Absolute Parameters of Young Stars: V Puppis
Edwin Budding, Tom Love, Mark G. Blackford, Timothy Banks, Michael D. Rhodes
MMNRAS , 000–000 (0000) Preprint 2 February 2021 Compiled using MNRAS L A TEX style file v3.0
Absolute Parameters of Young Stars: V Puppis
E. Budding , , , , T. Love , , M. G. Blackford , T. Banks , ,M. J. Rhodes Visiting astronomer, University of Canterbury Mt John Observatory, University of Canterbury, Private Bag 4800, Christchurch 8140, NZ; Carter Observatory, Wellington 6012, NZ; School of Chemical & Physical Sciences, Victoria University of Wellington, Wellington 6012, New Zealand. Variable Stars South, RASNZ; Nielsen, Data Science, 200 W Jackson Blvd 17, Chicago, IL 60606, USA. Physics & Astronomy, Harper College, 1200 W Algonquin Rd, Palatine, IL 60067, USA Brigham Young University‘, Provo, Utah, USA.
ABSTRACT
New spectrometric data on V Pup are combined with satellite photometry (HIPPARCOS and recent TESS) to allowa revision of the absolute parameters with increased precision. We find: M = 14.0 ± M = 7.3 ± (cid:12) ); R =5.48 ± R = 4.59 ± (cid:12) ); T ± T ± ± ±
10 (pc). The TESS photometry reveals low-amplitude ( ∼ β Cep kind, consistent withthe deduced evolutionary condition and age of the optical primary. This fact provides independent support to ourunderstanding of the system as in a process of Case A type interactive evolution that can be compared with µ Sco.The ∼
10 M (cid:12) amount of matter shed by the over-luminous present secondary must have been mostly ejected fromthe system rather than transferred, thus taking angular momentum out of the orbit and keeping the pair in relativeclose proximity. New times of minima for V Pup have been studied and the results compared with previous analyses.The implied variation of period is consistent with the Case A evolutionary model, though we offer only a tentativesketch of the original arrangement of this massive system. We are not able to confirm the previously reported cyclicalvariations having a 5.47 yr period with the new data, though a direct comparison between the HIPPARCOS andTESS photometry points to the presence of third light from a star that is cooler than those of the close binary, asmentioned in previous literature.
Key words: stars: binaries (including multiple) close — stars: early type — stars: variable β Cep type — stars:individual V Pup
Studies of massive young stars, forming part of a ‘South-ern Binaries Programme’, were presented by members of ourgroup in a number of previous papers. General backgroundwas given by Budding (2008) and in the summary of Idaczyket al. (2013). For a recent example see Blackford et al. (2019).Binary stars are still the main source of fundamental dataon stellar masses and radii. Our access to such advanced facil-ities as the high-precision photometry from the TESS satellite(Section 2) and the high-resolution HERCULES spectrome-ter (Section 3) for this application enables continued progressin refining our knowledge of the properties of stars. Popper’s(1980) contribution to this subject set accuracy limits of afew percent, that was refined to an estimated ∼
2% for the 45examples studied by Andersen (1991). These review papersreport an ongoing development of our understanding of stel-lar astrophysics, on the basis of data that has been confirmed to be reliable and of high quality. Andersen et al. (1993) alsodrew attention to the interesting role of close young binariesin understanding the relationship of stellar properties to theirgalactic environment. As well, Rucinski (2006) pointed outthe observational neglect of binaries with declinations southof declination –15 ◦ . Such discussion underlies and provides aspringboard for the work presented here.In this paper, we re-examine the early type eclipsing bi-nary V Pup. The system consists of at least two young starsin a very close orbit, apparently in a ‘Case A’ process ofinteractive binary evolution. V Pup has attracted recent at-tention regarding the possibility that it may contain a blackhole companion associated with its known high energy andmicrowave emissions (Giacconi et al., 1974; Groote et al.,1978; Bahcall et al., 1975; Qian et al., 2008; Maccarone etal., 2009). The issue may be probed more fully with the aid © a r X i v : . [ a s t r o - ph . S R ] J a n E. Budding et al. of up-to-date measurement and data-analysis procedures aswell as the observational facilities mentioned above.
V Pup ( = HD 65818, HIP 38597, WDS J07582-4915A, HR3129; Gaia DR2 55171716782683628800) is a bright ( V =4 . B − V = − . U − B = − .
