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

2. Sample selection and properties

The star sample we have analyzed was obtained by applying several selection steps. The stars were initially extracted from the Bright Star Catalogue (Hoffleit & Warren 1991) in the region of the H-R diagram with (B-V) and . The next step was the availability of ROSAT-PSPC pointed observations. These observations allow to reach a sensitivity limit about two orders of magnitude better than observations in the ROSAT All Sky Survey (RASS) (see Sect. 3). Moreover, we have selected only stars within from the field center (either pointed or serendipitous observations), to avoid observations affected by strong vignetting effects, and sources with too large apparent sizes, due to the increasing width of the Point Spread Function (PSF) with increasing off-axis distance. The sample at this stage comprised 219 stars in 316 ROSAT fields.

The selection of the stars in post-main-sequence evolutionary phases was made by using the evolutionary tracks of Schaller et al. (1992; see Sect. 2.1 for more details), transposed from theoretical to observational C-M diagram using the transformations of Flower (1996). The most appropriate set of tracks was selected taking into account the metallicity; to this aim, we have investigated the distribution of for the fraction ( of the total) of the selected stars for which metallicity was available from literature (Brown et al. 1989, McWilliam 1990, Cayrel De Strobel et al. 1992, Taylor 1994, Luck & Challener 1995). In Fig. 1 we can see that the distribution is centered around the solar value, with 90% of data in the range [-0.4, +0.2]. We have also tried to match the positions in the H-R diagram of main sequence stars and clump giants with those predicted for them by models assuming different metallicities. Both methods suggest that the tracks with solar metallicity are the most adequate for the selection of evolved stars, in line with the findings by Gondoin (1999). In Fig. 2 we show the H-R diagram with the adopted evolutionary tracks and the locus of the points near the end of the main-sequence phase (exhaustion of core hydrogen); we have then selected only the stars on the right of this locus. For ease of comparison, in Fig. 2 we also show the locus which would have been obtained assuming evolutionary tracks with . Our sample still includes few class-V star among those with B-V (as for example the F0V star HD 28052, Hyades member): their position in the H-R diagram suggests that these stars may be in the final core-hydrogen burning phases, but - in case of metallicities higher than solar - an earlier evolutionary stage could be inferred.

Fig. 1. Distributions of for of the selected sample including main sequence stars (solid line), and for % of the final sample of evolved stars only (dotted line).

Fig. 2. H-R diagram of the evolved stars with Schaller et al. (1992) evolutionary tracks for 1.0 to 3.0 solar masses; the meaning of the solid and the dashed line is explained in the text.

We have eventually checked the metallicity distribution of the sample of evolved stars selected at this stage: the general agreement (Fig. 1) with the distribution obtained for the sample including the main-sequence stars, confirms the adequacy of the set of tracks we have chosen. A further control on the evolutionary state of the stars was made using the evolutionary models of VandenBerg (1985; Sect. 2.1): nearly the same star sample would have been selected starting from the latter alternative set of tracks. The 143 stars in the final sample fall in 175 ROSAT-PSPC fields, with 36 of them observed more than once.

2.1. Determination of mass

In order to estimate masses and to check the evolutionary states of the stars in our sample we have used and compared results based on two different sets of evolutionary tracks: (a) the VandenBerg (1985) evolutionary tracks, which assume Y = 0.25 and Z = 0.0169, and use the mixing length theory of convection with and no overshooting, Los Alamos opacities (Huebner et al. 1977), and model atmospheres of Kurucz (1979) for the boundary conditions and for transposing the theoretical -L diagram into a C-M diagram; (b) the more recent Schaller et al. (1992) evolutionary tracks, with Y = 0.3 and Z = 0.020, mixing length parameter , overshooting with for stars with , Rogers & Iglesias (1992) opacities and Kurucz (1991) opacities at low temperatures, and updated nuclear reaction rates and neutrino loss rates.

The observational C-M diagram for our sample was based on Hipparcos parallaxes, and the stellar masses were computed via interpolation on the tracks, assuming all stars being in the first-crossing evolutionary phases. We have obtained consistent mass estimates, within 10%, using the two sets of tracks (Fig. 3), and we have eventually adopted the masses based on the Schaller et al. evolutionary tracks for our study. As we can see from inspection of Fig. 3, the error on the mass due to the uncertainty on the Hipparcos parallax (typically 1%) is smaller than the indetermination on the mass caused by the use of one or the other set of evolutionary tracks, so that the latter source of uncertainly is actually the dominant one. However, this indetermination has little impact on our work because we have eventually selected only four mass ranges for our study.

Fig. 3. Comparison of masses estimated by interpolating the VandenBerg (1985) evolutionary tracks vs. those obtained from the adopted Schaller et al. (1992) tracks.

We have initially chosen as a boundary value to separate stars with A-type (or earlier) progenitors on the main-sequence, from late-type stars. This selection is relevant for our investigation because early and late-type stars are expected to show different evolutionary histories of their magnetic activity, because of the differences in convection properties. Each of these two subsamples was further split in two, in order to study the gradual change of the stellar activity evolution for stars with masses increasing from to . Note that our sample includes five stars with estimated masses (HD 22468, HD 23249, HD 128620, HD 133640, HD 160691) which cannot be considered as evolved stars; while we have not taken them into account for the investigation on the coronal activity evolution, nonetheless we have kept them in the studied sample for comparison purposes.

