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

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6. Which properties determine the X-ray activity?

For the Pop II binaries, the photometric properties [FORMULA] and [FORMULA] of the secondary are unknown. Thus, we do not know whether the secondary contributes at all to the total X-ray luminosity or if it is even the more active component. For this reason, we use the integral luminosity [FORMULA] as the activity measure, not the more desirable surface flux [FORMULA] or the normalized luminosity [FORMULA]. For the same reason, we correlate [FORMULA] with other integral quantities rather than parameters referring to the primary alone. Therefore, amongst the photospheric parameters, we correlate only the metallicity with [FORMULA], assuming that both stellar components have the same [m/H]. Similarly, we use the orbital period [FORMULA] (corresponding to the rotational period in case of synchronous rotation) as rotational parameter, because the projected rotational velocity [FORMULA] is unknown for most systems, and the rotational velocity or the Rossby number can, at best, be estimated only for the primary.

6.1. X-ray activity vs. rotation

Under the assumption of synchronous rotation, [FORMULA] can be used as the rotational parameter even when the active component is unknown. In short-period (SP) systems, the stellar components will rotate synchronously due to the strong tidal coupling and the resulting short synchronization timescale. The division between SP and long-period (LP) systems is made at [FORMULA] d on the grounds that (i) subgiant systems with [FORMULA] d are expected to be closely synchronized ([FORMULA]) on evolutionary time scales (Zahn 1977), and (ii) Latham et al. (1992) have found for extreme metal-poor systems the longest-period circular orbit, which gives a lower limit of the longest-period synchronized orbit, to be at a period of about 19 d. In LP binaries, the rotational period may still be close to the orbital one, except for very long-period systems having correspondingly long synchronization timescales and, therefore, [FORMULA]. However, all the detected Pop II systems, except HD149162, have orbital periods [FORMULA] d and, thus, are synchronous rotators or, at least, do not deviate too strongly from synchronism. The X-ray activity of the very long-period binary HD149162 ([FORMULA] d) comes very likely from the secondary, which is itself a binary system with a presumably much shorter period.

In Fig. 3, the X-ray luminosity is plotted as a function of orbital (or, for the SP systems, rotational) period. At first glance, it is surprising that we did not detect all the SP systems, but did detect 7 LP systems. Specifically, all the four SP systems with [FORMULA] d, BD+13 13, HD85091, HD89499, and BD-00 4234, have been detected, while there are only 2 detections, BD+30 2130 and HD 22694, among the 16 systems with [FORMULA] d. The detected LP systems, HD3266, HD6286, HD195987, BD+381670, HD106516, BD+212442, and HD149162, have rotational periods up to [FORMULA] d. For some LP systems, the X-ray activity may be naturally explained: As mentioned above, the secondary of HD149162 is probably a SP binary. HD6286 is evolved; therefore, despite its longer period, it may have a high rotational velocity [FORMULA] and hence a large X-ray luminosity. Finally, HD195987 could possess a white-dwarf (WD) companion, because its X-ray emission is typical for WDs with respect to both the magnitude ([FORMULA] erg s-1) and softness ([FORMULA] ; Fleming et al. 1996). However, HD106516 and presumably also HD3266, BD+381670, and BD+212442 are dwarfs, thus having low rotational velocities.

[FIGURE] Fig. 3. X-ray luminosity plotted against orbital period for the X-ray detections (squares) and upper limits (arrows). Amongst the X-ray detections, we indicate those systems known to be evolved (open squares); the other detections are known or presumed to be dwarfs (filled squares). Note that all highly active detections are evolved, while all the less active detections are dwarfs.

For comparison, the chromospheric index [FORMULA] is plotted as a function of orbital period in Fig. 4. The correlation between [FORMULA] and [FORMULA] has already been investigated by Pasquini and Lindgren (1994). In Fig. 4, we have added our new [FORMULA] measurements. On the basis of this extended data set, we confirm the result found by Pasquini and Lindgren (1994) that systems with [FORMULA] less than about [FORMULA] d show chromospheric activity, while systems with longer periods typically possess no active chromospheres unless they are evolved (e.g., HD 6286). However, there seem to be a few exceptions to this trend, since we find evidence for chromospheric activity in BD+212442, HD195987, BD+381670, and HD149162. This result is consistent with our finding of coronal activity in these systems. The correlation between chromospheric and coronal activity will be studied below in detail.

