BRITE observations of $\nu$ Centauri and $\gamma$ Lupi, the first non-eclipsing members of the new class of nascent binaries

Results of an analysis of the BRITE-Constellation and SMEI photometry and radial-velocity observations, archival and new, of two single-lined spectroscopic binary systems $\nu$ Centauri and $\gamma$ Lupi are reported. In the case of $\gamma$ Lup AB, a visual binary, an examination of the light-time effect shows that component A is the spectroscopic binary. Both $\nu$ Cen and $\gamma$ Lup exhibit light variations with the orbital period. The variations are caused by the reflection effect, i.e. heating of the secondary's hemisphere by the early-B main sequence (MS) primary component's light. The modelling of the light curves augmented with the fundamental parameters of the primary components obtained from the literature photometric data and Hipparcos parallaxes, shows that the secondary components are pre-MS stars, in the process of contracting onto the MS. $\nu$ Cen and $\gamma$ Lup A are thus found to be non-eclipsing counterparts of the B2 IV eclipsing binary (and a $\beta$ Cephei variable) 16 (EN) Lac, the B5 IV eclipsing binary (and an SPB variable) $\mu$ Eri, and the recently discovered LMC nascent eclipsing binaries.


INTRODUCTION
Formation of close binaries with massive components is a challenging theoretical problem as the details of the formation processes cannot be tested observationally. This is because massive stars at the pre-MS stage of evolution are embedded in the parent cloud from which the stellar cluster is formed (e.g. Lada & Lada 2003). The stars become observable only after the cloud is dispersed by strong stellar winds of the most massive stars or core-collapse supernova explosions. Assuming coevality or near-coevality of the onset of star formation, one comes to the conclusion that if the binary has a low mass ratio = 2 / 1 , the system may become visible as a binary consisting of a massive MS primary and a pre-MS companion. Given the overall scarcity of massive stars, their fast evolution and observational selection effects, such systems will be rare and difficult to discover. Recently, using a sample of 174 000 eclipsing binaries in the Large Magellanic Cloud (LMC), selected from the third phase of the Optical Gravitational Lensing Experiment (OGLE-III) database (Graczyk et al. 2011), Moe & Di Stefano (2015) discovered 18 systems with low mass-ratios (0.06 < < 0.25), consisting of early Btype MS primaries with 1 ≈ 5 -16 M ⊙ and pre-MS secondaries. After correcting the observed number of these systems for selection effects, they found that (2.0 ± 0.6)% of early B-type MS stars would have companions with masses of 0.06-0.25 1 and orbital periods, orb , of 3.0-8.5 d. According to Moe & Di Stefano (2015), this fraction is ≈10 times larger than that observed around solar-type MS stars in the same mass ratio and period interval.
Such systems, referred to by Moe & Di Stefano (2015) as nascent eclipsing binaries with extreme mass ratios (NEBs henceforth), are interesting because it is not known how they were formed. In particular, there is the question whether these systems originate as a close binary from the beginning and both components accrete matter at the same time (see e.g. Sørensen et al. 2018, and references therein) or if they form as a wide binary and the orbit shrinks at a later stage of evolution leaving a much closer system as a product (e.g. Kiseleva, Eggleton & Mikkola 1998;Fabrycky & Tremaine 2007). Equally interesting is the future of these systems after the primary leaves the MS: the stars may coalesce or form a low-mass X-ray binary (Kalogera & Webbink 1998;Kiel & Hurley 2006). Fur-ther evolution may produce a type Ia supernova and a millisecond pulsar.
As discussed by Moe & Di Stefano (2017), early-type binaries identified by various observing techniques, such as spectroscopy, eclipses, interferometry, adaptive optics, common proper motion, etc., are distributed in distinct regions of theorb plane. Those with low-mass pre-MS secondaries are difficult to select because of the large difference in brightness between components. In the case of a wide binary observed by means of astrometric techniques, the pre-MS status of the secondary is hard to establish due to the limited possibilities of deriving its mass and radius. The systems with the shortest orbital periods can be detected as spectroscopic binaries (SBs) showing a measurable reflection effect. If there are no eclipses, an analysis of the reflection light-curves may constrain the radius of the secondary component, revealing its pre-MS status. In the present paper, we announce the discovery of two such systems, Cen and Lup, non-eclipsing counterparts of the NEBs. The presence of eclipses would be an additional asset allowing to constrain the secondary's radius even if the reflection effect is marginal or below the detection threshold. Examples illustrating this are the single-lined (SB1) eclipsing binaries 16 (EN) Lac and Eri. The B2 IV primary of the former is also a well-known Cephei variable, while the B5 IV primary of the latter is an SPB star. The pre-MS nature of the secondary of 16 (EN) Lac was suggested by Pigulski & Jerzykiewicz (1988) and confirmed by Jerzykiewicz et al. (2015), while that of Eri is established in Section 6 of the present paper.

