The Detection and Characterization of Be+sdO Binaries from HST/STIS FUV Spectroscopy

Close binaries are common among massive stars, and growing evidence suggests that many massive stars are evolutionary products of post-interacting binary systems that have experienced mass transfer (de Mink et al. 2014). There are two main routes of binary interaction. In the case where the companion star has a much lower mass, the more massive component will evolve and fill its Roche lobe and may engulf the companion in a common envelope stage that leads to a merger. Alternatively, for systems with more comparable masses, the more massive donor star will transfer its mass and angular momentum to the gainer star through Roche lobe overflow. The orbit shrinks and promotes further mass transfer until the two components reach comparable masses. Then continuing mass transfer will expand the orbit until the donor star is stripped of its outer envelope, leaving a hot core with a size much smaller than its Roche lobe. The gainer star will become a rapid rotator.

Be stars are B-type main-sequence stars, and their optical spectra display broad Hα emission that originates in an outflowing, circumstellar decretion disk. They are rapidly rotating stars, and their projected rotational velocities $V\sin i$ can reach up to 70%–80% or larger of their critical rotational velocities (Yudin 2001; Huang et al. 2010). Pols et al. (1991) and Shao & Li (2014) argue that Be stars were spun up through close binary interactions. If so, then many Be stars will have companions that are the remnants of the mass donor. The final stripped donor star may explode to create a neutron star in a Be X-ray binary, or it will evolve into a faint, hot, low-mass subdwarf (sdO) star and create a Be+sdO binary system. Pols et al. (1991) predict that majority of the evolved companions in Be binaries are He stars (sdO remnants). Recently, Bodensteiner et al. (2020b) showed that Be stars lack normal B-type companions, in stark contrast to regular B-type stars, and they argue that this implies that many Be stars are the products of binary interaction (either mergers or binaries with faint evolved companions).

The sdO spectral designation encompasses a wide range of hot objects with diverse evolutionary histories. Many sdO stars occupy the extreme horizontal branch in the Hertzsprung–Russell (H-R) diagram, and they typically have effective temperatures in the range of 35 kK–55 kK, gravities $\mathrm{log}g$ spanning the range of 5.1 and 6.4 (cgs units), and luminosities from 10 to 100 times solar luminosity (Heber 2009, 2016). Most of the sdO stars are probably descendants of red giant stars, although some have hot temperatures and high luminosities similar to those of the central stars of planetary nebulae (Heber et al. 1988; Rauch et al. 1991). The sdO stars with temperatures below 40 kK are probably He-core-burning objects, while the hotter ones have entered a subsequent He-shell-burning stage. The sdO companions of Be stars must have formed by stripping through binary interactions, and they typically have larger masses and radii than the general population of low-mass sdO stars.

The sdO components of Be binary systems are faint and hard to detect, but they are hot and contribute more flux in the shorter wavelength part of the spectrum due to their high temperature. Thus, searches for their spectral features are more favorable in the far-ultraviolet (FUV). The first detection of the spectrum of an sdO star in a Be binary ϕ Per was reported by Thaller et al. (1995) using the International Ultraviolet Explorer (IUE) FUV spectroscopy. They estimated that the sdO companion contributes ∼12% of the UV flux of the Be star. This result was confirmed by Gies et al. (1998) from FUV observations with Hubble Space Telescope (HST), and the sdO-to-Be flux ratio was estimated to be 16% at 1374 Å. The binary orbit of this system was subsequently resolved through long-baseline interferometry with the CHARA Array by Mourard et al. (2015). Continuing searches for sdO companion stars using IUE spectroscopy led to the discovery of another three Be+sdO systems: FY CMa (Peters et al. 2008), 59 Cyg (Peters et al. 2013), and 60 Cyg (Wang et al. 2017). The sdO companions in these systems contribute ∼4% of the FUV flux. One fainter sdO companion was found in HR 2142, which has an estimated flux ratio of only ∼1% (Peters et al. 2016). Wang et al. (2018) conducted an IUE survey study to search for additional Be+sdO systems, and they found another 12 candidates in a sample of 264 stars that were not known binaries. Chojnowski et al. (2018) reported a detection of an sdO companion through an investigation of a large set of optical spectra in Be binary system HD 55606, and several other systems are suspected of hosting a hot companion from clues in their optical spectra (Koubský et al. 2012, 2014; Harmanec et al. 2020). The detected sdO companions have temperatures in the range of 42–53 kK and masses between 0.7 and 1.7 M_⊙.

These Be+sdO binaries are important for studies of massive star evolution because a large fraction of massive stars have nearby stellar companions (Sana et al. 2012) and binary interactions play a key role in their destinies (de Mink et al. 2014). Hot sdO stars may contribute significantly to the UV flux of stellar populations (Han et al. 2010; Götberg et al. 2019) and constitute an important contribution to spectral synthesis models (Eldridge et al. 2017). Those sdO stars with a mass above the Chandrasekhar limit may explode as hydrogen-deficient supernovae (SN Ib and SN Ic; Eldridge et al. 2013). Binary systems at the high-mass end may also be closely related to the progenitors of neutron star pairs that can merge to create bright gravitational wave sources (Tauris et al. 2017).

Be+sdO binaries may also be related to several systems that are claimed to be black hole binaries. Liu et al. (2019) found that the LB-1 system consists of what appears to be a B-giant star with an invisible companion. More recently, Rivinius et al. (2020) reported that HR 6819 also hosts a B-giant orbiting an unseen companion. In both cases, the mass of the faint component is much larger than that of the B giant, so that the companions are possibly black holes but without the X-ray emission that characterizes the massive X-ray binaries. Also, in both cases, Balmer line emission is present, the defining criterion of Be stars. Subsequent work indicates that both the emission lines (Gies & Wang 2020; Liu et al. 2020) and faint, broad absorption lines (Bodensteiner et al. 2020a; Shenar et al. 2020; El-Badry & Quataert 2021) show the small-amplitude, reflex orbital motion around the B-giant component. If the Be-star component has normal mass, then the B-giant component must be an unusual, low-mass object. Furthermore, the atmosphere of the B-giant component in LB-1 is enriched in He and N (Irrgang et al. 2020; Shenar et al. 2020), and a N enrichment is found for HR 6819 (Bodensteiner et al. 2020a; El-Badry & Quataert 2021). These enrichments are associated with He-core burning through the CNO cycle, and their presence suggests that plasma from the core now occupies their atmospheres. Thus, the B-giant star in both cases may be the stripped remnant of mass transfer caught during a short transition stage leading to a Be+sdO system (Section 7).

It is vitally important to obtain FUV spectroscopy of Be+sdO systems because analysis of their rich spectra offers us the means to determine the physical parameters of the stripped-down remnants. Here we report on new FUV spectroscopy from the HST/Space Telescope Imaging Spectrograph (STIS) of the sample of candidate Be+sdO binaries from the work of Wang et al. (2018) and Chojnowski et al. (2018). We describe the FUV observations and associated reduction details in Section 2. In Section 3, we present measurements of the radial velocities of the Be stars. These are used in Section 4 to remove the Be-star contribution to cross-correlation functions (CCFs) of the observed spectrum with a model spectrum for the hot component. We detect the CCF signal from a hot sdO component in 10 of the 13 systems. In Section 5, we describe our methodology to determine the physical properties of the sdO stars for the detections. We use model fits of the observed spectral energy distributions in Section 6 to determine the angular diameters of the Be stars, and these are used with the estimated distances and radius ratios to estimate the radii of each stellar component. Section 7 presents a comparison of the derived temperatures and radii of the sdO components with evolutionary tracks. We summarize our work in Section 8.

