The nearby ellipsoidal variable TVPictoris - aa.springer.deaa.springer.de/papers/8331002/2300639.pdf · of Zrii even more so; at best the stronger lines of Vii mul-tiplet 33 and Zrii

Astron. Astrophys. 331, 639–650 (1998) ASTRONOMYAND

ASTROPHYSICS

The nearby ellipsoidal variable TV Pictoris?

K. Pavlovski1, J. Cuypers2, M. David3, R.E.M. Griffin4, H. Hensberge2, S. Ilijic5, H. Schneider6, and W. Verschueren3,??

1 University of Zagreb, Faculty of Geodesy, Kaciceva 26, 10000 Zagreb, Croatia2 Royal Observatory of Belgium, Ringlaan 3, B-1180 Brussel, Belgium3 University of Antwerp (RUCA), Astrophysics Research Group, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium4 6 London Place, Oxford OX4 1BD, UK; currently visiting Department of Physics, University of Oxford, UK5 Institute of Physics, Bijenicka 34, 10000 Zagreb, Croatia6 Universitats-Sternwarte, Geismarlandstr. 11, D-37083 Gottingen, Germany

Received 27 June 1997 / Accepted 6 November 1997

Abstract. TV Pic is identified as a bright, near-contact mid–A + early–F binary seen under a moderate inclination of 54◦.From the analyses reported in this paper, it appears that bothcomponents are undermassive (1.2 + 0.4 M�), and that thesecondary rotates not synchronously but more than twice asfast. These conclusions follow from the analysis of (1) high–dispersion spectra near both quadrature phases, to which thesecondary contributes roughly 10% in the visual light, and (2)light–curves in the Stromgren and Walraven system coveringthe interval 3200–5600 A and a time span of more than 2600rotational periods. The light–curves show a very pronouncedO’Connell effect, and only marginal colour variations. Mod-els assuming a temperature spot either on the primary or thesecondary explain the major part of the asymmetry in the light–curves, and are intended to provide useful initial estimates formore advanced mathematical codes. However, a more realisticphysical model will require more discriminatory data, includ-ing spectroscopic observations in other spectral windows, andspectroscopy over the whole orbital cycle.

Key words: stars: binaries: close; spectroscopic – stars: in-dividual: HD 30 861 (TV Pic) – stars: variables: other – stars:fundamental parameters – stars: rotation

1. Introduction

The light variability of TV Pic (HD 30 861) was discovered ac-cidentally by H.M. Maitzen, who used it as comparison star in a

Send offprint requests to: K. Pavlovski ([email protected])? Based on observations obtained at the European Southern Obser-vatory (ESO), La Silla, Chile?? Postdoctoral Fellow of the Fund for Scientific Research - Flanders(Belgium)

study of CP stars at ESO in 1979 (Hensberge et al. 1981). Subse-quent photometry revealed light variations with a double-waveshape and a period of about 0.852 d (Verschueren et al. 1987).Full amplitude exceeds 0.15 mag in all Stromgren and Walravenpassbands. The variations were presumed to arise from an ellip-soidal binary, but the pronounced difference in the light maximais quite uncommon and prompted a more detailed study, whichis reported here. This study includes the analysis of two high–dispersion spectra taken at the quadrature phases. We search forspectroscopic evidence of the secondary component, as well asfor chemical peculiarities in the primary. The photometry, in-cluding new measurements, is used to constrain models with a(temperature) spot on one component.

2. Observations and ephemeris

The observation log is summarized in Table 1. The echelle spec-tra have a S/N of 200 over the larger part of the covered wave-length region, but 100 or less below 3900 A. They were takenvery near quadrature, at HJD 2 447 191.542 and 2 447 193.691,and have been reduced with the software described in Ver-schueren et al. (1997). The original 2-pixel resolving power isR= 16300, and the spectra were rebinned to a slightly smaller binwidth of 8.4 km/s. The differential photometry is quite accurate.The scatter in the results for HD 31 587−HD 31 640 suggest anrms for the final HD 30 861−HD 31 640 data smaller than 7mmag in y, b− y and u− v and smaller than 9 mmag in v − b.The Walraven data have an rms of 5 mmag in −2.5V , 4 mmagin 2.5 (V − B), 2.5 (B − U ) and 2.5 (B − L), and 7 mmag in2.5 (U−W ) respectively, as judged from results obtained in thesame run for stars in the open cluster NGC 2244. Notice that it iscommon practice to express Walraven photometry in log units;the factor of 2.5 is introduced for ease of comparison with theStromgren photometry.

All differential photometry is listed in Tables 4, 5 and 6.Table 5 lists the data shown in Verschueren et al. (1987). Visual

640 K. Pavlovski et al.: The nearby ellipsoidal variable TV Pictoris

Table 1. Observation log

obs. run telescope instrument observer remarks

Nov. 1981 ESO 0.5 m uvby phot. HS comp. star HD 31 640, (HD 31 587)Dec. 1986 Dutch 0.9 m V BLUW phot. HH, WV comp. star HD 31 640Jan. 1988 ESO 0.5 m b phot. JC HD 31 640 and network of check stars (Balona et al. 1992)Jan. 1988 ESO 3.6 m CASPEC spec. HH CCD#3, 372–470 nm, exp. 3 min

Fig. 1. Light curve of TV Pic in Stromgren b, relative to HD 31 640.Different symbols refer to different runs. Circles refer to the Walravendata −2.5 (∆B − 0.35∆(V −B)) + 0.01, where the constant and thecolour term correct for the difference in luminosity and for the colourdependence of the variation between the effective wavelengths of theB and b filters. The data obtained after HJD 2 447 000 were shifted tothe differential scale fixed by the data obtained before HJD 2 447 000(∆b − y + ∆VJ) by subtracting 8.186 from the data given in Table 6.The phases at which the spectra were observed are indicated by verticaldashed lines. The full line corresponds to the model with the spot onthe secondary, while the model with the spot on the primary is shownas a dashed–line curve (see Table 8 for the model parameters). Forcomparison, the model without spot (fitted to the part of the light curvearound the secondary maximum) is shown as a dashed–dotted curve.

magnitudes, colours and indices are given in Table 2. The com-bined runs define the periodicity of the light variations and thenumber of cycles elapsed between the runs, without ambigu-ity (Fig. 1). The ephemeris published earlier is confirmed andconsiderably refined:

HJD(sec. max. b) = 2 447 193.693 + 0.851990 E±0.005±0.000005

The zero point for the phases is defined with respect to thesecondary light maximum, rather than to the deepest eclipse,because the two minima are almost indistinguishable in depth.The deepest eclipse in our data set occurs at HJD 2 447 183.664,at phase 0.229.