96; types B1Vp + B2)eclipsing variable of the ‘EB’ type, discovered by Williams(1886). It is located on the sky about 2.5 ◦ south-west of, andat a comparable distance ( ∼
300 pc) to, the massive multiplestar γ Vel. Early history of observations of the system isbriefly reviewed in the paper of Cousins (1947).There has been ongoing literature discussion about theabsolute parameters of V Pup, with effects attributed tothe presence of gas streams or mass transfer distortingradial velocity (RV) data on the stellar components (the‘Struve-Sahade effect’ — see e.g. Maury, 1920; Popper, 1947;Frieboes, 1962; York et al., 1976; Cester et al., 1977; Eaton,1978; Koch et al., 1981, Andersen et al., 1983, Stickland etal., 1998). The spectral types were given as B1 V and B3 Vby Freiboes (1962) with corresponding masses of about 17and 9 M (cid:12) (Popper, 1980). Andersen et al. (1983) revised theparametrization of the system with improved data and anal-ysis procedures, dropping the dwarf luminosity (V) of thesecondary, which could now be assigned a subgiant (IV) clas-sification. Their masses were reduced somewhat from thoseused by Popper to 14.8 and 7.8 M (cid:12) , with error estimatesof about 2% of these values. The orbital period is relativelyshort at 1.4545 d. Stickland et al. (1998) obtained noticeablylower masses from IUE spectrograms, though unfortunately,the coverage at one of the elongations was rather incomplete.V Pup appears to have at least one physical companion,associated with the double star h4025, the other star being an11th mag object at a separation of about 6 arcsec. Two otherfainter companions have also been linked to the massive early-type close binary. York et al. (1976), using UV data from theCopernicus satellite, deduced the presence of an HII regionaround the binary with an angular extent of ∼ µ Sco (Budding et al., 2015) in showing a semi-detached,near-contact configuration (cf. Schneider et al., 1979; An-dersen et al. 1983; Bell et al. 1987a, 1987b; Terrell et al.2005), and with this type of hot massive binary this is oftenassociated with Case A evolution, in which mass loss fromthe erstwhile primary continues while the star is still on thehydrogen-burning Main Sequence (Sybesma, 1986; Yakut &Eggleton, 2005).With its stable light curve and well defined eclipses, tim-ings of the light minima of V Pup may allow the stabilityof the binary orbit to be checked by use of the ‘O – C’ (ob-served minus calculated) diagram. Periodic residuals in suchdata (Kreiner et al., 2000) have suggested the presence of a ∼
10 M (cid:12) unseen companion to the binary, with an orbital pe-riod of about 5 years (Qian, Liao & Fernandez-Lajus, 2008).Absence of visible indications of such a massive component inthe optical region lead to the idea that this component maybe a black hole.Qian et al. (2008) argued that the X-ray emission from VPup is consistent with accretion of stellar winds from the hotbinary towards such a black hole. Interestingly, its mass could then be determinable from the observed orbital effects, andindependently of evolution scenarios for the overall system.Triple systems with accreting components have been in-voked in the past, for example, to provide a physically plausi-ble scenario for the Cygnus X-1 system (Bahcall et al. 1975).Also, the occurrence of long additional periods in systemswith accreting neutron stars and black holes (Priedhorsky& Terrell, 1983; Gies & Bolton 1984; Zdziarski et al. 2007)may be explained in this way. Longer timescale effects in theshort period neutron-star binary 4U 2129+47 were attributedto an observed F type wide companion (Garcia et al. 1989;Nowak, Heinz & Begelman 2002), further substantiating suchan hierarchical stellar system model. Maccarone et al. (2009)made observations aimed at testing the hypothesis that theX-ray emission from V Pup is from accretion onto the puta-tive black hole by searching for radio emission, since a highratio of radio to X-ray flux should be a characteristic signa-ture of accreting black holes of stellar mass. They invokedan X-ray image of the field using Chandra, thus confirmingthat the X-rays are indeed from V Puppis or its close ( ∼ µ Jy. V Pup was identified in its X-ray emis-sion with a luminosity of about 3 × erg/sec. This valueis much lower than what had been reported in low angularresolution surveys of the past. Maccarone et al.’s results wereinterpreted to show that the X-ray emission comes from masstransfer between the two B stars in the system. The possi-bility of X-ray emission from the black hole accreting stellarwind from one or both of the B stars could not be ruled out,however.In fact, massive early type stars, such as those in the V Pupsystem, are known to produce strong winds driven by the ra-diation pressure from the high temperature stellar surfaces.In a binary system consisting of two such stars the windswill interact, producing exotic shock effects observed acrossthe spectrum, but noticeably in the X-ray range (e.g. Pol-lock, 1987; Chlebowski & Garmany, 1991; Corcoran, 1996)and as synchrotron radio-emission. Such emissions tend tohave a complex, intermittent or highly variable behaviour,particularly in higher energy ranges, and observations do notalways support the predictions of basic models (e.g. Prilutski& Usov, 1976; Cherepashchuk, 1976; Stevens et al. 1992). Asmore data have been collected over the years, fuller recogni-tion of these anomalies has grown and theory developed tointroduce more refined models (Pittard, 2009; Parkin et al.2011; Rauw & Naz´e, 2016). It seems likely that the high en-ergy emissions noted for V Pup, as well as their variability,may be accounted for by such modelling, without requiringthe more extreme configuration invoked by Qian et al. (2008).In the next section, we present and analyse photometry ofV Pup. We follow this with some new spectroscopic data inSection 3. Combination of the results from the photometricand spectroscopic analyses lead to our derived set of absoluteparameters in Section 4, and we discuss O – C analysis ofthe system in Section 5. These findings are discussed andinterpreted in terms of relevant stellar astrophysical modelsin the Section 6. MNRAS , 000–000 (0000) bsolute Parameters of Young Stars −0.2 0.0 0.2 0.4 0.6 0.8 1.0 . . . . . Phase F l u x l e v e l −0.2 0.0 0.2 0.4 0.6 0.8 1.0 − . . Phase F l u x l e v e l Figure 1.
HIPPARCOS photometry of V Pup with Radau-modelfitting. Residuals (crosses) are shown distributed about the loweraxis.
As before in this programme we looked into previous pho-tometry, particularly that of the HIPPARCOS satellite (ESA,1997). The light-curve has been phased in the HIPPARCOSEpoch Photometry Annex according to the ephemeris Min I= 2448500.595 + 1.454507E. Since the data were gatheredover a ∼ WinFitter that follow from the principles set out in Bevington (1969),chapter 11. The procedure involves numerically inverting thedeterminacy Hessian of the χ variate in the vicinity of itsminimum. This Hessian matrix should be positive definitefor a properly posed inversion problem. The resulting errorsthen include the effects of inter-correlations between the pa-rameters selected for adjustment (see also Banks & Budding,1990, for further background on this topic).We can at once deduce, from the comparability of the lu-minosities despite the appreciable difference in masses, thatwe are not dealing with a Main Sequence pair. Kopal’s (1959,Table 3.3) approximation that r + r ≈ .