The targets of this investigation were identified as candidate Be+sdO binaries by Wang et al. (2018) through an examination of CCFs of high-dispersion, Short Wavelength Prime (SWP) camera spectra from IUE with a model spectrum with an assumed temperature of 45 kK. These 12 targets all displayed narrow CCF peaks (unlike the broader Be-star features), and the CCF peaks were generally velocity variable (in cases with multiple spectra), indicating Doppler shifts from orbital motion. The final target, HD 55606, was discovered to be a Be+sdO binary with a 93.76 day period by Chojnowski et al. (2018), who observed narrow components of He i lines from the sdO component in high-quality optical spectra. Table 1 summarizes the properties of the sample. It lists the Henry Draper Memorial (HD) catalog number, star name, spectral classification, and physical properties of the Be stars, including the effective temperature (T_eff), gravity ($\mathrm{log}g$), and projected rotational velocity ($V\sin i$), as well as source references for these estimates. We also include in the last column an estimate of $V\sin i$ that we applied in creating models of the Be-star spectrum to account for its contribution to the CCF analysis (see Section 4).

Table 1. List of Targets

HD	Star	Spectral	Reference	Teff	Reference	$\mathrm{log}g$	Reference	$V\sin i$	Reference	$V\sin i$ (HST)
Number	Name	Classification		(K)		(cm s−2)		(km s−1)		(km s−1)
29441	V1150 Tau	B2.5 Vne	1	20,350	2	4.0	11	338	3	380
43544	HR 2249	B3 V	1	21,500	4	3.9	4	260	7	260
51354	QY Gem	B3 Ve	1	20,000	11	4.0	11	330	5	330
55606	MWC 522	B2 Vnnpe	6	27,350	7	4.3	7	335	7	335
60855	V378 Pup	B3 IV	1	20,000	11	4.0	11	244	8	300
113120	LS Mus	B2 IVne	4	22,800	7	3.7	7	339	7	460
137387	κ Aps	B2 Vnpe	4	23,950	7	4.0	7	250	7	380
152478	V846 Ara	B3 Vnpe	4	19,800	7	3.7	7	295	7	300
157042	ι Ara	B2.5 IVe	1	25,860	7	4.2	7	340	7	320
157832	V750 Ara	B1.5 Ve	9	25,000	9	3.9	11	277	10	250
191610	28 Cyg	B3 IVe	1	20,470	7	3.7	7	300	7	300
194335	V2119 Cyg	B2 IIIe	1	25,600	7	4.3	7	360	7	360
214168	8 Lac A	B1 IVe	1	27,380	7	4.1	7	300	7	360

Note. Indices of references: (1) Slettebak (1982), (2) Hohle et al. (2010), (3) Jaschek & Egret (1982), (4) Levenhagen & Leister (2006), (5) Halbedel (1996), (6) Chojnowski et al. (2018), (7) Zorec et al. (2016), (8) Huang & Gies (2006), (9) Lopes de Oliveira & Motch (2011), (10) Yudin (2001), and (11) estimated values based upon spectral classification.

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We obtained FUV spectra of the 13 Be+sdO candidate systems with the HST and STIS (Kimble et al. 1998). The spectra were made with the MAMA detector and the E140M echelle grating. The spectra cover a wavelength range of 1144–1710 Å with a resolving power of R = 45,800 (Riley et al. 2019). Most of the stars are bright and required the use of the 0.2X0.05ND or other aperture with a neutral density filter in order to meet the bright flux limits of the MAMA detector. The sole exception was the fainter star, HD 55606, where the default 0.2X0.2 aperture was used. The observations were made for each target in three, single orbit visits between 2019 August and 2020 February at intervals of days to months. We usually obtained a signal-to-noise ratio (S/N) of 30 per pixel or better in the best-exposed parts of the spectrum.

The FUV spectra were reduced, and the wavelength and flux were calibrated, following the standard STIS pipeline (Sohn et al. 2019). We subsequently combined the echelle orders onto a single uniform wavelength grid on a $\mathrm{log}\lambda$ scale with an equivalent pixel size of 7.5 km s⁻¹. A number of prominent interstellar medium lines, such as Si iv λ λ 1394,1403 and C iv λ λ 1548,1550, were removed from the spectra by linear interpolation across the features. We also removed the geocoronal Ly α λ1216 line by interpolation. The spectra were rectified in flux by applying a spline fit to relatively line-free regions. The final working product was a rectified spectrum matrix as a function of wavelength and heliocentric Julian date (HJD). Figure 1 displays the observed spectra of a cooler Be star (HD 43544) and a hotter Be star (HD 55606). The observed spectrum is shown in black, and it is compared to model spectra for the Be star (offset by +1.0 and shown in blue) and the sdO star (offset by +2.5 and shown in green). These kinds of models are used in the CCF analyses described below (see Sections 3 and 4).

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Our main goal in this work is to find the spectral line patterns that correspond to the faint sdO companion star in these targets. It is very difficult to identify individual spectral lines from the sdO star because they are weak in the combined spectrum and blended with the rotationally broadened lines of the Be star. Instead, we calculate the CCFs of the observed spectra with a model spectrum for an adopted hot temperature for the sdO star. The CCF effectively multiplexes the spectral signal from all the faint lines into a single high-S/N CCF for investigation. However, there is usually some correlation between the spectral features of the Be star and the hot model spectrum, so that the CCF appears as a composite of a broad component from the Be star and a generally narrow component from the sdO star. We need to remove the Be-star component from the CCF in order to isolate the part of CCF due to the sdO spectral features. The first step in this process is to register the Be component in velocity space, and in this section, we describe how the radial velocities of the Be stars were measured.

The radial velocities of the Be stars were determined by forming the CCF of the observed spectrum with a model for the Be star itself. The Be-star model spectrum was constructed from the TLUSTY BSTAR2006 grid (Lanz & Hubeny 2007) by interpolation in solar abundance model spectra for the effective temperature (T_eff) and surface gravity ($\mathrm{log}g$) given in Table 1. The interpolated spectrum was convolved with a rotational broadening function for the projected rotational velocity ($V\sin i$) from Table 1 and an interpolated, linear limb-darkening coefficient from Kurucz LTE models derived by Wade & Rucinski (1985). The resulting CCFs are very broad (Figure 2), and their central peaks may be influenced by the correlation between the Be model and the central CCF peak from the sdO star. Consequently, we measured the Be-star velocity by finding the wing bisector position using the Gaussian sampling method described by Shafter et al. (1986). The radial velocity uncertainties were calculated using the maximum likelihood from Zucker (2003), which is associated with the second derivative of the CCF peak, the number of wavelength points within the CCF peak, and the peak height. Tests show that these errors are comparable to those obtained by selecting bisectors above and below the default value of 50% peak height. We report our radial velocity measurements and their uncertainties in columns 3 and 4, respectively, of Table 2.

