In earlier optical identification programs of X-ray sources very often possible candidates in the error box were observed until a "plausible'' counterpart was found. For the identification of the EMSS X-ray sources Stocke et al. 1991) e.g. used a plausibility criterion based on the X-ray-to-optical flux ratio.
In the present investigation we used a different strategy. As described above our instrumental setup allows multi-object spectroscopy and hence offers the possibility to observe all candidates in the error circle with just one or two exposures. The candidate selection is limited by the sensitivity of the instrument. The X-ray-to-optical flux ratio, together with other X-ray characteristics like hardness ratios and extension parameter, are used additionally only and as secondary criteria for the identification. In most cases an unambiguous identification of an object as optical counterpart of an X-ray source is possible with the CCD direct images and the spectra we observed.
Only in a few cases where known X-ray sources or obvious counterparts were
found in the SIMBAD or NED databases at distances smaller than 30
from the X-ray source position no new observations were carried out. Most of
these obvious objects are known QSOs, BL Lacs, or bright stars. If on the APM
blue finding charts other potential candidates were visible,
new observations were obtained.
Abell clusters were usually reobserved in order to check if e.g. AGN are
present in the error circle.
It has been repeatedly suggested, e.g. by Stocke et al. (1991),
to select different object classes (such as e.g. extragalactic sources) on the
basis of 
prior to spectroscopic identification.
In many cases this method leads to reliable
pre-identifications. However, we found numerous cases where this
quantity alone does not allow a decision whether an X-ray source is of
extragalactic or stellar origin. An example is shown in Fig. 5 (click here)
(RXJ0403.5+0837) for which an X-ray count
rate of 0.05 ctss
was measured. In the error circle a
star with 
and a fainter object with 
are present. Spectroscopy showed the star to be of type G to K and the
fainter object to be a QSO. Both would have a 
ratio suitable
for their class. An identification in such a case requires
additional higher resolution spectroscopic observations in order to check
if the star shows signs of coronal activity. In this special
case a further clue to the nature of the counterpart comes from the hardness
ratio HR1 which is +0.83 and therefore is more indicative for a QSO than
for a coronally active star. Note, however, that certain classes of coronally
active stars, like e.g. TTauri stars, also can exhibit rather hard X-ray
spectra.
Tracers for coronal activity in mid-to-late type stars are emission
components in the
CaII resonance lines and Balmer line emission. Both spectroscopic
characteristics are closely related to
coronal X-ray activity (e.g. Fleming et al. 1995)
and hence are an ideal tool for the identification
of coronally active sources as optical counterparts of X-ray sources.
Since LFOSC uses inexpensive glass optics and a "thick'' CCD,
observations
of the spectral region below 
4000Å were not possible.
Moreover, our spectral resolution would not have been sufficient to detect
emission components in the absorption troughs of CaII. For our
identification procedure we were therefore restricted to the use of Balmer
emission components.
Among the stellar counterparts the coronally active M dwarfs represent a
group of objects which can be reliably identified with our low resolution
spectra due to their molecular absorption bands and strong H
emission
lines. Occasionally also H
is visible in emission.
In K and G type stars very often the absorption strength of H
is
weaker than expected for the respective spectral type,
indicating that the photospheric absorption line is filled in by
chromospheric emission.
In several cases, however, with our low-resolution spectra we are not able to find direct spectroscopic indicators for chromospheric activitity. This is particularly the case for F to G type stars, among them also X-ray active binary systems e.g. of the RS CVn class. In most of these cases we observed all possible counterparts in the ROSAT error circle in order to search, e.g., for fainter AGN. Exceptions are a few very bright stars which do not allow to detect much fainter objects in their immediate vicinity. Occasionally, the presence of a distant cluster of galaxies in the field of a star near the X-ray position was indicated in the deep R image. If no other potential counterpart than the star was found and if the X-ray properties were in agreement with the average class characteristics the star was considered to be the X-ray emitter. In these cases the identification should be regarded as tentative requiring further higher resolution spectroscopic observations of the stellar object.
Although our sample contains
sources at high galactic latitude the presence of young objects cannot be
excluded as shown by Favata et al. (1993). In fact,
in the small sample of stellar counterparts observed at the 72 cm
telescope of the Landessternwarte (see Sect. 3 (click here)) we found
LiI
absorption characteristic for pre-main sequence
X-ray sources in several objects (Ziegler 1993).
These sources are listed in Table 4 (click here). A more detailed
study of stellar counterparts is under way in order to search for
binarity, for CaII emission, for LiI
absorption and
to determine the stellar rotational velocity (Metanomski et al.
1996).