3. Atmospheric parameters

3.1. Spectroscopic indicators

The Balmer lines dominate the spectrum; next in intensity arethe Ca ii K line and Mg ii λ 4481. The atoms and ions identi-fied in the visual spectrum include H i, Mg i, Mg ii, Al i, Si ii,Ca i, Ca ii, Sc ii, Ti ii, Cr i, Cr ii, Mn i, Fe i, Fe ii, Ni ii, Sr iiand Ba ii. An identification of V ii remains doubtful, and thatof Zr ii even more so; at best the stronger lines of V ii mul-tiplet 33 and Zr ii multiplet 41 (Moore 1945) coincide withonly very faint stellar features. Owing to significant rotationalbroadening, almost all metal lines are shallower than 10%. TheFWHM of the best isolated lines, i.e. Fe ii λ 4508, Ti ii λ 4501,Ti ii λ 4572, and Mg ii λ 4481, implies that computed profilesshould be blurred by a rotational broadening corresponding tov sin i = 115 ± 5 km s−1. This error estimate includes only theuncertainty in the continuum level and the internal rms scatterbetween results from different lines.

Houk (1978) classified TV Pic as A2 V, but it is well knownthat the spectra of a significant fraction of A dwarfs show dis-cordant spectral types according to the classification criteriaadopted: Balmer, Ca ii K or metallic lines. These ambiguitiesmay be present not only in TV Pic but also in the A–type starsthat we adopted to make a relative assessment of TV Pic: oPeg,a well-studied sharp-lined A1 V star (Maestre & Deutsch 1961,Conti & Strom 1968a, Adelman 1973) and the A–type starsin Conti & Strom (1968b). Comparisons show that the metal-lic spectrum of TV Pic corresponds to a lower temperaturethan A2 V. Relative to oPeg and other early–A stars, lines ofneutral atoms are more prominent than those of the ions: e.g.Cr i λ 4254.3 is stronger than Cr ii λ 4242.2, as in mid–A stars,while the opposite is true in A0–A2 V stars. The Fe i lines aremore numerous than in oPeg.

The most prominent difference between TV Pic and oPegis in the Ca i lines and the Ca ii K line, whose strengths growrapidly through the A–type spectral range. Ca i λ 4226.7 inTV Pic is stronger than Fe ii λ 4233.2; it is markedly strongerthan Fe ii λ 4178.8, whereas in any A0–A2 V star the Ca i lineis of no more than the same strength as that Fe ii line but 1.3–1.7 times greater in mid–A stars. The Ca i lines of multiplet 4(Moore 1945) in the λλ 4420–4460 region are clearly present.Ca ii K reaches a depth of about 70%, but the stronger (andsharper) component appears to be superposed on a weak broadcomponent (Fig. 3). We return to the interpretation of that pro-file in Sect. 4. In conclusion, the appearance of the metal lines

K. Pavlovski et al.: The nearby ellipsoidal variable TV Pictoris 641

Fig. 2. Model fit (Teff = 8400 K, log g = 3.7) to the Ca ii K, Hδ and Hγ line from which the contribution of the secondary was eliminated. Theobserved spectrum is shown as a full line, the model as a dashed line

Table 2. Stromgren and Walraven photometry of TV Pic (average overthe orbital period) and of the comparison stars. The Johnson magnitudeVJ is derived from the y and V filters

Name VJ b− y m1 c1

HD 31 640 8.064 0.131 0.191 0.825HD 31 587 9.450 0.238 0.154 0.615TV Pic 7.457 0.085 0.167 1.014

Name VJ V −B B − U U −W B − L

HD 31 640 8.068 0.095 0.406 0.148 0.205TV Pic 7.456 0.059 0.443 0.141 0.196

in the spectrum points to a mid–A spectral type rather than theA2 V classification of Houk (1978).

Sr ii in TV Pic is clearly weaker than in oPeg; the λ 4215.5line is as faint as Fe i λ 4202.0, as it is in most A stars (Conti& Strom 1968b). However, Conti & Strom (1968a) assign amild Am character to oPeg on the grounds that this Sr ii lineis anomalous relative to the nearby Sc ii λ 4246.8 line, but thisis not echoed in TV Pic. TV Pic appears to show a so-called‘normal’ A–type spectrum. None of the identified atoms or ionsshows lines whose strength deviates conspicuously from ‘nor-mal’.

3.2. Photometric information

3.2.1. Walraven photometry

The colour indices of TV Pic (Table 2) lead to the reddening-freeindices [B−U ] = 0.407 and [B−L] = 0.173. [U−W ] = 0.078is not useful in this spectral range, since the Kurucz models,on which the theoretical grids are based, do not give reliablepredictions (see e.g. Brand and Wouterloot 1988).

There are two photometric solutions; one (that TV Pic is ahighly reddened A0 V star) is incompatible with the spectro-scopic evidence. The colours of the system indicate an unred-dened star with Teff = 8180 K and log g = 3.98. In the grid of

Straizys & Kuriliene (1981) these parameters correspond tospectral type A6 IV. If we anticipate the estimated spectral typeof the secondary and its contribution to the total light (early–F,9 times fainter than the primary; see Sect. 4), we deduce thatthe colours of the primary must be near to (V −B)p ≈ 0.050,(B − L)p ≈ 0.196, (B − U )p ≈ 0.449, (U −W )p ≈ 0.138.This leads to an improved photometric solution: Teff = 8310 K,log g = 3.99, no reddening, and spectral type A5 IV.

3.2.2. Stromgren photometry

The literature contains numerous calibrations of Stromgren pho-tometry, including the β-index, in terms of atmospheric pa-rameters. Most rely on Kurucz model fluxes (cf. Smalley &Dworetsky 1993). Napiwotzki et al. (1993) recently intercom-pared them and found the calibration of Moon & Dworetsky(1985) to be the most reliable.