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In order to confirm the detection of the hot subdwarf companions in these candidate systems, we adopted the methodology described in Wang et al. (2018) to search for the spectral signature of the subdwarf O-type (sdO) star by forming CCFs of the observed FUV spectra with a model spectrum for a very hot star. The default model spectrum was derived from the OSTAR2003 grid of solar abundance models based upon the nonlocal thermal equilibrium (non-LTE) atmospheres code TLUSTY and the associated radiative transfer code SYNSPEC (Lanz & Hubeny 2003). The adopted parameters for the model spectrum are T_eff = 45 kK, $\mathrm{log}g=4.75$, and $V\sin i\,=0$ km s⁻¹, and these are typical of estimates derived for known Be+sdO systems (Wang et al. 2017). The adopted gravity parameter is the highest value available in the OSTAR2003 grid, but it may underestimate the actual value for the subdwarf companions.

The CCFs should ideally reflect the photospheric absorption lines of the components, so we omitted those regions with spectral features that are much broader than the line profiles associated with rotational broadening. The omitted regions included the deep and broad absorption line profiles of Ly α λ1216 and Si iii λ1300 blend, as well as the beginning and ending regions of the spectrum. In addition, we excluded the broad wind line features of Si iv λ λ1393,1402 in the cases of HD 43544, HD 55606, HD 60855, HD 137387, HD 152478, and HD 194335. Both the Si iv λ λ1393,1402 and C iv λ λ1548,1550 wind lines were omitted in spectra of HD 29441, HD 113120, and HD 157042.

We caution that the solar abundance model spectrum used to represent the sdO spectrum may not match the abundance patterns accurately. Many low-mass sdO stars have spectra that are He rich with metallic line enhancements. For example, Rauch (1993) examined the FUV spectrum of the low-mass sdO star HD 128220 based upon 38 high-resolution IUE spectra. Through a careful spectral analysis using non-LTE models, he found that the star has an effective temperature of T_eff = 40.6 ± 0.4 kK, $\mathrm{log}g=4.5\pm 0.1$, and a mass of 0.54 ± 0.01 M_⊙. Furthermore, the star is helium rich with n_He/n_H = 0.30 ± 0.05. Because this subdwarf star has measured T_eff and $\mathrm{log}g$ values that are similar to our model template, but with enhanced helium abundance, it provides a good test case of the applicability of our adopted solar abundance model. We downloaded from MAST ⁷ a high-resolution SWP spectrum of HD 128220 made on HJD 2,444,256.0. The spectrum was reduced and rectified following the procedures reported in Wang et al. (2018). In Figure 3, the spectrum of HD 128220 is illustrated in black in the left panel, and the TLUSTY model spectrum of the subdwarf component is offset by +1.0 and shown in green. In order to bring the observed spectrum into agreement with the rest frame of the model spectrum, we shifted the observed spectrum by adopting a radial velocity of RV = 15.2 ± 2.2 km s⁻¹ from Howarth (1987) for the date of observations. We then cross-correlated the observed spectrum with the TLUSTY model spectrum. The resulting CCF is shown in the right panel in Figure 3. A sharp peak is clearly seen indicating the detection of the subdwarf star in HD 128220 using the model spectrum. Therefore, we can safely assume that the TLUSTY model spectrum provides a sufficiently good match of an sdO spectrum for application in our search for their spectral signature in the observed HST spectra.

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The resulting CCFs generally are very broad because of the correlation of the model lines with the rotationally broadened lines of the Be star. In those cases of a positive detection, the CCF appears to show a sharp peak from the sdO spectral features that is superimposed on top of the broad CCF component from the Be star. We applied the following method to remove the Be component from the CCFs and isolate the signal from the sdO star. We first calculated a CCF for model spectra of both the Be star (using the parameters in Table 1) and the sdO star. This simulated CCF was shifted from the zero-velocity frame to the specific radial velocity of the Be star from Section 3 (Table 2), and the CCF amplitude was rescaled to match that of the wings in the CCF of the observed spectrum with the model sdO spectrum. In many cases, we found that the CCF of the model Be and model sdO spectrum did not match well with the observed CCF width, so we reset the value of the projected rotational velocity $V\sin i$ for the model Be-star spectrum in order to attain a better fit of the CCF wings. These adjusted $V\sin i$ values are listed in the final column of Table 1, and the uncertainties are of order 10% because the widths were set by visual inspection. Once the simulated Be model plus sdO model CCF was registered in velocity, adjusted in width, and rescaled in CCF amplitude, we then subtracted this model from the CCF of the observed spectrum and model sdO spectrum. This procedure is illustrated in Figure 4 for the case of one observation of HD 137837. We see that the simulated CCF from the model Be star and model sdO-star spectrum does match the observed CCF wings, and by subtracting this component, we form a residual CCF that clearly shows the narrow central peak from correlation with the sdO spectral lines alone.

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We examined the residual peaks formed this way for all the observed spectra, and we detected CCF peaks from a hot subdwarf companion in 10 Be+sdO targets. These positive detections were reanalyzed using a grid of test effective temperatures for the sdO component (see Section 5), and we adopted the temperature that maximized the residual CCF peaks as the default for the model sdO spectrum. We then repeated the procedure of subtracting the Be component in the CCF using a model with the adopted sdO temperature instead of the default T_eff = 45 kK value. The final residual CCFs are plotted for the 10 positive detection cases in Figures 5–7. No residual peaks were found that were significantly larger than the variation in the CCFs far from zero velocity for HD 157832, HD 191610, and HD 214168. The residual CCFs for these three nondetections are shown in Figure 8 and are based on the default T_eff = 45 kK model for an sdO component. It is puzzling that no obvious CCF peaks were found for these three cases, given that clear peaks were detected in CCFs constructed in a similar way for the lower-S/N IUE spectra (and often in multiple observations; Wang et al. 2018). This may result from temporal variations in the overall visibility of the spectral lines of the sdO component (Section 8).

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5.1. Radial Velocities

5.2. Projected Rotational Velocity

The width of the peak in the residual CCF is directly related to the projected rotational velocity $V\sin i$ of the sdO line profiles. We made a simulation of the dependence of the CCF peak FWHM (from Gaussian fits) as a function of assumed $V\sin i$ by calculating model spectra on the observed grid that were convolved with a rotational broadening function for a range in $V\sin i$. We then formed CCFs of these model spectra with the adopted model sdO spectrum, and we made Gaussian fits of the resulting CCF peaks to build a functional relation between $V\sin i$ and CCF FWHM. An example of this relation from the numerical tests is shown in Figure 9. Comparison of the observed FWHM results with these relations indicates that the sdO-star spectral lines are mainly unresolved in the R = 20,000 versions of HST/STIS spectra. The only exception is the case of HD 51354 that shows significantly broader CCF peaks than those in any of the other detected sdO targets. The derived value of $V\sin i$ for HD 51354 is given in column 3 of Table 3, and upper limits are reported for the other nine cases where the sdO signal is detected. The uncertainty in $V\sin i$ is the standard deviation of the derived values from the FWHM measurements in the residual CCFs of the three observations. The upper limits are set by the largest estimate from the three spectra or by the limit associated with the spectral resolution.

