Astron. Astrophys. 361, 614-628 (2000)

3. Results

Our final sample contains 42 single stars and 78 binaries (from SIMBAD database information), 44 of them being spectroscopic binaries (SB). From the observational point of view, a spectroscopic binary star or a multiple stellar system not resolved in X-rays may imply an overestimation of the flux associated to the evolved star under examination. From an interpretative point of view, multiple systems, with stars at a distance such that mass exchange between components or tidal effects may occur, can be characterized by a dynamo efficiency and level of X-ray emission different with respect to single stars of similar mass. Checking the PSPC images we have resolved 13 binary stars having an angular separation , according to the Bright Star Catalogue. To further increase the number of resolved stars we have examined also 16 images obtained with the High Resolution Imager (HRI) on board of ROSAT, having a better angular resolution ( on the axis) than the PSPC, and a useful field of view of . One more star was resolved in this way. These 14 stars were studied together with the other 42 single stars, already selected.

3.1. X-ray emission level vs. evolutionary phase

In order to monitor the variation of X-ray activity during the evolution across the Hertzsprung gap, we have studied the distribution of X-ray luminosities vs. B-V color for single and binary stars separately, in each selected mass range (Fig. 8 and Fig. 9). In fact, since the evolutionary tracks are almost horizontal in the H-R diagram, during early post-main-sequence phases, the B-V color can be used as a proxy of the evolutionary age. To the aim of looking for trends in the data with a non-parametric statistical approach, we have employed a procedure called LOWESS (for locally-weighted scatterplot smoother; Cleveland 1979), also known as robust locally-weighted regression ¹. The following scenario appears evident:

• : most of the stars with (G-type on the main-sequence) show relatively low X-ray emission levels ( erg s^-1) in the B-V range 0.4-0.9, and there is a tendency of decreasing vs. B-V. The only three stars with log  erg s^-1 in this subsample are GJ 732.1 (HD 175225), a suspected spectroscopic binary (Duquennoy & Mayor, 1991), and two of the five stars with , i.e. the well-known W UMa-type short period binary 44 Boo (HD 133640), and the RS CVn-type system HR 1099 (HD 28468). These two latter stars are indeed "peculiar", however their inclusion does not affect any of our results because they are recognized as outliers by our robust regression. We have no a priori clue on why GJ 732.1 shows such a high X-ray luminosity.

• : these stars (F and G-type on the main-sequence) appear on average slightly more X-ray luminous ( erg s^-1) with respect to lower mass stars with similar color, and there is little if any dependence of on B-V, up to B-V . Beyond B-V = 0.6 the only star in this mass range is  Ser (HD 168723), showing a low upper limit on its X-ray luminosity ( erg s^-1). One more W UMa-type system is present in this subsample (HD 175813, B-V=0.41,  erg s^-1), but -unlike the case of 44 Boo- its X-ray emission level is typical of other single and binary stars with similar mass and B-V color.

• : the single stars in this mass range (A-type on the main sequence) show instead, on average, an increasing X-ray emission level during the evolutionary phases across the Hertzsprung gap, from  erg s^-1 to  erg s^-1; the binary stars follow a similar trend up to B-V , but all the other stars with redder colors have X-ray luminosities below  erg s^-1, with the most notable examples (located around B-V ) being Boo (HD 121370), a G0 IV spectroscopic binary with  km s^-1, and 40 Her (HD 150680), a G0 IV spectroscopic binary with  km s^-1. There are also two binary stars with X-ray luminosity exceeding  erg s^-1 and B-V: the spectroscopic binary 71 Tau (HD 28052, F0 V), member of the Hyades cluster, with  km s^-1, and HD 10308, F2 III, member of a triple-system, having  km s^-1. The single star with the highest X-ray luminosity is the well-known gap giant 24 UMa (HD 82210; Ayres et al. 1998).

• : these stars show the same increasing trend as the previous subsample. The two X-ray luminous single stars with B-V = 0.6-0.7 are the bona-fide gap giants  Peg (HD 220657) and 31 Com (HD 111812), while the star with B-V  with the highest X-ray luminosity is  Tuc (HD 6793). The only star well below the average path is the binary HD 35162 at B-V . Among the stars with B-V we observe a large range of X-ray emission levels ( erg s^{- 1} erg s^-1), possibly due to mixing of stars ascending the giant branch for the first time and clump giants (see discussion below).

