3. Spectral analysis
The mean spectrum of PG1026+002 is shown in Fig. 2 along with a scaled spectrum of the M5 V standard star Yale 1755. The latter was taken from Jacoby et al. (1984). The shape of the continuum clearly indicates that blue-ward of H the white dwarf dominates, while further to the red the secondary star is brighter. Apart from the broad absorption line of H and the embedded narrow emission component the line features as well as the broad spectral bands are due to the late type secondary. Using spectrophotometric measurements up to the near infrared, Saffer et al. (1993) could determine the spectral type of the secondary in PG1026+002 quite accurately. Since the present spectra are restricted to a much narrower wavelength range, it will hardly be possible to improve their classification of M4 which we will adopt in the following.
3.1. Spectral decomposition
In order to determine the fractional contribution of the secondary star to the total light of PG1026+002, and in order to be able to remove the secondary star structures from the profile of the H absorption line, the spectrum of Yale 1755 of Jacoby et al. (1984), available in digital form, was multiplied by a suitable factor f and subtracted from PG1026+002. The resolution of the PG1026+002 spectrum was degraded by a Gaussian filter in order to match the lower resolution of the comparison star before this operation. We are aware that the spectrum of Yale 1755 is not ideally suited for this purpose since it is of type M5 V while the secondary of PG1026+002 is classified as a M4 dwarf (Saffer et al. 1993). However, no more suitable comparison spectrum being available, Yale 1755 is the best approximation.
In Fig. 3 the results of the secondary star subtraction for various values of f are shown. None of them is completely satisfactory. In particular, the strong TiO bands around 7 000 Å can only (approximately) be removed at the cost of grossly over-compensating the TiO 6159 Å (band-head) band. The best compromise appears to be the third graph from top in Fig. 3 which was calculated assuming the secondary to contribute 20% of the total flux at 6700 Å (the mean wavelength of the photometric R band). Most of the secondary star features red-ward of H as well at the TiO 6159 Å band are removed, although some features in the blue wing of H remain. Thus, we conclude that the veiling factor, defined as the fractional contribution of the primary to the total light, is approximately 0.8 at = 6700 Å.
3.2. The orbital period
Using observations covering a time base of 814 days, Saffer et al. (1993) were able to measure the orbital period of PG0026+002 without aliasing problems as 0.5972570 0.0000049 days. It is by far accurate enough to phase the current observations without cycle count ambiguities. This permits us to extend the time base for an improved period determination to 5116 days.
To do so, we measured the radial velocity (RV) of the narrow emission component of H. In order to remove possible distortions due to the underlying absorption, the absorption profile was first approximated by a spline fit, interpolating below the emission component. The division of the original spectrum by the spline yielded the rectified profile of the emission line. Its position was measured by a Gauss-fit. The derived RVs are listed in Table 2.
Table 2. Radial velocities of the H emission component of PG1026+002
After applying the heliocentric correction, these RV data were combined with the data of Saffer et al. (1993; their Table 2) and with two further radial velocity measurements of Schultz et al. (1996). The entire data set was then investigated with the analysis-of-variance (AoV) method of Schwarzenberg-Czerny (1989). The resulting AoV periodogram permits to unambiguously determine the period P as 0.5972584 days. The distribution in time of the RV data of Saffer et al. (1993) and of Table 2 permits a natural grouping of the data into subsets, each one containing only data closely neighbouring in time. In a final step these subsets were fitted by sinusoids where the amplitude, systemic () velocity and phase were left free to vary, but the period was fixed to the period of the peak of the AoV periodogram which is more than good enough for phase folding the subsets and keeping track of their cycle numbers. The resulting timings of the negative-to-positive crossing were then fitted by a linear relation, yielding the final value of the period P and the epoch of the crossing as quoted in Table 3. An diagram of the differences between the observed and the calculated epochs of crossing is shown in Fig. 4. The amplitude and the systemic velocity, also quoted in Table 3, were finally derived through a least squares sine fit to the entire data set, fixing P and to the previously found values. But note that and probably suffer from a systematic error as outlined in Sect. 3.3. The new orbital parameters are quite similar to those published by Saffer et al. (1993) but have a higher precision. The radial velocity curve, folded on the orbital period is shown in Fig. 5 together with a least squares sine fit.