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Table 3. Physical Properties of sdO Stars

HD	Teff	$V\sin i$	f2/f1	F2/F1	R2	$\mathrm{log}L$
Number	(K)	(km s−1)			(R⊙)	(L⊙)
29441	40,000	<15	0.027 ± 0.003	9.9 ± 2.4	0.28 ± 0.04	${2.26}_{-0.21}^{+0.14}$
43544	38,200	<15	0.090 ± 0.009	6.8 ± 1.5	0.51 ± 0.08	${2.70}_{-0.23}^{+0.15}$
51354	43,500	102 ± 4	0.099 ± 0.027	11.7 ± 2.7	0.47 ± 0.09	${2.85}_{-0.18}^{+0.13}$
55606	40,900	<24	0.041 ± 0.002	8.4 ± 1.9	0.31 ± 0.04	${2.38}_{-0.19}^{+0.13}$
60855	42,000	<27	0.041 ± 0.003	10.9 ± 2.6	0.50 ± 0.07	${2.85}_{-0.20}^{+0.14}$
113120	45,000	<36	0.041 ± 0.009	7.6 ± 3.6	0.30 ± 0.10	${2.52}_{-0.53}^{+0.23}$
137387	40,000	<17	0.032 ± 0.003	4.8 ± 1.0	0.44 ± 0.06	${2.65}_{-0.20}^{+0.14}$
152478	42,000	<15	0.049 ± 0.003	11.5 ± 2.7	0.27 ± 0.04	${2.31}_{-0.21}^{+0.14}$
157042	33,800	<36	0.026 ± 0.003	2.5 ± 0.6	0.61 ± 0.09	${2.64}_{-0.23}^{+0.15}$
157832	45,000 a	⋯	<0.007	5.2	<0.37	<2.70
191610	45,000 a	⋯	<0.024	11.5	<0.19	<2.13
194335	43,500	<15	0.047 ± 0.007	4.8 ± 0.9	0.52 ± 0.07	${2.94}_{-0.23}^{+0.15}$
214168	45,000 a	⋯	<0.019	3.6	<0.42	<2.82

Note.

^a Assumed sdO temperature value.

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5.3. Effective Temperature

The residual CCF peak heights are sensitive to the degree of agreement between the model sdO spectrum and the sdO line contribution to the observed spectrum. The model properties are primarily set by the assumed effective temperature, so for each positive detection, we calculated residual CCFs over a range in assumed sdO temperature in the same way as described above (Section 4), and then we measured the resulting peak height. Figure 10 shows the variation in peak height with assumed effective temperature T_eff for one observation of HD 43544 plus a spline fit of the relation. We took T_eff at the position of the maximum of the spline fit as the best estimate of the temperature of the sdO star, and these are listed for the 10 detected Be+sdO systems in column 2 of Table 3. The range in the resulting T_eff values between observations is generally small, but given the uncertainty in the other model parameters (such as how much the actual gravity differs from the assumed $\mathrm{log}g=4.75$), we estimate that temperature uncertainties are comparable to the grid step size in the OSTAR2003 models, △T_eff = 2.5 kK.

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5.4. Monochromatic Flux Ratio

The height of the residual CCF peak is closely related to the flux contribution of the sdO star to the combined FUV flux. We relied upon a simulation of the residual CCFs for models of the spectra of the Be star and sdO star that were made over a range of test values of monochromatic flux ratio r = (f₂/f₁). Each composite model was created using the best-fit parameters for the Be star from Table 1 (from the BSTAR2006 grid) and for the sdO star from Table 3 (from the OSTAR2003 grid), and then the two rectified spectra were added by

$$\begin{eqnarray}&&f(\mathrm{model})=(f(\mathrm{Be})+{rf}(\mathrm{sdO}))/(1+r).\end{eqnarray} \tag{ 1 }$$

This approach assumes a constant flux ratio across the observed wavelength range, which is a reasonable assumption given the high temperatures of both components. We then calculated the CCF of the model spectrum with an sdO model for the best-fit T_eff and $V\sin i=0$ km s⁻¹ in the same way as we did for the observed spectra (Section 4). The Be contribution to the resulting CCF was then removed as done previously, and the residual CCF peak height for the sdO component was measured. The result is a relation between the assumed flux ratio r and residual CCF peak height, and an example is shown in Figure 11. We interpolated within each of these target specific curves to determine the flux ratio r from the measured residual CCF peak heights. These flux ratio estimates and their standard deviations are listed in column 4 of Table 3.

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The observed flux ratio f₂/f₁ is related to surface flux ratios F₂/F₁ and area ratio ${\left({R}_{2}/{R}_{1}\right)}^{2}$ by

$$\begin{eqnarray}&&\displaystyle \frac{{f}_{2}}{{f}_{1}}=\displaystyle \frac{{F}_{2}}{{F}_{1}}{\left(\displaystyle \frac{{R}_{2}}{{R}_{1}}\right)}^{2}.\end{eqnarray} \tag{ 2 }$$

The surface fluxes were taken as the average fluxes from the TLUSTY/SYNSPEC flux models over the range 1450–1460 Å, which corresponds to the near-center part of the observed wavelength range. These fluxes depend mainly upon the adopted temperatures of the Be and sdO stars, and the surface flux ratio F₂/F₁ is given in column 5 of Table 3. The uncertainty in this ratio was determined by the errors in the effective temperatures (assumed as σ(T_eff) = 2.5 kK). Thus, we can use the observed flux ratio and surface flux ratio to arrive at the radius ratio. In Section 6 below, we derive estimates for the Be-star radius R₁ from the spectral energy distribution and distance. Then, we solve for the sdO-star radius R₂ from the radius ratio, and these radii are given in column 6 of Table 3. Finally, we estimate the luminosity of the sdO star in column 7 using

$$\begin{eqnarray}&&\mathrm{log}L/{L}_{\odot }=4\mathrm{log}T/{T}_{\odot }+2\mathrm{log}R/{R}_{\odot },\end{eqnarray} \tag{ 3 }$$

in which the nominal solar temperature is T_⊙ = 5772 K (Prša et al. 2016).

The radius of the sdO star can be found from the radius ratio (Section 5.4) and the radius of the Be star. In this section, we estimate the Be-star radius by comparing the observed spectral energy distribution (SED) with models for the composite Be+sdO system in order to determine the Be-star angular diameter. We then use a distance estimate to find the Be-star physical radius, which in turn leads to the sdO-star radius (Table 3).