75 for contact bi-naries, indicates that these stars must be relatively close tocontact at the internal Lagrangian point L . Indeed, the rel-ative size of the secondary points to a filling of its ‘Rochelobe’. This point, together with the closeness of the stars,confirms that this eclipsing binary is of the semi-detachedCase-A-evolution type that may be compared with µ Sco(cf. Introduction).A small shift from zero in the phase of minimum light ∆ φ is given in Table 1. The movement is in the sense that theobserved minimum was late from its predicted time by anamount of some 0.0019 in phase, or 0.0028 days from the pre- Table 1.
Curve fitting results for archival HIPPARCOS photome-try of V Pup using
WinFitter 6.2 . Parameters for which no errorestimate is given are adopted from information separate to thefitting. The HIPPARCOS raw data were phased according to theephemeris provided in the HIPPARCOS Photometry Annex (ESA,1997; – see text). Parameter Value Error M /M L L r (mean) 0.406 0.002 r (mean) 0.349 0.005 i (deg) 75.1 0.4 T h (K) 26000 T c (K) 24000 u u φ (deg) 0.7 0.2 χ /ν l dicted time using the HIPPARCOS ephemeris given above.We deduce that the time of observed minimum should be24448455.5081, or some 13618.01536 cycles after Kreiner’sepoch that is used as a basis for O –C studies. This leads toan O – C value of +0.0223 d, which is slightly greater thanthe +0.0198 d given by Qian et al. (2008). The Transiting Exoplanet Survey Satellite (TESS) waslaunched in April 2018, and began regular science operationsby the end of July in that year. This NASA-supported mis-sion is primarily aimed at a near complete survey of the wholesky, searching for exoplanet transiting systems (Ricker et al.,2015). In its first two years TESS should closely monitorover 200,000 Main Sequence stars with four wide-field opti-cal CCD cameras. Photometry of the target stars is recordedwith a 2 minute cadence. Additional images are taken of awide ( ∼ WinFit-ter was then used to experiment with photometric modellingof these data.Although the TESS data are of very high accuracy, en-abling a remarkably close modelling fit (Fig 2), at an initialstage it became clear that there were small short-term com-
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E. Budding et al. −0.2 0.0 0.2 0.4 0.6 0.8 1.0 . . . . Phase F l u x l e v e l −0.2 0.0 0.2 0.4 0.6 0.8 1.0 − . . Phase F l u x l e v e l Figure 2.
WinFitter model fit to the complete TESS photomet-ric data-set for V Pup, binned by a factor of 10 down to 1513 indi-vidual values. The scatter of individual readings is of order 0.0002,but systematic departures of up to an order of magnitude greaterthan that can be seen in the residuals in the regions of the eclipseswhen plotted about the mean flux level 0.55 in this diagram. Thisis mostly accounted for by the fitting function’s quadratic approxi-mation being inadequate to represent the stars’ photospheric limb-darkening effect with sufficient accuracy of detail. The parameterscorresponding to this fitting are given in Table 2. plications in the form of the data compared with expecta-tion for a standard binary system pattern of light variation.The complete data-set was then binned by a factor of 10 andan optimal model sought, using the results of Table 1 as aguide. The adopted model parameters are listed in Table 2.The fitted light curve is shown in Fig 2, and Fig 3 displays acorresponding illustration of the basic stellar model.These parameters have some noticeable differences fromthe ones in Table 1. But the forms of the light curves are alsoseen to be different: while both light curves show the peakbrightness at close to unity and the minima are in about thesame proportions, those in Fig 2 are more than 10% shal-lower than those of Fig 1. This is probably mainly due to thedifference in effective wavelengths of the HIPPARCOS andTESS photometers. The TESS detector bandpass spans from600 — 1000 nm and is centered on the Cousins I-band (7865˚A), but with the high temperature expected for the source( ∼ ∼
549 nm (Mann & von Braun, 2015).The possible contribution of an additional cooler compo-nent, or components, therefore arises (cf. Eaton, 1978). Whilethere is no question that the TESS data have a higher mea-surement precision than those of HIPPARCOS, (by a coupleof orders of magnitude, to judge by the scatter of individ-ual measures), the TESS pixels (21 arcsec in extent) includesignificantly more background sky than the field of HIPPAR-COS. The WDS (Worley & Douglass, 1997) lists four visualcompanions to V Pup, but none of the nearest 3 within 20 arc-sec are brighter than mag 11.5, while HJ 4025D, the bright-est at V = 9.88 and separated at 40 arcsec, can not haveadded significantly to background illumination, though thepossibility of error in the background subtraction procedure,given the large pixels of TESS, cannot be ruled out. Table 2
Figure 3.
Gnuplot illustration of V Pup using a standard Roche-model corresponding to the parameters of Table 2. The secondaryis close to contact with its ‘Roche lobe’. presents this as L : the additional light at the longer wave-length that reduces the apparent amplitude of the variationdue to the close binary alone.The residuals from the fitting to the binned complete data-set shown in Fig 2, whilst evidently less than those of Fig 1,reveal small systematic features, of amplitude < ≈ . ≈ . β Cep typevariable, with the rather low amplitude of ∼ β Cep variability is likely in view of the primary star’sproximity to the instability strip. This discovery potentiallyoffers an additional check on the system’s parametrization.Lomb-Scargle analysis (cf. Ruf, 1999) of the flux residualsreveals a complex pattern (Fig 7), with some 40 identifiedfrequencies significant at the 99% confidence level. Nineteenof these are close to multiples of the orbital frequency, andtherefore suspected to be aliases or artefacts from the closebinary light curve modelling. In this connection, complica-tions also arise from inadequacy of the limb-darkening seriesapproximation. This is known to introduce additional oscil-latory effects in the residuals from the eclipse phases. The
Period04 program (Lenz & Breger 2005) was also used tocheck on the pulsations. Its pre-whitening technique was ap-plied to data outside the two eclipses, from which some 13 sig-nificant frequencies were found, supporting the main clumpof strong contributions in the ∼ P /5 – P /10 range. Furtherwork is clearly needed to investigate and quantify the pulsa-tion spectrum and its source. Spectroscopic data were mostly gathered using the High Ef-ficiency and Resolution Canterbury University Large ´EchelleSpectrograph (HERCULES) of the Department of Physicsand Astronomy, University of Canterbury, New Zealand
MNRAS , 000–000 (0000) bsolute Parameters of Young Stars Figure 4.