TARGET STARS: ν CEN AND γ LUP
Cen (HD 120307, HR 5190, HIP 67464) is a member of the Upper Centaurus Lupus (UCL) subgroup of the association Sco OB2 (de Zeeuw et al. 1999). The MK type is B2 IV (Hiltner, Garrison & Schild 1969). According to Wilson (1915), Cen is an SB1 system with orb = 2.625172 d, a circular orbit and the semi-amplitude = 20.6 km s −1 . These parameters were confirmed by Ashoka, Surendiranath & Rao (1985) but Rajamohan (1977) obtained = 0.26 and = 29.9 km s −1 . In addition, Rajamohan (1977) maintains that the residuals from the orbital radial-velocity (RV) curve show a Cephei-type variation with at least two periods close to 0.1750 d. This period, albeit a single one, was found by Kubiak & Seggewiss (1982) in their RV and Strömgren -filter observations. Using residuals from the orbital solution and the RV data of Kubiak & Seggewiss (1982), Ashoka et al. (1985) updated this period to 0.1690156 d. Subsequently, Ashoka & Padmini (1992) added three nights of RV observations and revised the period to 0.1696401 d. However, Shobbrook (1978), Percy, Jakate & Matthews (1981) and Sterken & Jerzykiewicz (1983) failed to detect any shortperiod brightness variations in their Strömgren -filter observations. Moreover, from a number of 12 Å mm −1 spectrograms, Sterken & Jerzykiewicz (1983) found no evidence for a short-period RV variation. More recently, from a series of high-resolution CCD spectrograms, Schrĳvers & Telting (2002) discovered a pattern of moving bumps in the Si III 455.2 and 456.7-nm line profiles which they attributed to high-degree non-radial pulsations with ranging from 6 to 10, ruling out low-degree pulsations with a period of 0.17 d. A small-amplitude brightness variation of Cen with the orbital period was detected by Waelkens & Rufener (1983); these authors ascribed the variation to a reflection effect. From numerous observations in the Strömgren filter, Cuypers, Balona & Marang (1989) concluded that The observations [...] clearly show a variation with the same period as the orbital period. Minimum light corresponds to maximum positive RV. As discussed by Waelkens & Rufener (1983), the resulting light curve is most probably a reflection effect. A careful investigation did not reveal any signs of a variation at any other frequency with an amplitude exceeding 2 millimags.
In the General Catalogue of Variable Stars (GCVS) 1 , Cen is classified as BCEP (i.e. a Cephei-type variable) but Stankov & Handler (2005) have degraded it to the status of a candidate Cephei variable presumably because of the conflicting evidence for short-period RV and brightness variability summarized above. In the Hipparcos catalogue (ESA 1997), the type of variability is EB (i.e. a Lyrae-type eclipsing variable), the range is 3.318 -3.329 mag, and the period = 2.6249 ± 0.0003 d.
Lup (HD 138690, HR 5776, HIP 76297), is a close visual double with the separation ranging from 0.1 to 0.8 arcsec. It consists of components of very nearly equal brightness: the Hp magnitudes are equal to 3.397 and 3.511 for the A and B component, respectively (ESA 1997). The orbital elements listed in the US Naval Observatory's Sixth Catalog of Orbits of Visual Binary Stars (ORB6) 2 , computed by Heintz (1990) from the 1836 -1988 mainly micrometric observations, include a period of 190 yr, a semi-major axis of 0.655 arcsec, an inclination of 95. • 0 and an eccentricity of 0.51. In Notes to the 5th edition of the Bright Star Catalogue (Hoffleit & Jaschek 1991), an MK type of B2 IV-V is assigned to either component, but Hiltner et al. (1969) give a single MK type of B2 IV. One component is an SB1 system with orb = 2.80805 d and = 0.10 ± 0.02 (Levato et al. 1987). These authors note that both components fell on the slit of the spectrograph, so that-because of their similar brightness-either can be responsible for the RV variation. The star is listed in the GCVS as ELL: (i.e. a questionable ellipsoidal variable). According to the Hipparcos catalogue, the type of variability is P (i.e. periodic), the range is 2.693 -2.711 mag, and the period, = 2.8511 ± 0.0004 d. Note that the frequencies corresponding to the Hipparcos and the spectroscopic period differ by 0.0054 d −1 = 2 yr −1 . An excellent summary of the observations of Lup throughout 1987 was provided by Baade (1987).

BRITE and SMEI photometry
The photometry analysed in the present paper was obtained from space by the constellation of five BRITE (BRIght Target Explorer) nanosatellites (Weiss et al. 2014;Pablo et al. 2016) during two runs, in the fields Centaurus I (both stars) and Scorpius I (only Lup). These observations were secured by all five BRITEs, three red-filter, UniBRITE (UBr), BRITE-Toronto (BTr), and BRITE-Heweliusz (BHr), and two blue-filter ones, BRITE-Austria (BAb) and BRITE-Lem (BLb). Details of BRITE observations are given in Table 1. The Cen I observations were obtained in stare mode, the Sco I, in the chopping mode of observing (Pablo et al. 2016;Popowicz et al. 2017). The images were analyzed by means of two pipelines described by Popowicz et al. (2017). The resulting aperture photometry is subject to several instrumental effects ) and needs preprocessing aimed at the effects' removal. To remove the instrumental effects we followed the procedure designed by Pigulski et al. (2016) with several modifications proposed by Pigulski & Figure 1. The spurious 1 d −1 variation of the 2014 UBr magnitudes of Lup. Shown are the normal points computed in adjacent intervals of 0.005 phase of the frequency of 1 d −1 . The data were the 2014 UBr magnitudes of Lup decorrelated with respect to the CCD's temperature, the and coordinates of the image centre of gravity and the satellite orbital phase, and pre-whitened with the star's orbital frequency.
(2018). The whole procedure includes converting fluxes to magnitudes, rejecting outliers and the worst orbits (i.e. the orbits on which the standard deviation of the magnitudes was excessive), and oneand two-dimensional decorrelations with all parameters provided with the data (e.g. position in the subraster and CCD temperature) and the calculated satellite orbital phase. The 2014 UBr observations of Lup were additionally decorrelated with respect to the frequency of 1 d −1 because they showed a spurious variation with this frequency (see Fig. 1). After decorrelating, the magnitudes were de-trended and deviant magnitudes were rejected by hand.
The Solar Mass Ejection Imager (SMEI) time-series photometry has been already employed by a number of workers. Eg., Kallinger et al. (2017) used SMEI time-series photometry to bolster the BRITE data analysis of V389 Cygni, a triple system with an SPB star component. The time-series photometry of Cen and Lup was downloaded from the SMEI website 3 and reduced as described in section 6 of Kallinger et al. (2017). The details of the photometry are given in Table 1.

The radial-velocity data
For both target stars, several sets of archival RV data are available in the literature. They are listed in Table 2 as sets (1) to (15). In addition to sets (1) to (10) of the archival RVs of Cen, and sets (11) to (15) of Lup, we used three archival FEROS spectrograms of Lup, obtained in May 2004 and August 2013, to derive the RVs. This was done by least-squares fitting of rotationally-broadened template spectra to the observed spectra. The template spectra were calculated using BSTAR2006 grid of models (Lanz & Hubeny 2007), convolved rotationally with the rotin3 program provided on the Synspec 4 web page. These RVs, together with their estimated standard errors, are listed in Table 3 and are referred to in Table 2 as set (16). In addition to the archival data, new RVs of Lup were derived from spectrograms taken by one of the authors (MR) with the BACHES echelle spectrograph (Kozłowski et al. 2016) installed on the 0.5-m robotic telescope Solaris-1 Sybilski et al. 2014) located at SAAO. Eight spectrograms each of exposure time of 250 s and signal-to-noise ratios from 100 to 150 were taken between 29 February and 5 May 2016. In order to reduce the spectrograms, we used 3 http://smei.ucsd.edu/new − smei/data&images/stars/timeseries.html 4 http://nova.astro.umd.edu/Synspec43/synspec.html standard IRAF 5 procedures. The wavelength calibration was performed using the mean of wavelength solutions from the Th-Ar lamp frames taken before and after target frames. IRAF rvsao.bcvcorr task was used for barycentric velocity and time corrections. The RVs were calculated as straight means of the values obtained from Gaussian fitting to four He I lines,438.79,492.19,587.56,and 667.82 nm. Standard errors of these means serve as a measure of uncertainty. The new RVs together with the uncertainties are listed in Table 3 and are referred to in Table 2 as set (17).