The angular diameter of the limb-darkened disk θ (in units of radians) of a single star is found using the inverse-square law:

$$\begin{eqnarray}&&\displaystyle \frac{{f}_{\lambda }(\mathrm{observed})}{{F}_{\lambda }(\mathrm{emitted})}={\left({R}_{\star }/d\right)}^{2}\,{10}^{-0.4{A}_{\lambda }}=\displaystyle \frac{1}{4}{\theta }^{2}\,{10}^{-0.4{A}_{\lambda }},\end{eqnarray} \tag{ 4 }$$

where the ratio of the observed to emitted fluxes depends on the square of the ratio of stellar radius R_⋆ to distance d and the interstellar extinction A_λ . Here we create a model spectrum for the Be+sdO system F_λ that is scaled to the Be-star flux, and then we fit this to the observed flux f_λ to find the angular diameter θ and reddening E(B − V). We adopted an extinction curve law A_λ from Fitzpatrick (1999) that is a function of the reddening E(B − V) and the ratio of total-to-selective extinction R = A_V /E(B − V) (set at a value of 3.1).

Low-resolution (R = 500) model spectra were formed from surface fluxes from BSTAR2006 for the Be star and from OSTAR2003 for the sdO star using the atmospheric parameters listed in Tables 1 and 3, respectively. Then, the combined spectrum is given by ${F}_{\lambda }(\mathrm{Be})+{F}_{\lambda }(\mathrm{sdO}){\left({R}_{2}/{R}_{1}\right)}^{2}$, using the radius ratio determined in Section 5.4. In the cases of the sdO nondetections (HD 157832, HD 191610, HD 214168), only the Be-star flux is included in the model.

The flux versions of the HST/STIS spectra were averaged and rebinned into nine wavelength segments (effective resolution of ≈14) to represent the flux in the FUV. We then extended the wavelength range into the NUV by adding fluxes measured by the TD-1 mission (Thompson et al. 1978) and fluxes derived from the Johnson UBV magnitudes (Mermilliod 1987) using the flux calibration of Colina et al. (1996). Longer-wavelength fluxes were omitted because the Be-star disks become important flux contributors beyond the optical range. There were two exceptions to this general scheme. The target HD 113120 has a close visual companion that is excluded from the small aperture for the HST/STIS observations but is present in the longer-wavelength measurements, so the latter were corrected to correspond to the Be+sdO system alone (see the Appendix). The other target with a close companion is HD 214168, and the three HST/STIS spectra record different amounts of companion flux (see the Appendix). In this case, we selected the spectrum with the lowest flux as the most representative of the Be star (no sdO detection) and then adjusted the longer-wavelength fluxes for the Be-star alone.

The composite model spectra were fit to the observed SED using the relation above and the nonlinear, least-squares-fitting code MPFIT (Markwardt 2009) to find the best-fit values of E(B − V) and θ that are listed in columns 2 and 5 of Table 4, respectively. The observed and model fit SEDs are plotted in Figures 12–14 for systems with sdO detections (Be+sdO model fluxes) and in Figure 15 for the sdO nondetections (Be model fluxes only). The fluxes increase toward the shorter FUV wavelengths because of the hot temperatures of the targets and their companions, and the extinction and reddening values are relatively small in all cases. Column 3 of Table 4 lists published estimates of E(B − V) from references cited in column 4. These published values agree with our measurements within 0.1 mag. We include in column 6 of Table 4 the Be-star angular size estimates from the JMMC Stellar Diameters Catalog (Bourgés et al. 2014) for comparison with our result θ. In most cases, there is satisfactory agreement, but we caution that the JMMC results do not account for the flux of the sdO and other companions.

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Table 4. Spectral Energy Distribution Fitting Parameters

HD	$E{\left(B-V\right)}_{\mathrm{HST}}$	E(B − V)	Reference	θ	θJMCC	d	RBe
Number	(mag)	(mag)		(mas)	(mas)	(pc)	(R⊙)
29441	0.198 ± 0.014	0.202	1	0.0673 ± 0.0033	0.0763 ± 0.0030	737 ± 38	5.34 ± 0.38
43544	0.155 ± 0.024	0.054 ± 0.013	2	0.1315 ± 0.0113	0.1169 ± 0.0042	314 ± 6	4.44 ± 0.39
51354	0.172 ± 0.015	0.07	3	0.0779 ± 0.0042	0.0876 ± 0.0030	608 ± 21	5.09 ± 0.33
55606	0.220 ± 0.012	0.151 ± 0.100	2	0.0343 ± 0.0014	⋯	1090 ± 45	4.01 ± 0.23
60855	0.204 ± 0.016	0.295 ± 0.054	2	0.1586 ± 0.0092	0.1877 ± 0.0078	483 ± 25	8.24 ± 0.64
113120	0.176 ± 0.014	0.295 ± 0.054	2	0.1246 ± 0.0059	⋯	307 ± 57	4.11 ± 0.79
137387	0.125 ± 0.012	0.107 ± 0.009	2	0.1558 ± 0.0066	0.1599 ± 0.0060	326 ± 11	5.45 ± 0.29
152478	0.252 ± 0.011	0.241 ± 0.037	2	0.1274 ± 0.0051	0.1576 ± 0.0055	308 ± 7	4.21 ± 0.20
157042	0.187 ± 0.015	0.111 ± 0.027	2	0.1931 ± 0.0103	0.1845 ± 0.0164	291 ± 15	6.04 ± 0.44
157832	0.229 ± 0.011	0.138	1	0.1025 ± 0.0041	0.1341 ± 0.0052	1078 ± 85	11.88 ± 1.05
191610	0.182 ± 0.012	0.064 ± 0.019	2	0.2144 ± 0.0095	0.2140 ± 0.0079	188 ± 8	4.34 ± 0.27
194335	0.122 ± 0.017	0.045 ± 0.019	2	0.1311 ± 0.0078	0.1225 ± 0.0046	373 ± 11	5.26 ± 0.35
214168	0.025 ± 0.051	0.093 ± 0.024	2	0.0943 ± 0.0170	0.0899 ± 0.0035	590 ± 25	5.98 ± 1.11

Note. Indices of references: (1) Kervella et al. (2019), (2) Zorec et al. (2016), and (3) Gontcharov & Mosenkov (2018).

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We multiply the angular sizes by the distance to arrive at the physical radii of the Be stars. The distances from the Gaia DR2 survey (Bailer-Jones et al. 2018) are given in column 5 of Table 4, with the exception of the case of HD 113120 where the Hipparcos distance is adopted (see the Appendix). The Be-star radii appear in the final column of Table 4, and they are close to expectations for B-type main-sequence stars (except perhaps for HD 157832; see the Appendix). We used these Be-star radii estimates together with the ratio of the radii derived from the flux ratios to find the sdO-star radii that are given in column 6 of Table 3 (Section 5.4).