Panels (a) and (c) show the light-level of the out-of-eclipse phases resulting from the binning of the 14+ individualTESS light curves of V Pup. This appears to have mostly smoothedout the intrinsic β Cep variation visible in individual light curves,as shown in panels (b) and (d) (although traces of some predomi-nating low-amplitude tendency can be seen in the binned data).
Figure 5.
The character of the short-term oscillatory behaviouris confirmed by plotting the difference between the residuals fromthe single light curve fit and those of the 14 combined and binnedlight curves. The apparent damping out of the oscillator behaviourthrough the primary eclipse is indicative that it is the primary starwhich undergoes the pulsations, but this evidence, by itself, is notconclusive.
Table 2.
Curve fitting results for TESS photometry of V Pupusing
WinFitter 6.5 . Parameters for which no error estimate isgiven are adopted from information separate to the fitting.Parameter Value Error M /M L L L r (mean) 0.366 0.002 r (mean) 0.307 0.002 i (deg) 80.5 0.3 T h (K) 26000 T c (K) 24000 u u u –0.03 u –0.03∆ φ (deg) –2.04 0.02 χ /ν l Figure 6. β Cep stars in the HR diagram. The revised instabilitystrip (copied from Fig 2 in Pamyatnykh, 2007), that uses improvedOP opacities, is delineated by the thick-line border. The dense bluecross locates the primary of V Pup as an incipient β Cep typevariable in the H-R diagram. (Hearnshaw et al., 2002). This was attached to the 1m McLel-lan telescope at the University of Canterbury Mt John Obser-vatory (UCMJO) near Lake Tekapo ( ∼ ◦ (cid:48) S, 174 ◦ (cid:48) E).Over 120 spectra of V Pup were collected during fairly clearweather during the period Feb 5-12, 2020.The phase coverage of these UCMJO observations was
MNRAS000
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E. Budding et al. frequency (d −1 ) no r m a li s ed po w e r Figure 7.
Lomb-Scargle periodogram of pulsational effects in theV Pup system. This may include a possible β -Cep type behaviourof the primary star. Solid blue lines indicate significant (p=0.01)frequencies that are within 0.1 of an integer multiple of the orbitalfrequency. Other significant frequencies are indicated by red lines.The two strongest signals are at 8.8555 d − (= 2.71 h) and 10.2030d − (=2.35 h). about 65% of the complete cycle. Uncovered phases have beenobserved subsequently (TL) from the Saesteorra Observatoryin the Wairarapa region of New Zealand (41 ◦ (cid:48) (cid:48)(cid:48) S; 175 ◦ (cid:48) (cid:48)(cid:48) E) with a 12 inch f/8 Ritchey-Chretien telescope. Thespectroscopic equipment there consisted of a Lhires Littrowdesign spectrograph (Thizy, 2007), having a 35 micron slitand a 2400 lines/mm grating. This has a nominal resolutionof approximately R=13400. The spectral coverage was set tobe from 6607 to 6813 ˚A, so as to encompass the He6678 line.The UCMJO spectral images were collected with a 4k × µ fibre, which is suited to typical seeing conditions at MtJohn, enables a theoretical resolution of ∼ ∼
100 seconds for this 4th mag star. The raw observa-tions were reduced using an updated version of the softwarepackage hrsp (Skuljan, 2012), that produces wavelength cali-brated and normalized output conveniently in fits formattedfiles.Some 45 clear orders of the ´echelle were set up for inspec-tion. These have been studied using iraf software. One of the iraf subroutines ( splot ), for example, allows image statis-tics to be checked. We could determine in this way a signalto noise ratio (S/N) for continuum pixel regions (away fromflaws or telluric effects) to be usually of order 70 (with a ∼
10% deterioration from orders 85 to 121: the orders exam-ined in this study). The spectra were also examined usingthe software package Visual Spec ( vspec ; Desnoux & Buil,2005), which is an MS-Windows TM based package that al-lows convenient analysis of spectra, including line fitting andidentification functions. Table 3.
Identified spectral lines for V Pup (p ≡ primary; s ≡ secondary).Species Order no. Adopted λ CommentHe I 85 6678.149 well-defined p & sH α
87 6562.817 strong, complexHe I 97 5875.650 well-defined p & sC II (*) 110 5145.16 p weakHe I 112 5047.736 weak, ill-defined p & sHe I 113 5015.675 weakHe I 115 4921.929 strong p & sH β
117 4861.332 strong, complexHe I 121 4713.146 weak p & sHe II 122 4685.7 p onlyC III+ OII 122 4649.1 strong blendSi III 125 4574.78 edge of orderSi III 125 4567.87 blendSi III 125 4552.65 blend
Table 4.
