3 Results

3.1 Characteristics of sample

The distribution of the distances for our objects is shown in Fig. 1. It is clear that most of our sources lie within 200 pc from the Sun (86% of our sample). Only 15 stars (14% of the sample) lie at distances greater than 200 pc, with only one star as far out as $\sim$700 pc.

  

Figure 1: Distribution of the distances for our sample

  

Figure 2: Distribution of the separation between X-ray and Counterpart positions

Figure 2 shows the distribution of the separation between the optical counterpart position and the ROSAT X-ray position. Most of the optical counterparts lie at 30$^{\prime\prime}$ or less from the X-ray position. Voges (1993) determined that for the RASS 68% of the optical counterparts are within 20$^{\prime\prime}$ of the X-ray position. In our sample, 72% lie within that distance, in excellent agreement with Voges' results.

Both the errors in X-ray flux and distance contribute to the uncertainty in the X-ray luminosity, the flux error giving the major contribution. The error for $L_{\rm X}$ is typically about a factor 2.

  

Figure 3: Cumulative distributions of X-ray luminosities for our RASS sample (continuous line) and the EMSS sample (broken line) as taken from Fleming (1988 and 1995)

  

Figure 4: The X-ray to visual luminosity as a function of spectral type, represented here by the (B-V) colour index. The F stars are represented with (+), the G stars with ($\ast$) and the K stars with (X).The continuous line represents the saturation level of $F_{\rm X} \sim 7 \ 10^7\ {\rm erg} \ {\rm s}^{-1} \ {\rm cm}^{-2}$ detected by Fleming in his sample (Fleming 1988). The dashed line is the upper limit for $L_{\rm X}$ as calculated by Vilhu & Walter (1987). The dash-dot line is a constant $\log (L_{\rm X} / L_V)$ of -1.8

  

Figure 5: The distribution of the hardness ratio in our sample. Most sources have hardness ratios between -0.5 and 0.7

Figure 3 shows the cumulative X-ray luminosity function for our sample. Although nearly all objects are clearly active, none displays extremely high activity with high X-ray luminosity ($\log (L_{\rm X}) \ge 32$). The median value of the X-ray luminosity is $\log (L_{\rm X})=29.88$. This value is higher by two orders of magnitude than the $\log (L_{\rm X})$ observed for the active Sun. 63% of the sample has X-ray luminosity of $\log (L_{\rm X})$ between 29.5 and 30.0. We only have four objects so far with $L_{\rm X}$ of the order of $10^{31}\ {\rm erg} \ {\rm s}^{-1}$.

The X-ray to visual luminosity as a function of spectral type is shown in Fig. 4. Noticeable is the spread in $L_{\rm X} / L_V$ in every spectral class, a spread that is larger than the uncertainty in X-ray luminosity. This spread shows the range of activity levels present in the observed objects. For $(B-V) \leq 0.64$, $L_{\rm X} / L_V$ is confined to less than 10^-3, with one source only, a binary (F8V+G4V), having a higher value. For $(B-V) \geq 0.64$, the maximal value of $\log (L_{\rm X} / L_V)$ rises to $\sim -1.8$. Only one source shows a higher value of $L_{\rm X} / L_V$, and that source is so far a good candidate for a PMS object. The turning point value of (B-V) corresponds to the value found by Fleming (1988), where the stars show a constant maximum value of $F_{\rm X} \sim 7 \ 10^7\ {\rm erg} \ {\rm s}^{-1} \ {\rm cm}^{-2}$.For the stars with a bluer (B-V), Fleming finds that the maximal value of $F_{\rm X}$ (or $L_{\rm X}$) rises with later spectral types, as calculated by Vilhu & Walter (1987). The corresponding limiting $\log (L_{\rm X} / L_V)$ (for main-sequence stars) are shown in Fig. 4: the values of Vilhu and Walter by a dashed line, Fleming's maximal value for the surface flux by a continuous line. Also plotted is a line for $\log (L_{\rm X}/L_V) = -1.8$.Most of our stars seem to confirm Fleming's maximal value for $F_{\rm X} \sim 7 \ 10^7\ {\rm erg} \ {\rm s}^{-1} \ {\rm cm}^{-2}$.There are only a few objects above this limit. The nature of these sources with high X-ray surface flux will be investigated further once high resolution spectroscopic observations are available and have been analyzed.

