2 RASS data and detection of late-type stars

2.1 The ROSAT all-sky survey (RASS)

During it's first half year of operations, the ROSAT observatory carried out the first all-sky survey with an imaging X-ray telescope between July 1990 and January 1991. Further survey observations were carried out in February 1991 (2 days) and August 1991 (10 days). The whole sky was scanned along great circles perpendicular to the direction to the Sun. Because of the Earth's motion around the Sun, the plane of these circles slowly rotated around an axis through the ecliptic poles, thus covering the whole sphere within 6 months. Each point of the sky was observed several times as the scan paths of 2 degrees width (i.e., the field of view of the PSPC detector) progressed along the ecliptic. Therefore, the data of any particular source consist of a number of "snapshots'' of up to 30 s duration, separated by the orbital period of the satellite ($\approx$ 90 min) and distributed over an interval of at least 2 days. Towards the ecliptic poles, the cumulative exposure time increases due to the larger number of scans covering a particular position. Depending on the ecliptic latitude (and down-time due to radiation belts of the Earth), the effective exposure time varies between $\sim\!100$ s and $\sim\!40\,000$ s (at the poles), with typical values of $\sim\!400$ s on the ecliptic. Given a typical energy-conversion factor for soft sources of $6\ 10^{-12}$ ergcts^-1 cm^-2 (cf. Sect. 2.4) the typical detection limit of RASS observations (i.e., $\approx$0.015 ctss^-1) amounts to $f_{\rm x}\approx 10^{-13}$ergcm^-2 s^-1. For a more detailed description of the RASS we refer to Voges (1992) and Belloni et al. (1994). Details of the ROSAT observatory in general can be found in Trümper (1983) and Trümper et al. (1991), the PSPC detector used during the RASS is described by Pfeffermann et al. (1986).

In February 1997 the remaining gaps left in the all sky survey were filled with a sequence of pointed, partially overlapping PSPC observations so that with the exception of a small region around the strong X-ray source Sco X-1 the whole sky has been imaged with the ROSAT PSPC. In the catalog presented in this paper we include sources detected in this "survey repair'' pointed observations; they are marked with an asterisk.

The source detection was performed by means of a maximum likelihood algorithm (Cruddace et al. 1988) in the course of the standard analysis software system (SASS; Voges et al. 1992). The significance of an X-ray source is expressed by the likelihood Li = $-\ln (1-P)$,where P is the probability of existence; e.g., a likelihood of Li = 7 corresponds to a source existence probability of 99.9%. The result of the SASS is a comprehensive list of several 10⁴ sources, each source described by the sky position in right ascension and declination, its source detection likelihood, count rate, hardness ratio, extent, and corresponding errors. The data for the brighter X-ray sources have recently been released as the ROSAT All-sky Survey Bright Source Catalogue (Voges et al. 1996b), which contains sources with Likelihood $\ge$ 15, count rate larger than 0.05 s^-1, and with at least 15 detected photons.

2.2 Selection of stars

We used the Bright Star Catalogue (BSC; Hoffleit & Warren 1991) as input sample for our search of X-ray bright late-type stars. In particular, we extracted all stars of spectral types A, F, G, and K and luminosity classes IV and V (including subtypes like IV-V, IVa, but not III-IV). Note that there are no M-type stars in this sample except for the MV star HR 1703, which is obviously a misclassified giant, according to its Hipparcos parallax. We also included those stars lacking an MK classification but with a suffix "d'' or "sg'', and the composite-spectrum stars that do not have one or both companions classified as a giant (these are treated in HSV98). Finally, we included stars of the above mentioned spectral types but without any indication of luminosity (no MK type, no suffix). This also holds for the many Ap-, Am-, Fp- and Fm-stars. Thus in total, our input sample consists of 3054 stars.

One has to keep in mind that because of the large spread in absolute magnitude of main-sequence stars, very different space volumes are covered by our magnitude-limited sample. While A-type stars are almost completely covered by the BSC up to a distance of $\approx\!50$ pc, K-types stars are only listed in the BSC if they are within a few pc from the Sun. This selection effect obviously introduces a strong bias to any derived X-ray luminosity function.