Equivalent width measures of the λ The better-defined He I lines in Table 3 have a depth of ∼
5% of the continuum and a width at base of up to ∼ ∼
350 pixels. The lines hardly make a complete separa-tion even at the highest observed elongation. The position-ing of a well-formed symmetrical line (notably the primary’s λ ∼ ∼ − . (The re-sulting distribution of ∼
130 measured RV displacements foreither star is seen in Fig 8, while the He I λ vspec also allows the equivalent width (W λ ) of featuresto be directly read from its on-screen spectrometry bar. Wecould check, in this way, the spectral type assignations in theliterature. Direct measures of equivalent widths have to bescaled against the relative luminosities of the two stars. Theresults of measuring a dozen pairs of the well-recorded λ λ values indicates errors of ∼
500 K inthe assigned temperatures. There is some support for the ap-proaching hemispheres to show slightly stronger absorptions(by ∼ The RVs listed in Table 5 derived from profile fitting to deter-mine the selected He I lines’ centre-of-light wavelengths and
MNRAS , 000–000 (0000) bsolute Parameters of Young Stars − − Phase R ad i a l v e l o c i t y ( k m / s ) − Phase R ad i a l v e l o c i t y Figure 8.
Orbital RV variation of the close binary V Pup (upperpanel) with residuals (lower panel), (red for the primary, blue forthe secondary). Full circles correspond to the UCMJO data; opencircles to the data from the Saesteorra Observatory. the corresponding Doppler displacements. The well-definedHe I line at 6678 has been used mostly, with additional checksmade with the He I 5876 line. The He I lines have the bestS/N ratios in our spectra, apart from the hydrogen lines thatare difficult to model due to their highly blended wings. Eachuseful line was fitted separately at least three times and afinal RV value obtained by averaging, noting the standarddeviations in the same process.The RVs in Table 5 have been corrected to solar system he-liocentric values using hrsp and vspec data-reduction tools.The listed orbital phases are derived from the ephemeris givenby Andersen et al. (1983), i.e.MinI : HJD2445367 . . E (1)This ephemeris is cited in the GCVS of Khopolov et al.(1987), and appears to be an accurate representation of earlyobservations of the system. The adopted period is close to themean value given by Kreiner et al. 2000, though it appearsclear from more recent data that there is some variation inthe period. This will be discussed in Section 5.Measured RVs are presented with an accuracy 0.1 km s − ,but that overestimates the accuracy of individual points (seeabove). Line-positioning depends mainly on the line prop-erties, rather than the available spectrographic resolution,which is relatively high for HERCULES. But while RV mea-sures are given with one significant decimal place in Table 5,equivalent to ∼ λ a can be determined fromthe RV amplitudes using the inclination obtained from the Table 5.
Radial velocity data for V Pup.HJD Orbital RV1 RV22458880+ phase km s − km s −000
Radial velocity data for V Pup.HJD Orbital RV1 RV22458880+ phase km s − km s −000 , 000–000 (0000) E. Budding et al.
Table 5.
Radial velocity data for V Pup (continued).HJD Orbital RV1 RV22458880+ phase km s − km s − Table 6.
Out-of-eclipse curve fitting results for measured MJUORVs for the close binary system V Pup. Symbols have their usualmeanings. Parameter Value Error K sin i (km s − ) 175.4 3.2 K sin i (km s − ) 338.8 5.4∆ φ (deg) 23.6 1.2 V γ (km s − ) 28.9 1.5 ν
74 (p) 63 (s) χ /ν σ (km s − ) 7(p) 9(s) Table 7.
Line-modelling parameters for V Pup at elongation.Parameter 1st elong. 2nd elong. Error I , –0.059 –0.047 0.002 I , –0.040 –0.036 0.002 λ λ v rot , km s −
218 246 5 v rot , km s −
187 209 6 s km s − s km s −
17 12 5∆ f χ /ν photometric analysis. We have, a = P ( K + K ) √ − e π sin i , (2)where symbols have their usual meanings (Smart, 1960). Onsubstitution of the foregoing values for the Eqn 1 period P (in seconds) and the Table 6 RV amplitudes K and K ,and adopting the eccentricity e to be negligible, we find a ≈ . × km, or 14.96 R (cid:12) . Using the relative radii fromTable 2 the mean radii turn out to be 5.48 and 4.59 R (cid:12) . The profiles of the He I lines, particularly the 6678 feature,are well-defined and capable of yielding rotational and turbu-lence parameters. We show the results of such profile fittingin Table 7 and Fig 9.The entries in Table 7 follow a similar arrangement to theother tables of model-fitting in this paper. The quantities I correspond to the central depths on the same relative scale.Mean wavelengths λ , are self-explanatory. The rotationalvelocities v rot , , are calculated with an inclination i = 80 . ◦ (Table 2) to apply a correction for the projection. The pa-rameters s , represent the widths of the gaussian broadeningthat is convolved with the rotational broadening. These maybe interpreted as a measure of the turbulence in the source.The secondary appears relatively more disturbed in this waythan the primary, perhaps reflecting its Roche lobe instabilitycondition.The angular velocity of the system, using the period given MNRAS , 000–000 (0000) bsolute Parameters of Young Stars . . . Phase F l u x l e v e l − . . Wavelength (Angstroms) F l u x l e v e l Figure 9.
Profile fitting to the HeI λ in Section 2, is 5.00 × − radians s − . With the stellarradii given in the previous section, mean synchronized ro-tation speeds ( ωR ) then turn out to be 191 and 160 km s − .These speeds are appreciably less than the measured valuesin Table 7, though they are in the same ratio ( ∼ ∼ v rot , (sync) and v rot , (2 × sync) on the Rossitereffect is barely noticeable against the scatter in the relevantphase range (0.0 to 0.1 in Fig 8). Table 8.