[FIGURE] Fig. 4. Chromospheric index [FORMULA] as a function of orbital period.
[FIGURE] Fig. 5. a X-ray luminosity vs. projected rotational velocity for all sample stars with known [FORMULA]. b  X-ray luminosity vs. rotational velocity of the primary for all X-ray detections (open squares indicate LP systems, filled squares SP systems) and the SP non-detections (arrows). HD 149162 is not included in this figure, because its secondary is itself a probably SP binary.

Obviously, the X-ray luminosity is not very strongly correlated with the orbital period. The fact, that all the highly X-ray luminous systems are evolved (cf. Fig. 3), indicates that the X-ray luminosity depends not only on the orbital (or rotational) period, but also on the stellar surface, or radius. Therefore, it may be more appropriate to compare the rotational velocity, which involves both period and radius, rather than the period, to the X-ray luminosity of stars of different luminosity classes. In Fig. 5a, the X-ray luminosity is plotted as a function of the projected rotational velocity for all stars with known [FORMULA] values. Unfortunately, [FORMULA] values have been measured only for 18 sample stars (Spite et al. 1994, Henry et al. 1995), of which 7 are X-ray detections. Evidently, all the non-detections have rotational velocities [FORMULA] below 8 km s-1, while the detections typically have higher [FORMULA] values with [FORMULA]. However, the data are too sparse to allow firm conclusions about the correlation between [FORMULA] and [FORMULA].

In Fig. 5b, the X-ray luminosity is shown as a function of the rotational velocity [FORMULA] of the primary for the X-ray detections and the SP non-detections. The rotational velocities, listed in Table 3, are derived from the relation [FORMULA], with the radius of the primary being determined from the evolutionary models of Van den Berg and Bell (1985). The [FORMULA] values are, for the most part, lower than the corresponding [FORMULA] values, as would be expected due to the projection effect. The rotational velocity is a better intrinsic rotational parameter than [FORMULA], because it does not suffer from the projection effect and, consequently, it covers a more extended parameter range compared to the rather narrow range of [FORMULA] values. However, one has to keep in mind that the primary might not be in any case the active component and its radius is not known very accurately. These uncertainties lead to an additional scatter in the activity-rotation relation. Nevertheless, for the X-ray detections, the X-ray luminosity obviously correlates better with the rotational velocity than with the orbital period. This is shown quantitatively by calculating the correlation probability of these quantities for the X-ray detections (except HD149162): The linear correlation probability (cf. Bevington 1969) between [FORMULA] and [FORMULA] ([FORMULA]) amounts to 0.9999 (0.9935). It is interesting to note that the RS CVn systems seem to show a similar correlation between rotation and activity as the Pop2 binaries. Drake et al. (1989) found that, for the RS CVn systems, the 6 cm radio luminosity, which is correlated significantly with the X-ray luminosity and is thus a good measure of activity, does not show any significant correlation with either orbital or rotational period; instead, a fair correlation with the rotational velocity of the active component was found.


Table 3. Derived rotational velocities [FORMULA] for all the SP and LP X-ray detections (except HD 149162) and the SP non-detections with known distances. If available, the measured vsini values (Spite et al. 1994, Henry et al. 1995) are given for comparison.

The SP binaries and the evolved LP system HD 6286 have moderately high rotational velocities [FORMULA] km s-1. The detected LP dwarf systems have low rotational velocities around [FORMULA] km s-1, which however might be sufficient to maintain activity levels of [FORMULA] erg s-1. Fig. 5b further shows that the SP non-detections have rotational velocities [FORMULA] km s-1, from which we would expect X-ray luminosities [FORMULA] erg s-1 according to the rotation-activity relation for optically selected (i.e., mostly non-saturated) stars (Pallavicini et al. 1981). Clearly, some of the non-detected SP systems have upper limits greater than this, indicating a short exposure and/or high background as the explanation for why they were not detected. But a few non-detected SP systems have upper limits which indicate X-ray luminosities [FORMULA] erg s-1, which would be inconsistent with the [FORMULA] - [FORMULA] relation. Longer pointed observations are required to decide whether these systems actually deviate from the rotation-activity relation, or whether the associated parameters are too uncertain.

