For our investigation originally six "study areas'' north of
, designated I to VI, have been selected. Each area has
a size of about 144 square degrees. One of the areas chosen is located close
to the North Ecliptic pole (NEP), area V, a second one around the North
Galactic pole (NGP), area IV. The other four
areas are in regions of medium-to-high X-ray sensitivity
outside the galactic plane (
) at R.A.s allowing
year-round follow-up observations. The coordinates of the study areas are
given in Table 1 (click here).
Table 1: Coordinates (right ascension R.A.(2000.0) and declination
DEC(2000.0)) of the selected study areas. Areas IVac and Va are
subsections of areas IV and V, respectively (see
Sect. 2.1 (click here)). In the last column the total number of
RASS sources with a detection likelihood of 
is given for each study
area
As described in detail in PaperI, the individual RASS scan stripes covering
our study areas were
merged to produce a final data set. Then sources were identified by applying
standard maximum-likelihood search algorithms. For the source detection a
minimum detection likelihood L of 10 was adopted corresponding to
detections on a 
level, where 
with 1-P being the
probability of a spurious detection. This detection limit was reached for
count rates of 
ctss
in area V and 
ctss
in all other areas. The final data set of the six
study areas comprises 1629 X-ray sources for which positions, integrated
X-ray count rates CR in the 0.1 to 2.4 keV energy band, hardness ratios
HR1 and HR2, extension parameter EXT, and detection likelihoods are
available.
The hardness ratios are defined as
and
where [A], etc. are
the count rates in
the respective energy bands A = 0.11-0.41keV, B =
0.52-2.01keV, C = 0.52-0.90keV, and D = 0.91-2.01keV.
The extension parameter EXT gives a measure for the deviation of the source shape from a point source and can thus be used to identify extended sources like clusters of galaxies.
After the superposition of the scan stripes the total number of sources detected in the originally selected study areas was larger than anticipated and also larger than required for the statistical investigation. Moreover, the different sensitivity resulted in very different source numbers in the original study areas.
Figure 1: Number of the detected sources as a function of
the count rate for the combined study areas I, II, III, and VI
(upper panel) and
for areas IV and V (two lower panels). Incompleteness starts below
0.01 ctss
in area V and below 0.03 ctss
in the other areas
Figure 2: Signal-to-noise ratio (S/N) of the X-ray fluxes in the
six study areas I to VI as a function of the X-ray count rates. The broken
vertical line indicates the flux limits adopted for our complete sample. Note
the different behaviour of the NEP field V, where typical integration times
were higher and less uniform
To reduce the sample to a manageable but still statistically meaningful size,
we removed all sources below a minimum count rate. These
minimum count rates were selected using histograms of 
(source number)
over 
. As can be seen in Fig. 1 (click here), the X-ray sample
becomes incomplete at count rates lower than about 0.01 ctss
in
area V, and about 0.03 ctss
in the other areas. For the count-rate
limits adopted the S/N ratio of the X-ray fluxes is equal to or larger
than about 3 (see Fig. 2 (click here)).
In addition, we decreased the sample further by restricting the condition of
complete identification in the NGP and NEP areas to smaller
sub-areas. They are designated IVac and Va in Table 1 (click here). Area IVac
contains the western half of area IV with count
rates 
0.03 ctss
. During the course of the
project, area Va which consists of the
sources in the western quarter of area V with count rates 
0.01
ctss
was extended in R.A. towards the east until it finally
resulted in a 
field size. For areas I, II, III and VI we
adopted count rate limits of 
0.03 ctss
for the entire
areas. The so-defined final subsample contains 674
sources and the number of sources in each field is about equal.
Table 2 (click here) summarizes basic informations about this
subsample.
Table 2: Statistics of the
count-rate and area limited complete subsample. The size of the
areas is given as R.A.
DEC. 
is the median
integration time in the respective study area. "CR limit'' denotes the
adopted count-rate limit. The median values of the column density of neutral
hydrogen, 
, for the individual areas are from Dickey &
Lockman (1990).
SIM/NED: Identifications based exclusively on cross-correlation with
SIMBAD and NED data bases, respectively, i.e. for these sources no new
observations were obtained
We note that the median column density of neutral hydrogen, 
,
(taken from Dickey & Lockman (1990)
varies by a factor of about 7
between the different study areas (see Table 2 (click here)) with
a scatter of about a factor of 
within each area. In area I the
scatter is larger with 
ranging between 6 and
1910
cm
.
The median integration time in area Va is about 5 to 7 times longer than in
the other areas resulting in a 2-3 times higher signal-to-noise ratio for the
same count-rate level.
While a complete identification was carried out only for the subsample defined by Table 2 (click here), our final catalog presented in Paper III will also contain identifications outside these areas but inside the areas defined by Table 1 (click here).
For the optical identification it is helpful to obtain an estimate for
the visual brightness of the faintest expected counterpart for the
various object classes in the studied sample.