Absolute parameters of V Pup system from combinedresults of data fittings. The column of comparison numbers comefrom the work of Andersen et al. (1983). There is closer agree-ment between the parameters of the present paper and those ofthe comparison than with the other papers cited by Andersen etal., though the formal errors given by the latter for the radii andmasses are more stringent than ours (see text). On the other hand,our estimates of the V magnitudes, given with lower uncertainties,produce a significantly closer photometric parallax to the indepen-dent HIPPARCOS value.Parameter Value Error Comparison Error P d 1.4544859 — — — a (R (cid:12) ) 14.96 0.2 15.27 0.09 R (cid:12) R (cid:12) T K 26000 1000 28200 1000 T K 24000 1000 26600 1000 M (cid:12) M (cid:12) L (cid:12) L (cid:12) V mag 5.10 0.05 4.83 0.16 V mag 5.59 0.07 5.50 0.16 V γ (km/s) 20.0 1.1 13.2 2.5distance pc 320 10 380 — 30 —age Myr 5 0.8 The foregoing orbital semi-major axis and radii of compo-nents are listed in Table 8. Using the HIPPARCOS period(0.0039822 yr) with the value of a as 0.06961 AU, we find thesum of the close binary components’ masses directly fromKepler’s third law to be 21.27 M (cid:12) . Given the mass ratio q = K /K = 0.518, we then find the listed individual masses,which are sensitive to the derived RV amplitude and incli-nation parameters. The absolute radii, R , that come frommultiplying the relative radii of Table 2 by a , are determinedwith higher precision than the masses. These radii, togetherwith the temperatures from Table 2, produce the luminositiesgiven in Table 8.The set of comparison parameters in Table 8 come fromthe work of Andersen et al. (1983). There is a good generalagreement between our derived parameters and and those ofAndersen et al., though the formal errors given by the latterfor the radii and masses are about twice as low as ours. Thedifferences on the mass values come mainly from the analysisof the radial velocity curves. In Section 3 we gave reasonswhy individual RV measures should have errors on the orderof 10 km s − , and this would also appear to apply to themeasures listed by Andersen et al. (their Table 1), where theaverage datum error is close to 10 km s − . Andersen et al.(1983) corrected their initial RV measures according to theprescription of a selected model. It is seen in Table 3 of An-dersen et al. (1983) that the differences between their initialand corrected model results are significantly greater than theformal errors of the modelling parameters, while our radialvelocity amplitudes (Table 6) are between the two parametersets produced by Andersen et al. An empirical stance with MNRAS000
Absolute parameters of V Pup system from combinedresults of data fittings. The column of comparison numbers comefrom the work of Andersen et al. (1983). There is closer agree-ment between the parameters of the present paper and those ofthe comparison than with the other papers cited by Andersen etal., though the formal errors given by the latter for the radii andmasses are more stringent than ours (see text). On the other hand,our estimates of the V magnitudes, given with lower uncertainties,produce a significantly closer photometric parallax to the indepen-dent HIPPARCOS value.Parameter Value Error Comparison Error P d 1.4544859 — — — a (R (cid:12) ) 14.96 0.2 15.27 0.09 R (cid:12) R (cid:12) T K 26000 1000 28200 1000 T K 24000 1000 26600 1000 M (cid:12) M (cid:12) L (cid:12) L (cid:12) V mag 5.10 0.05 4.83 0.16 V mag 5.59 0.07 5.50 0.16 V γ (km/s) 20.0 1.1 13.2 2.5distance pc 320 10 380 — 30 —age Myr 5 0.8 The foregoing orbital semi-major axis and radii of compo-nents are listed in Table 8. Using the HIPPARCOS period(0.0039822 yr) with the value of a as 0.06961 AU, we find thesum of the close binary components’ masses directly fromKepler’s third law to be 21.27 M (cid:12) . Given the mass ratio q = K /K = 0.518, we then find the listed individual masses,which are sensitive to the derived RV amplitude and incli-nation parameters. The absolute radii, R , that come frommultiplying the relative radii of Table 2 by a , are determinedwith higher precision than the masses. These radii, togetherwith the temperatures from Table 2, produce the luminositiesgiven in Table 8.The set of comparison parameters in Table 8 come fromthe work of Andersen et al. (1983). There is a good generalagreement between our derived parameters and and those ofAndersen et al., though the formal errors given by the latterfor the radii and masses are about twice as low as ours. Thedifferences on the mass values come mainly from the analysisof the radial velocity curves. In Section 3 we gave reasonswhy individual RV measures should have errors on the orderof 10 km s − , and this would also appear to apply to themeasures listed by Andersen et al. (their Table 1), where theaverage datum error is close to 10 km s − . Andersen et al.(1983) corrected their initial RV measures according to theprescription of a selected model. It is seen in Table 3 of An-dersen et al. (1983) that the differences between their initialand corrected model results are significantly greater than theformal errors of the modelling parameters, while our radialvelocity amplitudes (Table 6) are between the two parametersets produced by Andersen et al. An empirical stance with MNRAS000 , 000–000 (0000) E. Budding et al. . . . . . . . Age (Myears) S o l a r r ad ii Figure 10.
Increasing radius of a 14 M (cid:12) star is shown as a func-tion of age from the Padova models (Marigo et al., 2017), togetherwith the determined radius (horizontal line) and its uncertaintylimits (dotted). An age of about 5 Myr is deduced. regard to deviations of data from modelling predictions thenallows that the real errors of parameters may be appreciablygreater than the formal ones of a particular modelling result.Our more conservative assessment of the modelling accuracycomes after various curve-fitting experiments with differentassumptions on the non-adjustable parameters.The photometric parallax π is derived from the formula(Budding & Demircan, 2007; Eqn 3.42)log π = 7 . − log R − . V − F (cid:48) V , (3)where R is the absolute radius, V the visual magnitude and F (cid:48) V the flux parameter (= log T e − . T e being the effec-tive temperature and BC the corresponding bolometric cor-rection). The reciprocal of π would give the distance ρ to be360 ±
12 pc, but Eqn 3 refers to a V magnitude without in-terstellar extinction. The adopted B − V colour of –0.17 forthe components (Ducati, 2002), when compared with the rep-resentative unreddened colour of –0.27 for this pair of earlyB-type stars (Budding & Demircan, 2007, Table 3.6) yieldsa colour excess of 0.10. From this, we can estimate an inter-stellar absorption value of A V = 0 .