6.2. X-ray activity vs. metallicity

In Fig. 6, we plot the X-ray luminosity versus the metallicity. Twelve out of the 13 X-ray detections have intermediate metallicities with [FORMULA], while there is only one X-ray detection (HD 89499) amongst the extreme Pop II stars. Thus, the detection rate is much lower for the extreme metal-poor stars than for the intermediate Pop II. Just to illustrate, if the line between the two metallicity groups would be drawn at [FORMULA], then the detection rate would be [FORMULA] and [FORMULA] for the intermediate and the extreme Pop II systems, respectively. One may ask whether the different detection rates are actually caused by observational and/or intrinsic biases: First, systematically shorter RASS exposures times for the extreme Pop II subsample, as would arise from a concentration towards the ecliptic plane, are not present; both metallicity groups have about the same mean exposure time. Second, the extreme Pop II systems are located on average at larger distances than the intermediate Pop II. Consequently, the extreme metal-poor sample has on average higher luminosity upper limits than the intermediate Pop II, as is evident from Fig. 6. Third, the extreme metal-poor stars might have systematically longer rotation periods, and hence lower levels of X-ray activity. To check this suspicion, we show the correlation between metallicity and orbital period in Fig. 7. Obviously, the intermediate Pop II systems cover a more extended range of periods than the extreme Pop II. But, the fraction of SP systems is only moderately larger for the intermediate Pop II than for the extreme Pop II stars shown in Fig. 6 and 7 ([FORMULA] compared to [FORMULA]). Thus, there is no obvious metallicity-period correlation which would explain the higher detection rate of the intermediate Pop II stars.

[FIGURE] Fig. 6. X-ray luminosity plotted against metallicity for the X-ray detections (filled squares) and upper limits (arrows). Orbital periods between 1-20 (20-100, [FORMULA]) d are marked by large (intermediate, small) symbols. HD 149162 with [FORMULA] d has probably a SP secondary.
[FIGURE] Fig. 7. Correlation between metallicity and orbital period for those Pop II stars with known distances (i.e., the same stars as in Fig. 6). The X-ray detections are marked by filled squares, the upper limits by open squares. Again, HD 149162 with [FORMULA] d has probably a SP secondary.

Since our upper limits are rather conservative, we conclude from Fig. 6 that the majority of the extreme Pop II stars have X-ray luminosities below [FORMULA] erg s-1, although HD 89499 has an extremely high [FORMULA]. In contrast, the X-ray luminosities of the intermediate systems appearently are distributed more homogeneously over 4 orders of magnitude. Therefore, intermediate and extreme Pop II stars may have different X-ray luminosity functions. As there is only one X-ray detection amongst the extreme Pop II systems, their XLDF cannot be computed at the present stage. Thus, firm conclusions can be drawn only after further detections of extreme metal-poor systems.

Fig. 8 shows the hardness ratio as a function of metallicity. Very low hardness ratios of [FORMULA] indicate coronae having only a cool temperature component with [FORMULA] K or a WD. Intermediate values of the hardness ratio are representative of coronae which have a hot temperature component with [FORMULA] K, i.e. the hardness ratio increases with temperature and with the emission measure ratio between the high and low temperature components. Very high hardness ratios of [FORMULA] will be obtained only for X-ray spectra with very high temperatures and high absorption. Fig. 8 shows that the intermediate Pop II stars typically have slightly negative hardness ratios centered around [FORMULA], indicating coronal temperatures around [FORMULA] K and low interstellar absorption. In contrast, the extreme metal-poor system HD 89499 has a distinctly higher hardness ratio of [FORMULA], indicating correspondingly high coronal temperatures and high interstellar absorption. Indeed, ASCA SIS and ROSAT PSPC spectra have shown HD 89499 to have a coronal temperature of [FORMULA] million K and [FORMULA] (Fleming and Tagliaferri 1996). The high coronal temperature of HD 89499 is consistent with our theoretical understanding that extreme metal-poor coronae can not release their energy by line emission, but only by thermal bremsstrahlung, which is efficient above [FORMULA] million K. HD 6286, being on the boundary between intermediate and extreme Pop II, is the only other star with a similarly high hardness ratio, [FORMULA], again indicating a high temperature and [FORMULA] value (therefore, its distance is probably somewhat larger than [FORMULA] pc as quoted in Table 1). Again, it requires the detection of more extreme metal-poor stars to draw conclusions about a correlation between metallicty and coronal temperature.