According to Moon’s (1985) code, the mean colour in-dices of TV Pic (Table 2) give Teff = 8150 K, log g = 3.86 andδ m1 = 0.035. If the secondary does indeed have an F2–F5type spectrum, the improved colours for the primary become(b− y)p ≈ 0.067, m1p ≈ 0.170, c1p ≈ 1.038 and correspondto an unreddened star with Teff = 8310 K and log g = 3.90. Themetallicity indicator δ m1 = 0.031 points to an older PopulationI star.

3.3. Temperature and gravity of the primary

The synthesis code SPECTRUM (Gray & Corbally 1994),which depends on Kurucz’s (1979) model atmospheres, wasused to estimate Teff and log g. A straightforward fit to the ob-served spectrum reveals a time–dependent asymmetry in theBalmer lines, indicating a small but probably non–negligiblecontribution from the secondary spectrum. A theoretical sec-ondary spectrum, modelled according to the luminosity ratio andradial–velocity shifts deduced in Sect. 4, was therefore first sub-tracted from the observed spectra, and the residues (intended torepresent the spectra of the primary alone) were compared with a


suitable grid of SPECTRUM models. Simultaneous matching tothe observed Balmer lines, the Ca ii K line and the global metal-lic spectrum yielded the spectroscopic parametersTeff = 8400 Kand log g = 3.7. Fig. 2 shows the fit to the primary’s Balmerlines and to its Ca ii K line. Spectroscopy and photometry in-dicate thus a somewhat different gravity, while the temperatureestimates are compatible within the uncertainties. The main dis-crepancy lies in the fact that the observed Ca line is too narrowfor the photometrically suggested gravity; the weight given tothis line also pushed the spectroscopic temperature estimate toa marginally higher value. Noting that the Ca ii K line shows apeculiar profile in a number of stars, it seems reasonable to givethe line lower weight and to adopt at present Teff ≈ 8300 Kand log g ≈ 3.8, which is more closely compatible with theobserved colours and with the other spectral lines. Dynamicalarguments in Sect. 5 will provide independent information onthe gravity.

4. The secondary component

A careful inspection of the high–resolution spectra taken at thetwo quadrature phases reveals differences which can only beexplained as contributions from the spectrum of the secondary;the most prominent example is the extended wings of the Ca ii Kline, as shown in Fig. 3. We therefore treated the observed spec-tra as though they were indeed composite, and attempted toisolate and analyse any features that might be characteristic ofthe spectrum of the secondary. The observed spectra were re-processed by two different techniques: (1) ‘difference’ spectraand (2) spectral subtraction.

4.1. ‘Difference’ spectra

Small and blended differences between two observations of acomposite spectrum taken at different phases can be highlightedsimply by subtracting the two spectra such as to eliminate thespectrum of the primary. One spectrum must first be shifted inwavelength (amounting in the present case to about 100 km s−1)in order to align the two primary spectra. The ‘difference spec-trum’ thus obtained, in the sense ‘HJD 2 447 191.542 − HJD2 447 193.691’, exhibits some distinct features, well above thenoise level for λ > 3900 A, in the vicinities of the Balmerlines Hγ to Hε and of the Ca ii K line. The fact that numerousless conspicuous differences are found at other wavelengths sug-gests that the difference spectrum may in fact hold quite a lotof information on the secondary. It was therefore quantitativelycompared with theoretical models. The underlying broad com-ponent in the Ca ii K line (Fig. 3) yielded an initial estimate of(Teff , log g) in the region of (6250–7000 K, 3.0–4.0).

A 2-D grid of theoretical spectra, atTeff = 6250, 6500, 6750and 7000 K and log g = 3.0, 3.5 and 4.0, was calculated with theSPECTRUM code. Each spectrum was broadened correspond-ing to a set of rotational velocities 90, 95, ..., 130 km s−1, and foreach rotational velocity a template for the difference spectrumwas obtained by shifting the broadened spectrum with respectto itself and subtracting it; the latter shift represents the sum

Fig. 3. The broad component of Ca ii K underlying the sharper line ofthe primary. The two spectra were recorded near phases of oppositequadrature. The spectrum observed at HJD 2 447 193.691 is shifteddown by 0.15 in intensity, and is shifted in wavelength by 1.3 A tocompensate for the Doppler shift between the spectra

of the total orbital velocity ranges of both components (plusa small correction because the exposures were not taken ex-actly at the the quadrature phases), and was chosen from the set46, 46.5, . . . , 51.5 pixel.

The observed difference spectrum was cross–correlatedwith each of the templates to find the best–matching set ofparameters. Strictly speaking, this method is only valid whenthe stellar spectra do not vary throughout the orbital cycle andwhen their relative contributions are equal at both quadratures;we do not yet know whether or not this is true for TV Pic, butthe method should at least supply some useful information. Astraightforward search in the four–dimensional parameter spaceintroduced above, using the whole spectrum, is inefficient be-cause information about the secondary’s temperature and grav-ity is principally in the calcium and hydrogen lines, and in-formation on rotational velocity is to be found only in the othermetal lines. These narrower lines also constrain better the orbitalvelocity shift. Therefore, as a first step, we estimated the rota-tional velocity and the orbital–velocity shift at each fixed Teff

and log g from five 90 A intervals with starting wavelengths of4135, 4225, 4410, 4500 and 4590 A. The differences betweenthe results from different wavelength regions exceed those cor-responding to a variation of the atmospheric parameters acrossour grid; they appear to be due to a residual mismatch, be-tween the difference spectrum and the templates, which persiststhroughout the parameter grid. Weighting the results for a sub–grid (Teff = 6500 K, 6750 K, 7000 K and log g = 3.5, 4.0) withthe corresponding correlation coefficients, we finally estimate


the rotational velocity of the secondary to be 112 ± 5 km s−1,and its shift in the difference spectrum to be 413 ± 4 km s−1.These values were used to construct new templates for the at-mospheric parameter grid. The quoted errors were estimatedfrom the scatter between the values obtained from five differentwavelength regions; this scatter exceeds both the uncertaintiesin the position of individual cross-correlation maxima and thescatter in the values over the acceptable domain in the grid ofsynthetic spectra used for modelling the secondary. However,they do not account for any bias due to structural imperfectionsin the synthetic spectrum, or due to intrinsic spectral variability.

