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Astron. Astrophys. 353, 25-40 (2000)

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2. The ROSAT surveys used in the analysis

We have used soft X-ray sources identified with AGNs with redshift information from a combination of ROSAT surveys in various depths/areas from a number of already published and unpublished sources. In order to avoid the possible bias from the large-scale overdensity and the distortion of the redshift-distance relation based on bulk-flows in the nearby universe (e.g. Tully & Shaya 1984), we have excluded objects within [FORMULA] from the analysis.

The surveys we have used are summarized in Table 1. Two optical followup programs from the ROSAT All-Sky Survey (RASS) (Voges 1994), a serendipitous survey of the ROSAT PSPC pointed observations (RIXOS), and a number of deep pointings specifically aimed for deep surveys. Here we describe the AGN sample from each survey.


Table 1. ROSAT surveys used in the analysis.
a) Abbreviations - RBS: The ROSAT Bright Survey, SA-N: The Selected Area-North, RIXOS: The ROSAT International X-ray Optical Survey, NEP: The North Ecliptic Pole UKD: The UK Deep Survey, RDS-Marano: The ROSAT Deep Survey - Marano field, RDS-LH: The ROSAT Deep Survey - Lockman Hole. See text for references.
b) Excluding AGNs with [FORMULA].

All surveys, except for a part of the the Lockman Hole, are based on the ROSAT PSPC count rates in the pulse-invariant (PI) channel range corresponding to 0.5-2 keV. For most sources in the Lockman Hole, we have used the deeper HRI count rates (see below) with no spectral resolution and sensitive to the 0.1-2 keV.

In order to convert the countrate to flux, we have to assume a spectrum. Hasinger et al. (1993) obtained the value of [FORMULA] for the average spectral photon index in the Lockman Hole. Other works (Romero-Colenero et al. 1996; Almaini et al. 1996) also found similar spectral index for AGNs, but a harder index [FORMULA] for the "NELGs". The same class as a part of the population they have classified as NELGs may fall into our sample. In any case, the ROSAT countrate to the unabsorbed 0.5-2 keV flux conversion has been made assuming a power-law with a photon index of [FORMULA] and corrected for the Galactic absorption. In effect, the Galactic column density changes the response curves for the flux-to-countrate conversion. However, the extragalactic surveys are mainly concentrated on the part of the sky where the Galactic absorption is low. Typical values are [FORMULA] [FORMULA] for the deep surveys and a maximum of [FORMULA] [FORMULA] for a small portion of the sky covered by the RBS. Within this range, the conversion between the [FORMULA] (here and hereafter, [FORMULA] represents the 0.5-2 keV flux and [FORMULA] is the same quantity measured in units of [FORMULA]) the ROSAT PSPC countrate (in the corresponding channel range) only weakly dependent on the spectral shape and varies by about [FORMULA]% for spectral indices [FORMULA]. We discuss the conversion for the HRI case in Sect. 2.7.

For the computation of the SXLF, it is important to define the available survey area as a function of limiting flux. In case there is incompleteness in the spectroscopic identifications, we have made the usual assumption that the redshift/classification distribution of these unidentified sources is the same as the identified sources at similar fluxes. This can be attained by defining the `effective' survey area as the geometrical survey area multiplied by the completeness of the identifications. This assumption is not correct when the source is unidentified due to non-random causes, e.g., no prominent emission lines in the observed spectrum. However, given the high completeness of the samples used in our analysis, this does not affect the results significantly, except for the faintest end of RDS-LH. We discuss the effects of the incompleteness at this faint end in Sect. 3.5.

Below we summarize our sample selection and completeness for each survey.

2.1. The ROSAT Bright Survey (RBS)

The RBS program aims for a complete identification of the [FORMULA] 2000 brightest sources in the ROSAT All-Sky Survey (RASS) for [FORMULA] (Fischer et al. 1998; Schwope et al. in preparation) measured in the entire ROSAT band (0.1-2.4 keV). For our purposes, we have extracted a subset selected by the ROSAT Hard band (0.5-2 keV) countrate of [FORMULA] [FORMULA], which makes a complete hard countrate-limited sample. Five sources in this subsample have further been identified as AGNs since M99a and included in the analysis. This subsample now has been completely identified.

Since the absorption in our galaxy varies from place to place, the same countrate limit corresponds to different 0.5-2 keV flux limits based on different galactic [FORMULA] values. The [FORMULA] value range from [FORMULA] [FORMULA].

2.2. The RASS selected-area survey - North

This survey uses several high galactic latitude areas of RASS (a total of [FORMULA]) for optical identification of the sources down to about an order of magnitude fainter than the RBS. The fields selected for the survey have the Galactic column ranging [FORMULA] [FORMULA]. Details of the survey have been described in Zickgraf et al. (1997) and the catalog of source identifications has been published by Appenzeller et al. (1998). We have further selected our sample such that each field has a complete ROSAT hard-band (0.5-2 [keV]) countrate-limited sample with complete identifications ([FORMULA] 0.01-0.05 [FORMULA]).

2.3. The RIXOS survey

The ROSAT International X-ray Optical Survey (RIXOS), Mason et al. (1999) (see also Page et al. 1996) is a serendipitous survey of [FORMULA] PSPC fields covering 15 deg2 of the sky. The flux limit of the deepest field is [FORMULA], while the actual completeness limit varies from field to field. The identification is [FORMULA] complete, thus the effect of the identification incompleteness is negligible considering statistical errors.