Finally, note that the stars with B-V and suffer of the additional source of uncertainty due to the difficulty of establishing whether they are true first-crossing giants or rather clump giants.

2.2. Determination of X-ray luminosity

The ROSAT data were reprocessed with the Palermo-CfA pipeline (Mackie et al. 1996), where source detection and count rate (or upper limit) evaluation are performed with the wavelet transform algorithm of Damiani et al. (1997). The best way to determine X-ray fluxes from count rates, corrected for vignetting effects and background contamination, is that of generating the spectrum of the source and fitting it with a thermal emission model. Then, fluxes can be evaluated from the best-fit model. To this aim, we have fitted spectra with more than 200 total counts, so to get robust fitting results and to reduce the error on the computed flux. One- or two-component isothermal models have been used for the fit, including an interstellar absorption term with the hydrogen column density fixed to the value , where  cm^-3 is the average number density of H atoms in the solar neighborhood ( pc; Paresce 1984), and D is the star distance. The statistics was used to test the goodness of our fitting results, as reported in Table 1. The search of the best-fit parameters and the 90% confidence limits on the fitted temperatures, for each model component, were searched within a grid of 55 thermal spectra, computed at constant steps over the range - K.

Table 1. One- or Two-temperature model of ROSAT/PSPC spectra.
Notes:
a) The 90% joint confidence ranges on and have been computed with the criterium .
Hydrogen column density was kept fixed to a value estimated from the star distance.
b) Last PSPC channel used for the the spectral fitting.
c) Plasma emission measure, in units of  cm^-3
d) X-ray fluxes in units of  erg cm^-2 s^-1, at the source, in the 0.2-4 keV band.

Unfortunately, only 56 observations of the selected stars satisfy the previous condition on the total counts. For the other stars we have adopted a count rate-to-flux conversion factor estimated from the available fitting results. Since the distribution of conversion factors shows a small scatter ( 3%, Fig. 4), we have used the median value  erg cm^-2 s^-1 per count s^-1 to evaluate X-ray fluxes for the stars for which spectral fits have not been performed, including those for which only an upper limit on the count rate is available.

Fig. 4. X-ray fluxes computed from spectral fits vs. fluxes estimated using count rates and the median of the count rate-to-flux conversion factors obtained from the spectral fitting results.

We have then studied the variations of the X-ray fluxes measured in multiple ROSAT observations of the same star at different times, searching for possible large flares. In Fig. 5 we show the distribution of the ratios between measured fluxes and the corresponding minimum value for each star: the median of these ratios is 1.45, 85% of the stars vary less than a factor two, only five stars vary more then a factor two, and none more than a factor five. This result excludes the occurrence of very large flares. After this check we have calculated the average of the fluxes measured for each star observed more than ones; this value has been used in the rest of this study.

Fig. 5. Integral distribution of the ratios for the multiple detections in the ROSAT observations.

The X-ray fluxes so evaluated have been used to compute X-ray luminosities, , or upper limits for the non-detected stars, and surface X-ray fluxes by means of stellar radii estimated with the Barnes-Evans relation (Barnes et al. 1978) involving the B-V color. The 1 errors on these parameters take into account the statistical uncertainties on the count rates and the (minor) uncertainties on the parallaxes (on only).

Fig. 6 shows the distribution of X-ray luminosities, , vs. stellar distance: the sample adopted so far, being limited in visual magnitude and in X-ray flux, shows an increasing number of stars and a trend of increasing for increasing stellar distance. In order to obtain a pseudo-volume-limited sample of stars, we have decided to retain for our following analysis only stars with distance  pc. Our final distance-limited sample contains 120 evolved stars within 100 pc, and from inspection of Fig. 6, we can see that it is nearly free of distance-related observational biases.

Fig. 6. X-ray luminosity vs. stellar distance. The dashed line indicates the sensitivity threshold for ROSAT-PSPC observations,  erg s-1 cm-2, which could be achieved with an exposure time of  s; the parallel solid line shows instead the sensitivity of a typical ROSAT-PSPC observation, corresponding to a flux of  erg s-1 cm-2. The vertical line marks the distance limit of our final sample.

In order to check for other possible observational biases due to the sample selection, we have also studied the dependence of X-ray luminosity vs. stellar mass (Fig. 7). There is a tendency for the higher mass stars to be more X-ray luminous, but there exist also high luminosity sources ( erg s^-1) with relatively low masses (). This characteristic makes us confident that any residual selection effect is small.

Fig. 7. Scatter plot of X-ray luminosity (or upper limit) vs. stellar mass for the stars in the ROSAT sample with  pc.

For the stars in the final distance-limited sample we have also collected values of the projected rotational velocity, , available for 100 objects in literature (see Table 2 for references). In particular, we have given preference to the most recent determinations by De Medeiros & Major (1995, 1999) and De Medeiros et al. (1997), obtained from CORAVEL data. All the stellar data required for our following analysis are listed in Table 2.

Table 2. Data of the distance-limited star sample.

Table 2. (continued)
Notes:
1) Single/Binary flag
References for and : (a) De Medeiros & Mayor (1995, 1999), De Medeiros et al. (1997); (b) BSC5; (c) Simbad database; (d) Balachandran (1990); (e) Fekel (1997) References for (only for spectroscopic binaries): (d) Batten et al. (1989); (e) Strassmeier et al. (1993)

© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000
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