30 (Cardelli et al., 1989).The effect of the absorption implies the distance would be re-duced by ∼ ±
30 pc).Table 8 also gives and age estimate, that is determined frommatching the calculated radius of the MS component withPadova evolutionary models (Fig 10). This result is discussedfurther in Section 6.
If we plot the difference between observed times of minimafor V Pup and those predicted by the reference ephemeris ofKreiner et al. (2000) (Fig 11), i.e.Min : I = HJD2428648 . . E , (4)we can see directly the general parabolic trend pointed outby Qian et al. (2008). It is worth noting the O-C Gateway
Figure 11.
Parabolic trend in the O – C eclipse timings of V Pupusing the ephemeris of Kreiner et al. (2000). revision however , where a longer mean period also gives areasonable fit if we admit somewhat larger timing uncertain-ties. Our procedure is a little different to that of Qian et al.,in that we have added some more recent times of minimaand separated out the parabolic trend before addressing theresiduals, but our result is fairly similar. We find a second or-der term in the epoch number E of order 3.5 × − , a slightreduction in the mean period from that given by Kreiner etal. (2000) of around 5 × − and a slight positive shift in thereference epoch of about 10 minutes. The uncertainties inthese parameters are on the order of 10% of their values. Theimplied rate of period variation is ˙ P ≈ . × − d yr − ;slightly less than that found by Qian et al., but within theerror measures of the determinations.From a close examination of the residuals from theparabolic fitting, Qian et al. (2008) found an additional sinu-soidal variation as a 2.5 σ effect, with a period of ∼ ; Skarka (Ho˘nkov´a et al. 2013); the BRITEcollaboration (Popowicz et al., 2017) and TESS (Ricker et al.,2015); the fit significantly deteriorates. These times of min-ima have been listed by MB on the VSS website . Accordingto the ephemeris of Kreiner et al. (2000), given as Eqn 4, themean time of inferior conjunction for the radial velocity curveshown in Fig 8 should have occurred at HJD 2458888.520 —the 20791st such conjunction after the reference epoch. Ascan be seen in Fig 8, the conjunction was a little later thanthis, by 0.107 ± E , thatis T ( E ), follow the parabolic form T ( E ) = A + BE + CE (5)The period at E , usually given in days, is then given by the http://var2.astro.cz/ocgate/ocgate.php?star=V+Pup&submit=Submit&lang=en , 000–000 (0000) bsolute Parameters of Young Stars Wide orbit cycle number O − C ( da ys ) − . − . . . . Figure 12.
Sinusoidal effect in the O – C eclipse residuals afterremoving the parabolic trend in Fig 11. 17 selected points (opencircles) conform well to the wide orbit period (5.47 yr) of Qianet al. (2008). Later values (filled circles), however, include somedistinct discrepancies with the sinusoidal model (see text). uniformly increasing slope P ( E ) = B + 2 CE , (6)where, in practice, C is very small compared to B .After selecting some reference epoch T where E = E = 0,the O – C diagram is formed from the difference between T ( E ) and corresponding T -values calculated along the line T c = P c E + const., where P c = B c , say, and the constantterm in the expression for T c is A c , say. The constants A c , B c would be assigned to give the best position of the lineto match the observed trend in the given E, T interval. Wewould expect them to be close to A and B in practice. TheO – C values are thenO − C = T ( E ) − T c = ( A − A c ) + ( B − B c ) E + CE , (7)in days. This is again of parabolic form, and with the samecoefficient of the E term. Reasonably measurable values of C , for an O – C of order 0.1 d or greater, involve a suitablycovered interval with a half-range for E reaching to ∼ C should be typically greater than about 10 − for a very confident determination.The change of period ∆ P with each event (∆ E = 1) be-comes dP/dE = 2 C . and the rate of change of period peryear at E is then 730 . C/P ( E ). The amount of mass lostper year ∆ M , follows as (Kreiner & Zi´o(cid:32)lkowski, 1978),∆ M = 243 . M Cg ( x ) P yr − , (8)where g ( x ) is a function of the mass ratio x = M / ( M + M )that depends on what happens to the matter, as a whole, shedby the mass-losing star, here identified as M – the originallymore massive component. In the case where total mass andangular momentum of the binary are conserved g ( x ) can beshown to equal (2 x − / (1 − x ); so its value would be currentlyclose to –0.5, from the data in Table 8. We then derive amass transfer rate of about 6 × − solar masses per year.If most of the mass is lost from the system, then at low M , g ( x ) → −
1; so a lower mass loss rate, say ∼ × − solar masses per year, would achieve the same period increase (i.e.a lower C in Eqn 8).In fact, we can deduce that, if the age of the system is only ∼ ∼ − M (cid:12) yr − , andprobably more than that, in keeping with the lack of appre-ciable separation of the stars that would have occurred withthe decline to a mass ratio of 0.5 in a conservative regime.We can compare the mass loss rate with what follows fromthe mass loss formula (cf. Awadalla & Budding, 1982; Murad& Budding, 1984): ˙ M ≈ − ηsM /R (9)where we can take the mass-losing star’s mass and radius( M and R ) from (Table 8) and give consideration to therelative density parameter η and rate of surface expansion s . The value s might be considered on the basis of a CaseA mass-transfer model, in which the loser remains in hydro-static equilibrium as a Main Sequence star but with a modi-fied evolution timescale. That would allow it to be comparedwith a 7.3 solar mass star of age close to 28 Myr. The corre-sponding value of s then works out as 1 . × − solar radiiper year, using the Padova evolution models (Marigo et al.,2017). Eqn(9) then yields˙ M ≈ − η × − (10)solar masses per yr. The parameter η = ρ s / ¯ ρ : the ratio of thedensity in the subphotospheric layer where the predominatingsystematic motion is the outward expansion, to the meandensity of the star as a whole, appears to be relatively small.Using continuity of the flow, we can write ρ s = ρ R v R (cid:15) /s ,where v R is the velocity of sound in the atmospheric layerswhere the mean density is ρ R , and (cid:15) = Ω a/v R = h/ R ≈ / h the mass-transferring stream’s width (cf. Lubow & Shu, 1975). With v R estimated at 6 × − (Cox, 2000), we find η ≈ . (cid:12) . Also, η is largerat earlier stages of interactive evolution, as can be seen fromthe (cid:15) parameter, in the Lubow and Shu (1975) discussion,being greater as a result of both increased mass and proxim-ity. If we adopt η = 0 . M of around 15 M (cid:12) , we find anexpansion approaching 1 . × − solar radii per year withinthe time-frame of a few million years. Eqn (9) then allows afair agreement between the amount of mass lost by M anda Case A model for the binary evolution. The V Pup system has been long recognized as a benchmarkexample for studies of massive close binary Algol-type evolu-tion. It may be compared with µ Sco, where Budding et al.
