the less frequent and deeper ones may be due to the variable circumstellar extinction.

Periodogram analysis of the visual brightness variations (excluding the minima with $V > 13.2$ mag) performed using the Lomb-Scargle method<fnref n="15" /> shows several peaks in the power spectrum above the confidence level; these peaks correspond to the periods of 69, 145, and 295 days (see top panel of Figure 7). The longest period (~650 days) is unreliable, as the data cover only a few such cycles. Phase curves folded with these periods have an amplitude of ~0.3 mag and a large scatter of data points (see bottom panel of Figure 7). Nevertheless, we note that the application of Fourier analysis to a random sample of data longer than the presented periods does not give any stable peaks in the power spectra, and the discussed signals can have quasi-periodic characters. Thus, neither of the periods can be linked to binarity, because they do not keep the same phase from one observing season to another. Similar cyclic variations are typical for objects with gaseous and dusty envelopes, such as B[e] stars (Miroshnichenko 1998) and protoplanetary nebulae. They are typically attributed to an inhomogeneous distribution of the circumstellar material orbiting the underlying star or binary system.

<footnote n="15">¹⁵ https://exoplanetarchive.ipac.caltech.edu/cgi-bin/Pgram/nph-pgram</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Comparison of the absorption line spectra of MWC 645 and MWC 623 with a model spectrum. The model atmosphere was calculated for $T_{\text{eff}} = 4250$ K, surface gravity $g = 1.5$, and a projected rotational velocity of $v \sin i = 10 \text{ km s}^{-1}$. The contribution of the cool component is 25% in the 6100–6175 Å range and 30% in the 6700–6775 Å range. The intensity is normalized to the local continuum, and the wavelength scale is heliocentric.</figcaption></figure>

### 3.4. Spectral Energy Distribution

The SED data of MWC 645 were taken from different sources, which included both ground- and space-based photometric data. For the optical range, we used the average brightness and color indices at the brightest state, which seems to be least affected by the circumstellar extinction.

These data include $V = 13.02 \pm 0.05$ mag, $U - B = -0.09 \pm 0.10$ mag, $B - V = 0.86 \pm 0.04$ mag from Table 2, and $g - V = 0.39 \pm 0.02$ mag from the ASAS SN data using the $B - V$ to $g - V$ conversion from Smith et al. (2002). The color index $V - R = 2.17 \pm 0.09$ mag contains a strong contribution from the Hα emission line and cannot be used in the SED analysis. The near-IR JHK data were taken from Table 3, while the longer-wavelength data came from all-sky surveys, which are listed in the Figure 8 caption.

In order to take into account the interstellar extinction, we used published relationships between DIBs EW and the color excess $E(B - V)$. The calibrations by Herbig (1993) and Kos & Zwitter (2013) for EWs of the DIBs at 5780 Å and 6613 Å result in a color excess of $E(B - V) = 1.0 \pm 0.1$ mag.

The aforementioned average color indices $U - B$ and $B - V$ at the object's brightest state suggest a total color excess of $E(B - V) \approx 1.0$ mag using a typical Galactic color-excess ratio of $E(U - B)/E(B - V) = 0.72 \pm 0.05$ (see Figure 8, left panel). A correction to the UV magnitudes (0.00, 0.05, and 0.15 mag, respectively) was applied to the $U - B$ and $B - V$ color indices using the cool component contributions derived above (see Section 3.2) and extrapolated to shorter wavelengths. This assessment implies that the object should have a spectral type of B2 with an uncertainty of one subtype.

The reddening of MWC 645 can also be estimated from the ratio of the O I lines at 0.8446, 1.1287, and 1.3165 µm (Rudy et al. 1991). From the 2005 July 3 Lick spectrum, this yields $E(B - V) = 0.94$ mag for the reddening curve from Schlafly & Finkbeiner (2011). Nearly the same result is found for the color excess using both these methods, pointing to a small amount of circumstellar reddening.

