Astron. Astrophys. 322, 785-800 (1997)

5. X-ray luminosity function

5.1. The entire Pop II sample

For those Pop II binaries in our sample which have X-ray luminosities, we computed the cumulative X-ray luminosity distribution function (XLDF). The XLDF was derived using the Kaplan-Meier Product Limit Estimator which includes the information contained in the upper limits (e.g., Schmitt 1985). The resulting XLDF is shown in Fig. 2. First, the median of the distribution , which is coincident with the least luminous X-ray detection. However, as there are only few detections at low X-ray luminosities, the median is not very robust. To be precise, we can only say that the median lies below . If, for comparison, the XLDF were calculated by taking into account only the detections, but not the upper limits, then the median would lie at . This indicates that the XLDF of the whole Pop II sample is dominated by upper limits rather than by X-ray detections. Second, despite the low detection rate, the median of the distribution still lies within the luminosity interval spanned by the X-ray detections. This is due to the fact that the upper limits are distributed over a large luminosity range as a result of the different exposure times and background levels, instead of being concentrated at low X-ray luminosities, as would be the case for a more homogeneous sample of observations (e.g., stellar clusters). Third, since the median denotes the 50th percentile of the distribution function, half of the Pop II binaries have X-ray luminosities below the median. With , it follows that at least of the Pop II stars have X-ray luminosities below erg s^-1. Fourth, Fig. 2 clearly shows that the XLDF has a high-luminosity tail, which extends over two orders of magnitude in luminosity between erg s^-1 and contains about of the stars. This high-luminosity tail is essentially due to the fact that our sample of Pop II binaries is not complete (i.e., volume-limited), but contains too large a fraction of distant stars contributing high luminosities and upper limits. Therefore, we explicitly mention that the XLDF of Fig. 2 represents the luminosity function of all Pop II binaries known so far, hence being slightly biased towards higher luminosities, rather than the intrinsic one. We see no way to define a complete, volume-limited subsample out of the entire sample of Table 1. Thus, the intrinsic XLDF can be constructed only after significantly enlargening the present sample of Pop II binaries.

Fig. 2. Cumulative X-ray luminosity distribution function for the entire sample of Pop II binaries (solid curve), for the emission Pop II subsample (dashed-dotted curve), and for a complete sample of RS CVn binaries (dooted curve). The XLDF at the position gives the probability that a star has an X-ray luminosity .

5.2. Comparing emission Pop II with RS CVn systems

The RS CVn systems constitute the most active class of late-type binaries (e.g., Schmitt et al. 1990, Dempsey et al. 1993). Hall (1976) proposed the following definition: The classical RS CVn binaries have orbital periods between 1-14 d, show significant Ca II H & K line emission, and have a primary of spectral type F-G, V-IV. The long-period RS CVn systems have periods beyond 14 d, and a primary of type G-K IV-II. Hall (1976) notes that lightcurve variations are a characteristic but not required property of RS CVn systems (cf. Table 4 in Hall 1976). Consequently, the 'emission Pop II' systems, i.e. those stars in our spectral types F-K comprising sample which exhibit significant Ca II H & K line emission, may be considered the halo component analogs to the RS CVn systems of the Galactic disk. In a quantitative way, we define the emission Pop II as systems with a chromospheric index . Unfortunately, we know both chromospheric indices and X-ray luminosities for only a quarter of the Pop II sample stars. Therefore, our emission Pop II subsample is statistically not very significant, comprising only 12 systems - CD-48 1741, BD+13 13, HD85091, BD+30 2130, HD89499, HD6286, BD+5 3080, BD-00 4234, HD195987, HD22694, BD+38 1670, BD+21 2442 - amongst them being 10 X-ray detections. We note that for 8 out of the 12 emission Pop II systems observations to search for photometric variability have been performed. Lightcurve variations attributed to star spots have been reported for BD+13 13 (Rodono et al. 1994, Henry et al. 1995), for HD85091, BD+30 2130, BD-00 4234, HD22694 (Henry et al. 1995), and for HD6286 (Hooten and Hall 1990). Further, variability in the V-amplitude has been detected for HD89499 (Ardeberg and Lindgren 1991), which might be caused by star spots. Only for CD-48 1741, no significant light variability has been found (Lindgren et al. 1987). These results indicate at least half of our emission Pop II sample to have star spots; thus, also from the aspect of lightcurve variability a comparison with the RS CVn binaries seems to be justified.

The emission Pop II binaries and the RS CVn systems, as a class, significantly differ in proper motion, age, and (photospheric) metallicity. We note that the entire Pop II sample covers a metallicity range , and the emission Pop II sample covers . Randich et al. (1993, 1994) also find many RS CVn binaries to be metal deficient with , but they note, as different [Fe/H] values are derived for the two components of several SB2 binaries, that "the spectral lines could be significantly affected by surface activity (spots and plages) and may not represent a true metal deficiency". On the other hand, Fekel and Balanchandran (1993) derive abundances for a sample of 10 SB1 RS CVn binaries. Specifically, for 4 stars common in both samples, abundances much closer to the solar photospheric values were derived by Fekel and Balanchandran (1993). Assuming the RS CVn to belong to the disk population, then, from a theoretical point of view, one would expect photospheric abundances close to solar due to their spatial proximity. Thus, although there may be a small overlap in metallicity between the Pop II and the RS CVn binaries, which is difficult to quantify at present, the metallicity ranges covered by the two stellar classes are distinctly different.

The XLDF of the emission Pop II subsample is shown in Fig. 2. The median , but is not very well constrained due to the small sample size. Next, we constructed the XLDF for a complete, volume-limited sample of RS CVn binaries. The sample of all RS CVn systems known so far, which has been compiled by Strassmeier et al. (1988) and analyzed in X-rays using the RASS by Dempsey et al. (1993), is estimated to be complete out to a distance of about pc (Drake et al. 1989, Ottmann and Schmitt 1992). Selecting those stars within pc, we find 27 systems, all of which are detected in the RASS. In Fig. 2, we plot the XLDF of the complete RS CVn subsample. Obviously, the median of the emission Pop II XLDF is about one order of magnitude smaller than that of the RS CVn sample, while its width is much broader. For a complete sample of Pop II binaries, the median is expected to be even lower, and the width substantially smaller. Thus, the emission Pop II halo binaries typically are at least one order of magnitude, probably more, less X-ray luminous than the disk component RS CVn binaries. But the high-luminosity tail of the emission Pop II XLDF is entirely within the luminosity range of the RS CVns, indicating that the most luminous emission halo binaries have X-ray luminosities as high as those of the most active disk binaries.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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