In the second step the difference spectrum was cross–correlated with the new templates, over four narrow (20–40 A)wavelength intervals surrounding respectively (1) Ca ii K, (2)the blend of Ca ii H with Hε, (3) Hδ and (4) Hγ . In all the in-tervals, the cross-correlation results exhibit a similar behaviourwith varying atmospheric parameters provided that interval (2)is chosen not too narrow and (3) not too wide. On the basis ofall these results, the atmospheric parameters for the secondarycan be constrained to:

6500 K ≤ Teff ≤ 6900 K, 3.3 ≤ log g ≤ 3.7

Actually these constraints were obtained after the whole proce-dure was iterated once, with an improved value for the radial–velocity shift of the primary between both exposures: after thefirst run, assuming the values Teff = 6750 K, log g = 3.5 forthe atmospheric parameters of the secondary, we provisionallysubtracted the estimated contribution of the secondary from theobserved spectrum; as a result the radial–velocity shift of theprimary between both exposures was corrected from 11.6±0.5to 11.9±0.2 pixels, i.e. by 2.5 km s−1. Remarks similar to thosemade on the error quoted for the shift in the secondary spectrumapply here.

Fig. 4 shows two portions of the observed difference spec-trum and the computed model, which assumes that the contin-uum of the primary is 9 times brighter than that of the secondary.The major part of the high–frequency structure in the data is wellreproduced, but some shortcomings of the model remain.

4.2. Spectral subtraction

Another technique for identifying the characteristics of the spec-trum of the secondary is to subtract away the spectrum of theprimary, using a third spectrum which is a close analogue to it.Details of this method have been given elsewhere (Griffin 1986).This technique has a definite advantage in that it relies on ob-served spectra and has no dependence on model atmospheres,and moreover all the features of the residue from the subtraction(i.e. the secondary’s spectrum) are made visible at once. On theother hand the introduction of a third spectrum as an analogue,however close, to that of the primary will undoubtedly introduceextraneous errors and artefacts which grow rapidly as increas-ingly large fractions of the primary are subtracted away (as hap-pens in the case of TV Pic, where the primary heavily dominatesthe composite spectrum). Nevertheless, the subtraction methodcomplements nicely the ‘difference’ technique. Both methods

Fig. 4. Difference spectra in the vicinity of the Ca ii K line and around4440 A. The contribution of the primary was eliminated from the spec-tra recorded near opposite quadrature phases by applying an appropri-ate velocity shift and subtracting them. Dots show the observed data.The full line is computed from the model atmosphere for the secondaryand then scaled down by a factor 10 to account for the light ratio be-tween primary and secondary

share the disadvantage that subtraction reduces the signal butadds (quadratically) the noise.

The composite spectrum of TV Pic stretches the capabili-ties of the subtraction technique to its limits. The original pro-gramme was developed for use with composite systems con-taining cool giants and hot dwarfs, and its supporting libraryof standards is accordingly much richer in cool giants than inhot dwarfs. It proved to be not possible to match the spectrumof the primary in TV Pic (TV Pic A) unambiguously to any oneof the available standards, the chief problem being the growingstrengths of Ca ii at 3933 A and Mg ii at 4481 A coupled with acorresponding lack of decline in the widths of the Balmer lines.The best available compromise was the A3 IV starψ Sco, afterbeing blurred to mimic an additional rotational velocity of 120km s−1.

The two uncovered spectra of the secondary (TV Pic B) areshown in Fig. 5. Both show rather large deviations in the appar-ent continuum level, some of which is attributable to residuals


in the blaze function of the echelle, and some to mismatch (be-tween TV Pic A and ψ Sco) that has become magnified until itlooks much more serious in these residual spectra than it doesin a system whose components are more similar in luminosity.However, there also appear to be intriguing systematic differ-ences between the two spectra of TV Pic B, and a subtractionwhich produced a tolerably clean secondary spectrum in onecase did not seem able to do so in the other, indicating that notall the peculiarities that we see in Fig. 5 (excluding the obviousone at 3933 A) are artefacts of mismatch.

The spectrum of TV Pic B corresponding to phase 0.47 (pri-mary light maximum) and red–shifted by≈ 150 km s−1 relativeto the primary, conveys reasonably faithfully the characteristicsof an F dwarf; it matches Procyon (F5) slightly better than γ Vir(F0) except in the strength of the Ca ii K line. On the other hand,the spectrum of TV Pic B that corresponds to phase 0.0 and isblue–shifted relative to the primary, looks distinctly differentfrom the former and somewhat strange. One possible interpre-tation is that the lines have split into two narrow componentsdisplaced from the primary by (very approximately) −230 and+40 km s−1 respectively. As is seen in Fig. 5, several of the metallines show quite a convincing split, whilst each of the Balmerlines appears to be composed of two unresolved components:a short–wavelength member that is as deep as in the spectrumat primary light maximum, together with a shallow but broad,red–shifted component.

4.3. Preliminary conclusions

Both methods demonstrate that the secondary is cooler than theprimary, though any spectral variability which the secondarymay exhibit will have to be sampled at more phases than thetwo that are presently at our disposal. High-resolution spectracovering the orbital phases are needed in order to unravel thesystem’s geometry.

5. Fundamental parameters for the binary and its compo-nents

Since the two maxima in the light curve of TV Pic are not thesame, we cannot derive the physical elements (radii and masses)of the component stars in the classical way. One solution is toconstruct a specific model for the light curve by including a spoton one or both stars. It is therefore instructive to investigate firstthe constraints placed on that model by the observations, beforeadditional degrees of freedom are introduced.