However, the SED can still be affected by free-free and bound-free continuum and circumstellar extinction, both of which are capable of producing reddening and are expected given the strong emission-line spectrum and IR excess of
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Light curve of MWC 645 in the *V* and *K* bands. Data are taken from the ASAS SN survey and our observations (an average uncertainty of ~0.02 mag is shown in the corner of the top panel). Top panel: black circles show our data in the *V*-band, red circles are the ASAS SN *V*-band data, blue circles represent ASAS SN *g*-band data to match the *V*-band light curve using the relationship described in the text, and triangles show data taken at TShAO. Bottom panel: *K*-band data. The open circle shows the OAN SPM observation, while plus signs show the Lick observatory data integrated with the *K*-band response curve.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Results of a periodogram analysis of the ASAS SN light curve (see text for the description of used fragments). Top panel: Fourier power spectrum with a confidence level show by the dashed line. Bottom panel: The light curve folded with the 145-day period and a sinusoidal fit with an amplitude of 0.2 mag. The *g*-band data were shifted to the *V*-band scale using the transformation described in the text.</figcaption></figure>

MWC 645. Since the reddening vectors in the left panel of Figure 8 suggest reasonable spectral types of the hot component, we can adopt an upper limit on the circumstellar contribution to the observed continuum of $\le 30\%$, similar to what was found for MWC 728, another binary system with a B-type and a G-type component of the FS CMa-type (Miroshnichenko et al. 2015). Although this value is not strongly justified, it cannot be very high, as it would reduce the luminosity of the hot component and make its $T_{\text{eff}}$ higher and inconsistent with the absence of the He I lines in the spectrum of MWC 645. As shown in Section 4, adopting or neglecting this contribution would not change the main conclusions of the study.

A separate method of assessing the interstellar reddening is using a 3D reddening map based on Gaia distances and photometric data for projectionally close stars from the Pan-STARRS 1 and 2MASS catalogs (Green et al. 2019). It implies a reddening of $E(g-r) \simeq E(B-V) = 0.78 \pm 0.03$ mag in the object's direction (galactic coordinates $l=98^\circ, b=-1^\circ$) at a distance of $6.5 \pm 0.9$ kpc.

The discrepancy between the methods may be due to a scatter in the DIB data collected from a wide range of lines of sight, or a lack of data for main-sequence stars at distances over 6 kpc indicated on the reddening map in the object's direction.16 The latter cause seems to be more probable, as the reddening calculated by the 3D map tool reaches $E(g-r) = 1.0$ mag in just 0.2 toward the galactic plane from the object's position. The assurance is amplified by a very good agreement between the values of $E(B-V)$ derived using the DIB and reddening line methods.

Adopting $E(B-V) = 1.0$ mag and applying an average wavelength dependence of the interstellar extinction (e.g.,

<footnote n="16">16 http://argonaut.skymaps.info/query?lon=98.0&lat=-1.0&coordsys=gal&mapname=bayestar2019</footnote>
<figure><img src="image_10.png" /></figure>

**Figure 8.** Left panel: Color–color diagram. The circle with error bars shows the average color indices of MWC 645 corrected for the cool component contribution (see text). The filled circles show intrinsic color indices from Straizys (1977); open squares show those for O- and early-B stars from Pecaut et al. (2012), for comparison. The dots on the intrinsic color-index lines show positions of stars with various spectral types, some of which around the suggested type for the hot component of MWC 645 are labeled. The dashed lines from the object's position show the interstellar reddening vectors for $E(U - B)/E(B - V) = 0.67$ (lower line) and $E(U - B)/E(B - V) = 0.77$ (upper line). The lengths of both lines correspond to $E(B - V) = 1.0$ mag. Right panel: Spectral energy distribution of MWC 645 corrected for a total reddening of $E(B - V) = 1.0$ mag. Symbols: Filled circles represent optical photometry, open circles show near-IR photometry (JHK), squares are WISE data (Wright et al. 2019), plus signs represent MSX data (MSX Team 2019), crosses are for AKARI data (AKARI Team 2020a, 2020b), and filled triangles are IRAS data (Neugebauer et al. 2019). The red line shows the model SED for $T_{\text{eff}} = 18,000$ K, log g = 3.0, the blue line shows the model SED for $T_{\text{eff}} = 4250$ K, log g = 1.5, and the black line shows a combination of the two with 85% contribution of the hot model and 15% contribution of the cool model at $\lambda = 0.55$ µm. The fluxes are normalized to that in the V band, and the wavelengths are shown in microns.

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

**Figure 9.** Hertzsprung–Russell diagram with positions of some FS CMa objects (black circles) and the components of the MWC 645 system (red and blue circle). Open circles show the positions of the MWC 623 system components (Zickgraf 2001). Evolutionary tracks of single rotating stars are shown by solid lines (Ekström et al. 2012). Numbers at the evolutionary tracks are initial masses in solar units.