Götberg et al. (2018) explored the properties of the stripped stars in binaries by calculating MESA evolutionary tracks for the mass donor stars. These models assume a Case B scenario in which mass transfer occurs as the initially more massive star expands as it evolves toward the red giant phase. After losing the outer envelope, the remnant spends about 10% to ∼20% of its lifetime as a He-core-burning, hot subdwarf. We show examples of the evolutionary tracks from Götberg et al. (2018) in the $(\mathrm{log}{T}_{\mathrm{eff}},\mathrm{log}R/{R}_{\odot })$ and $(\mathrm{log}{T}_{\mathrm{eff}},\mathrm{log}L/{L}_{\odot })$ diagrams in Figures 16 and 17, respectively. These particular tracks assume an initial solar composition for the star. Four tracks are illustrated in each case for initial masses of 3.30, 3.65, 4.04, and 7.37 M_⊙ for the mass donor star (sdO progenitor). In both diagrams, we see how the star evolves from the main sequence to cooler temperature and larger size. In the case of the low-mass sdO progenitor (3.30 M_⊙), the star grows to fill its Roche limit after a period of 300 Myr. Once large-scale Roche lobe overflow commences, the donor star is quickly transformed to a hotter and smaller (less luminous) object, a stage that may last only 3 Myr. The star then continues He-core burning for another 60 Myr in the portion of the tracks just beyond the first minimum in radius and luminosity (see also Figure 2 in Götberg et al. 2018). The masses of sdO remnant at this stage are 0.67, 0.74, 0.85, and 1.85 M_⊙ for the four mass tracks, respectively.

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We include in Figures 16 and 17 our estimates for the sdO stellar parameters as summarized in Table 3. We also plot the parameters for the five Be+sdO systems that were known prior to our study. We see that most of the sdO companions do indeed have temperatures, radii, and luminosities that are comparable to the predictions from Götberg et al. (2018) for progenitors with masses in the range of 3–5 M_⊙. The sdO companions in four of our stars (HD 29441, HD 55606, HD 113120, and HD 152478) are shown at the He-core-burning stage on the evolutionary track, and the rest of the sdO stars are at an inflated stage either from an early contraction phase or the later inflation phase at the He-shell-burning stage. If the masses of the sample Be stars are typical of those of single B stars (≈4–8 M_⊙), then these systems probably began in near-equal-mass binaries, and systemic mass loss during the mass transfer phase was probably minimal.

The only system in the sample with a known orbit and mass estimates is HD 55606, and Chojnowski et al. (2018) find a mass for the sdO star in the range 0.83–0.90 M_⊙. The evolutionary tracks suggest there is an approximately linear mass—luminosity relation during the He-core-burning stage (see Figure 3 in Götberg et al. 2018). Using the luminosity estimate for the sdO star in HD 55606 from Table 3, the tracks predict a mass in the range of 0.77–0.91 M_⊙, in agreement with the observed estimate for the sdO star from Chojnowski et al. (2018).

Schootemeijer et al. (2018) created similar evolutionary tracks to study the current stage of the Be+sdO system ϕ Per. They concluded that the sdO star's luminosity was large for its mass (1.2 M_⊙), and consequently, the star may have entered the subsequent and short-lived He-shell-burning stage of evolution. This also appears to be the conclusion from the tracks from Götberg et al. (2018) that show that the parameters of ϕ Per fall on a track for a more massive remnant (1.85 M_⊙). Schootemeijer et al. (2018) argued that most of the Be+sdO binaries would have fainter sdO components found in the longer-lasting He-core-burning stage. The sdO companions discovered in the HST/STIS sample all have lower luminosities than ϕ Per, and this supports the idea that most such systems will be found in the fainter, He-core-burning phase.

The faintest of the sdO companions plotted in Figures 16 and 17 is that in the HR 2142 system. Peters et al. (2016) described how the CCF peak strength from the sdO companion has an orbital phase dependence in the case of HR 2142, and they argued that the sdO star was obscured by varying amounts by circumstellar gas. Thus, the implied radius and luminosity of the sdO component in HR 2142 are both lower limits to the actual values.

The primary goal of this investigation was to verify the presence of the spectral lines of hot subdwarf stars through a CCF analysis of FUV spectra from HST/STIS. We succeeded in detecting the CCF signal from the sdO star in 9 of 12 candidates identified from lower-quality IUE spectroscopy and in one case, HD 55606, where the sdO spectral features were first seen in optical spectra (Chojnowski et al. 2018). We can be confident that these detections are reliable because the CCF peaks of the sdO component in these Be+sdO binaries are much narrower than the rotationally broadened component of the Be star, the peaks attain a maximum using a model CCF template for a star much hotter than the Be star, and the peaks display radial velocity variations indicative of Doppler shifts from orbital motion. On the other hand, the peak heights indicate that the sdO companions are relatively faint compared to their Be-star primaries, which makes their detection difficult by other means. In fact, in our sample of 10 confirmed Be+sdO systems, only HD 55606 was known to be a binary prior to this work.

The radial velocity measurements of the sdO components are an important first step in determining the orbital elements of the binaries and placing limits on the masses. The only system in the sample with a known orbit is HD 55606 with an orbital period of 93.76 days derived by Chojnowski et al. (2018), and the velocities from the HST/STIS spectra are consistent with their radial velocity curve for the sdO star. We combined the HST/STIS and IUE velocity measurements to make a preliminary orbit for HD 194335 that indicates an orbital period of 60.3 days (see the Appendix). We can make a rough estimate of the orbital period P of the other systems by assuming a probable Be-star mass M₁, system mass ratio q = M₂/M₁, and inclination i. For a circular orbit, the semiamplitude of the sdO star will be

$$\begin{eqnarray}&&{K}_{2}=\displaystyle \frac{\sin i}{1+q}\displaystyle \frac{2\pi }{P}{M}_{1}^{1/3}{\left(1+q\right)}^{1/3}{P}^{2/3}.\end{eqnarray} \tag{ 5 }$$

If we assume M₁ = 6 M_⊙, q = 0.1, and i = 60°, then the predicted semiamplitude is K₂ = 315 km s⁻¹ P^−1/3, where the period is measured in days.

We can then make a numerical fit of the three observed radial velocities from HST/STIS by solving for three parameters: the period P, the epoch of maximum velocity T₀, and the systemic velocity γ. The results range from P = 84 days for HD 137837 to P = 346 days for HD 60855. These are nominally upper limits on the period because we make the simplifying assumption that the HST/STIS spectra cover only part of one orbit. Nevertheless, orbital periods on the order of months are what are found in the six other systems with known orbits and are consistent with the expectations for the enlargement of the orbit with mass transfer following mass ratio reversal (Wellstein et al. 2001).

The CCF peaks from the sdO components are generally narrow, and the derived projected rotational velocity $V\sin i$ is small (unresolved) except in the case of HD 51354 where $V\sin i=102$ km s⁻¹. We expect that the progenitors of the sdO stars attained synchronous rotation due to tidal forcing when they filled their Roche lobe, and consequently, their projected rotational velocities are small because of the long orbital periods and very small radii. The large $V\sin i$ of HD 51354 may be the result of spin-up by reverse mass transfer. The Be primary star loses mass into its outflowing equatorial disk, and some of this gas may end up being accreted by the sdO companion. The angular momentum carried by the accreted gas could lead to spin-up. However, it is unknown why this process would occur in this Be+sdO system and not the others.

The peak heights of the sdO CCF component vary with the assumed temperature of the model spectrum used to form the CCF. We adopt a temperature that maximizes the CCF peak strength, and this yields effective temperatures in the range of 34–45 kK (Table 3). These are all much hotter than those of the Be stars and are close to model expectations for stripped stars (Section 7).