MNRAS , 000–000 (0000) E. Budding et al. (2015) found that the primary was fairly consistent with theproperties of a single star of its age and mass. In turn, thatimplies that the matter shed by the over-luminous secondarywas probably mostly ejected from the system rather thantransferred, thus taking angular momentum out of the orbitand keeping the pair in relative close proximity. This also ap-pears to be the case for V Pup. This is then the regular CaseA situation discussed by Andersen et al. (1983), whose Fig 6shows the primary close to the trend of the Main Sequencefor young massive stars as quantified by Popper (1980), whilethe secondary is significantly more luminous than an MS starwould be at its present mass of ∼ (cid:12) . Although our modelis ∼
10% less massive than that of Andersen et al. the param-eters are essentially similar.We support this view from the results of the present pa-per in two ways. Firstly, the photometric fittings of Section 1show the system to be consistent with a secondary star thatis near to contact with its surrounding Roche lobe, i.e. anAlgol configuration. It is difficult to establish a clear picturefor the original arrangement of this massive system, but aninteraction that preserves the angular momentum of the orbitwould require the star centres to be implausibly near to eachother at around 1 solar radius when at their closest. The gen-erally adopted scenario thus implies that matter shed by theloser is mostly driven out of the system by intense radiationpressure, taking with it a fair proportion of the original sys-temic angular momentum. If about half the system’s angularmomentum was lost in this way, an original pair of near equalmasses totalling around 30 M (cid:12) would have had a separationof order 10 solar radii, the two near-contact components hav-ing mean radii of about 0.4 of this.The Padova modelling (Marigo et al., 2017) giving rise toFig 10 shows that a ZAMS star of 15 M (cid:12) would be expandingat a rate of ∼ β Cep pulsational effect. This pri-mary star, then, appears to be behaving much as a singlePopulation I star would behave at its deduced age and mass.We believe that this is the fourth β cepheid variable to be re-ported having a precise mass measurement after V453 Cyg A(Southworth et al., 2020), one component of CW Cep (Lee &Hong, 2010), and VV Ori (Southworth, 2021). A preliminaryexploration of the pulsation spectrum was carried out, givingsupport to the likely nature of the low-amplitude variability,but it is likely that the power spectrum is affected by compo-nents associated with submultiples of the close binary period.This subject is rather outside the scope of the present article,but further study of the bright object V Pup is clearly calledfor in this connection.The ongoing mass-loss of the secondary does raise the is-sue of detectable period variation, and we have confirmedthe general trend of period increase reported by Qian et al.(2008), though with about a 15% lower rate. We could notconfirm the 5.47 yr additional cyclical variation found byQian et al. after admitting more new times of minima (ToMs), though there remain relatively large discrepancies betweenindividual ToMs and the longer term parabolic trend, partic-ularly in the ToMs reported by Skarka (Ho˘nkov´a et al. 2013).It is possible that some periodic term in the calculated timesof minima may reduce these discrepancies, but we could notestablish this with a high degree of confidence.In this connection we note that we found an improvementin the quality of fit to the TESS data could be achieved bythe inclusion of a small amount ( ∼ ∼
3% in the V range. A mid-to-late Btype MS third star would meet the implied relative luminos-ity. We could not find any clear evidence of this star in thespectral data, however; though this is unsurprising given thenature of the early type rapidly rotating stars involved andtheir relative light levels in the optical range. The question ofa third major body in the V Puppis system thus appears stillunresolved and awaits further more detailed investigation.
It is a pleasure to express our appreciation of the high-qualityand ready availability, via the Mikulski Archive for SpaceTelescopes (MAST), of data collected by the TESS mission.Funding for the TESS mission is provided by the NASA Sci-ence Mission DirectorateGenerous allocations of time on the 1m McLellan Telescopeand HERCULES spectrograph at the University of Canter-bury Mt John Observatory in support of the Southern Bina-ries Programme have been made available through its TACand supported by its Director, Dr. K. Pollard and previousDirector, Prof. J.B. Hearnshaw. Useful help at the telescopewas provided by the UCMJO management (N. Frost) assistedby F. Gunn. Considerable assistance with our use of the hrsp
All data included in this article are available as listed in thepaper or from the online supplementary material it refers to.
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