The orbital period
We shall now derive the orbital period of Cen from the available RV and photometric observations. The RV data sets we could use, i.e. those in which the measurements were well distributed over orbital phase, include six sets listed in Table 2: (1), (2), (3), (4), (7), and (9). For set (9) straight means of the RVs of the Si III 455.2 and 456.7 nm lines (Schrĳvers & Telting 2002) were taken. We fitted each data set with the sine curve where orb = 0.38092 d −1 and is reckoned from the middle of the interval spanned by the observations. Using a sine curve is justified because the orbit of Cen is circular (see Section 4.2). In fitting Eq.
(1), we used the method of least squares with weights inversely proportional to the squares of the standard errors of the velocities. In sets (1) and (2), the standard errors were obtained by multiplying the overall probable error given by Wilson (1915) by / /0.6745, where is the number of lines measured; if two values of were listed by Wilson (1915), a mean was taken, if none (one case), was set equal to , the overall mean of . In sets (3) and (9), the standard errors were assumed to be those of an equal-weight fit of Eq. (1) to the data. In sets (4) and (7), the standard errors were computed from the probable errors given by Levato et al. (1987) and Ashoka et al. (1985), respectively. Then, we computed the epochs of crossing the -axis from the smaller to greater RV (i.e. from approach to recession), HJD , and their standard deviations. These numbers are given in the second column of Table 4.
The photometric observations of Cen we used consisted of the following sets: 1987 and 1988 magnitudes of Cuypers et al. (1989), Hipparcos Hp magnitudes, SMEI data divided into five adjacent segments of approximately equal duration, and BRITE blue and red magnitudes (see Section 3.1). We fitted the magnitudes with the sine curve with orb = 0.38092 d −1 and reckoned from the middle of the interval spanned by the observations; in the case of the Hp and BRITE fits, we applied weights inversely proportional to the squares of the standard errors of the magnitudes. The epochs of maximum light computed from the fits, HJD max , and their uncertainties are listed in the first column of Table 5. Assuming that at a given epoch the orbital phase of HJD is equal to that of HJD max , an assumption  Table 3 to be verified shortly, and using HJD from Table 4 and HJD max from Table 5 we arrived at the following ephemeris: The number of cycles that elapsed from the = 0 epoch and the residuals O -C from the ephemeris are listed in Tables 4 and 5. In order to verify our assumption that the orbital phase of HJD is equal to that of HJD max , we computed the = 0 epoch using the RV and brightness data separately. The results, HJD 2450893.6678 ± 0.0015 and 2450893.696 ± 0.013, differ by about 2 . We conclude that at maximum light the secondary component is at superior conjunction, i.e. the primary component is the closest to the observer, with the secondary behind. This phase relation between the RV and light variation is compatible with the reflection effect. Note that this conclusion is in conflict with that of Cuypers et al. (1989) quoted in Section 2.   Figure 2. Archival RVs of Cen plotted as a function of orbital phase. The phases were computed from ephemeris (3). The solid line is the RV curve computed from the spectroscopic elements listed in Table 6.

The RV curve and the spectroscopic orbit
The RVs of Cen are plotted in Fig. 2. For the Schrĳvers & Telting (2002) points, the error bars (not shown) would be of about the same size as the symbols plotted in the figure because we assumed the standard error to be equal to 0.6 km s −1 , the standard deviation of the least-squares fit of the sine-curve to these points (see Section 4.1). In addition to the data referenced in Table 4 (filled symbols), the RV measurements of Sterken & Jerzykiewicz (1983), Kubiak & Seggewiss (1982) and Jilinski et al. (2006), i.e. sets (5), (6) and (10) detailed in Table 2, are shown (open symbols). In the case of Sterken & Jerzykiewicz (1983), we plotted only the first and the last of their 49 data-points with the standard errors provided by them. In the case of Jilinski et al. (2006), we converted the MJD of the exposure beginning (which they call HJD in their table 1) to HJD of the middle of the exposure by adding 2400000.5 d, the heliocentric correction and half of the exposure time. In addition, we estimated the standard error from the range of the RVs on HJD 2452413 (the two asterisks at phase ∼0.99 in Fig. 2) to be 4.5 km s −1 . As can be seen from the figure, most measurements scatter around those of Schrĳvers & Telting (2002); the two exceptions are the measurements of Rajamohan (1977) and Kubiak & Seggewiss (1982). The former show a systematic shift toward smaller RVs, the latter, toward greater RVs. Omitting the Rajamohan (1977) and Kubiak & Seggewiss (1982) data, we computed a spectroscopic orbit by means of the non-linear least squares method of Schlesinger (1910) with weights inversely proportional to the squares of the standard errors of the velocities. The parameters of the orbit are determined by RVs of Schrĳvers & Telting (2002) but their standard deviations, by the remaining data. The eccentricity of the orbit turned out to be an insignificant = 0.009 ± 0.007. We conclude that the orbit is circular, confirming the result of Wilson (1915). The elements of the orbit are listed in Table 6 and the RV curve computed from these elements is shown in Fig. 2 with the solid line.