The CCF peak height also depends on the fractional flux contribution of the sdO spectrum to the total combined flux, and we used numerical simulations of model spectra for the Be and sdO stars to derive the monochromatic flux ratio in each case (Table 3). We can then compare the observed flux ratio with the surface flux ratio from the estimated temperatures of the components to find the radius ratio. We then determined the Be-star radius from a fit of the spectral energy distribution and the distance (Section 6) to finally arrive at estimates of the sdO stellar radii (Table 3). Although the sdO stars contribute a minor fraction of the overall flux, it should be possible to find evidence of their spectral lines in high-S/N optical spectra and to determine visual orbits for the closer systems through long-baseline optical interferometry (Mourard et al. 2015).

The question remains as to why we did not detect any clear sdO CCF peak in the HST/STIS spectra of HD 157832, HD 191610, and HD 214168, even though such peaks were detected in CCFs from lower-quality IUE spectra (Wang et al. 2018). We note that in the latter two cases, there are many archival IUE spectra, but Wang et al. (2018) were only able to find significant CCF peaks for about half of those spectra (see the Appendix). This suggests that there is inherent temporal variability in the contribution of the sdO component to the combined FUV spectrum. A similar situation was found by Peters et al. (2016) for the Be+sdO system HR 2142, in which the detection of the peak was limited to certain parts of the orbit. We suspect that this variability is due to changes in the obscuration of the sdO star by nearby circumstellar gas. Thus, the nondetection of the sdO CCF peaks in these three cases does not necessarily imply that these are single Be stars that lack sdO companions.

We found that the derived temperatures and radii of the sdO components are broadly consistent with model predictions for stars stripped of their envelopes by binary interaction (Götberg et al. 2018). These parameters agree with the long-lived stage of He-core burning in the remnants that lasts about 10% ∼to 20% of the star's lifetime. There is a predicted relation between mass and luminosity at this stage, and our derived luminosity for the sdO in HD 55606 corresponds to a mass that agrees within uncertainties with that derived from the observations presented by Chojnowski et al. (2018).

The HST/STIS spectra of this sample of Be stars have given us a remarkable picture of how stars are transformed through binary interactions to create hot, stripped-down subdwarfs. These spectra reveal the temperatures, radii, and hence, luminosities of the sdO stars, but what remains is to determine their masses by determining the full orbital elements. This is a difficult task because the sdO spectral lines in the optical part of the spectrum are weak and few in number, and the lines of the Be star are very shallow and broad ($V\sin i\approx 300$ km s⁻¹) compared to the orbital semiamplitude (K₁ < 10 km s⁻¹). Nevertheless, this observational work is essential in order to derive the component masses and to make detailed comparisons with model predictions (Götberg et al. 2018). Searches for Be+sdO systems among Be stars in clusters are particularly important to compare their ages to model predictions. The fact that Be stars lack main-sequence companions compared to normal B stars is evidence that many Be stars are the descendants of pairs of interacting binaries (Bodensteiner et al. 2020b), so there should be many examples of this hidden stage of evolution that remain to be discovered.

We thank Denise Taylor of STScI for her help in planning the observations with HST. This work was supported by NASA through a grant from the Space Telescope Science Institute, under program GO-15659. Institutional support was provided from the GSU College of Arts and Science.

Facilities: HST (STIS) - , Gemini:Gillett (Àlopeke). -

HD 29441 (V1150 Tau). There is only one IUE high-dispersion spectrum for this target, and the CCF peak of the hot component appears with a radial velocity of V_r = −60.7 ± 2.5 km s⁻¹ (Wang et al. 2018), compared to the positive radial velocities found here (Table 2). Slettebak et al. (1997) note that the star is distant from the Galactic plane, with z = −308 pc for the Gaia DR2 distance (Table 4). Slettebak et al. (1997) describe the broad lines in the optical spectrum, which they classify as B2 III/IVe.

HD 43544 (HR 2249). Levenhagen & Leister (2006) determined parameters for this star that they classify as B2/3 Ve, and they estimate an evolutionary mass of 8.5 M_⊙ for the Be star. The HST/STIS spectra CCF peaks show a large velocity range that spans the single IUE measurement (Wang et al. 2018). Huang et al. (2010) find a small velocity variation for the Be component between two observations.

HD 51354 (QY Gem). The CCFs of the hot companion are remarkably broad compared to all the other detections, and this was also found in the CCFs from two IUE spectra (Wang et al. 2018). These CCF peaks show large velocity variations, while velocity measurements of the Be star display relatively little scatter (Chojnowski et al. 2017).

HD 55606. The orbital variations of the hot, narrow-lined component were discovered in optical spectra by Chojnowski et al. (2018), who determined a double-lined orbital solution. The HST/STIS spectra CCF velocities are consistent with their orbit. There are no IUE observations for this target.

HD 60855 (HR 2921; V378 Pup). This star is a candidate blue straggler in the open cluster NGC 2422 (Pols et al. 1991), and it has several wide and faint companions listed in the Washington Double Star catalog. There are six IUE CCF velocity measurements, all of which are lower than the three measurements presented in Table 2.

HD 113120 (HR 4930; LS Mus). There are large velocity variations in both the three IUE (Wang et al. 2018) and HST/STIS spectra CCF measurements for the hot component. This star has a nearby companion at a separation of 056 (Hartkopf et al. 1996). It was also resolved by Hipparcos with a magnitude difference of △H_p = 2.84 ± 0.04 mag (ESA 1997). This companion falls outside the HST/STIS aperture, but its flux does contribute to the TD-1 and Johnson UBV measurements. Consequently, we used △H_p to add 0.077 ± 0.003 mag to correct the TD-1 and UBV measurements (assuming similar colors for both components) to estimate the magnitudes and fluxes without the companion's contribution. The SED fitting was made using these adjusted supplementary fluxes. The distance from Gaia DR2 is very uncertain (756–1496 pc; Bailer-Jones et al. 2018) probably due to complications from the companion's flux. Krełowski et al. (2017) list three distance estimates: 250 pc from the Ca ii interstellar line strength, 307 pc from Hipparcos (van Leeuwen 2007), and 351 pc from spectrophotometric fits. We adopt the Hipparcos result in Table 4.

HD 137387 ( κ¹ Aps; HR 5730). Boubert & Evans (2018) suggest that the object is a runaway star with a peculiar space velocity of 57 km s⁻¹, but Jilinski et al. (2010) derive a much lower value of 32 km s⁻¹. Jilinski et al. (2010) obtained seven radial velocities for the Be star and concluded that it is a binary. There are large velocity variations for the hot component in both the four IUE and three HST/STIS spectra CCF measurements.

HD 152478 (HR 6274; V846 Ara). There are two IUE velocity measurements with a large difference (Wang et al. 2018), while all three HST/STIS spectra CCF measurements are similar and redshifted. Jilinski et al. (2010) found that the Be-star absorption lines are too broad ($V\sin i=370$ km s⁻¹) for reliable radial velocity measurements.