Also of note in the plot is the absence of any low-activity objects in the late-K types (for spectral types later than K4). The reason for this absence of low-luminosity objects is most probably the detection limit of the RASS, which lies at a flux of $f_{\rm X} \sim 2 \ 10^{-13}\ {\rm erg} \ {\rm s}^{-1} \ {\rm cm}^{-2}$. This means that late K stars with $\log (L_{\rm X}/L_V)= -4$ (or $\log (L_{\rm X}) \sim 28.5$) can only be observed if they lie within 36 pc of the Sun, and those with $\log (L_{\rm X}/L_V) = -5$ (or $\log (L_{\rm X}) \sim 27.5$) only up to a distance of 10 pc. A study of nearby ($\le$ 7 pc) K stars made by Schmitt et al. (1995) has shown that high X-ray luminosity is not very frequent among late K stars. The sample they studied contained only 43% of stars of spectral type K4 or later with an X-ray luminosity of $\log (L_{\rm X}) \ge 27$, and only 27% have $\log (L_{\rm X})$ of 27.5 or higher, making them detectable with the RASS at distances of $\sim$10 pc. In our studied areas there are only 15 K stars belonging to the Gliese catalogue and of spectral type K4-K7. Out of these only two lie within 10-11 pc and another two lie within 12 pc. Therefore, according to the Schmitt and Fleming statistics, we would expect to detect at the most one of these nearby K stars, and this produces the observed gap in Fig. 4.

The distribution of the hardness ratio for the ROSAT sample is given in Fig. 5. Clearly, most of our stars have HR1 values between -0.5 and 0.7. The mean value of the hardness ratio lies near 0, being $<{\rm HR}1\gt$ = 0.13 $\pm$ 0.35. Three stars have very high HR1 values and only one has value smaller than -0.5, RXJ 0440.3-5856, with HR1 = -1.05. Such a soft X-ray emission is usually characteristic of white dwarfs. The counterpart for this source, though, is a wide binary composed of two dwarf G-stars. In this case we have rather a X-ray quiet source ($\log (L_{\rm X})=28.2$), which may explain the soft spectrum. Another possibility is that we have a binary system with a white dwarf companion.

3.2 Selection criteria

Considering the large amount of sources ($\sim$$60\ 000$) that compose the RASS catalogue, an automated search for objects of interest, using for instance the guide Star Catalogue, would be of definite advantage. For this reason, we have tried to determine good selection criteria for solar-type stars using our sample.

First of all, the considered objects should be close to the X-ray position, at maximum 20$^{\prime\prime}$ distance. 72% of our objects lie within this radius of the X-ray position. The optical sources should be brighter than 15 mag in the visual range.

The hardness ratio for our sources is mostly between -0.4 and 0.7. 92% of the stars have a HR1 included in this interval. So in an automated search only X-ray sources with HR1 between these two values should be considered.

The X-ray flux of the ROSAT source can be calculated using either a constant conversion factor for the countrates, or the formula given by Fleming et al. (1995) and used in this work (see Eq. 1). Since a high photometric accuracy is not required for a first selection, candidates can be directly selected, and their approximate visual flux determined, from existing large surveys. The ratio of X-ray to visual flux determined using these values should not exceed $\log (f_{\rm X}/f_V) = -3$ for F stars and early G stars ($(B-V) \le 0.64$), and $\log (f_{\rm X}/f_V) = -1.8$ for later spectral types ((B-V) > 0.64).

3.3 Comparison with EMSS and EXOSAT samples

  

Table 2: Distribution of our sources among the spectral types F, G and K, as well as distribution in the EMSS and EXOSAT samples

Table 2 lists the distribution of our sources, as well as for the sources from the EMSS and EXOSAT surveys, between the spectral types A, F, G and K (including the primaries of binary systems, for which the secondaries have not been included). The EMSS sample has been taken from Stocke et al. (1991) and the EXOSAT sample from Cutispoto et al. (1996).

Table 2 shows clearly that the RASS sample and the EMSS sample have the same distribution between the four studied spectral types. The EXOSAT sample has a different distribution. But the sample being rather small (28 late-type stars), the difference cannot be considered significant.

  

Figure 6: X-ray luminosities as a function of distance for our RASS sample ($\ast$) and for the EMSS sample ($\diamond$) as taken from Fleming et al. (1995). The line drawn represents the X-ray luminosity as a function of distance for a constant observed flux $f_{\rm X}$

  

Figure 7: X-ray luminosities as a function of distance for our RASS sample ($\ast$) and for the sample of RS CVn stars ($\triangle$) of Dempsey et al. (1993). For some of the RS CVn stars only upper limits for the X-ray luminosities were given. These objects are those indicated with the downwards pointing arrows

Figures 3 and 6 compare the cumulative X-ray luminosity function and the X-ray luminosities as a function of the distance from the Sun for our sample and the EMSS sample (Fleming 1988). For this we used the ROSAT data available for the EMSS sources (Fleming et al. 1995), allowing a direct comparison of the samples. For some of the EMSS sources, only an upper limit for $f_{\rm X}$ was given. These sources are given in Fig. 6 by downwards pointing arrows. Also shown in Fig. 6 is the curve of the X-ray luminosity as a function of distance, for a given flux $f_{\rm X}$. This curve describes the effect of having stellar distances badly determined.