The orbital light-curves and the W-D modelling
The light-curves of Cen are presented in Fig. 3. The data shown are normal points formed in adjacent intervals of 0.02 orbital phase from the blue and red BRITE magnitudes (the upper and lower panel, respectively). The error bars are not shown because they would barely extend beyond the plotted circles: the standard errors ranged from 22.30 ± 0.12 km s −1 Projected semi-major axis, 1 sin The light-curves of Cen. Plotted are normal points formed in the adjacent intervals of 0.02 orbital phase from the blue (upper panel), and red (lower panel) BRITE magnitudes. The phases were computed from ephemeris (3). The lines are the theoretical W-D light-curves. 0.27 to 0.42 mmag for the blue normal points, and from 0.26 to 0.39 mmag for the red normal points. The lines plotted in the figure are the theoretical light-curves, results of the Wilson-Devinney (W-D) modelling to be discussed presently. A least-squares fit of a sum of the orb and 2 orb sines to the normal points yields blue amplitudes of 5.47 ± 0.22 and 0.11 ± 0.22 mmag, and red amplitudes of 8.70 ± 0.16 and 0.14 ± 0.16 mmag, respectively. The 2 orb amplitudes are consistent with the conclusion of Appendix A1 that no detectable ellipsoidal light-variation is present. Thus, the orbital light-variation is caused solely by the reflection effect.
The light curves were subject to modelling by means of the 2015 version of the W-D code 6 (Wilson & Devinney 1971;Wilson 1979). In addition to the light curves, the input data for the code included the orbital elements from Table 6 and the primary component's fundamental parameters eff,1 = 22 370 K and log 1 = 3.76 from Appendix B1. The eff,1 was fixed throughout but the final log 1 , used only in deriving the limb darkening coefficients, were taken from the W-D solutions after several iterations. The limb darkening coefficients were from the logarithmic-law tables of Walter V. Van Hamme 7 . For the primary component we assumed [M/H] = 0 and used 421 and 620.5 nm monochromatic coefficients for the blue and red data, respectively. A radiative-envelope albedo of 1.0 was assumed. In treating the reflection effect, we used the detailed model with six reflections (MREF = 2, NREF = 6). For the secondary component, bolometric limb-darkening coefficients and a convectiveenvelope albedo of 0.5 were adopted.
The mass function, ( ), depends on the primary's mass, 1 , the secondary's mass, 2 , and the inclination, , or -alternatively -on 1 , , and the mass ratio = 2 / 1 . Once two of these parameters are fixed, the third can be calculated from ( ) given in Table 6. The evolutionary mass 1 = 8.7 ± 0.3 M ⊙ derived for the primary component of Cen in Appendix B1 is model dependent. Therefore, in order to be certain that the range of 1 adopted in the W-D modelling comprises the true primary mass, we assumed a range five times wider than the formal uncertainty of 1 , i.e. 7.2 to 10.2 M ⊙ . In a preliminary run we found that the range of should be limited to 30 • ≤ < 75 • because for ≥ 75 • the W-D light-curves showed an eclipse not seen in the observed light-curves, while for < 30 • an ellipsoidal effect, also not present in the observed lightcurves, showed up in the W-D light curves. In the < 30 • models, the distortion of the primary causing the ellipsoidal effect was a consequence of a higher 2 and a tighter orbit. In addition, a higher 2 and hence greater brightness would be also inconsistent with the lack of the secondary's lines in the spectrum. The final W-D modelling was therefore done assuming a grid of ( 1 , ) ∈ (7.2 -10.2 M ⊙ , 35 • -75 • ). As it turned out, the calculated for the whole grid was confined to a rather narrow range of 0.074 -0.169.
In the ( 1 , ) grid, we fitted the W-D light-curves to the normal points shown in Fig. 3 assuming equal weights. The overall standard deviation of the fits were very nearly the same over the whole grid. This is a consequence of the fact that there are three free parameters in the models, the secondary's effective temperature, eff,2 , and the components' radii, 1 and 2 (formally, the surface potentials), that can be adjusted to get a satisfactory fit. Thus, the fits do not discriminate between different ( 1 , ). The solid lines plotted in Fig. 3 are the W-D light-curves computed with 1 = 8.695 M ⊙ and = 35 • . At the resolution of the figure, the light-curves computed with other ( 1 , ) values would be impossible to distinguish from those shown. The ranges of the parameters of the components obtained from the W-D modelling are given in Table 7; they are an order of magnitude greater than the formal standard deviations of the W-D solutions. It is interesting that the primary's W-D surface gravity is much better constrained than that derived in Appendix B1 from the photometric indices. In Fig. 4, the components of Cen are plotted using the effective temperature and luminosity of the primary from Appendix B1, and those of the secondary from Table 7; the ranges of log eff,2 and log( 2 /L ⊙ ) listed in the table define the full lengths of the error  bars and the open inverted triangles are placed at their intersection. Also shown in the figure is the ZAMS for the = 0.014 models from Ekström et al. (2012). Given coevality of the components, the position of the secondary relative to the ZAMS indicates its pre-MS status. The secondary's evolutionary status will be further discussed in Section 6.

The SB1 RV curve
All sets of the RV observations of Lup detailed in Section 3.2 and Table 2 (17), the RV measurements are distributed in orbital phase sufficiently well to be fit with the sine curve in which orb = 0.35090 d −1 . Using a sine curve is justified because the SB1 orbit of Lup is circular (see Section 5.4). In fitting Eq. (1), we used the method of least squares with weights inversely proportional to the squares of the standard errors of the velocities. For sets (11) and (14), the standard errors were obtained by multiplying the standard error of an equal-weights fit by / , where is the number of lines measured and is the overall mean of . For set (15), the standard errors were computed from the probable errors provided by Levato et al. (1987). For set (17), the standard errors are given in Table 3. The fits yielded the velocities to be used in Section 5.2, and the epochs of crossing theaxis from the smaller to greater RV (i.e. from approach to recession), HJD , to be used in Section 5.3.

Component A is the SB
Given the elements of the Lup AB visual binary orbit, the parallax of the system and the mass ratio of the components, the temporal variation of the RVs of the components A and B can be computed. After Heintz (1990) derived the elements mentioned in Section 2, a number of interferometric determinations of the position angle and angular separation of Lup B relative to A became available. In order to update the orbital elements, we compiled a list of and from the US Naval Observatory's Fourth Catalog of Interferometric Measurements of Binary Stars 8 , assigning weights to the measurements depending on the number of observations used in computing and , the scatter of the observations and the telescope size. Zero weight was given to the measurements with grossly deviating from the average run; this was never the case for . The updated elements were estimated by bootstrapping with 1 000 resamplings. The elements are listed in Table 8 and the corresponding apparent relative orbit is plotted in Fig 5. The value of = 0. ′′ 970 from the table and the revised Hipparcos parallax, equal to 7.75 ± 0.50 mas (van Leeuwen 2007), yield the semi-major axis of the relative orbit = 125.2 AU. Inserting this value and the period of the AB system AB = 167.3 yr into Kepler's third law, we get the mass of the system A + B = 70.1 M ⊙ , a value much too large for a pair of B2 stars. The lower bound of the orbital period, AB = 160.1 yr, yields a value still greater. Using the upper bound of the orbital period allowed by the solution, AB = 188.8 yr, and the corresponding = 1.394 × 10 10 km, we get A + B = 22.7 M ⊙ , a value still 5.5 M ⊙ greater than the overall mass of the system derived in Section B2.
Taking the above-mentioned three values of AB and the corresponding , , and from Table 8, and assuming = 0.00 km s −1 , we computed the RV curves shown in Fig. 6. Also plotted are the velocities from the fits carried out in Section 5.1 decreased by 4.12 km s −1 , so that sets' (14) (triangle) coincides with the computed RVs of component A for AB = 167.3 yr and = 1.0 (blue 8 http://www.usno.navy.mil/USNO/astrometry/optical-IR-prod/wds/int4

The light-time effect
Because of the orbital motion around the centre of mass of the AB system, the epochs of observations of Lup A include a term arising from the light-time effect (LiTE). In particular, the epochs of crossing the -axis from the smaller to greater RV, HJD , derived in Section 5.1, and the epochs of maximum light, HJD max , to be derived shortly, will be affected. HJD are listed in the second column of Table 9 while HJD max , in the first column of Table 10. The latter were computed from the least-squares fits of Eq.
(2) with orb = 0.35090 d −1 to the Hipparcos, SMEI, and BRITE data. The SMEI data were divided into five adjacent segments of approximately equal duration. Before fitting, the 2014 BRITE magnitudes were prewhitened with the 1.5389 d −1 term, and the 2015 blue magnitudes were pre-whitened with the 1.6913 d −1 term derived in Appendix A3.
In Fig. 7 there are shown the LiTE O -C curves computed for Lup A from equation (3) of Irwin (1952) with the 167.3, 160.1 and 188.8-yr elements of Table 8 (the solid, short-dashed and dashed lines, respectively) for two values of the B to A mass ratio, = 1.0 (upper panel) and 0.5 (lower panel). Assuming that at a given epoch the orbital phase of HJD is equal to that of HJD max , i.e. that the maximum light of the SB light-curve occurs when the secondary is at superior conjunction, one can fit the LiTE O -C curves to the HJD and HJD max from Tables 9 and 10. In the ephemerides 0 + 0 obtained in this way, the period 0 is equal to the Lup SB A orbital period, orb , for the epoch of   = 1.0 residuals fit the computed O -C curve with a slightly smaller standard deviation (0.0071 d) than the = 0.5 residuals (0.0076 d).

