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

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4. X-ray detections and upper limits

The results of our source detection analysis for the total PSPC bandpass are given in Table 2. For each star, the Maximum Likelihood value for X-ray source existence and the difference between X-ray and optical position are listed. For the X-ray detections, the total PSPC countrate and its [FORMULA] error, the hardness ratio and its [FORMULA] error, and the derived X-ray luminosity based upon the distance given in Table 1 are provided. For the non-detected stars, the upper limits (corresponding to [FORMULA] confidence) on countrate and X-ray luminosity are indicated. At the chosen detection threshold ([FORMULA]), there are 15 X-ray sources detected in the total PSPC band (cf. Table 2). In addition, 1 source was detected only in the soft band, and 2 sources were detected only in the hard band.


Table 2. The Pop II Binaries in the RASS (total PSPC bandpass).


Table 2. (continued)

Next, we have to estimate the maximum positional offset between the optical and X-ray positions to be used for identification. The cumulative distribution [FORMULA] of the radial positional offsets [FORMULA] may be approximated by a Gaussian distribution, [FORMULA], with [FORMULA] denoting the characteristic radial positional error. The X-ray position as determined by the ML algorithm has a radial positional error of [FORMULA]. Out of the 18 X-ray detections, 12 detections have an optical to X-ray positional offset [FORMULA], despite the fact that the optical position is not corrected for proper motion. As the mean density of RASS sources amounts to about [FORMULA] arcsec-2, the number of background sources within a circle of [FORMULA] radius is only [FORMULA]. Thus, these 12 X-ray detections (containing the soft band detection) are true identifications. Furthermore, for HD 89499, which has a large proper motion, the positional offset is reduced to [FORMULA] if the correction for proper motion is applied. This gives us 13 true identifications. The remaining two detections in the total bandpass, G 103-50 and BD +13 308, are probably not true identifications, because their positional offsets (cf. Table 2) are too large to be explained either by proper motion or statistical fluctuations of the X-ray positional error. Instead, the X-ray detection for BD +13 308 is close to the position of MRK 1146. Similarly, the two X-ray detections in the hard bandpass only, CD -37 14010 and HD 23439B, are [FORMULA] and [FORMULA], respectively, from their optical positions, so we discount them as identifications. Finally, HD 20507 is a marginal case: Its proper motion is not sufficiently high to explain the large positional offset ([FORMULA]), but the X-ray source properties (i.e., the X-ray luminosity and the hardness ratio) are consistent with what would be expected for a long-period binary. We choose to be conservative and not add this star to the sample of true identifications. In summary, we detect 13 out of 86 Pop II binaries in the RASS, which corresponds to a detection rate of [FORMULA]. HD 195987 is detected only in the soft band and its X-ray properties as given in Table 2 refer to this bandpass only.

Consequently, 73 systems in our Pop II sample are not detected in X-rays at the chosen detection threshold. Because the detection algorithm allows the X-ray position to vary, it will find an X-ray peak in any case, and the ML value will always be [FORMULA] (note, that a value of [FORMULA], as quoted in Table 2, is accurate only to the first digit). However, for most of the non-detections the X-ray peak is actually too far away from the optical position to be associated with the Pop II star.

The countrates are obtained by dividing the number of counts as determined by the ML algorithm by the exposure time corrected downward for telesope vignetting. Since the off-axis vignetting depends strongly on photon energy, different correction factors are applied to the exposure time of the soft, hard, and total bandpasses. The hardness ratios are defined as [FORMULA], with H and S being the countrates in the hard and soft bandpasses. For all stars in our sample, the number of counts obtained in the RASS is not sufficient to determine the spectral shape of the X-ray flux. Therefore, X-ray flux is obtained by multiplying the countrate by a conversion factor which assumes a spectral distribution. Clearly, a conversion factor which depends on hardness ratio would be best. For coronal sources observed with the ROSAT /PSPC, the HR-dependent conversion factor was determined by Fleming et al. (1995) as [FORMULA] erg cm-2 ct-1, where interstellar absorption is neglected. This conversion factor, along with the distances given in Table 1, are used to derive the luminosities given in Table 2. For non-detections, we use the same conversion factor evaluated at the mean hardness ratio of the detections, [FORMULA]. Due to differences in the exposure time and the X-ray background over the sky, the limiting detectable X-ray flux varies strongly at the positions of the individual Pop II stars. As shown in Fig. 1, the limiting PSPC countrate ranges from [FORMULA] ct s-1 for exposures [FORMULA] up to [FORMULA] ct s-1 for exposures [FORMULA]. This corresponds to a limiting energy flux of about [FORMULA] erg cm-2 s-1. Depending on stellar distance, we obtain limiting X-ray luminosities between [FORMULA] erg s-1.

[FIGURE] Fig. 1. Upper limits to the PSPC countrate ([FORMULA] confidence) as a function of exposure time for undetected Pop II binaries.
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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998