[FIGURE] Fig. 8. Dependence of the hardness ratio on the metallicity.

In Fig. 9, the dependence of the chromospheric indices [FORMULA] (cf. Sect. 2) on the metallicity is shown. Clearly, the Pop II binaries with metallicities larger than about [FORMULA] exhibit on average significantly higher chromospheric activity levels than the systems with lower metallicities. Hence, chromospheric activity shows the same dependence on metallicity as coronal activity. Thus, for the extreme Pop II binaries, the chromospheric and coronal activity appearently is reduced compared to the intermediate metallicity systems.

[FIGURE] Fig. 9. Chromospheric index shown as a function of metallicity.

6.3. X-ray activity vs. atmospheric structure

In this section, we investigate the dependence of the X-ray activity on other atmospheric parameters. First, we correlate the X-ray luminosity with the hardness ratio as an indicator of the coronal temperature (cf. Sect. 6.2). Second, we study the relation between the coronal and chromospheric activity levels. However, a possible correlation between the coronal activity measure [FORMULA] and the chromospheric index [FORMULA] may be obscured by a large scatter for the following reasons: (i) [FORMULA] is an integral property while [FORMULA] is normalized to the stellar surface flux. (ii) [FORMULA] is only a relative activity index and not the absolute Ca II K line flux. (iii) The X-ray and optical data are not taken simultaneously but are spread over an interval of a few years, during which time the activity levels may have changed.

In Fig. 10, the X-ray luminosity is plotted as a function of the hardness ratio for the 13 detected Pop II systems. There appears to be only a weak correlation between [FORMULA] and HR. Actually, one would expect a correlation between [FORMULA] (or [FORMULA]) and T, as it was observed in several previous studies. For example, for a sample of 130 late-type stars detected by the EINSTEIN IPC, Schmitt et al. (1990) found the X-ray luminosity to be correlated with the temperature obtained in a single-temperature fit according to [FORMULA]. Furthermore, for a sample of late-type stars covering a large range of activity levels, Ottmann (1993) derived a relation between more physical quantities, the stellar surface flux and the maximum loop temperature, which was [FORMULA]. However, the hardness ratio is not linearly correlated with the coronal temperature, because it depends on both the emission measure and the temperature in the case of two-temperature fits, and it is also affected by interstellar absorption.

[FIGURE] Fig. 10. X-ray luminosity vs. hardness ratio for the 14 X-ray detections.

Fig. 11 shows the dependence of the X-ray luminosity on the chromospheric index for all the X-ray detections and upper limits for which both the [FORMULA] values and the distances are known. For the X-ray detections, the X-ray luminosity and the chromospheric index are correlated according to [FORMULA], although there is a large scatter due to the reasons outlined above. The systems which were not detected in X-rays and, thus, have low [FORMULA] values, also have low [FORMULA] values. There is only one exception, BD+53080, which has quite a large [FORMULA] value and an X-ray luminosity less than [FORMULA] erg s-1. Again, this discrepancy may arise from the facts that the [FORMULA] value does not represent the absolute chromospheric flux, and that the optical and X-ray data are not taken simultaneously.

[FIGURE] Fig. 11. X-ray luminosity vs. chromospheric index for all the X-ray detections and upper limits for which both [FORMULA] values and distances are known.
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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998