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Astron. Astrophys. 318, 215-230 (1997)

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4. Discussion

4.1. Detection thresholds

The number of sources detected in an X-ray survey obviously depends on the adopted lower acceptance threshold, which is to some extent arbitrary and depends on the value of contamination through spurious sources one is willing to tolerate. As in Schmitt et al. (1995), a likelihood threshold of 6 was used as a criterion to decide between source detections and upper limits. In the likelihood range between 6 and 10 there is a total of 4 sources, i.e., Gl 124, Gl 914A, Gl 780, and Gl 454. Visual inspection of these images indeed shows the presence of sources in all these cases. I also inspected the distribution of the position offsets between X-ray source and optical star, where care was to taken to apply an appropriate proper motion correction to the actual epoch of the ROSAT observations. None of the survey detections reported here has a position offset larger than 60 arc sec, and for the pointing data the position accuracy is greatly improved. I therefore conclude that essentially all of the reported detections are real and that the sample is not contaminated by incorrectly associating "background" X-ray sources with "foreground" stars.

4.2. Survey sensitivity

The ROSAT all-sky survey is obviously a flux-limited all-sky X-ray survey. Its typical limiting flux of [FORMULA] in the 0.1 - 2.4 keV pass band corresponds to a typical limiting intrinsic X-ray luminosity of [FORMULA]. Thus at larger distances only the intrinsically brighter objects can be detected, and consequently in flux-limited samples one tends to find a correlation between distance and intrinsic luminosity. However, because of the pointed follow-up observations this effect is not present in the sample discussed in this paper. In Fig. 2 I plot X-ray luminosity [FORMULA] (or upper limits thereof) vs. distance (in pc) for my sample stars; obviously, the limiting luminosity [FORMULA] stays essentially constant throughout the sample and only for larger distances especially in the 12 - 13 pc bin the pointed follow-up observations become incomplete.

[FIGURE] Fig. 2. Plot of X-ray luminosity [FORMULA] vs. distance d (in parsec) for our sample stars. A-type stars are drawn as squares, F-type stars as triangles, and G- and K-type stars as diamonds; upper limits are additionally indicated by downward arrows. Note that the sample is unbiased in terms of limiting X-ray luminosity with intrinsically faint stars being detected at large distances.

4.3. X-ray detection completeness

Inspection of Table 1 shows that 60 objects out of the total sample of 73 systems were detected as X-ray sources; if attention is restricted to stars within 12 pc, 46 out of 53 objects are detected. Among the 7 non-detections, there are 3 A-type stars (with spectral types between A0 and A3), and all of the non-detections of stars not classified as A-type are due to lower sensitivity survey data. Thus it is very suggestive to assume that lack of sensitivity is the only reason for not achieving a 100 percent detection rate for F and G type stars. On the other hand, the A-stars Vega, [FORMULA] Leo, and Fomalhaut remained undetected in quite deep PSPC pointings, exceeding (for Vega and [FORMULA] Leo) 10 ksec and resulting in rather low upper limits.

4.4. X-ray luminosity and spectral type

In Fig. 3 I plot the derived ROSAT X-ray luminosities [FORMULA] vs. absolute magnitude [FORMULA] for my sample stars. The three upper limit for stars with [FORMULA] correspond to the A-type stars [FORMULA] Lyr (A0 V), [FORMULA] PsA (A3V) and [FORMULA] Leo (A3V). The "earliest" late-type star in my sample is the A7V star Altair, already detected by the Einstein Observatory (cf., Schmitt et al. 1985). From Fig. 3 it is clear that X-ray emission sets in rather abruptly for stars with [FORMULA], and for F-type stars between [FORMULA] one immediately obtains the full range of the X-ray luminosity distribution function. It is worthwhile noting that among the F-type stars the detection rate is close to 100 percent, the hottest non-detection being Gl 364 classified as F9 IV. Among the G-type stars the formal detection rate is 83 percent and hence lower. However, all G type stars studied in the pointed program have been detected, and hence there is no reason to assume that the non-detected stars have X-ray luminosities very much different from the detected ones. In other words, I strongly argue that the observed range of X-ray luminosities as shown in Fig. 3 is identical to the true range of X-ray luminosities of solar-like stars.