• : only 7 stars in this mass range are included in our sample, including just one single star, and most of them (6 out of 7) have B-V , so we are unable to study in detail their evolutionary history; however, their X-ray luminosities (or upper limits) are comprised in the wide range spanned by the stars in the previous subsample with similar red colors.

Fig. 8. Distributions of X-ray luminosities (or upper limits) vs. B-V color for single and resolved binary stars (filled symbols) and unresolved binaries (open symbols), in the two mass ranges indicated in the upper panels. Five stars with estimated masses , indicated with diamonds, are included for comparison purposes only. Note that the errors on X-ray luminosities are often smaller than the symbol size. The lines are the result of a LOWESS regression (see text) applied separately to the subsamples of single (solid line) and binary (dotted line) stars, in the single range of masses . The bottom panels show the corresponding H-R diagrams, including the Schaller et al. (1992) evolutionary tracks.

Fig. 9. Similar to Fig. 8, but for two different mass ranges. The LOWESS regression has been applied separately to single and binary stars in each indicated mass range.

Since in these phases the stellar radius increases appreciably, and the X-ray luminosity may depend on the available stellar surface, we have inspected also the distributions of surface X-ray fluxes vs. B-V color (Fig. 10). Even using this parameter, there is a clear decay of the coronal emission for the lower mass stars (), and a trend for increasing emission levels for the intermediate-mass stars, up to B-V, followed by a large spread for redder stars.

Fig. 10. Surface X-ray fluxes vs. B-V color for single stars in the mass ranges (open symbols) and (filled symbols), with LOWESS regression curves.

3.2. Coronal temperatures

In Fig. 11 we show our spectral fitting results. Inspection of the scatter plot of vs. temperature, for the individual thermal components, suggests that two effects occur as the total coronal X-ray luminosity increases: the temperatures of the individual components tend to increase, and at the same time the relative contribution to the X-ray emission of the cooler vs. the hotter component gradually shifts from dominant low-temperature components ( 1-2 MK) to dominant high-temperature components ( 4-16 MK). The latter results is confirmed by the scatter plot of the total X-ray luminosity vs. the hot/cool emission measure ratio, shown in Fig. 11 b: for , the trend found with a lowess regression can be well approximated with the power law , and the emission measure ratio becomes greater than one (hotter component dominant) for  erg s^-1. Finally, we have evaluated average temperatures from the 2-T model fits, weighting the two components with the respective emission measures: these "effective" coronal temperatures, combined with those derived from the 1-T model fits, scale with the total X-ray luminosities as shown in Fig. 11 c: the LOWESS result can be well approximated with the following linear relationship:

Fig. 11. a X-ray luminosities vs. temperature, for stars whose spectra have been fitted with 1-T models (plus symbols) or 2-T models (open and closed circles for the two components). Two dashed lines connect the components of the two stars with the lowest and highest total X-ray luminosity; the solid lines are the result of a LOWESS regression applied separately to the low- and high-temperature components (for 2-T model fits only). b  X-ray luminosity vs. ratio of emission measures, for stars with 2-T model fits. The solid line has been obtained with a LOWESS regression, while the dotted line is a least-squares linear approximation to the LOWESS result, for . c  X-ray luminosity vs. average coronal temperature, with LOWESS regression (solid line) and linear approximation (dotted line).

We have also investigated on the possible biases introduced by the differences in iron abundance on the distributions of the X-ray luminosity vs. temperature and vs. the ratio of the emission measures. We have performed the spectral fitting for all the stars in Fig. 11 using two different metallicities, and , corresponding to the 90% range of the photospheric Fe/H distribution (see Fig. 1), in order to check how the best-fit parameters change. We have found that both the emission measures associated to the two thermal components decrease by factors 3-4 for increasing , in such a way that their ratio becomes lower by 30% in going from the low to the high metallicity extreme. At the same time we have checked that variations of the average coronal temperature and of the X-ray luminosity computed by assuming different metal abundances are less than 5%. We conclude that the correlations noted above are not significantly affected by the assumed coronal metallicity.