Savage & Mathis 1979), we calculated a reddening-free object's SED (see Figure 8, right panel). The dereddened SED was modeled by combining different temperatures of the cool and hot component to reproduce the optical continuum slope. In particular, we used the SED of the model atmospheres (Kurucz 1994) for $T_{\text{eff}}$ between 3500 K and 5000 K for the cool component and between 14,000 and 20,000 K for the hot component.

The best agreement was found for $T_{\text{eff}} = 18,000$ K and $T_{\text{eff}} = 4250$ K and the relative contributions at 5500 Å of 85% (hot component) and 15% (cool component), respectively. The cool component's temperature and contribution to the visual continuum flux are virtually the same as found from the absorption-line spectrum fitting, while the hot component's

temperature closely matches the typical one for a dwarf of the spectral type B2.5 (Pecaut et al. 2012) and is in agreement with the reddening vector method. The resulting SED model is shown in the right panel of Figure 8.

The SED of MWC 645 shows weak emission peaks around $\lambda10$ µm and $\lambda18$ µm, indicating that the circumstellar dust is nearly optically thin and mainly consists of relatively small silicate particles. Such a dust is supposed to produce an additional reddening of the objects' optical fluxes. Since the slope of the dereddened SED in the optical range is consistent with the expected intrinsic SED of the binary system, one can conclude that the dusty disk is tilted with respect to the line of sight and the observed SED is weakly affected by the dust. The presence of a wavelength-independent circumstellar extinction is still possible, and this is discussed in Section 4.

## 4. Discussion

The results of the data analysis clearly show that MWC 645 is a binary system, which consists of a B-type and a K-type star, surrounded by large amounts of the circumstellar gas and dust. The ionized part of the circumstellar gas is responsible for the strong emission-line spectrum, while the dusty part of the envelope produces a strong IR excess suggesting a compact dust distribution manifested from a steep decrease of the IR flux past the maximum at a wavelength of ~5 µm. This qualitative information, along with the derived quantitative parameters (e.g., $T_{\text{eff}}$, reddening, and fractional contributions of the stellar components to the observed continuum flux), gives us an opportunity to put constraints on the system's nature and evolutionary status.

We found neither emission nor absorption lines of He I and He II in our optical spectra. There are several possibilities to explain this fact: (1) emission may fill in the absorption lines, (2) rapid rotation of the star may make photospheric line profiles shallow and undetectable at a low signal-to-noise ratio in the continuum, (3) there may be a helium deficiency in the
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Theoretical evolutionary tracks for a 7.0 $M_\odot$ + 2.8 $M_\odot$ binary system with an initial orbital period of 15 days that includes a phase of a strong nonconservative mass transfer (van Rensbergen et al. 2008). The blue line shows the track for the mass donor (7.0 $M_\odot$), while the red line shows that of the mass gainer (2.8 $M_\odot$). The letters indicate the beginning and ending of the Roche overflow phase. The inset shows the mass transfer process in relative time since the beginning of the evolution. The red and blue circles show the position of the hot (initially less massive) and cool (initially more massive) components of MWC 645 with the derived uncertainties on both $T_{\text{eff}}$ and luminosity.</figcaption></figure>

star's atmosphere, and (4) weak helium lines may be contaminated with absorption lines of the cool component.

The absence of He II lines, which are usually observed only in O-type stars, in our spectra puts an upper limit on the hot star $T_{\text{eff}}$ as ~28,000 K. Studies of various early-type emission-line stars show that emission components, which originate in the circumstellar medium, show up in He I lines at $T_{\text{eff}}$ ~20,000 K (e.g., Miroshnichenko 2007). It has also been shown that hotter stars with the Be and B[e] phenomenon exhibit stronger emission-line spectra compared to cooler stars (e.g., Miroshnichenko 2008). Therefore, one can roughly assign an early-B subtype for the spectral type of the hot component. This issue has been nearly avoided in the literature, where only B-type with no subtype was mentioned by Allen & Swings (1976) and Jaschek et al. (1996). Also, He I lines in emission have been observed in the IR spectra of objects with the B[e] phenomenon while also being detected in absorption in the optical spectra (e.g., Miroshnichenko et al. 2002).