The fact that the spectra were not taken exactly at quadratureimplies that the velocity semi-amplitudesKp andKs are slightlylarger than the observed velocity differences. We assume a sinu-soidal velocity curve, and apply a correction of 1.01; hence, weestimateKp = 50± 1 km s−1andKs = 158 ± 3 km s−1(seeSect. 4.1 for the meaning of the errors), implying a mass ratioq = Ms

Mp= 0.318± 0.009 and a mass function

f (m) =P K3

p

2πG= Ms sin3 i (

q

1 + q)2 = 0.0112± 0.0008 M�

Table 3. Preliminary solutions for masses, separation, and Roche–loberadii using the mass ratios derived from different assumptions

q i Mp Ms A RLp RLs

[◦] [M�] [M�] [R�] [R�] [R�]

0.318 65 0.82 0.26 3.88 1.86 1.110.318 60 0.94 0.30 4.06 1.95 1.160.318 55 1.11 0.35 4.29 2.06 1.220.318 50 1.36 0.43 4.58 2.20 1.31

0.273 65 1.20 0.33 4.36 2.15 1.190.273 60 1.37 0.37 4.55 2.25 1.250.273 55 1.62 0.44 4.81 2.37 1.320.273 50 1.98 0.54 5.14 2.54 1.41

where P is the orbital period in days, and Ms the sec-ondary’s mass. Thus, Ms sin3 i = 0.194 ± 0.014 M� andMp sin3 i = 0.61 ± 0.05 M�. The Roche lobe geometrymay be computed from Eggleton (1983):

RLp

A=

0.490.6 + q2/3 ln(1 + q−1/3)

where RLp is the radius of a sphere with the same volumeas the primary Roche lobe, and A is the binary separation.We find RLp

A = 0.480 ± 0.002 and, using the inverse of q,RLsA = 0.286 ± 0.002.

In view of the large light amplitude due to ellipticity andof the absence of deep eclipses, it follows, conservatively, that50◦ < i < 65◦. This is because the ellipticity of the systemcannot cause a sufficiently large light amplitude at smaller in-clinations, while the (grazing) eclipse of the primary becomesmuch to deep for inclinations exceeding the upper limit givenabove. Moreover, the width of the shoulders of the light curveshows that the primary must be nearly filling its Roche lobe;a 5% smaller radius produces unacceptably broad shoulders.These bounds to the inclination also set bounds to the separa-tion A between the components, through the relation

A = 4.206 (Mp +Ms)1/3 P 2/3

and on their masses (Table 3). If the period is given in days andthe mass in solar masses, this formula will yield the separationin solar radii. Even before carrying out a more precise deter-mination of the inclination by detailed light curve modelling,we are finding that the masses of the stars are too small for(near–) main–sequence stars of the inferred spectral types. Ifwe anticipate the inclination of 53◦–54◦ derived in Sect. 6.2,we deduce a dynamical estimate of log g = 3.85 for the primary– between the spectroscopic and the photometric estimates –and log g = 3.95 for the secondary; the value of 3.5 obtainedspectroscopically for the latter is very uncertain.

When a star fills its Roche lobe, synchronous rotation re-quires

vsyn sin i = K1 + qq

RL

A


Fig. 5. Uncovered spectra of TV Pic B near phase of primary light maximum (top panels) and near phase of secondary light maximum (bottompanels). The smooth line represents the template spectrum derived by blurring the observed spectrum of γ Vir (F0) to mimic an additionalrotational velocity of 120 km s−1. The spectra of TV Pic B have been shifted to coincide in wavelength with the template

If the star is smaller, the right-hand side of this equation gives anupper limit to the required apparent rotational velocity. We thusderive vp syn sin i ≤ 100 km s−1 and vs syn sin i ≤ 60 km s−1.However, the widths of the lines in the secondary indicate sig-nificantly faster rotation (112 km s−1), so either the secondaryis not in synchronous rotation, or rotation is not the dominantsource of line broadening.

If we assume that the primary fills its Roche lobe and is ro-tating synchronously, then from the above equation we obtainthe slightly smaller mass ratio q = 0.273±0.014. The uncer-tainty does not include that associated with derivation of rota-tional line broadening from the simple line-broadened model,as noted in Sect. 3. The latter is estimated by Collins & Truax(1995) to be about 10% for single stars, so q ≈ 0.31 appearscompatible with the radial–velocity amplitudes as well as withthe primary’s line broadening. The possible solutions presentedin Table 3 and the rotational broadening of the primary suggeststrongly that TV Pic is a near–contact binary (see Shaw 1994and references therein).

6. Light-curve modelling

6.1. Observational evidence

The observed light–curves refer to a broad wavelength rangeand to a fairly large time span: more than 2600 rotational peri-ods between the first and the last observing runs. The fact that

the light maxima are unequal (known as the O’Connell effect)precludes a complete explanation for the light variations basedmerely on the ellipticity of the stars and grazing eclipses. How-ever, the analysis presented in Sect. 5 and general considerationson the stability of the light–curve and on its colour dependenceindicate which kind of models are excluded.

Several observational facts put strong constraints on thesource of the additional light variability were it to be associatedwith the primary. Indeed, the spectrum emitted by the primary ateither phase of quadrature is apparently not very different, andthe colour variation in the light–curves is marginal (Fig. 6). Ifthe variability is caused by a spot on the surface of the primary,then the spot must be small (≤ 30◦ radius) and hotter than thelarger part of the stellar surface. Only such spot can leave theb−y colour almost unchanged while also causing the differencebetween the light maxima observed in the passbands. The tem-perature contrast must therefore be smaller than those publishedfor AG Vir (Bell et al. 1990) and similar systems. The parameterrange for spots on the surface of the secondary is much less con-strained because the influence of the spot on the total spectrumand on the colour variation is very diluted. However, such a spotcannot remain in a fixed position on the secondary’s surface inview of the evidence for non-synchronous rotation and the factthat the light curve remained stable over the time span of theobservations. There is no significant indication of any changein the light curve between November 1981 and January 1988.Undetected changes must be below the 0.01 mag level. Finally,


Table 4. Differential Stromgren photometry in the sense TV Pic − HD 31 640. HJD are expressed relative to a zero point at HJD 2 440 000. VJ

refers to Johnson’s V magnitude as derived from our photometry. Remarks are coded as follows: ‘c’ = TV Pic measured relative to HD 31 587only; ‘+’ = longer series of observations (accuracy higher than average); ‘?’ = observations not absolute (accuracy probably lower than average)