Table 3. Revised orbital parameters of PG1026+002
The RVs measured by Wood et al. (1999) refer to H instead of H. Therefore, they were not considered when the orbital parameters of PG1026+002 were revised. Nevertheless they agree very well with the H radial velocities and are therefore included in Fig. 5 as filled triangles 1.
3.3. The emission line profile
In order to study the profile of the H emission component, the contribution of the secondary star was first removed from each spectrum according to the veiling factor derived in Sect. 3.1. All spectra were then normalized to the continuum, regarding the H absorption profile as the local continuum. Subsequently, the spectra were shifted in wavelength in order to reduce them to the rest frame of the emission component.
After co-adding these spectra a narrow absorption component appeared in the red flanc of the line profile. This is probably a blend of telluric water vapor at 6564.2 Å and the sharp core of the H absorption of the white dwarf which is not easily removed by interpolating the spline fit to the total absorption profile beneath the emission component. The presence of water vapor lines can be seen in the insert in Fig. 6 which is a simple sum of all spectra in the terrestrial rest frame. Some telluric lines which are not severely blended with strong late type absorptions as seen e.g. in the spectrum of Yale 1755 are marked. However, although telluric features definitely contaminate the spectra, the absorption at 6564.2 Å is too strong to be soley explained by water vapor. Moreover, the minimum of the absorption corresponds to a RV of 20.7 km s-1. This is in very good agreement with the expected mean velocity of 19.1 km s-1 of the white dwarf (taking into account the distribution of the observations in phase), assuming a mass ratio (Saffer et al. 1993), and supports the assumption that the absorption is dominated by the core of the H line of the white dwarf. In any case the sharp absorption is not part of the emission line profile.
In order to remove this feature, the normalized emission lines were co-added in the expected rest frame of the primary, calculated from the mass ratio of Saffer et al. (1993) and the values of and taken from Table 3. A spline was fitted to the mean emission profile, interpolating above the absorption component (tests with Gaussian profiles proved unsatisfactory). The difference between the spline and the original profile is considered as a fair approximation of the residual absorption component. If was shifted in wavelength according to the expected primary radial velocity and subtracted from the individual emission profiles. These were then again co-added in the rest frame of the secondary, yielding the mean profile shown in Fig. 6.
The shape of the emission consists basically of a narrow feature which in its main part is very well fitted by a Gaussian with Å. Comparing this to the instrumental line broadening as derived from the lines of the comparison spectra which can be considered to be intrinsically infinitely narrow this leads to a true linewidth of the emission component of 0.76 Å, corresponding to 35 km s-1. This is in contrast to the results of Wood et al. (1999) who found the H emission line in PG1026+002 to be intrinsically unresolved ( km s-1). However, it is in line with the intrinsic width of the emission components of the PCBs RE1016-053 and RE2013+400, also observed by Wood et al. (1999). We presume that the line width determined by Wood et al. (1999) is biased by the absorption core of the white dwarf for which they apparently did not correct their line profiles, and which could mimick a smaller emission line width. RE1016-053 and RE2013+400 are not subject to this effect because their H emission lines are much stronger than that of PG1026+002. Thus, in contrast to the conclusion of Wood et al. (1999), the emission line width of PG1026+002 is not different from that in other PCBs.
Apart from the narrow Gaussian emission component there is a broad base on the blue flanc of the line. Regarding the individual spectra, it is not always visible. In order to investigate if it appears preferably at certain orbital phases, the line profiles observed in the individual spectra were studied as a function of phase. The displacement of the line due to orbital motion is neatly visible on a corresponding plot, however, the limited signal-to-noise ratio makes it difficult to decide if there are significant phase-dependent variations in the emission profile.
The H absorption core of the white dwarf in the emission profiles raises concern as to which extent it can cause a systematic error of the measured RVs. In order to investigate this question radial velocities measured by Gauss fits to the emission profiles before and after subtracting the absorption core were compared. Least squares fits to the uncorrected and corrected RVs revealed an amplitude which is 10.6 km s-1 smaller after correction. The velocity is 3.7 km s-1 higher. Thus, any conclusions based on the dynamical properties of the secondary star as derived from the Balmer emission line component should take into account this correction.