The SB RV and the mean light-curves of γ Lup A
Using the AB = 188.8 yr, = 1.0 LiTE O -C curve (dashed line in the upper panel of Fig. 7), we corrected the epochs of the RV and the BRITE observations of Lup for the LiTE, i.e. reduced the epochs to the centre of mass of the AB system. In addition, we reduced all RV measurements using component's A computed RVs (blue dashed line in the upper panel of Fig. 6) and removed a systematic difference of 6.4 km s −1 between sets (14) and (17). Then, we re-determined HJD and HJD max . The ephemeris obtained from these data HJD = HJD 2457482.7996(39) + 2.8497690(47) × .
(4) will be unaffected by the orbital motion of component A provided that the true AB and are equal to those we assumed. The initial epoch and the period in ephemeris (4) are close to those of the    The reduced RVs are plotted in Fig. 8 as a function of phase computed using the LiTE-corrected epochs of observations and orb from ephemeris (4). These data were then used in computing a spectroscopic orbit by means of the non-linear least squares method of Schlesinger (1910) with weights inversely proportional to the squares of the standard errors. The standard errors of sets (11), (14), (15), and (17) were the same as in Section 5.1 while those of set (16) were taken from Table 3. For set (12), we obtained the standard errors from the probable errors Buscombe & Morris (1960) provide, while for set (13) we estimated the standard error from the scatter in the phase diagram. The eccentricity of the orbit turned out to be equal to an insignificant = 0.044 ± 0.045. It is thus feasible to assume that the orbit is circular. The elements of a circular orbit are listed in Table 11 and the RV curve computed from these elements is shown in Fig. 8 with the solid line.
An anonymous referee has suggested that the orbital period of the AB binary could be obtained from an assumed value of the mass of the system equal to a sum of masses of two B2 stars. We carried out this exercise using the mass of the system of 17.2 ± 0.7 M ⊙ derived in Section B2 and the same data as in the first paragraph of Section 5.2. We obtained AB = 198.3 ± 5.4 yr and the remaining orbital elements rather close to those of Heintz (1990) mentioned in Section 2. If plotted in the upper panel of Fig. 6, the RVs computed with the AB = 198.3-yr elements would very nearly coincide with those computed with the AB = 188.8-yr elements. A similar result is obtained for the − shown in Fig. 7. In addition, the elements of the Lup A spectroscopic orbit obtained from the HJD and RV corrected for LiTE with the AB = 198.3-yr elements differ from those in Table 11 by much less than 1 : 1 , 1 sin and ( ) differ by 0.5 ± 1.4 km s −1 , 0.03 ± 0.08 R ⊙ and 0.0003 ± 0.0008 M ⊙ , respectively. Clearly, there exists an interval of mass of LupAB such that for a mass from this interval there is a value of AB which accounts for the observed temporal variation of RV and − . We believe that more measurements of and of the system are needed to narrow down this interval. Whether the model-independent mass of the system derived from the observed orbit will then agree with the model-dependent mass obtained in Section B2 remains to be seen.
Let us now turn to the question whether correcting the epochs of observations for the LiTE would affect results of frequency analysis of the BRITE data. As can be seen from Fig. 7, the LiTE corrections to the epochs of observations over the time interval covered by the BRITE data can be expressed by a linear function of time, + , where and are constants. In other words, the LiTE-corrected epochs of observations are shifted by and scaled by 1 + . From the well-known properties of the Fourier transform it follows that the time shift translates in the frequency domain into a phase shift, while the scaling, into scaling the frequencies and amplitudes by the reciprocal of 1 + . Since ≈ 1.5 × 10 −5 , the answer to our question is no. More precisely, the LiTE corrections would have negligible effect on the frequencies and amplitudes derived in Appendices A2 and A3.
Using the 2014 and 2015 blue and red magnitudes (see Appendix A3) with the LiTE-corrected epochs of observations and orb from ephemeris (4), we plot the blue and red phase diagrams in Fig. 9. The data plotted in the figure are normal points, computed in the adjacent intervals of 0.01 orbital phase. The standard errors, ranging from 0.25 to 0.35 mmag for the blue normal points and from 0.24 to 0.36 mmag for the red normal points, are not shown. The solid lines are the theoretical light-curves, results of the W-D modelling detailed in Section 5.5. A least-squares fit of a sum of the orb and 2 orb sines to the normal points yields the blue amplitudes of 5.92 ± 0.10 and 0.14 ± 0.10 mmag, and the red amplitudes of 8.54 ± 0.12 and 0.44 ± 0.12 mmag. In the latter case, the phase difference between the orb and 2 orb sines is equal to 0.21 ± 0.14 rad, excluding ellipsoidal effect as the cause of the 2 orb term. We conclude that the orbital light-variation is caused solely by the reflection effect. The amplitudes and the phase difference agree with the results presented in Section A3.

The W-D modelling
In the W-D modelling of the light curves of Lup we used the orbital elements from Table 11 and the fundamental parameters eff,1 = 20 790 K and log 1 = 3.94 from Appendix B2. As in the case of Cen, the eff,1 was fixed throughout but the final log 1 were taken from the W-D solutions after several iterations. The remaining details of the W-D modelling were also the same as in the case of Cen (see Section 4.3), except that a third light was included in order to account for component B. The third light's brightness was kept as a free parameter because fixing it at a level consistent with the Hp magnitudes of the components (see Section 2) resulted in a divergent solution. As in the case of Cen, the range of 1 was assumed to span five times the uncertainty obtained in Appendix B2. The results of the W-D modelling, listed in Table 7, bear many similarities to the results for Cen (Section 4.3): (i) the mass ratio is low, = 0.15 +0.09 −0.05 , (ii) the W-D light-curves fit the normal points with very nearly the same overall standard deviation over the whole ( 1 , ) grid, (iii) the position of the secondary relative to the ZAMS indicates its pre-MS status (see Fig. 4). The secondary's evolutionary status will be further discussed in Section 6.