HJD ∆VJ ∆(b− y) ∆(v − b) ∆(u− v) R HJD ∆VJ ∆(b− y) ∆(v − b) ∆(u− v) R

4912.770 -0.572 -0.050 -0.068 0.115 + 4924.720 -0.588 -0.037 -0.069 0.1184912.850 -0.640 -0.038 -0.073 0.116 4924.766 -0.616 -0.039 -0.069 0.123 +4914.728 -0.579 -0.055 -0.056 0.103 4924.805 -0.642 -0.032 -0.073 0.1134914.774 -0.540 -0.047 -0.071 0.117 4925.818 -0.599 -0.038 -0.070 0.103 c4914.851 -0.552 -0.042 -0.075 0.105 4926.716 -0.559 -0.035 -0.076 0.100 c4915.647 -0.539 -0.045 -0.073 0.110 + 4927.834 -0.683 -0.040 -0.073 0.131 c4915.730 -0.564 -0.046 -0.077 0.110 4928.846 -0.564 -0.052 -0.075 0.112 c4915.859 -0.684 -0.052 -0.077 0.119 4929.638 -0.612 -0.049 -0.066 0.1134916.616 -0.604 -0.053 -0.067 0.129 4929.671 -0.584 -0.046 -0.067 0.1144916.656 -0.645 -0.052 -0.070 0.126 + 4929.695 -0.572 -0.039 -0.066 0.1244916.753 -0.685 -0.052 -0.062 0.135 ? 4930.640 -0.548 -0.049 -0.070 0.1274917.663 -0.658 -0.052 -0.077 0.129 4930.672 -0.582 -0.046 -0.066 0.1204917.759 -0.583 -0.045 -0.069 0.132 4930.702 -0.592 -0.049 -0.063 0.1184917.873 -0.567 -0.053 -0.067 0.157 4930.727 -0.620 -0.040 -0.072 0.1234918.611 -0.581 -0.054 -0.070 0.130 4930.795 -0.643 -0.048 -0.062 0.112 +4918.694 -0.556 -0.040 -0.079 0.121 ? 4930.830 -0.637 -0.048 -0.068 0.1174919.625 -0.601 -0.039 -0.074 0.120 4933.578 -0.531 -0.041 -0.071 0.1054919.741 -0.638 -0.048 -0.065 0.105 ? 4933.611 -0.545 -0.045 -0.078 0.1174920.607 -0.638 -0.049 -0.057 0.108 4933.812 -0.673 -0.051 -0.074 0.1234920.711 -0.561 -0.047 -0.076 0.113 4933.838 -0.664 -0.051 -0.074 0.1184921.710 -0.586 -0.046 -0.073 0.116 + 4934.759 -0.616 -0.044 -0.069 0.1184922.606 -0.627 -0.052 -0.073 0.117 + 4935.569 -0.652 -0.041 -0.075 0.1204922.700 -0.685 -0.051 -0.074 0.122 + 4936.567 -0.559 -0.039 -0.072 0.1114923.636 -0.657 -0.040 -0.068 0.122 4936.610 -0.564 -0.037 -0.074 0.1224923.688 -0.618 -0.038 -0.073 0.141 + 4936.661 -0.591 -0.044 -0.067 0.1104923.747 -0.570 -0.039 -0.067 0.124 4936.698 -0.623 -0.041 -0.072 0.1084923.808 -0.551 -0.051 -0.064 0.133 4936.779 -0.637 -0.046 -0.064 0.1124923.850 -0.575 -0.047 -0.068 0.122 +

the light curve does not show evidence of transient phenomenacharacteristic of strongly interactive systems.

The light curve in Stromgren b is shown in Fig. 1. The colourvariations (Fig. 6) are marginal and are dominated by a sinu-soidal term; only in u−v and 2.5 (U−W ) does the full range ofvariation exceed 10 mmag. The colours well above the Balmerjump all vary in phase with each other, and their amplitude isroughly proportional to the separation in wavelength betweenthe filters used (Table 7) at a rate of 8 mmag full range per 1000 Aseparation of the filters. The binary appears reddest when theprimary is in front of the secondary, one tenth of the orbital pe-riod before the following quadrature; at the Balmer jump andshortwards of it, the phase of reddest colour is shifted about onequarter period in the direction of the preceeding quadrature.While a sinusoidal representation is useful for a first estimateof the amplitude and the phase relation, it is obvious from thephysical background that the precise shape might be much morecomplex and the above statements should be interpreted accord-ingly. The evidence for the phase shifts and the small colourvariability is presently not sufficiently detailed to warrant anattempt to model it.

The light–curves and colour characteristics are very similarto the observations for TU Hor in the Geneva photometrical sys-

tem (Waelkens 1982). The visual light–curve of TU Hor has twomaxima differing by 0.05 mag, and a fairly sinusoidal colourvariation of 6 mmag amplitude in theB2−V1 index. This ‘tem-perature’ index is reddest about 0.1 period before the secondarymaximum in visual light. Waelkens showed that the mV light–curve can be transformed in a normal close–binary light–curve,with equal maxima separated by exactly half the orbital pe-riod, by subtracting a sinusoidal variation whose amplitude (30mmag) and phase in mV are compatible with the observed am-plitude and phase in theB2−V1 index (the variation in the indexis ascribed to a 75 K variation between the stellar hemispheresvisible at opposite quadratures). In our case, a slightly smallersinusoidal correction in b (26 mmag) removes the O’Connell ef-fect from the light–curve of TV Pic and brings the phase differ-ence between the maxima to half the orbital period if the colourindex is reddest 0.08± 0.03 P before the secondary maximumin b. Such correction implies an amplitude of ≈ 4.3 mmag inb− y and≈ 5.8 mmag in 2.5 (V −B). The predicted phase forthe ‘temperature’ index variations is compatible with the ob-served one, while the predicted amplitude is marginally largerthan observed (Table 7).