2.4. The North ecliptic pole (NEP) survey

The data are from Bower et al. (1996), which gave a catalog of 20 sources in the [FORMULA] radius region with [FORMULA]. One object, RX J1802.1+6629 did not have a redshift entry in Table 2 of Bower et al., but in the text, they argued that the most probable interpretation of this object was a weak-lined QSO at [FORMULA]. Thus we have assigned a redshift of 1.0 to this source. There is one unidentified source, making the identificaton of the sample 95% complete. Thus we have set the effective survey area of the NEP survey as 95% of the geometrical area.


Table 2. Best-fit PLE and PDE Parameters.
a) Units - A: [[FORMULA]], [FORMULA]: [[FORMULA]], [FORMULA]: [FORMULA] in 0.5-2 keV. Parameter errors correspond to the 90% confidence level (see Sect. 3.3).

2.5. The UK deep survey

Based on a 115 [ks] of ROSAT PSPC observation, McHardy et al. (1998) published a list of sources and identification of X-ray sources down to [FORMULA]. A significant fraction of their identifications are "NELGs" (Narrow Emission-Line Galaxies) and the fraction increases towards fainter fluxes. As mentioned in Sect. 1, a part of these NELGs are likely to be misidentifications. The identifications of other NELGs might be correct, but those would have been classified as AGNs with the criteria of Schmidt et al. (1998).

To include the results of the UKD survey in our sample, we would like to include their NELGs in the latter category, but exclude those in the former category. We find that the redshift distribution of the AGN+NELG classes in the UKD survey is significantly different from the AGN+galaxy classes in the Lockman survey if we include all sources down to [FORMULA]. If we limit the sample to brighter sources ([FORMULA]), the redshift distributions are consistent with each other. Thus, in this work, we limit the samples from UKD and other deep PSPC surveys to [FORMULA], assuming that the misidentification problem would not affect the analysis significantly above this limit.

2.6. The ROSAT deep survey - Marano field

For the same reason as the UKD case, we have also used the same flux cutoff [FORMULA] for the survey in the 15´- radius region on the Marano field (Zamorani et al. 1999), based on a deep PSPC exposure. Source fluxes of their catalog have been updated since the version used by M99a. The identifications are 100% complete for the 14 sources in [FORMULA] and 4 of the 27 sources remain unidentified or ambiguous (85% complete) in [FORMULA]. As before, we have reduced the survey area by 15% in this flux range to define the effective survey area used in the SXLF calculations.

2.7. The ROSAT deep survey - Lockman hole

There are 200 ks of PSPC and 1 Msec of HRI observations on this field (Hasinger et al. 1998). The source list and identifications for the brightest 50 sources ([FORMULA]) have been published (Schmidt et al. 1998). In this work, we have included further unpublished identifications down to [FORMULA]. These include identifications and redshifts based on spectra obtained in March 1998 with the Keck 10m telescope (Hasinger et al. 1999), which have also been included in M99a. Further four spectroscopic identifications obtained with the Keck telescope in February 1999 have been added to the sample since M99a.

The conversion between the HRI countrate and the 0.5-2 keV flux has been determined from the mean values of overlapping sources between the HRI and PSPC. The convsersion carries more uncertainties based on spectra, because the HRI has practically no spectral resolution and has some sensitivity down to 0.1 keV. With the HRI, the conversion factor varies by [FORMULA] for photon indices [FORMULA].

The basic strategy of defining the combined PSPC-HRI sample has been explained in Hasinger et al. (1999). In this paper, we have slightly modified the flux-limit and areas of the HRI sample in order to optimize our AGN sample in the presence of new identifications:

  • We use the deeper HRI-detected sample and HRI fluxes for the region 12.0 arcminutes from the HRI center (0.126 deg2). At the faintest fluxes ([FORMULA]), we have further limited the area to 10.1 arcminutes from the HRI center (0.090 deg2). This choice allows us to avoid the problem of incomplete source detection due to source confusion (see Fig. 2b of Hasinger et al. 1999). A total of 48 AGNs are present in this HRI sample.

  • Outside of the HRI region defined above, and within 18.4 arcminutes from the PSPC center, we have used the PSPC detected sources and PSPC fluxes. This corresponds to 0.175 deg2. For completeness, we have imposed a flux cutoff of [FORMULA] for PSPC off-axis angles smaller than 12´.5 and [FORMULA] for PSPC offaxis angles between 12.5 and 18.4 arcminutes respectively.

  • The sources in the HRI/PSPC combined sample have been 100% identified for [FORMULA]. Four of the 31 sources in [FORMULA] remain spectroscopically unidentified. Thus we have reduced the effective survey area by 13% for [FORMULA] to compensate for the identification incompleteness.

2.8. The combined sample

In our combined sample, there are 691 AGNs ranging from [FORMULA] to [FORMULA]. The effective survey area for the combined sample is plotted as a function of the limiting flux in Fig. 1, overlaid with the value of [FORMULA], showing that the combined sample indeed covers the above flux range continuously.

[FIGURE] Fig. 1. The survey area of the combined sample are plotted as a function of the limiting 0.5-2 keV flux limit (solid line). For reference, [FORMULA] for all the X-ray sources is overplotted (dashed line).

The redshift - luminosity scatter digrams of the sample objects are shown in Fig. 2 for the [FORMULA] universe. In any case, the luminosities have been calculated by:


where [FORMULA] is the luminosity distance as a function of redshift, which depends on the choice of cosmological parameters. This corresponds to the no K-correction case. Explanation on our K-correction policy is explained in Sect. 3.1. Hereafter, the symbol [FORMULA] refers to the quantity defined in Eq. (1) expressed in units of [FORMULA], unless otherwise noted.

[FIGURE] Fig. 2. The AGNs in the combined sample are plotted in the [FORMULA] for ([FORMULA]) =(1.0,0.0). Different symbols correspond to different surveys as labeled.

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Online publication: December 8, 1999