DISCUSSION AND CONCLUSIONS
Using stellar parameters and the results of the W-D modelling of the reflection effect in Cen and Lup A, we concluded in Sections 4.3 and 5.5 that the secondaries in both systems are in the pre-MS stage of evolution. Thus, as we already mentioned in Section 1, the systems can be regarded as non-eclipsing counterparts of the NEBs, to be referred to in the following as NnonEBs. In order to strengthen this conclusion, we compare in Fig. 10 the radii, the age, and the range of reflection effect of Cen and Lup A with those of the LMC NEBs using the parameters of Cen and Lup A from Table 7 (the ranges of the parameters are plotted as error bars) and those of the LMC NEBs from tables 1 and 2 of Moe & Di Stefano (2015). First of all, the radii of the secondaries are significantly larger than the zero-age main sequence (ZAMS) values for stars with the same masses (upper left-hand panel of the figure). A more convincing argument that Cen  Table 11. The two lower panels of Fig. 10 show parameters characterising the light curves. The NnonEBs Cen and Lup A can be plotted only in the left-hand panel, in which they occupy a shortorb extension of the area occupied by the LMC NEBs. Also shown in Fig. 10 are two SB1 eclipsing binaries 16 (EN) Lac and Eri mentioned in Section 1. 16 (EN) Lac is plotted with the parameters from Jerzykiewicz et al. (2015), while Eri, with the parameters computed using the data from tables 3 and 4 and fig. 11 of Jerzykiewicz et al. (2013). Because of the ratio of the radii = 2 / 1 of only ≈ 0.25 and a relatively long orbital period of 12.1 d, the range of the reflection effect in 16 (EN) Lac is smaller than 5 mmag. The pre-MS status of the star's secondary component is based on the analysis of the ground-based eclipse lightcurve (Pigulski & Jerzykiewicz 1988;Jerzykiewicz et al. 2015) and an unpublished eclipse light-curve obtained by one of the authors (MJ) from the NASA Transiting Exoplanet Survey Satellite (TESS, Ricker et al. 2015) observations. In the case of Eri, the orbital period is about 1.6 times shorter than that of 16 (EN) Lac but the reflection effect is below the detection threshold because of the small ≈ 0.135. Still, as can be seen from Fig. 10, the pre-MS status of the secondary is evident. We conclude that 16 (EN) Lac and Eri should be regarded as bona fide NEBs. Note that since it was the reflection signature in the eclipsing light-curves which Moe & Di Stefano (2015) used to single out the NEBs from the OGLE data, objects similar to 16 (EN) Lac and Eri would have passed undetected in their search.
As far as we are aware, Cen and Lup A are the only known NnonEBs, i.e early B-type non-eclipsing SB systems such that (i) their observed orbital light-variation is caused solely by the reflection effect, and (ii) the secondary component is in a pre-MS evolutionary phase. In order to verify this and prepare the ground for a future photometric program, we have searched the literature for the light-variability information about all 169 B0 -B5 non-eclipsing SB systems listed in The Ninth Catalogue of Spectroscopic Binary Orbits 9 (Pourbaix et al. 2004). Apart from Cen and Lup A, we found only 17 systems with the orbital period equal to the light-variation period, all with primaries of spectral type B3 or earlier. In three cases the secondary component is known to be a compact object, a neutron star or a white dwarf, while in 13, the light curve is a double wave implying an ellipsoidal variation. Only one system, CX Dra, with an orbital period equal to 6.696 d, exhibits a sinusoidal light-variation of this period, albeit with a large amount of scatter, and the phase relation between the RV and light variation characteristic of the reflection effect (Koubský et al. 1980). The scatter is mainly due to the fact that CX Dra is an interacting Be binary showing variations on time-scales from days to years. Koubský et al. (1980) suggest that a combination of ellipsoidal and reflection effects is responsible for the orbital lightvariation. However, using the well-known formula for the amplitude, , of the ellipsoidal light-variation (see e.g. Ruciński 1970) and the spectroscopic orbital parameters of the system (Koubský 1978) we find < ≈ 0.3 mmag. Thus, CX Dra meets condition (i). G. D. Penrod ( , private communication to Horn et al. 1992) detected the lines of the secondary component and estimated the MK type to be F5 III. The orbit of the secondary component was derived by Horn et al. (1992). These authors concluded that the component is a mid-F luminosity III star filling its Roche lobe. This conclusion is at variance with the result of Guinan, Koch & Plavec (1984), obtained by means of a thorough W-D modeling, that the system is detached. In any 9 http://sb9.astro.ulb.ac.be case, CX Dra does not meet condition (ii). We conclude that no other NnonEBs than Cen and Lup A are known. However, there is a number of B0 -B5 non-eclipsing SB systems which in the Hipparcos Epoch Photometry have Hp ranges from two to several mmags but were not classified as periodic variables. Re-observed with satellite photometers, some of these systems may turn out to be NnonEBs.
As discussed in some detail by Moe & Di Stefano (2015), the study of nascent binaries may be of great importance for our understanding of the formation of low-mass-ratio binaries and the origin of such objects as type Ia supernovae, low-mass X-ray binaries and millisecond pulsars. The discussion would benefit from including Galactic counterparts of the LMC nascent binaries, eclipsing or otherwise. They should be searched for among young binaries. We have already found several candidates in young open clusters and associations but a detailed discussion of these objects is beyond the scope of this paper.

DATA AVAILABILITY
The raw BRITE data are available from BRITE Public Data Archive (https://brite.camk.edu.pl/pub/index.html). The raw SMEI data are available via the link given in Section 3.1. The processed (decorrelated) BRITE and SMEI data are available from the first author upon request. The other data are available from their respective public databases.

APPENDIX A: FREQUENCY ANALYSIS A1 ν Cen
For the purpose of frequency analysis, the reduced BAb and BLb magnitudes of Cen (Table 1) were combined into one data set of blue-filter magnitudes, and the reduced BTr and UBr magnitudes, into one data set of red-filter magnitudes. We shall refer to the two data sets as the red and blue data, respectively. The periodograms using these data were computed in the frequency range from 0 to 20 d −1 . The highest peaks in the periodograms of both data sets occurred at the orbital frequency (Section 4.1). The periodograms of the blue data, the red data and the blue and red data combined, Figure A1. The periodograms of the blue (top), red (middle) and blue and red combined (bottom) BRITE magnitudes of Cen pre-whitened with the orbital frequency. The mean noise levels and four times those are indicated (the white and red lines, respectively).
pre-whitened with the orbital frequency, are shown in Fig. A1. Also shown in the figure are the mean noise levels, , and 4 , the popular detection threshold set by Breger et al. (1993). As can be seen from the figure, there are no peaks in the periodograms exceeding 0.7 mmag. In particular, the blue and red amplitude at 2 orb is equal to 0.1 mmag, so that an ellipsoidal light-variation, if any, would have the amplitude less than or equal to 0.1 mmag in both colours. At the frequencies corresponding to the putative Cephei-type periods of 0.1750, 0.1690156 and 0.1696401 d, found by Rajamohan (1977), Kubiak & Seggewiss (1982) and Ashoka et al. (1985), the blue and red amplitudes do not exceed 0.2 mmag. One peak in the top panel of Fig. A1 has / slightly greater than 4, and a few ones in the middle panel have / slightly smaller than 4, but none has a counterpart in the other panel. We conclude that in the data prewhitened with the orbital frequency there are no periodic terms with an amplitude exceeding 0.7 mmag. In the periodogram of the prewhitened blue and red data combined (bottom panel), there are no peaks exceeding 0.5 mmag. We thus confirm the results of Shobbrook (1978), Percy et al. (1981) and Sterken & Jerzykiewicz (1983) who found no short-period brightness variation, and strengthen that of Cuypers et al. (1989) who found no variation, other than the orbital one, with an amplitude exceeding 2 mmag (Section 2).