Table 5. Differential Walraven photometry in the senseTV Pic−HD 31 640. V B,BU ,UW andBL stand for ∆2.5 (V −B),etc. HJD are expressed relative to a zero point at HJD 2 440 000

HJD -2.5 ∆V V B BU UW BL

6775.5513 -0.542 -0.087 0.090 -0.012 -0.0266775.5948 -0.549 -0.094 0.094 -0.024 -0.0186775.6795 -0.616 -0.095 0.092 -0.012 -0.0206776.5344 -0.611 -0.091 0.092 -0.029 -0.0246776.5518 -0.641 -0.097 0.093 -0.018 -0.0296776.6033 -0.675 -0.095 0.094 -0.015 -0.0276776.7169 -0.641 -0.086 0.100 -0.020 -0.0226777.5350 -0.661 -0.091 0.093 -0.003 -0.0226777.5558 -0.657 -0.090 0.092 -0.011 -0.0236777.6092 -0.618 -0.093 0.094 -0.006 -0.0206777.6826 -0.557 -0.085 0.093 -0.006 -0.0276778.6941 -0.611 -0.085 0.086 -0.019 -0.0306778.7737 -0.646 -0.088 0.094 -0.021 -0.0156779.5868 -0.631 -0.084 0.091 -0.016 -0.0196779.6751 -0.642 -0.086 0.089 -0.023 -0.0196779.7633 -0.570 -0.088 0.089 -0.011 -0.0226780.5318 -0.627 -0.086 0.090 -0.025 -0.0236780.5908 -0.592 -0.088 0.095 -0.019 -0.0246780.6794 -0.535 -0.094 0.096 -0.029 -0.0176780.7783 -0.608 -0.093 0.097 -0.020 -0.024

6.2. Spot models

By using the Binary Maker code (Bradstreet 1993) we have in-vestigated whether the light–curve can be reproduced by modelswith one temperature spot on either the primary or the secondary.We assumed that the light variability is mainly due to the ellip-soidal shape of the star and the occurrence of grazing eclipses.We had to position the (hypothetical) spot on the stellar sur-face so as to explain primarily the different luminosity seen atthe quadrature phases; an appropriate starting point was in theorbital plane but 90◦ out of the inner Lagrangian point.

Fig. 1 shows that much of the light–curve asymmetry canbe explained by such a simple model, and equally well witha spot on the primary as with a spot on the secondary. Themodels deviate nowhere more than 0.01 mag from a smoothspline representation of the data, and the parameters listed inTable 8 can be regarded as appropriate initial estimates for morepowerful light–curve fitting codes. The most uncertain ones arethe latitude of the spot and its extent (both affect the resultingtemperature contrast). The primary has to fill its Roche lobe toreproduce the observed light–curve amplitude and the radius ofthe secondary cannot be varied appreciably without violatingthe spectroscopically–observed light ratio. TV Pic is a near–contact binary. The light–curve is fitted slightly better whenthe temperature of the secondary lies near the spectroscopicallyallowed maximum value. Fig. 7 shows the configuration at phasezero for both models. The lack of uniqueness (only the modelincluding a single cool spot on the primary can be excluded) willpresumably not be avoided by more powerful codes. Progressrather has to come from spectroscopic observations at morephases, in visual light and also at wavelengths where interacting

Table 6. Stromgren b photometry of TV Pic. HJD are expressed relativeto a zero point at HJD 2 440 000

HJD b HJD b HJD b

7180.5915 7.518 7184.6578 7.486 7188.6941 7.5597180.6273 7.554 7184.6946 7.468 7190.5802 7.5417180.6844 7.589 7184.7181 7.451 7190.6286 7.4887181.5748 7.581 7184.7519 7.457 7190.6690 7.4597181.6107 7.568 7185.5885 7.450 7190.6955 7.4487181.6505 7.540 7185.6227 7.451 7190.7147 7.4487181.6982 7.523 7185.6607 7.481 7191.5712 7.4557181.7376 7.508 7185.6994 7.507 7191.5908 7.4657182.5748 7.510 7186.5773 7.540 7191.6337 7.4907182.6118 7.499 7186.6101 7.565 7191.6747 7.5267182.6480 7.504 7186.6510 7.588 7192.5800 7.5717182.6864 7.523 7186.6928 7.580 7192.6234 7.5907182.7250 7.552 7186.7304 7.566 7193.5740 7.5487182.7650 7.587 7187.5738 7.577 7193.6070 7.5347183.5744 7.561 7187.6100 7.552 7193.6494 7.5197183.6148 7.587 7187.6503 7.524 7193.6887 7.4937183.6612 7.601 7187.6903 7.503 7195.5800 7.6077183.7037 7.584 7187.7306 7.490 7195.6368 7.5917183.7489 7.535 7188.5836 7.499 7195.6773 7.5577184.5798 7.579 7188.6169 7.5067184.6214 7.532 7188.6546 7.529

Table 7. Amplitude and phase of reddest colour for sinusoidal fits to thecolours. The final fits were coupled by imposing the same phase relationwithin groups of colours. (Note that the sequence of effective wave-length of the passbands from UV to red is:W,u,U, L, v,B, b, V ≈ y).The last column lists the rms of the fit to the observations

colour amplitude phase of max. σmmag mmag

2.5 (U −W ) 5.6 ± 2.0 −0.375 ± 0.03 6.2u− v 8.2 ± 1.2 −0.375 ± 0.03 7.6

2.5 (B − U ) 1.5 ± 0.9 −0.375 fixed 2.92.5 (B − L) 0.7 ± 1.4 −0.114 fixed 4.0

v − b 2.8 ± 0.6 −0.114 ± 0.02 4.72.5 (V −B) 4.9 ± 0.8 −0.114 ± 0.02 2.3

b− y 2.9 ± 0.9 −0.114 ± 0.02 4.9

matter may be more prominent (e.g. Lyman α emission, X–rays). We note that TV Pic is not detected as a bright sourcein the ROSAT survey (Voges et al. 1996); however, many ofthe nearby near–contact binaries are no bright sources as shownby Shaw et al. (1996). A more detailed analysis of X–ray datanear TV Pic and TU Hor is necessary. Moreover, the slightlydiscordant MK classification of Houk (1978) may hint at a largerspectral variability over the orbital cycle than was recorded fromcomparing spectra taken at different quadratures. Clearly, suchvariation – if real – must be exploited and reproduced by futuremodels.


Fig. 6. Color changes of TV Pic, relative to HD 31 640, and fitted rela-tions (Table 7). Ticks on the vertical axis indicate 5 millimag intervals

6.3. Does the model need spots?

The spectroscopic evidence (Fig. 5) is that the spectrum of thesecondary seems to have altered significantly between phase0.5 (when it is red–shifted) and phase 0.0 (the lower light maxi-mum). The puzzling aspect is the apparent doubling of the linesof the secondary at phase 0.0; the spectrum of the secondaryitself is not visible at a velocity displacement that would mirrorits red–shift at the other phase, nor do the two sets of split linesappear to be symmetrically placed around the velocity expectedby comparison with its red–shifted displacement. One (admit-tedly generous) explanation is that the secondary is veiled bythe presence of some sort of accreted material; such a modelmight account qualitatively for the fall in brightness and for thebehaviour of the spectral lines. On the other hand, one wouldrather expect to find accreted material in the wake of the sec-ondary (in the red–shifted situation) rather than ahead of it in itsorbit. Further spectra are essential before we can make furtherprogress in understanding the system better.