As mentioned above, Jaschek et al. (1996) suggested the possible presence of weak He I lines at 6678 Å and 7065 Å. Our spectra with the highest signal-to-noise ratios show absorption features near these wavelengths that we identified as Fe I lines, as their RVs are close to those of the cool component (see Section 3.2 and Table 6). However, we also detected no He I lines at shorter wavelengths (e.g., 5876 Å, 5015 Å, 4921 Å), where the contribution of the cool component is much weaker. Summarizing this analysis, we cannot rule out any of the outlined possibilities, but the former two look more probable because helium emission lines are present in the IR spectrum.

Assuming that the circumstellar extinction is roughly balanced by the circumstellar continuum emission, and taking into account that the emission lines make a very small amount of additional to the continuum (0.04 mag to the V-band flux), one can estimate the luminosity of the system components. To do that, we use the system's average V-band brightness at the brightest level ($V = 13.02 \pm 0.05$ mag), the interstellar extinction $A_V = 3.1 \times E(B-V) = 3.1$ mag, and the GAIA EDR3 distance ($D = 6.5 \pm 0.9$ kpc; Bailer-Jones et al. 2021).

We also need to separate the contributions of the stellar components and assume a certain contribution of the

circumstellar continuum. As the cool component contributes 15% to the V-band flux of the system, its visual brightness comes to $V = 15.1$ mag, the absolute magnitude $M_V = -2.9_{-0.7}^{+0.9}$ mag, and the luminosity $\log L/L_\odot = 3.1_{-0.4}^{+0.3}$ (with a bolometric correction of $BC_V = -0.9 \pm 0.2$ mag for $T_{\text{eff}} = 4250 \pm 250$ K; Pecaut et al. 2012). An upper limit for the hot component's luminosity is set by assuming a zero contribution of the circumstellar continuum and comes to $\log L/L_\odot = 4.2_{-0.4}^{+0.3}$ for $T_{\text{eff}} = 18,000 \pm 2000$ K and $BC_V = -1.7 \pm 0.3$ mag. A lower limit that is based on a 30% contribution of the circumstellar continuum is $\log L/L_\odot = 3.9_{-0.4}^{+0.3}$. Figure 9 shows a Hertzsprung-Russell (HR) diagram with positions of some FS CMa objects and the components of the MWC 645 system.

Evolution of intermediate-mass binary systems has been studied theoretically. In particular, van Rensbergen et al. (2008) calculated a grid of models for conservative evolution as well as for a weak and strong tidal interaction between the stars. The grid includes detailed calculations of physical and orbital parameters from the beginning of the main-sequence evolution through the entire mass-transfer phase and beyond. In this grid, we found reasonably good matches for the current positions of the MWC 645 system's components. These models have initial masses 7.0 $M_\odot$ and 2.8 $M_\odot$ with initial orbital periods of 15–20 days and a strong mass transfer. Figure 10 shows the evolutionary tracks of one of these models.

In these models, the initially more massive donor star loses a mass of ~1.5–2.0 $M_\odot$ in ~$10^4$ yr. Currently, the mass-transfer rate is ~$2 \times 10^{-4} M_\odot \text{yr}^{-1}$, as the donor overfills its Roche lobe. The strong emission-line spectrum observed supports the suggestion about such a large mass-transfer rate. The nonconservative character of the latter is, in turn, consistent with the existence of the large amount of the circumstellar matter. This also implies that the periods found in the periodogram analysis (see Section 3.3) cannot be considered as orbital periods, because in this case neither companion would fill its Roche lobe.

An additional support for the current state of the system comes from a qualitative comparison with $\beta$ Lyrae, a binary with an ongoing mass transfer. Brož et al. (2021) presented a model of the complicated structure of the circumstellar
environments of $\beta$ Lyrae, including a disk, a spherical envelope, and a jet. All these components contribute to the emission-line profiles, which are morphologically similar to those of MWC 645 (double-peaked with a stronger redshifted peak). In particular, the jet, which comes from the gainer's disk, can be more powerful in the MWC 645 system, due a stronger mass-transfer rate than that in $\beta$ Lyrae ($\sim 10^{-5} M_{\odot} \text{yr}^{-1}$), and can cause a much stronger redshifted emission peak in the line profiles. The emission-line profiles in the spectrum of $\beta$ Lyrae are double-peaked with an almost equal width of the peaks, which can be different from those of MWC 645, due to a different tilt angle with respect to the line of sight ($\beta$ Lyrae is viewed nearly edge-on).

