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Astron. Astrophys. 347, 583-589 (1999)

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2. An improved period: coherent variations over 15 years

There is no question that the winds of hot stars are variable in general (Howarth and Prinja 1989), and thus, non-periodic variability is expected to be present even in the most established of binary star systems. The variability due to non-spherically symmetric wind distributions, wind instabilities and/or other mechanisms intrinsic to the stellar winds is expected to act as noise superposed on the periodic trends in the data. The relative amplitude of the periodic vs. the non-periodic variations will determine whether the observed spectral feature predominantly displays phase-dependent effects, or non-periodic wind variations. This amplitude is related to the amount of wind material involved in each of the different processes. Clearly, a perturbation involving a small fraction of wind material cannot provide as much flux variability in the observed spectrum as a perturbation involving a significant fraction of the wind. Let us assume for a moment that the star is a binary. The variations due to binary interaction effects, by their very nature, arise in a limited portion of the stellar wind. Thus, if the companion is not comparable to the primary, its perturbing effects on the primary's stellar wind are not very prominent. Intrinsic wind variations, however, are expected to arise throughout the wind, not just in the region between the two stars nor the line-of-sight to the companion. Thus, spectral features which arise in very extended regions of a stellar wind in which intrinsic variations are present, will tend to mask the periodic variations. This is the case, for example, of the resonance lines in the UV spectra of these stars. However, for spectral lines which are formed in a smaller, more limited region, the effects due to the binary companion are more comparable to those of wind instabilities, and allow the periodic variations to be more easily detected.

In the optical spectral region, the N V 4604, 4620 doublet provides an excellent diagnostic tool because the majority of this line's emission arises very close to the stellar core in HD 50896 (Hillier 1988), and both transitions display a P Cygni-type absorption component. The P Cygni absorption components arise only in the column of wind projected onto the stellar continuum-emitting core, and thus reflect physical conditions in an even more limited region of the wind than the emission components. This absorption component for the [FORMULA] line is superposed on the [FORMULA] emission, making any variations in its strength easy to detect. Hence, we have started the analysis with the N V 4604-20 doublet, first in order to analyze the problem of the coherence of the variations in HD 50896, and thus to determine whether any support for the presence of a binary companion can be found. The N V 4604-20 has been shown to present persistent variations from epoch to epoch (Ivanov at al., 1996; 1999).

The observations that were used include two of the most complete optical data sets in existence for HD 50896, obtained at the Observatorio Astronomico Nacional (OAN) in Tonanzintla in 1978 and 1979 (Firmani et al. 1980) and in San Pedro Martir (SPM) in 1991 (Cardona et al. 1999). These data have been complemented with observations obtained at the Bulgarian National Observatory between 1990-1993 (Ivanov at al. 1996). We mesuared two parameters from the optical spectra: a) Window averaged flux (WAF) - the average flux in a given spectral range - is calculated for two windows [FORMULA] for [FORMULA] and [FORMULA] for [FORMULA] centered on their P Cyg absorption components; b) The kurtosis defined as:


is calculated for the HeII 4686, using only the line profile at level higher than 2.5 times the continuum level. In order to reduce the uncertainty, additional parameters and additional sets of data are used. We measured the skewness of the N IV 1718 line from the IUE archival data, defined as:


Here we used only the line profile at level higher than 2 times the continuum level. This provides a totally independent parameter, calculated from an independent set of data, obtained over the years 1983-1995, including the IUE MEGA campaign (St-Louis et al. 1995).

In Table 1 we list the characteristics of these data sets.


Table 1. List of the photometric data.
a) Based on photon statistics.
b) Improved by averaging several spectra.
c) Calculated as average/st.dev. in the windows used for continuum normalisation.
d) Binned onto fixed wavelengt grid of [FORMULA] intervals
e) Binned onto fixed wavelengt grid of [FORMULA] intervals
(1) Firmani et al. 1980; (2) Cardona et al. 1999; (3) Ivanov et al. 1996; (4) Willis et al., 1989; (5) St. Louis et al., 1993; (6) St. Louis et al., 1995;