Fig. 7. The configuration of the binary at phase zero (secondary lightmaximum) for the spotted models described in Table 8 (upper: spot onprimary; lower: alternative model with spot on secondary)

Table 8. Parameters for the two ‘spot’ models shown in Fig. 1. The lon-gitude of the centre of the spot is measured from the inner Lagrangianpoint opposite to the sense of rotation. Co–latitude is measured fromthe ‘upper’ to the ‘lower’ pole. The phase of quadrature, φq, refers tothe quadrature nearest to the secondary light maximum. The primaryfills its Roche lobe. The radius given for the secondary is the ‘backradius’ (Wilson & Devinney 1971) in units of the distance betweenboth components. See Table 9 for the stellar and orbital parameters

Parameter Spot on Primary Spot on Secondary

inclination 53◦ 54◦

Rs/A 0.26 0.25Tspot 8800 K 8100 KRspot 30◦ 50◦

longitude 80◦ 260◦

co–latitude 90◦ 90◦

φq 0.008 0.006

7. Conclusion

High–dispersion spectroscopy near the quadrature phases to-gether with accurate photometry over a broad wavelengthrange have been used to identify TV Pic as one of the bright-est near–contact binaries: the list of Shaw (1994) containsonly 3 stars brighter than magnitude 7.5. All 130 stars inthat list have larger light amplitudes than TV Pic. PresumablyTV Pic, and the very similar, brighter (mV ≈ 6.0) A–typestar TU Hor = HR 1 081 = HD 21 981 (Waelkens, 1982), es-caped attention because they do not show pronounced eclipses.Shaw’s distance scale places TV Pic at 125 pc. These bright


Table 9. Predicted orbital and stellar parameters

Parameter Value

Porb 0.851990 de 0.0 (assumed)i 54◦

A 4.3 R�Mp 1.2M�Ms 0.4M�Rp 2.1R�Rs 1.0R�Tp 8300 KTs 7000 Klog gp 3.8log gs 3.5–4.0

near–contact binaries are very interesting candidates for detailedhigh–dispersion spectroscopic studies.

Indeed, several properties of TV Pic described in this paperindicate that these binaries deserve further study:(1) Both components are undermassive. This is characteristic ofa small group of near–contact binaries (Yamasaki et al. 1990).(2) To our knowledge, TV Pic is the first double–lined spectro-scopic binary in this subgroup of near–contact binaries.(3) The spectral types of primary and secondary (mid–A, early–F) are not too different.(4) There is strong evidence that the F–type component ro-tates much faster than would be required for synchronous ro-tation. The stability of the light–curve indicates that no sourceof light variability co–rotates with this component. We suggestthat checks for synchronous rotation should be made in similarsystems, through the method applied here.(5) TV Pic demonstrates that a strong O’Connell effect in thelight–curves may occur when the system is seen at very moder-ate inclination.

Our analysis has led to the system parameters summarizedin Table 9. Although the analysis of the light–curve is hamperedby the very unequal brightness of its shoulders, several physicalparameters have been determined to an informative degree ofprecision. Some improvements may be expected from more de-tailed light–curve solutions, but our analysis has indicated thatambiguities cannot at present be resolved. A more discrimina-tory data base, including spectroscopic observations in severalother spectral windows, and over the whole orbital period, wouldprovide a more direct foundation for a better physical model.

Some improvements may be expected from more detailedlight–curve solutions, but our analysis has indicated that am-biguities cannot at present be resolved. A more discriminatorydata base, including spectroscopic observations in several spec-tral windows, would provide a more direct foundation for abetter physical model.

8. Provisional note on the HIPPARCOS measurements

After submission of this paper, the measurements of the HIP-PARCOS satellite became public. The photometry made by the

TYCHO project confirms the stability of the light–curve. TheHIPPARCOS ephemeris (ESA, 1997),

HJD(prim.min.) = 2 448 500.8410

P = 0.851987d ± 0.000008

agrees very well with the period and phasing of our observations,within the uncertainties quoted; the shape and the amplitude ofthe light–curve are indistinguishable from those measured froma smooth spline representation of our observations. The HIP-PARCOS astrometry places TV Pic at a distance of 200+30

-20 pc,i.e. significantly further away than suggested by Shaw’s distancescale adopted in this paper. The HIPPARCOS distance measure-ments suggest that TU Hor and TV Pic are intrinsically brighterin the visual (MV = 0.7 for TU Hor and 0.9 for TV Pic) thanany of the eclipsing near–contact binaries of the list of Shaw(1994) and which HIPPARCOS considers to be nearer than 250pc. The majority of the latter are within 1.6 < MV < 2.2, andsome are still fainter. This could be seen as a suggestion thata statistical relation between intrinsic brightness and orienta-tion with respect to the observer might exist, but that shouldbe confirmed by studying larger samples of eclipsing and non–eclipsing near–contact binaries. Such relation might find its ori-gin, for example, in the presence and distribution of obscuringmaterial in the system.

Acknowledgements. KP acknowledges funding through researchproject 007002 of the Croatian Ministry of Science and Technology.He thanks Dr. R. Gray for providing the SPECTRUM code. REMG isgrateful to the Royal Observatory of Belgium for the support enjoyedwhile a visiting researcher. Part of this research was carried out byMD and WV in the framework of the project SC/005 ‘Service Cen-tres and Research Networks’, initiated and financed by the BelgianFederal Scientific Services (DWTC/SSTC), and by HH in the frame-work of the latter project and of the project ‘IUAP P4/05’ financed byDWTC/SSTC. JC and HH acknowledge funding by project G.060.91 ofthe Belgian Fund of Joint Basic Research, MD acknowledges researchgrants from the National Fund for Scientific Research (Belgium) andfrom the Special Research Fund of the University of Antwerp (NOIBOF UA).

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