[FIGURE] Fig. 3. Plot of X-ray luminosity [FORMULA] vs. absolute magnitude [FORMULA] for my sample stars. Detections are drawn with diamonds, upper limits by downward arrows. Note the absence of any detections for values of [FORMULA] despite the availability of extremely sensitive (pointed) observations. On the other hand, the few upper limits for stars with [FORMULA] are all due to survey data with reduced sensitivity; see text for details.

4.5. X-ray luminosity distribution functions

Next, I construct X-ray luminosity distribution functions for my sample stars using the the Kaplan-Meier product limit estimator (cf., Schmitt 1985 and references therein) for the full sample (excluding all stars classified as spectral type A), as well as the F and G star sample. Inspection of Fig. 3 shows that the X-ray luminosities of these stars are rather similar except for a slight trend for the F-type stars to be somewhat more luminous than G-type stars.

In Fig. 4 I plot the overall cumulative XLDF (stepped curve) for the 13 pc sample; the position of the few upper limits is noted in the plot by small vertical bars. Also shown is the best fit log-normal distribution function (dashed smooth curve) of the form


to the data; the parameters µ and [FORMULA] denote median and dispersion of the distribution function respectively. Note that for the log-normal distribution the mean of the distribution is related to the median and dispersion through


log-normal distribution function fits to X-ray selected samples of M stars from the Einstein Medium Sensitivity Survey have been presented by Schmitt & Snowden (1990) and for volume-complete samples of K and M stars by Schmitt et al. (1995).

[FIGURE] Fig. 4. Cumulative X-ray luminosity distribution function for the 13 pc sample (stepped curve) excluding the five A-type stars; the smooth line is the best log-normal distribution fit to the data, the four vertical bars indicate the positions of the non-detected stars in [FORMULA].

In Table 3 I list the fit parameters for various distribution functions, i.e, derived median, dispersion and mean values. In Fig. 5 I plot XLDFs for the stars in the color range [FORMULA] (dashed stepped curve), [FORMULA] (solid stepped curve) and, for comparison, the full sample (dotted stepped curve). As is obvious, the distribution function for the F-type stars lies systematically above the one for the G-type stars, with the full sample being in between. The same is true if these XLDFs are approximated by log-normal distributions (cf., Table 3); these distributions have virtually identical dispersions, and only the mean shifts towards systematically lower values.


Table 3. Mean X-ray properties

[FIGURE] Fig. 5. Cumulative X-ray luminosity distribution functions F-type stars contained in our 13 pc sample (dashed stepped curve), the G-type stars (solid stepped curve), and the full sample (dotted stepped curve).

4.6. X-ray luminosity and kinematics

Fleming et al. (1995) showed that in their complete sample of nearby K and M dwarfs small space motions, i.e., "Young Disk" kinematics, do not necessarily lead to large X-ray luminosities, and hence called in question the use of kinematic age indicators. With the sample of F and G stars one can again check the relationship between space motions and X-ray luminosity; in Fig. 6 I show X-ray luminosity vs. U and V space motion as an X-ray "bubblegram" with Eggen's (1969) "Young Disk" box; note that one X-ray detected star with very large space motions, i.e., Gl 451 A, is not plotted in Fig. 6. Figure 6 shows that indeed many, albeit not all, X-ray luminous stars are contained in "Eggen's box", while stars with lower X-ray luminosity have much less concentrated space motions. A statistical analysis rejects the null hypothesis, that stars within and outside "Eggen's box" have the same X-ray luminosity distribution functions with very high confidence. Thus, I conclude that for the more massive nearby F and G stars kinematic class does provide a reasonable activity indicator.

[FIGURE] Fig. 6. X-ray luminosity "bubblegram", showing X-ray luminosity (represented by the radius of the symbols plotted) vs. space velocity components of our sample stars; Eggen's (1969) box indicating the space velocity of a young disk population is shown.