The results of the EMSS (Stocke et al. 1991) have shown that
different classes of X-ray emitters represent different rather narrow ranges
in the X-ray-to-optical flux ratios 
with 
and 
being the X-ray and visual fluxes, respectively. The knowledge of
thus can help
in the identification process by allowing to exclude or include objects of a
certain visual brightness as possible counterparts. In order to estimate the
optical brightness of the faintest expected counterparts we therefore
made use of the flux ratios 
from the EMSS.
The visual flux, 
, was calculated with the relation given by
Stocke et al. (1991). Due to the energy bands of the detectors,
RASS sources could have X-ray-to-optical flux ratios differing
from those derived with EINSTEIN. For AGN an estimate for the difference
between EMSS 
values and the expected corresponding
ROSAT ratios can be obtained by assuming a power law energy distribution.
For a photon index of 
as adopted below the difference 
is on the order of 
; for 
it is 
. For coronal emitters Raymond-Smith models (Raymond &
Smith 1977) with temperatures of 0.2keV and 1keV (see
below) lead to 
and -0.1, respectively. This leads to
differences of the visual magnitude limits of
. For the estimates derived in
the following we neglect effects due to the different
energy bands of the RASS and of the EMSS.
The X-ray flux limits for our subsample are given by the applied count rate
limits which have to be converted to fluxes. To obtain the conversion factor
for coronal emitters we assumed a bremsstrahlung X-ray spectrum of a
thermal plasma with metal absorption lines. It can be described by a
Raymond-Smith model.
Because the stellar sources are mostly nearby for our purpose
the foreground absorption due to neutral hydrogen can be assumed to be
similar in all study areas. Typical temperatures in stellar coronae are
between 810
to 210
K. Assuming a Raymond-Smith model then
leads to an energy conversion factor, ECF, between count rate and
X-ray flux of 
ctscm
erg
(cf. also Schmitt et al. 1995)
for the ECF of
low-mass stars). With this conversion factor the X-ray flux limits are
about 
ergcm
and
1.8
ergcm
in
area Va and in the other areas, respectively.
X-ray flux limits for extragalactic sources depend on the shape of the
spectrum
and, in particular, on the column density of neutral hydrogen, 
,
due to the dependence of the conversion factor on these quantities.
For each study area the median value for 
was taken from Dickey
& Lockman (1990).
For AGN the flux limits given in Table 3 (click here)
were obtained for a power law spectrum 
with 
corresponding to a photon index 
. For
clusters of galaxies a thermal bremsstrahlung spectrum with 
K was
assumed. Likewise, for normal galaxies thermal bremsstrahlung with
K was assumed corresponding to a thermal energy of
1keV as derived by Kim et al. (1992) for ellipticals
(cf. also Read et al. 1996 and Peace & Sansom
1996). For spirals Kim et al. found 
3keV.
We give the flux limits for ellipticals
which generally have higher X-ray luminosities than spirals (see also Sect.
4.3 (click here)).
The highest ratio 
for coronal emitters was found for M
type stars (Stocke et al. 1991). With
to -0.5 from the EMSS
our flux limits correspond to 
for area Va and 
for the other areas, respectively.
Assuming
the upper limits of
the EMSS 
values for AGN
the expected visual magnitude limits in the subsample are:
in area I,
in areas II, III, and VI,
in area IVac,
in area Va,
with a scatter on the order of 0.5
due to the variations of 
within the individual study areas.
AGN with V as faint as 20
to 21
could be identified
despite the low exposure levels in the continuum by means of their
emission lines. A problem are the X-ray bright but optically faint BL Lac
objects. Due to their 
values they can be as faint as
21
in area Va. With the 2.15m telescope in Cananea, which we used for
the optical identification, it is not possible to
obtain spectra with sufficient S/N to identify reliably the featureless
spectrum of a BL Lac fainter than about 19th magnitude (see Sect.
3 (click here)). For the identification
of these faint BL Lac objects we therefore use additionally their
characteristic intrinsic optical variability
(see below).
Table 3: Estimated X-ray flux limits in the 0.1 to 2.4keV energy band
(in 
ergs
cm
) for coronal
emitters, 
, AGN, 
, clusters of
galaxies, 
, and normal galaxies, 
,
in the individual
study areas. Count rates CR are given in units of ctss
.
The fluxes depend on the intrinsic spectral energy distribution
and on 
(given in 
cm
).
For AGN a power law with a photon index of 
was used. For normal galaxies (ellipticals) and
clusters of galaxies we assumed a spectrum of thermal bremsstrahlung with
temperatures of 
and 8, respectively
The flux limits given in Table 3 (click here) for clusters of galaxies
correspond to visual magnitudes of the brightest galaxies in the clusters of
about 
in area Va, and 
in all other areas. Assuming a Schechter cluster luminosity function
(Schechter
1976) the limiting magnitude of 23
in the
direct imaging mode (see below) thus allows the detection of distant clusters
of galaxies contained in our flux-limited subsample.
Normal elliptical galaxies are expected to be brighter than about
in area Va, and brighter than about 17
in the other
areas.
These estimates show that with the exception of faint BL Lacs the different classes of X-ray emitters are within the range of sensitivity of the instrumentation we used for the optical identification and which is described in the following section.