HD 157042 (ι Ara; HR 6451). This star displays relatively large velocity variations in both the four IUE and three HST/STIS spectra CCF measurements for the hot companion. The violet and red peaks of the Hα emission show relative strength variations (Dachs et al. 1986, 1992; Mennickent & Vogt 1991) that may be related to the orbital phase.

HD 157832 (V750 Ara). This candidate binary was identified by Wang et al. (2018) from CCF weak peaks observed in two IUE spectra. The residual peaks from the HST/STIS spectra CCFs are also weak (Figure 7), which suggests that any hot component in this system is faint. The Gaia DR2 distance of 1078 pc (Bailer-Jones et al. 2018) may be too large. For example, Kozok (1985) gives a lower distance of 780 pc, and Lopes de Oliveira & Motch (2011) suggest an even smaller value of 530 pc. Thus, the Be-star radius given in Table 4 may be an overestimate. Lopes de Oliveira & Motch (2011) discuss the hard and intense X-ray flux from this target, making this star an analog of the Be-star X-ray-emitter γ Cas. Langer et al. (2020) argue that such X-ray emission may originate where the wind from a hot sdO star strikes the outer region of the Be-star disk.

HD 191610 (28 Cyg; V1624 Cyg). The CCF residuals shown in Figure 7 indicate little or no evidence of a hot component. Wang et al. (2018) examined 46 high-dispersion SWP spectra from IUE to search for evidence of a CCF peak from a hot companion, and a peak was measured for only 25 of the 46 spectra (with CCF peak amplitude of ≈0.025). This suggests that there is some kind of temporal variability that makes detection more favorable at some epochs rather than others. Thus, we still regard HD 191610 as a viable Be+sdO candidate system, despite the nondetection in the HST/STIS CCFs. Becker et al. (2015) obtained 64 measurements of the Be-star radial velocity from high-S/N and high-dispersion optical spectra, and they measured a residual "jitter" of 13.4 km s⁻¹, which is probably comparable to the orbital semiamplitude of the Be star.

HD 194335 (HR 7807; V2119 Cyg). The CCF peaks show large velocity variations in the four IUE measurements (Wang et al. 2018) and in the three HST/STIS measurements (Table 2). We combined these to make a preliminary circular orbital fit with period P = 60.286 ± 0.010 days, epoch of maximum velocity T₀ = HJD 2,458,721.2±0.6, systemic velocity γ = − 18.9 ± 1.2 km s⁻¹, and semiamplitude K₁ = 75.5 ± 2.4 km s⁻¹. The derived systemic velocity is comparable to the median from four measurements of the Be star, −30 km s⁻¹, made by Costado et al. (2017).

HD 214168 (8 Lac A; HR 8603). This star is a member of the Lac OB1 association (Kaltcheva 2009) and is the northern and brighter component of a pair separated by 22''. The target is also a close binary resolved by speckle interferometry (CHR 112 Aa,Ab; McAlister et al. 1987). Recently Tokovinin et al. (2019) presented an orbital solution based upon speckle measurements that yields an orbital period of 42 yr and an angular semimajor axis of 0057. The derived total mass is 17 ± 8 M_⊙ based upon the distance from Gaia DR2 (542 ± 30 pc; Bailer-Jones et al. 2018). We obtained speckle observations with the Àlopeke instrument on the Gemini North Telescope on 2019 October 12 and with the 562 and 832 nm filters. The measured separation was 0041 and position angle 1334 east from north, and this position is consistent with the orbit from Tokovinin et al. (2019). The average magnitude difference in the optical range from the Àlopeke and Tokovinin et al. measurements is Δm = 0.43 ± 0.10 mag.

The HST/STIS observations are centered on the brighter object within an aperture with a projected size of 0.2 × 005 on the sky, so some flux from the Ab component may be recorded in the spectra. We found that the measured flux in the 1300–1400 Å range was (4.27, 4.72, 3.71) × 10⁻¹⁰ erg cm⁻² s⁻¹ Å⁻¹ for the three observations consecutively, a much larger relative variation than observed in other targets, so we assume that the spectrum recorded more (less) flux from component Ab in the second (third) observation. However, there is no discernible difference between the three spectra, which suggests that the Ab component has a similar spectral appearance with broad lines and a temperature like that of the Be star.

We performed a CCF analysis to search for the spectral lines of the Ab component by constructing CCFs for a grid of lower-temperature models and then removing the associated contribution to the CCF from the Be star in the same way as we did in the search for the signal of a hot companion. We detected a weak and narrow signal in the residual CCFs that is shown in Figure 18. The residual peaks attained maximum strength for CCF model spectra with T_eff = 23 ± 4 kK, and the width and height of the peak suggest $V\sin i=31\pm 5$ km s⁻¹ and f₂/f₁ ≈ 0.07, respectively. The measured velocities from Gaussian fits of the peaks are −31.6 ± 1.6, −15.2 ± 1.8, and −24.1 ± 1.3 km s⁻¹ for the three consecutive observations. We doubt that these peaks originate in the Ab component, because the flux ratio is much too small for the bright Ab component and because there is no evidence in published optical spectra for a narrow-lined spectral component as bright as Ab. It is unlikely that this CCF peak corresponds to a cooler, stripped companion, because the associated temperature of the feature is lower than that of the Be star, and in all the other cases, we find that the stripped-down donor star is hotter than the bright mass-gainer star. We also rule out an origin in interstellar lines, because we avoided these in forming the CCFs and the peaks appear to have a variable radial velocity. Instead, we suspect that this spectral signature is the result of line absorption from the disk of the Be star. Gies et al. (1998) found evidence of such absorption features in the Be+sdO system ϕ Per that appeared when the hot companion was in the foreground in the orbit. They surmised that these narrow "shell" absorption lines (mainly Fe iv) are formed as we view the Be star through heated portions of the outer disk. If the weak CCF signal shown in Figure 18 is related to shell absorption lines, then the likely occurrence of these in the spectrum of ϕ Per suggests that HD 214168 may also have a close hot companion. However, there is no obvious signal from a hot companion in the CCF residuals (Figure 8).

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We fit the SED of HD 214168 by assuming that the third (faintest) HST/STIS spectrum has a flux representative of the Be star alone, and then we adjusted the observed Johnson UBV magnitudes to give the Be-star (assumed component Aa) magnitude by adding 0.56 ± 0.04 mag (assuming no significant color difference between Aa and Ab). The fit of the SED together with the Gaia DR2 distance yields a stellar radius of 6.0 ± 1.1 R_⊙ for Aa. The radius of Ab from the optical magnitude difference is then 4.9 ± 0.9 R_⊙ or somewhat larger if Ab is cooler than Aa. We caution that these values may be slightly overestimated because the FUV flux recorded in the third HST/STIS spectrum may include a small contribution from Ab.

Wang et al. (2018) were able to measure a CCF peak for an sdO companion in 9 of the 20 IUE spectra they analyzed. This suggests that there are temporal variations that influence the visibility of the sdO star's photospheric flux, as found in the case of HD 191610. Thus, the nondetection in the CCFs from the HST/STIS spectra may be due to the observations being made at a time when the sdO star was obscured from view.