4.7. X-ray luminosity and spectral hardness

Schmitt et al. (1995) reported a correlation between observed ROSAT PSPC spectral hardness and total X-ray output measured in terms of X-ray luminosity. It is natural to ask to what extent such a correlation is also present for the more massive stars considered in this paper. As in Schmitt et al. (1995), most of the F and G star observations were geared towards source detections only; this particularly applies to the RASS data as well as the follow-up observations of stars not detected in the RASS data. I therefore characterize the spectral properties of the X-ray emission by the measured PSPC hardness ratios (cf., col. 8 in Table 1 and Sect. 3.1). Also, in order to be able to compare different groups of stars I use X-ray surface fluxes instead of X-ray luminosities as activity indicator; stellar radii were computed from the Barnes-Evans relation (Barnes & Evans 1976) using the measured B-V colors, apparent magnitudes and distances. In Fig. 7 I plot X-ray surface flux [FORMULA] vs. spectral hardness HR for the X-ray detected sample stars (diamonds); for comparison I also plot the nearby K and M stars (shown in triangles) discussed by Schmitt et al. (1995). The clustering of points at [FORMULA] is due to data points with low signal-to-noise, where only a signal in the soft PSPC band could be significantly detected; for clarity, the F and G stars have been slightly offset from the later type dwarfs. As is clear from Fig. 7, just like nearby K and dwarfs, the F and G dwarfs populate the hardness ratio range between [FORMULA], and increasing X-ray surface flux is correlated with increasing hardness, which in turn implies an increase in the emission measure weighted temperature (cf., discussion by Schmitt et al. 1995). To summarize, I conclude that with respect to the correlation between surface flux and spectral hardness, all late-type dwarf stars behave in the same fashion. In this context it appears worthwhile to point out that studies trying to relate the spectral properties of coronal X-ray emission with its intensity have also been carried out with data from the Einstein Observatory (cf., Vaiana 1983; Schmitt et al. 1990); however, these studies had to characterize the observed stellar pulse height spectra parametrically (through fitted coronal temperatures), which very quickly leads to ambiguities in the permissible temperature distributions once more complicated emission measure distributions are allowed.

[FIGURE] Fig. 7. Plot of X-ray luminosity [FORMULA] vs. spectral hardness between soft and hard PSPC counts for F and G stars (diamonds) and K and M stars (triangles; from Schmitt et al. 1995). The correlation between hardness and total X-ray output is obvious, but a large scatter around the regression curve is also apparent. A typical value in terms of [FORMULA] and HR for a solar coronal hole is also shown.

A salient but interesting feature of Fig. 7 is the fact that apparently no surface fluxes significantly below [FORMULA] erg/cm2 /sec were measured.

In order to explore this further I plot in Fig. 8 the surface fluxes vs. [FORMULA] color for all of the sample stars of this paper (rather than only the detections) as well as the K and M dwarf sample studied by Schmitt et al. (1995). Figure 8 shows that the apparent cutoff at surface fluxes of [FORMULA] erg/cm2 /sec is not a question of lacking sensitivity. The non-detected A-type stars do indeed have upper limits below [FORMULA], but because of the completeness of the samples both for the F and G stars as well as the K and M stars, I can state that among cool dwarfs stars with X-ray surface fluxes below [FORMULA] do not exist (in the considered volumes of space). The star with the lowest detected surface flux is the G star Gl 512.1, which was barely detected as a very soft source in a 3 ksec PSPC pointing; this star incidentally is 70 Vir, recently proposed to be surrounded by a planetary companion (Marcy & Butler 1996). The minimum flux maybe slightly increasing with color, i.e., towards redder stars, which have larger surface gravities. Hence, if anything, the minimum flux will increase rather than decrease with surface gravity.

[FIGURE] Fig. 8. Mean X-ray surface brightness [FORMULA] vs. [FORMULA] color for my sample stars (including A-type stars drawn as upper limits). F and G stype stars are plotted with diamonds, K and M type stars (as discussed by Schmitt et al. 1995) with upward triangles. For comparison the typical X-ray surface flux level (in the PSPC band pass) from solar coronal holes is shown by the two dashed curves. Clearly the observed solar coronal hole surface flux provides a good description of the observed stellar minimum X-ray flux. See text for details.
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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998