A2 γ Lup: the 2014 and 2015 data analyzed separately
After combining the reduced 2014 BAb and BLb magnitudes of Lup into one set of blue magnitudes, and the reduced 2014 UBr and BTr magnitudes, into one set of red magnitudes, we computed periodograms in the same way as we did previously for Cen (Section A1). In both periodograms, the frequency of the highest peak was equal to the orbital frequency of 0.35090 d −1 to within 0.015 of the frequency resolution of the data. The periodograms of the blue and red magnitudes pre-whitened with the orbital frequency are shown in the upper and lower panels of Fig. A2, respectively. In both panels, the highest peak occurs at 1.5389 d −1 . At this frequency, the ampli- tude is equal to 0.7 mmag and the signal-to-noise ratio / > 4 in the upper panel, and the amplitude is equal to 0.6 mmag and / ≈ 4 in the lower panel. The blue to red amplitude ratio and the blue minus red phase difference of the 1.5389 d −1 sinusoid amount to 1.13 ± 0.16 and 0.43 ± 0.14 rad, respectively. These numbers are well within the range of values predicted for high radial-order, low harmonic-degree g-mode pulsations of B-stars models (see e.g. Townsend 2002). The periodograms of the 2015 blue and red magnitudes prewhitened with the orbital frequency are shown in the upper and lower panel of Fig. A3, respectively. The highest peak in the upper panel occurs at 1.6913 d −1 , while the highest peak in the lower panel, at 0.3441 d −1 . The former has / > 4, while the latter, / ≈ 4. However, none has a counterpart in the other panel, so that both are probably spurious. The 2014 1.5389 d −1 term was not present in 2015.

A3 γ Lup: the 2014 and 2015 data combined
Before combining the 2014 and 2015 blue magnitudes into a single data set, we pre-whitened the 2014 blue magnitudes with the In the middle panel, the two highest peaks, with / = 3.9 and 3.6, occur at 0.3176 and 0.7014 d −1 . The latter frequency is close to 2 orb . The amplitude of the sinusoid of this frequency is equal to 0.5 mmag and the phase differs from that of the orb sinusoid by an insignificant 0.2 ± 0.2 rad. Thus, the red orbital light-curve does not deviate within errors from a strictly sinusoidal shape. The same is true for the blue orbital light-curve because the amplitude of 2 orb in the top panel of Fig. A4 amounts to 0.1 mmag. Finally, the periodogram of the blue and red data combined (bottom panel of Fig. A4) shows peaks close to the above-mentioned frequencies 0.3176, 0.7014 and 0.9554 d −1 , and also peaks at 0.3725 and 1.4077 d −1 , all with / ≈ 4.0. It is doubtful that any of these frequencies, except the 0.7014 d −1 one, represents a variation intrinsic to Lup. Note that (i) because of the ambiguity mentioned in Section 2, either component A or B would be responsible for any of the frequencies discussed above except orb and 2 orb (Section 5.2), and (ii) the amplitude of a variation of component A would suffer from light dilution caused by component B, and vice versa.