3.4. The equivalent width of the H emission component
The emission components in the spectra of pre-cataclysmic binaries are generally interpreted as being due to re-processing of UV radiation of the hot primary in the atmosphere of the cool secondary (e.g. Thorstensen et al. 1978). They are thus restricted to the side of the secondary facing the primary. Depending on the orbital inclination of the system, its visibility from earth changes with orbital phase, leading to periodic variations of the equivalent width (EW) of the lines. Such an EW modulation was also observed by Saffer et al. (1993) in PG1026+002.
However, as Saffer et al. (1993) point out, the re-processing model does not work in the present case because the white dwarf in PG1026+002 is too cool and the component separation is too large for the secondary to intercept enough radiation of the primary to explain the observed EW variations of the H emission component. Saffer et al. (1993) favour intrinsic emission of the red dwarf. The modulation of its strength is then due to an asymmetric distribution of the emission on the stellar surface. The observed phasing being such that the emission comes predominantly from the side facing the primary can then be either due to some interaction with the white dwarf or it may be accidental. In the latter case Saffer et al. (1993) draw parallels to migrating waves seen in the light curves of many late type binaries. This hypothesis could be tested by measurements of the phasing of the EW curve at different epochs.
We therefore measured the EW of the H emission component in the present spectra. To minimize the influence of the secondary absorption spectrum, all spectra were first corrected for the veiling effect as measured in Sect. 3.3. The strength of the emission line was measured and referred to the strength of the local continuum interpolated above the broad absorption component to yield the EW (due to the non-photometric observing conditions, the observed line strength itself has no significance). These EW values were finally corrected for the contribution of the secondary which had been subtracted from the spectrum in order to refer it to the true continuum of the binary system. The resulting EW values, folded on the orbital period and binned in cells of widths are shown in Fig. 7.
The EW definitely varies, however, not with the orbital period but it rather shows two minima and maxima per orbit. A least squares sine fit with the period fixed at (solid line in Fig. 7), representing the observed data quite well, yields a mean EW of 1.45 0.02 Å and an amplitude of 0.32 0.02 Å (where the errors are formal fit errors). This is compatible with the observations of Saffer et al. (1993). The phase of the observations is such that the minima occur at orbital phases -0.02 and 0.48 (which in view of the uncertainties is definitely compatible with phases 0.0 and 0.5).
Thus, at the phases of upper and lower conjunction of the secondary star the EW assumes minima. This doublessly rules out re-processing of primary star radiation in the atmosphere of the red dwarf as the origin of the emission component (at least concerning the modulated part), confirming the view of Saffer et al. (1993). The maxima of the EW are seen when the line of sight forms a right angle with the line connecting the system components, i.e. when the secondary is seen sidewise. Thus, there seem to be two regions of enhanced emission roughly on opposite sides of the star.
But note that this view does not rule out a contribution to the H emission by reprocessing. In fact, as will be shown in Sect. 4, PG1026+002 exhibits a slight continuum variation which can very well be explained as being due to reflection. The favoured model requires a low orbital inclination. Thus, any modulation of a reflection induced emission line component would also be small (and diluted by the emission intrinsic to the red dwarf).
PG1026+002 is not the only pre-cataclysmic binary where the H emission component is not (exclusively) due to re-processing of light of the primary white dwarf. Bruch (1999) recently showed that also in the system RR Cae - where the H emission has a considerably larger equivalent width than in the present case - the emission is intrinsic to the red dwarf. Thus, although there are doubtlessly pre-cataclysmic binaries where the emission is due to illumination, this is not a general rule in this kind of systems.
3.5. The H absorption line
Due to its broadness and the distortion of its shape by the light of the secondary, the radial velocity of the H absorption component is much more difficult to measure than that of the emission line. In order to remove the influence of the secondary absorption lines the spectrum of Yale 1755 was subtracted from the individual spectra of PG1026+002, considering the veiling factor derived in Sect. 3.1. In spite of normalizing the spectra to the continuum, masking the H emission component, smoothing the spectra by different degrees and applying several techniques for radial velocity measurements [Gaussian fits, cross-correlations, double Gaussian convolution (see Schneider & Young 1980)] in no case a convincing radial velocity curve resulted. There is a tendency for a variation in anti-phase with the emission component at an amplitude which is not in contradiction with the expected amplitude, considering the mass ratio of 0.34 given by Saffer et al. (1993). However, the radial velocity curve is too noisy to permit more specific statements.
© European Southern Observatory (ESO) 1999
Online publication: November 3, 1999