Because the data in the three sets are clustered around different epochs and are not distributed uniformly in time, the standard period-searching routines are not applicable. Thus, instead we use the fact that the 3.76 day period is accurate for short time intervals. This period has been shown to exist in all data sets published by diverse autors (see the introduction) and it is unique (Antokhin et al. 1995). We searched for periods close to this value which produce a coherent phase-dependence in the different sets of data. We refined the period using the same events of the phase curve, using the fact that the curves for the NV doublet WAFs are similar in shape at different epochs. Following Massey and Niemela (1981) and Massey (1981), we first determine the time at which the ascending branch of the NV 4620 WAF reaches half its maximum intensity (at [FORMULA]), which for the SIT spectra occurs at [FORMULA]. Then, we select the points with similar values of the WAF, again in the ascending branch of the curve for the SPM data, and thus determine the second time [FORMULA]. Using the first approximation to the period 3.766, we determine the possible integral number of cycles between [FORMULA] and [FORMULA] to be 1284 and 1285. The corresponding possible periods are 3.7679 and 3.7650 days. The same procedure was applied to the 1988 and 1992 epochs of IUE data. The times are [FORMULA] and [FORMULA], and with the corresponding number of cycles 303 and 304 yields the periods 3.7771 and 3.7647 days, respectively. The consistent period between the two pairs of times ([FORMULA],[FORMULA]) and ([FORMULA],[FORMULA]) is [FORMULA] days so we adopt this as the refined period. Taking into account that the precision of [FORMULA] and [FORMULA] is on the order of 0.01 days and that 1285 cycles have passed between them, the formal error of the period should be better than 0.00005 days. We adopt the more conservative value of 0.0001 days.

In Figs. 1a and 1b we plot the [FORMULA] and [FORMULA] WAFs, respectively, using all optical spectral data, and with [FORMULA] and [FORMULA]. A clear modulation of the data is evident, despite the fact that the different data sets span a timescale of 15 years (1977-1992) and were obtained with different instruments and by different observers.

[FIGURE] Fig. 1a and b. Window Averaged Flux of the NV 4620 a and NV 4604 b line as a function of phase using P=3.7650 days and [FORMULA] = 2443199.53. Circles correspond to SPM data (1991), filled-in diamonds to the SIT-Tonanzintla data (1977-78), and squares to the BNAO data (1990-1993).

Two maxima are present in these figures (near phases 0.3 and 0.6) as well as one pronounced minimum (between phases 0.6 and 1.1), and a second narrower minimum near phase 0.4. The maxima in the values of the WAFs indicate that there is a larger area contained between the flux levels in the NV 4604 line and the continuum. This occurs when the the P Cygni absorption components are weaker. On the other hand, Morel et al. (1997, 1998) have recently shown that there is a correlation between the strength of the P Cyg absorption components in this line and the intensity of the continuum, in the sense that a more intense continuum is associated with weaker P Cyg absorptions (and hence the larger WAF). It is important to note that for a line which is formed primarily by absorption processes, the strength of the P Cyg absorption component increases when the underlying continuum increases, assuming constant ionization structure. Thus, the N V variations indicate that the ionization structure does not remain stable or that there is a significant scattering contribution to the formation of this line. This could either result from an intrinsic variation at the base of the wind as proposed by Morel et al. (1998), or an interaction effect due to the presence of a very hot companion.

In Fig. 2 we present a montage of the N V 4604-20 line profiles corresponding to the two OAN data sets (SPM - left and SIT-Tonanzintla - right), side by side, plotted in order of increasing phase with the same ephemeris. One can appreciate in this figure that both sets present stronger P Cyg absorptions in the phase interval 0.8 to 1.0 and weaker P Cyg absorption components in the phase interval 0.1 to 0.3, consistent with the WAF measurements on Fig. 1.

[FIGURE] Fig. 2. Plots of the N V 4604, 4620 doublet stacked in order of increasing phase computed as in Fig. 1. Phase increases from bottom to top; SPM data are on the right and the SIT-Tonanzintla data are on the left. The vertical dashed lines mark the wavelength regions within which the WAFs plotted in Fig. 1 are computed.

The data of the WAF's and the kurtosis used for Figs. 1 and 3 are given in Table 3a,b,c available in electronic form only.

Coherent variations over the entire 15 year timespan are present also in other features in the optical spectra. In Figs. 3a and 3b we plot the Kurtosis of the He II 4686 and He II 4530 lines as a function of phase, with the same ephemeris as above, and for the same data sets as in Fig. 1, illustrating a fairly stable pattern of variability with one maximum near phase 0.5 and a minimum near phase 0.9.

[FIGURE] Fig. 3a and b. Kurtosis measurements of the two He II optical lines, plotted with the same ephemeris and symbols as in Fig. 1. a  He II 4686 and b  He II 4540.

Thus, the spectral variations in the optical lines present in data obtained over a 15 year timespan can be plotted to yield coherent phase curves adopting the revised period of [FORMULA].

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Online publication: June 30, 1999