B1 ν Cen
We shall now derive the fundamental parameters of Cen. From the star's Strömgren indices − and 1 given by Hauck & Mermilliod (1998) we obtain 0 = 0.082, ( − ) 0 = −0.109, ( − ) = 0.007, and ( − ) = 0.009 mag by means of the canonical method of Crawford (1978). From 0 we get the effective temperature, eff = 22 267 K, and the bolometric correction, BC = −2.25 mag, using the calibration of Davis & Shobbrook (1977), eff = 22 550 K using UVBYBETA 10 and 22 289 K using the calibration of Sterken & Jerzykiewicz (1993). The close agreement of these eff values is due to the fact that the three temperature calibrations rely heavily on the OAO-2 absolute flux calibration of Code et al. (1976). Taking a straight mean of the above three values we arrive at eff = 22 370 K. Realistic standard deviations of the effective temperatures of early-type stars, estimated from the uncertainty of the absolute flux calibration, amount to about 3 % (Napiwotzki et al. 1993;Jerzykiewicz 1994) or 670 K for the eff in question. The standard deviation of BC we estimate to be 0.20 mag.
The surface gravity of a B-type star can be obtained from its index. Taking the index of Cen from Hauck & Mermilliod (1998) and 0 from the preceding paragraph, we get log = 3.76 by means of UVBYBETA. According to Napiwotzki et al. (1993), the uncertainty of the -index surface gravities of hot stars is equal to 0.25 dex; we shall adopt this value as the standard deviation of the star's log .
The revised Hipparcos parallax of Cen is equal to 7.47 ± 0.17 mas (van Leeuwen 2007). Taking the star's magnitude from Mermilliod (1991), ( − ) from the first paragraph of this section and assuming = 3.2 we get = −2.25 ± 0.05 mag. This value and BC yield bol = −4.50 ± 0.21 mag and log /L ⊙ = 3.70 ± 0.08. In computing log /L ⊙ , we assumed M bol⊙ = 4.74 mag, a value consistent with BC ⊙ = −0.07 mag, the zero point of the bolometric-correction scale adopted by Davis & Shobbrook (1977). In summary, the fundamental parameters of Cen are: eff = 22 370 ± 670 K, log = 3.76 ± 0.25, log /L ⊙ = 3.70 ± 0.08. 11 Percentage-wise, eff is best constrained, while log , the worst. In the PASTEL catalogue of stellar atmospheric parameters (Soubiran et al. 2016) one finds eff = 22 570 ± 1810 K, a value obtained by Sokolov (1995) from the continuum between 320 and 360 nm. No log of Cen is listed in the catalogue.
Since the bolometric magnitude of the secondary component of Cen is at least 7.4 mag fainter than that of the primary (Table 7), so that it is at least 5 mag fainter in than the primary, the fundamental parameters eff , log /L ⊙ and log just derived pertain to the latter; in Section 4.3 we refer to them as eff,1 , log 1 /L ⊙ and log 1 . Using the first two parameters, we plot the primary component in Fig. B1. Also shown in the figure are evolutionary tracks computed by means of the Warsaw-New Jersey evolutionary code (see e.g. Pamyatnykh et al. 1998), assuming no convective-core overshooting, the initial abundance of hydrogen = 0.7, the metallicity = 0.015, the OPAL equation of state (Rogers & Nayfonov 2002) and the OP opacities (Seaton 2005) for the heavy element mixture of Asplund et al. (2009). The tracks were kindly provided by Professor J. Daszyńska-Daszkiewicz. As can be seen from Fig. B1, the primary component of Cen is in the MS stage of evolution. The evolutionary mass and age, estimated from the position of the inverted triangle in the figure relative to the rot = 80 km s −1 evolutionary tracks, are equal to 8.7 ± 0.3 M ⊙ and 11.1 +5.2 −7.6 Myr. The most recent value of rot sin , measured on high signal-to-noise-ratio spectrograms, is equal to 65 ± 6 km s −1 (Brown & Verschueren 1997), so that the 10 A FORTRAN program based on the grid published by Moon & Dworetsky (1985). Written in 1985 by T.T. Moon of the University London and modified in 1992 and 1997 by R. Napiwotzki of Universitaet Kiel (see Napiwotzki, Schoenberner & Wenske 1993). 11 Gaia's Early Data Release 3 (https://www.cosmos.esa.int/web/gaia /earlydata-release-3) parallax of 8.05 ± 0.35 mas yields log /L ⊙ = 3.63 ± 0.09.   Figure B1. The primary components of Cen and Lup A (inverted triangle and filled circle with error bars, respectively) in the HR diagram plotted using the effective temperature derived from photometric indices, and the luminosity from the magnitude, photometric indices and the Hipparcos parallax (see Section B1 for Cen and B2 for Lup A). The lines are the = 0.7, = 0.015 evolutionary tracks for 8 and 9 M ⊙ and the rotation velocity listed in the bottom right corner. rot value we assumed corresponds to the inclination of the rotation axis of 54 +8 −6 deg. We believe that in view of the large errors of log eff,1 and log 1 /L ⊙ , the contribution of the uncertainty in rot to the final error of the evolutionary mass and age is negligible. The evolutionary age we derived is smaller than the MS turnoff age of 17 ± 1 Myr obtained for UCL by Mamajek, Meyer & Liebert (2002), but the difference is still within the errors. Our value is close to the age of ∼10 Myr obtained from the strength of Li 670.8 nm absorption line by Song, Zuckerman & Bessell (2012).

B2 γ Lup
We shall now derive fundamental parameters of Lup A assuming that the components A and B, because of their very nearly equal brightness (Section 2), have identical photometric indices, equal to the observed, combined values. From the star's Strömgren indices − and 1 (Hauck & Mermilliod 1998) we get 0 = 0.141, ( − ) 0 = −0.103, ( − ) = 0.006 and ( − ) = 0.008 mag by means of the canonical method of Crawford (1978). Then, using the same procedures and calibrations as in the case of Cen (Section B1), we obtain eff = 20 790 ± 620 K, BC = −2.10 ± 0.20 mag and log = 3.94 ± 0.25. In order to derive component's A logarithmic luminosity, log( A /L ⊙ ), we first computed the magnitudes from the Hp magnitudes (Section 2) using the Harmanec (1998) transformation with the − and − indices from Mermilliod (1991). The result is A = 3.468 and B = 3.582 mag. The combined magnitude of Lup computed from A and B is 2.771 mag, in good agreement with = 2.780 ± 0.013 mag given by Mermilliod (1991). Moreover, the B minus A -magnitude difference implies an insignificant − difference of 0.005 mag, consistent with the assumption made at the beginning of this paragraph. From the revised Hipparcos parallax, equal to 7.75 ± 0.50 mas (van Leeuwen 2007), the ( − ) derived above and = 3.2 we get = −2.11 ± 0.14 mag. This value and BC yield bol = −4.21 ± 0.24 mag. In summary, the fundamental parameters of Lup A are: eff = 20 790 ± 620 K, log = 3.94 ± 0.25 and log( /L ⊙ ) = 3.58 ± 0.10. As in the case of Cen, eff is best constrained, while log , the worst.
The secondary component of Lup A is about 4.5 to 5.5 mag fainter than the primary (Table 7). Thus, the fundamental parameters eff , log /L ⊙ and log just derived pertain to the latter; in Section 5.5 we refer to them as eff,1 , log 1 /L ⊙ and log 1 . Using the first two parameters, we plot the primary component in Fig. B1. As can be seen from the figure, the primary component falls very nearly on the MS branch of the 8 M ⊙ , rot = 250 km s −1 evolutionary track. Its evolutionary mass and age, estimated from the position of the circle relative to the track, are equal to 8.0 ± 0.4 M ⊙ and 16.7 +5.0 −6.6 Myr. According to Głębocki & Gnaciński (2005), rot sin of Lup is equal to 236 ± 5 km s −1 , so that the rot value we assumed is close to a lower limit because it corresponds to the inclination of the rotation axis of 71 +4 −3 deg. However, the evolutionary mass and age are rather insensitive to rot (see below). Unlike the case of Cen, the evolutionary age we derived is very nearly equal to the UCL's MS turnoff age of 17 ± 1 Myr (Mamajek et al. 2002). Component B is not plotted in Fig. B1 because it would almost coincide with A. Its evolutionary mass and age would be very nearly equal to those of A, provided it had rot = 250 km s −1 . If rot = 0 km s −1 , the evolutionary mass and age would become 7.8 ± 0.4 M ⊙ and 17.5 +5.0 −6.6 Myr. Since the difference between the evolutionary masses is much smaller than 1 , we conclude that the sum of evolutionary masses of the spectroscopic primary of A and that of B is equal to about 15.9 ± 0.6 M ⊙ . Assuming the mass of the spectroscopic secondary of A to be equal to 1.3 ± 0.3 M ⊙ , i.e. the middle of the range of 2 in Table 7 with an estimated uncertainty, and assuming that B is single, we get 17.2 ± 0.7 M ⊙ for the overall mass of the AB system, and 0.86 ± 0.12 for the B to A mass ratio. The overall mass of the AB system is thus about 5.5 M ⊙ smaller than A + B derived in Section 5.2 for AB = 188.8 yr. Hopefully, this discrepancy will be removed when more measurements of the position angle and angular separation of Lup B relative to A, and therefore a better visual orbit of Lup AB than that given in Table 8 become available. This paper has been typeset from a T E X/L A T E X file prepared by the author.