At the same time, the comparison with $\beta$ Lyrae is somewhat limited. A thick accretion disk around the mass gainer, which produces both an absorption- and an emission-line spectrum, is thought to be present in $\beta$ Lyrae (Ak et al. 2007; Brož et al. 2021). However, its properties (e.g., a high temperature and rotation velocity that cause broad spectral lines of ionized metals) are very different from those of MWC 645 (narrow absorption lines of neutral metals). Therefore, we suggest that, if an accretion disk is present in the MWC 645 system, it does not manifest itself through the observed absorption-line spectrum.

The observed photometric variations, which include nearly simultaneous fading of the visual and near-IR brightness accompanied with a decrease of the B-V color index and an increase of the J-H and H-K color indices, can be qualitatively explained by denser parts of the orbiting circumstellar dust passing in front of the binary. The “blueing” in the optical part of the spectrum may be due to an enhanced scattering off a larger number of dusty particles in the line of sight, while the “reddening” in the near-IR part may be due to blocking of hotter dust by cooler dust in the attenuating denser and more distant fragment. If the long-term fadings are regular with a period of $\sim 4$ yr, then such denser fragments should be located at a distance of $\sim 5$ au from the pair that is not the inner edge of the dusty envelope, thus justifying the latter effect.

## 5. Conclusions

We have presented the results of high-resolution spectroscopic and multicolor photometric observations of the FS CMa-type object MWC 645. The main findings of our study include the detection of a cool secondary component, quasi-cyclic photometric variability in both visual and near-IR region, and constraining the fundamental parameters of the system components.

MWC 645 can be classified as an FS CMa-type object based on its binary nature and the system components' positions in the HR diagram. Although relevant evolutionary models do not exactly describe the properties of the components, the observed strong emission-line spectrum is consistent with a strong current mass transfer between the components. The unusual profiles of many emission lines (a broad blueshifted peak and a

stronger and narrower redshifted peak) may present further evidence for the ongoing transfer.

MWC 645 is the first FS CMa group member with a seemingly ongoing mass transfer, while binaries found earlier most likely have finished the mass-transfer process (e.g., Miroshnichenko et al. 2015; Khokhlov et al. 2018; Miroshnichenko et al. 2020). A closer study that includes higher signal-to-noise, high-resolution spectroscopy at large telescopes and multicolor photometric monitoring would allow determination of more properties of the system, such as the orbital period and inclination, as well as those of its circumstellar envelope. In particular, constraining the cyclicity of possible brightness variations would help to extend theoretical studies of mass-transferring binaries to studying the structure of the circumstellar environments.

This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (grant No. AP08856419). It has made use of the SIMBAD database, operated at CDS, Strasbourg, France; SAO/NASA ADS, ASAS, Gaia, data products as well as those from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration; the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation; the Midcourse Space Experiment (MSX) Point Source Catalog; and the AKARI Infrared Astronomical Satellite All-Sky survey. 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 6 m telescope of the Russian Academy of Sciences, 2.7 m Harlan J. Smith telescope of the McDonald Observatory (Texas, USA), and the 2.1 m telescope of the Observatorio Astronómico Nacional San Pedro Martir (Baja California, Mexico). 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.K. acknowledges Al-Farabi Kazakh National University for a postdoc position. V.G.K. thanks the Russian Science Foundation for support (grant No. 22-12-00069). S.Z. acknowledges PAPIIT grants IN102120. Some of the observational data were obtained via the unique scientific facility SAO RAS, and the data processing was supported under the Ministry of Science and Higher Education of the Russian Federation grant 075-15-2022-262 (13. MNPMU.21.0003).
Appendix
Spectral Atlas

<figure><img src="image_14.png" /><figcaption>**Figure 11.** The most informative parts of a high-resolution CFHT spectrum of MWC 645 (R = 65000). The intensity is normalized to the continuum, and the wavelength scale is heliocentric.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Figure 12.** A continuation of Figure 11.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>Figure 13. A continuation of Figure 11.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Figure 14. A continuation of Figure 11.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure 15.** A continuation of Figure 11.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Figure 16.** A continuation of Figure 11.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Figure 17.** A continuation of Figure 11.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Figure 18. A continuation of Figure 11.</figcaption></figure>

## 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

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

V. G. Klochkova https://orcid.org/0000-0002-7981-0916

K. N. Grankin https://orcid.org/0000-0001-5707-8448

V. M. Larionov https://orcid.org/0000-0002-4640-4356

R. J. Rudy https://orcid.org/0000-0003-3096-759X

R. B. Perry https://orcid.org/0000-0002-4717-7837

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