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Astron. Astrophys. 331, 639-650 (1998)

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4. The secondary component

A careful inspection of the high-resolution spectra taken at the two quadrature phases reveals differences which can only be explained as contributions from the spectrum of the secondary; the most prominent example is the extended wings of the Ca II K line, as shown in Fig. 3. We therefore treated the observed spectra as though they were indeed composite, and attempted to isolate and analyse any features that might be characteristic of the spectrum of the secondary. The observed spectra were reprocessed by two different techniques: (1) 'difference' spectra and (2) spectral subtraction.

[FIGURE] Fig. 3. The broad component of Ca II K underlying the sharper line of the primary. The two spectra were recorded near phases of opposite quadrature. The spectrum observed at HJD 2 447 193.691 is shifted down by 0.15 in intensity, and is shifted in wavelength by 1.3 Å to compensate for the Doppler shift between the spectra

4.1. 'Difference' spectra

Small and blended differences between two observations of a composite spectrum taken at different phases can be highlighted simply by subtracting the two spectra such as to eliminate the spectrum of the primary. One spectrum must first be shifted in wavelength (amounting in the present case to about 100 km s-1) in order to align the two primary spectra. The 'difference spectrum' thus obtained, in the sense 'HJD 2 447 191.542 - HJD 2 447 193.691', exhibits some distinct features, well above the noise level for [FORMULA] Å, in the vicinities of the Balmer lines [FORMULA] and of the Ca II K line. The fact that numerous less conspicuous differences are found at other wavelengths suggests that the difference spectrum may in fact hold quite a lot of information on the secondary. It was therefore quantitatively compared with theoretical models. The underlying broad component in the Ca II K line (Fig. 3) yielded an initial estimate of ([FORMULA], [FORMULA]) in the region of (6250-7000 K, 3.0-4.0).

A 2-D grid of theoretical spectra, at [FORMULA]  = 6250, 6500, 6750 and 7000 K and [FORMULA]  = 3.0, 3.5 and 4.0, was calculated with the SPECTRUM code. Each spectrum was broadened corresponding to a set of rotational velocities 90, 95, ..., 130 km s-1, and for each rotational velocity a template for the difference spectrum was obtained by shifting the broadened spectrum with respect to itself and subtracting it; the latter shift represents the sum of the total orbital velocity ranges of both components (plus a small correction because the exposures were not taken exactly at the the quadrature phases), and was chosen from the set [FORMULA] pixel.

The observed difference spectrum was cross-correlated with each of the templates to find the best-matching set of parameters. Strictly speaking, this method is only valid when the stellar spectra do not vary throughout the orbital cycle and when their relative contributions are equal at both quadratures; we do not yet know whether or not this is true for TV Pic, but the method should at least supply some useful information. A straightforward search in the four-dimensional parameter space introduced above, using the whole spectrum, is inefficient because information about the secondary's temperature and gravity is principally in the calcium and hydrogen lines, and information on rotational velocity is to be found only in the other metal lines. These narrower lines also constrain better the orbital velocity shift. Therefore, as a first step, we estimated the rotational velocity and the orbital-velocity shift at each fixed [FORMULA] and [FORMULA] from five 90 Å intervals with starting wavelengths of 4135, 4225, 4410, 4500 and 4590 Å. The differences between the results from different wavelength regions exceed those corresponding to a variation of the atmospheric parameters across our grid; they appear to be due to a residual mismatch, between the difference spectrum and the templates, which persists throughout the parameter grid. Weighting the results for a sub-grid ([FORMULA]  = 6500 K, 6750 K, 7000 K and [FORMULA]  = 3.5, 4.0) with the corresponding correlation coefficients, we finally estimate the rotational velocity of the secondary to be [FORMULA]  km s-1, and its shift in the difference spectrum to be [FORMULA]  km s-1. These values were used to construct new templates for the atmospheric parameter grid. The quoted errors were estimated from the scatter between the values obtained from five different wavelength regions; this scatter exceeds both the uncertainties in the position of individual cross-correlation maxima and the scatter in the values over the acceptable domain in the grid of synthetic spectra used for modelling the secondary. However, they do not account for any bias due to structural imperfections in 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 Å) wavelength intervals surrounding respectively (1) Ca II K, (2) the blend of Ca II H with [FORMULA], (3) [FORMULA] and (4) [FORMULA]. In all the intervals, the cross-correlation results exhibit a similar behaviour with varying atmospheric parameters provided that interval (2) is chosen not too narrow and (3) not too wide. On the basis of all these results, the atmospheric parameters for the secondary can be constrained to:


Actually these constraints were obtained after the whole procedure was iterated once, with an improved value for the radial-velocity shift of the primary between both exposures: after the first run, assuming the values [FORMULA]  = 6750 K, [FORMULA]  = 3.5 for the atmospheric parameters of the secondary, we provisionally subtracted the estimated contribution of the secondary from the observed spectrum; as a result the radial-velocity shift of the primary between both exposures was corrected from [FORMULA] to [FORMULA] pixels, i.e. by 2.5 km s-1. Remarks similar to those made on the error quoted for the shift in the secondary spectrum apply here.