Both samples show a similar distribution of X-ray luminosities with distance, as well as similar X-ray luminosity functions. This leads to the conclusion that both samples come from the same population. This hypothesis was checked using a Kolmogorov-Smirnov test. The result was a disproof probability for the null hypothesis of P = 2.5%, or a probability of both samples coming from the same population of 97.5%, which we take as a confirmation that indeed both samples are representative of the X-ray emitting solar-type population in the solar neighbourhood.

The major difference between the two samples is the high X-ray luminosity tail, composed of four stars with X-ray luminosities of the order $10^{32}\ {\rm erg} \ {\rm s}^{-1}$, present in the EMSS sample. Out of these four stars one is a K giant, one a G subgiant, one a close binary (F8V + ?) and one a PMS star. All these sources are situated at more than 1000 pc from the Sun. Only two of them have been listed as observed by ROSAT: their ROSAT luminosity is also of the order of $10^{32}\ {\rm erg} \ {\rm s}^{-1}$, and their PSPC countrates are well above the detection threshold of this survey. If such active stars were present in the study areas they were likely to be detected, but our sample does not contain such distant, extremely luminous sources. This difference could be due to slightly different spectral classification criteria adopted in the EMSS identification program and in the present work. Distinguishing between dwarfs and subgiants can be difficult, and a misclassification in luminosity class would lead to a huge difference in distance, and therefore in X-ray luminosity. In any case, these extremely active stars are very rare, as can be inferred by following the comparison with RS CVn systems.

Figure 7 shows a comparison of our sample of solar-type stars with the sample of RS CVn studied by Dempsey et al. (1993). For some of the RS CVn (marked with downwards pointing arrows), only an upper limit for the X-ray luminosity was given. Obvious is the greater spread in luminosity shown by the RS CVn sample. All our stars have similar X-ray luminosities as the low-luminosity RS CVn stars. So should our sample include RS CVn, those would only be at the low-activity end for this type of binaries. The reason for this could just be due to statistics, X-ray bright RS CVn not being all that numerous. Considering the number of objects in the sample of Dempsey et al. (1993), we should have $\sim$1.5 RS CVn in our sample, and $\sim$0.4 RS CVn if considering only the high-luminosity ones ($\log (L_{\rm X}) \ge 31$). Under such conditions, it is not so surprising that our sample does not contain any of the brightest RS CVn, and this suggests that the number of presently known very active, nearby RS CVn is probably not too underestimated.

3.4 A-type stars

The results of studies from previous X-ray observations, as well as the models used to explain the X-ray emission in stars, have led to the view that if X-ray emission was to be expected from A-stars, or more precisely, from single B7-A5 stars, it would be at only very weak levels of $\log (L_{\rm X}) \le 10^{27}\ {\rm erg} \ {\rm s}^{-1}$ (see Golub et al. 1983). Exceptions to this rule are chemically peculiar Ap stars, and A-star binary systems, in which the X-ray emission is believed to come mainly from a later-type companion.

Our sample contains only one A-type star: RXJ 1446.3+0153 identified as 109 Vir, an A0V star. This star doesn't show photometric variability (see for example Lockwood & Thompson 1989). It doesn't display any peculiarity either, and is not known as a binary. It has been used as standard star in various studies. For instance as normal template A-star in a study of Ap stars (Gerbaldi et al. 1989) and as a spectrophotometric standard in the study of HH 46/47 (Raga & Mateo 1987). So far the most peculiar aspect of this star is its high rotational velocity, found to be $340~{\rm km} \ {\rm s}^{-1}$ by Andrillat et al. (1995). Further studies of this object will be necessary to check out and confirm its identification as an X-ray source. With an $L_{\rm X}$ of $\sim 10^{28}\ {\rm erg} \ {\rm s}^{-1}$ the possibility of an X-ray coronal, low-mass companion cannot be excluded. Photometric studies (Lockwood & Thompson 1989) indicate that, if such a companion exists, it is much fainter than the A star, and not detectable with standard photometry. A search for radial velocity variations in the primary spectrum could be carried out, but the very high rotational velocity of the star makes the use of this technique very difficult.