About 1 percent of the sky was not included in the original RASS, and we list in Table 1 those stars with less than 50 s exposure time. Note that the stars HR 813 ($\mu$ Cet), HR 997, HR 5234, HR 5325, and HR 5568 were detected in the pointed survey repair observations and are included in Table 2.

  

Table 1: Stars of the input sample with less than 50 s exposure time or which are located in the region of the X-ray bright Vela supernova remnant. Stars marked with * in the last column were detected in the survey repair

2.3 Matches between input stars and RASS-sources

The procedure whereby the positions of RASS sources were matched with the stars of our input sample has been extensively described in HSV98. Here, we only report that we have accepted sources with a likelihood greater than 7 within 90 arcsec distance from the input stars. The choice of this cut-off radius is justified by means of a Monte Carlo simulation of 10000 random positions, i.e., approximately the same number as our BSC input catalog; see HSV98 for details. That means, at 90 arcseconds offset between optical and X-ray position the probability that the X-ray source can be attributed to the star (and not to a background object) is 50%. This differential probability increases very rapidly for smaller values of positional offset (see Fig. 2 in HSV98).

For about 400 X-ray sources extracted in this way and not included in the Bright Source Catalogue (Voges et al. 1996b), we checked the X-ray images by eye for reality. Specifically, we rejected photon distributions that are significantly contaminated by nearby strong sources or that are obviously extended. In questionable cases, we ran the standard source detection algorithm of EXSAS on the source images in different passbands and decided on the basis of the results which sources to retain in our final catalog.

Confining now attention to the 3054 BSC positions identified with late-type main-sequence stars and subgiant stars, we detected X-ray emission from 980 stars, i.e., the average detection rate is 32%. Since the total search area around these 3054 stars is $3054\cdot \pi \cdot (1.5\hbox{$^\prime$})^2 = 6.00\ifmmode\hbox{\rlap{$\sqcap$}... ...$\sqcap$}$\sqcup$} \parfillskip=0pt\finalhyphendemerits=0\endgraf}\fi^{\circ} =$0.0145% of the sphere, and the total number of RASS sources amounts to $\sim$150000, we would expect 21.8 chance coincidences of late-type main-sequence stars or subgiants with background (or foreground) X-ray sources (i.e., 2.2% of our detected sources).

2.4 Determination of X-ray fluxes and luminosities

The procedure of determining X-ray fluxes has also been described in HSV98. In this paper, we followed the same procedure, except using a slightly different formula for the calculation of individual energy-conversion factors

$${\rm ECF} = (5.30 \cdot hr + 8.31)\;\;\; 10^{-12}~{\rm erg\,cm}^{-2}{\rm cts}^{-1}$$ (1)

which was derived by Schmitt et al. (1995) from an X-ray study of a complete sample of the nearby main-sequence stars; here hr denotes the hardness ratio defined through

$$hr = \frac{{\rm H - S}}{{\rm H + S}},$$ (2)

where H and S denote the source counts in the hard (0.5-2.0 keV) and soft (0.1-0.4 keV) passbands of ROSAT. The hardness ratio is an "X-ray colour'' that is influenced by both the plasma temperature and the hydrogen column density.

Since the SASS source detection was separately performed in both passbands, and since most of our X-ray sources were detected in both bands, the hardness ratios can be estimated for many stars, although in some cases with quite substantial errors. In a few cases, when the sources were not detected in either the soft or the hard passband, we set hr = +1.0 or -1.0 by definition, respectively. We refrain from estimating individual errors for $f_{\rm x}$since the error in ECF is very difficult to quantify. In general, we estimate this error to be within a factor of two for the weaker sources and less for the brighter sources. The X-ray luminosities are calculated using the recently available Hipparcos parallaxes. We only accepted those parallaxes which exceed their corresponding error by at least a factor of 3. Fortunately, this is the case for almost all of the input stars. Where this criterion is not fulfilled, the distance and X-ray luminosity column entries in Table 2 are left open. The X-ray luminosities are then calculated by the relation

$$L_{\rm x} = 4 \pi d^2 \times f_{\rm x} ,$$ (3)

where d is the distance to the star.