The above results, together with those found in Sect. 3.1, suggest that - during stellar evolution - coronal temperatures and X-ray luminosities follow similar trends; in particular, the coronae of lower-mass stars () tend to become cooler with advancing evolutionary phases, while for intermediate-mass stars () higher X-ray emission levels correspond to hotter coronae.

3.3. Activity vs. rotation

In Fig. 12 and Fig. 13 we have plotted the distributions of X-ray luminosities vs. and vs. B-V, for single and binary stars in each of the mass ranges already considered. Different behaviors are evident also in these distributions, for stars in different mass ranges. In the upper plots we have also drawn a solid line representing the well-known Pallavicini et al. (1981) law , in order to see how this law compares with the actual behavior of evolved stars. In practice, (a) stars with are loosely scattered around the Pallavicini's law, with the exception of the suspected spectroscopic binary HD 175225 (GJ 732.1), having high X-ray luminosity in spite of a low projected rotational velocity, suggesting that it may be viewed nearly pole-on; (b) stars with and  erg s^-1, having  km s^-1 and B-V, show similar X-ray luminosities in spite of a factor 10 spread in rotational velocities, while the less X-ray luminous and redder stars are clustered close to the Pallavicini's law; (c) stars with show instead a trend of decreasing X-ray luminosity with increasing rotational velocity; (d) finally, among the stars with , those bluer than B-V show the same trend observed in the previous mass range, but most of the gap giants with  B-V , like  Peg and 31 Com, are close to the Pallavicini's law, and most of the stars redder than B-V rest well above the Pallavicini's law.

Fig. 12. Distributions of X-ray luminosities (or upper limits) vs. for single and resolved binary stars (filled symbols) and unresolved binaries (open symbols), in the two mass ranges indicated on top of each panel (upper row). The bottom panels show the corresponding distributions in the B-V vs. diagram. Note that the B-V axis has been inverted to ease inspection of the vs. B-V decreasing trend, shown by the LOWESS regression (dotted line) applied to all stars in each mass range.

Fig. 13. Similar to Fig. 12, but for the two subsamples of intermediate mass stars.

On the other hand, all stars follow similar trends of decreasing rotational velocity for increasing B-V, in each mass range. Note in particular that the stars with have similar low values of 1-4 km s^-1 (whenever reliable measurements are available), but show a spread in X-ray luminosities of more than three orders of magnitude. On the basis of our previous results (Sect. 3.1), one can be tempted to identify the high X-ray luminosity stars ( erg s^-1, like  Her and  Cyg) with first-crossing evolved stars at the blue edge of the Hertzsprung gap, and the stars with lower X-ray luminosities with clump giants; unfortunately, this is a necessary but not sufficient condition for discriminating between the two classes of stars: in fact, there are well-known examples of true clump giants, like Tau in the Hyades cluster or the field star  Cet (not in our sample; see Maggio et al. 1998), which show high X-ray emission levels in spite of their low rotational velocities.

3.4. Close binaries

Finally, we have investigated the possibility of a connection between X-ray activity and mass in spectroscopic binaries with different orbital periods. Melo & De Medeiros (1996) noticed higher levels of X-ray emission in short-period spectroscopic binaries ( days) with respect to long-period binaries ( days). In particular, these authors found, for binaries with  days, X-ray to visible flux ratios about two orders of magnitude higher than for longer period binaries. They argued that this behavior may be due to synchronization between orbital motion and rotation, caused by tidal effects, in the shorter period binary stars, and consequent enhancement of the magnetic activity. We have checked this result with our larger sample, retrieving from literature the values of orbital periods for 35 out of the 44 spectroscopic binaries (Batten et al. 1989; Strassmeier et al. 1993). For these binary systems we have plotted in Fig. 14 the X-ray to visible flux ratio vs. the orbital period, maintaining the distinction between stars with mass and stars with . It appears that the trend noted by Melo and De Medeiros may be valid only for the lower-mass stars, while it is not followed by the more massive stars. This is somewhat surprising since their sample includes only late-G and early K giants with masses likely larger than 2-3 .

Fig. 14. Scatter plot of X-ray to visible flux ratio vs. the orbital period, for 35 spectroscopic binaries in our sample. Open and filled symbols refer to stars with and , respectively, and the dotted and solid lines are the corresponding LOWESS regression curves.

© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000
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