Fig. 4 shows two portions of the observed difference spectrum and the computed model, which assumes that the continuum of the primary is 9 times brighter than that of the secondary. The major part of the high-frequency structure in the data is well reproduced, but some shortcomings of the model remain.

[FIGURE] Fig. 4. Difference spectra in the vicinity of the Ca II K line and around 4440 Å. The contribution of the primary was eliminated from the spectra recorded near opposite quadrature phases by applying an appropriate velocity shift and subtracting them. Dots show the observed data. The full line is computed from the model atmosphere for the secondary and then scaled down by a factor 10 to account for the light ratio between primary and secondary

4.2. Spectral subtraction

Another technique for identifying the characteristics of the spectrum of the secondary is to subtract away the spectrum of the primary, 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 observed 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 the other hand the introduction of a third spectrum as an analogue, however close, to that of the primary will undoubtedly introduce extraneous errors and artefacts which grow rapidly as increasingly large fractions of the primary are subtracted away (as happens in the case of TV Pic, where the primary heavily dominates the composite spectrum). Nevertheless, the subtraction method complements nicely the 'difference' technique. Both methods share the disadvantage that subtraction reduces the signal but adds (quadratically) the noise.

The composite spectrum of TV Pic stretches the capabilities of the subtraction technique to its limits. The original programme was developed for use with composite systems containing cool giants and hot dwarfs, and its supporting library of standards is accordingly much richer in cool giants than in hot dwarfs. It proved to be not possible to match the spectrum of the primary in TV Pic (TV Pic A) unambiguously to any one of the available standards, the chief problem being the growing strengths of Ca II at 3933 Å and Mg II at 4481 Å coupled with a corresponding lack of decline in the widths of the Balmer lines. The best available compromise was the A3  IV star [FORMULA]   Sco, after being blurred to mimic an additional rotational velocity of 120 km s-1.

The two uncovered spectra of the secondary (TV Pic B) are shown in Fig. 5. Both show rather large deviations in the apparent continuum level, some of which is attributable to residuals in the blaze function of the echelle, and some to mismatch (between TV Pic A and [FORMULA]  Sco) that has become magnified until it looks much more serious in these residual spectra than it does in a system whose components are more similar in luminosity. However, there also appear to be intriguing systematic differences between the two spectra of TV Pic B, and a subtraction which produced a tolerably clean secondary spectrum in one case did not seem able to do so in the other, indicating that not all the peculiarities that we see in Fig. 5 (excluding the obvious one at 3933 Å) are artefacts of mismatch.

The spectrum of TV Pic B corresponding to phase 0.47 (primary light maximum) and red-shifted by [FORMULA]  150 km s-1 relative to the primary, conveys reasonably faithfully the characteristics of an F dwarf; it matches Procyon (F5) slightly better than [FORMULA]  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 is blue-shifted relative to the primary, looks distinctly different from the former and somewhat strange. One possible interpretation is that the lines have split into two narrow components displaced from the primary by (very approximately) -230 and [FORMULA] km s-1 respectively. As is seen in Fig. 5, several of the metal lines show quite a convincing split, whilst each of the Balmer lines appears to be composed of two unresolved components: a short-wavelength member that is as deep as in the spectrum at 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 the primary, though any spectral variability which the secondary may exhibit will have to be sampled at more phases than the two that are presently at our disposal. High-resolution spectra covering the orbital phases are needed in order to unravel the system's geometry.

[FIGURE] Fig. 5a and b. Uncovered spectra of TV Pic B near phase of primary light maximum (top panels) and near phase of secondary light maximum (bottom panels). The smooth line represents the template spectrum derived by blurring the observed spectrum of [FORMULA] Vir (F0) to mimic an additional rotational velocity of 120 km s-1. The spectra of TV Pic B have been shifted to coincide in wavelength with the template

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© European Southern Observatory (ESO) 1998

Online publication: February 16, 1998