Table 4: Stellar counterparts with strong LiI 
absorption
line. W(Li): equivalent width of LiI
in mÅ
The spectroscopic identification of most AGN (i.e. Seyfert galaxies, QSOs, and
LINER; for BL Lac objects see below), is based on the detection of emission
lines. With the low resolution grism LFOSC allows the detection of the
typical lines of H
[OIII ] and H
for redshifts below
about 0.3, the exact range of z depending on the position of the holes (see
Sect. 3 (click here)). At higher redshifts up to
H
[OIII ] are contained in the observed wavelength
range. At 
the emission feature of
MgII
becomes detectable at the blue edge of the spectra. At
even higher redshifts the emission features of e.g. MgII
and
CIII ]
are contained in the observed range.
At 
MgII
disappears from the observed wavelength range, however,
CIII ]
CIV
are visible.
At 
Ly
becomes detectable at the short wavelength limit.
Hence for a wide range of redshifts one
or more typical AGN emission feature is contained in the wavelength range of
the classification spectra obtained with the lower resolution grism of
LFOSC.
Most of the objects identified as AGN show broad emission lines of H
or H
. In a few cases H
is not in the observed wavelength range
and H
is too weak to measure the line width although H
and
[OIII ] are obviously present. In these cases the AGN type cannot be
established from our data.
The identification of individual non-AGN type galaxies as X-ray emitters is
sometimes ambiguous. Generally, normal galaxies are not
expected to be strong X-ray emitters. As discussed e.g. by Fabbiano et al.
(1992), Peace & Sansom (1996)
and Mackie et al. (1996) X-ray luminosities for spirals are
of the order of 
ergs
to less than
ergs
, elliptical and S0 galaxies are more luminous with
to
ergs
. Thus
the most luminous normal galaxies are at least one order of magnitude
less luminous than AGN and therefore only nearby galaxies or
the most luminous E and S0 type galaxies are expected to be detectable in
the X-ray band.
Most of the galaxies found at ROSAT positions seem to be members of groups or even of clusters of galaxies and hence it is not clear whether the X-ray emission is caused by an individual galaxy or whether extended gas in the group or cluster is the origin of the the X-ray emission. Occasionally the ROSAT extension parameter indicates extended emission suggesting that the X-ray emission is produced by the hot IGM gas distributed between the galaxies of a cluster or group. However, in normal galaxies the sources producing the X-ray emission are either spatially distributed individual sources or extended halos of hot gas. Therefore the extension parameter by itself is not a sufficient criterion for the identification of galaxy clusters. In cases of galaxies present at the position of extended X-ray emission we identified the X-ray source as individual galaxy only if the emission is well-centred on the candidate galaxy, if no neighbouring galaxies with similar redshifts are visible nearby, and if the X-ray luminosity is not too high for a normal individual galaxy.
Galaxy clusters were detected by the redshifts of its galaxy members or, when the galaxies were too faint, by the gradient of the number density of objects on the CCD direct image and/or by the distribution of the luminosities of its galaxy members, the cluster luminosity function.
The magnitude of the central galaxy of the faintest possible cluster
counterpart is about 
(see Sect.
2.2 (click here)).
Assuming a Schechter luminosity function (Schechter 1976) the tenth
brightest galaxy member should be less than a magnitude fainter, that is,
easily detectable with direct imaging. Assuming an absolute magnitude of the
brightest member of 
(Sarazin 1988)
and a Hubble constant of H = 75 km
the Abell radius of such a cluster is 
50
,
and even the faintest clusters are therefore resolvable as such.
The cluster luminosity function can be estimated
if the cluster radius is smaller than the size of our CCD image frame of
6
10
such that the
background source distribution can be roughly subtracted. This is the case for
an Abel radius smaller than about 3
. (A gradient in the number
distribution might be detected even up to an Abel radius of 6
).
X-ray emission of clusters is caused by hot virialized gas which traces the
cluster potential. Therefore the center of the cluster and with it the highest
projected number density should coincide with the center of the X-ray emission.
If this was the case we identified the X-ray source as a galaxy cluster.
When the direct image showed indications for the existence of a galaxy
cluster in the field of view, spectra of posible member galaxies were taken
even outside the ROSAT positional error circle. A detailed study
of these sources was carried out by Kneer (1996) and will be
discussed in a forthcoming paper.
A spectroscopic detection is possible if about the five brightest cluster
members are brighter than our magnitude limit for spectroscopy
(
= 19
) and if they are within our field of view.
Since the fifth brightest member of a cluster has typically an absolute
magnitude of about 
= 
(Sarazin 1988)
we can detect a cluster spectroscopically up to a distance of 2500Mpc,
i.e. a redshift of 0.63, when assuming a Hubble constant of
75km 
. This corresponds to an Abell radius of
2.7
.
Fainter, that is more distant clusters will have a smaller cluster
radius so that a gradient in the number distribution of objects inside
our CCD image frame of 6
10
will be visible and
they can be detected as described above.
When the Abel radius of a cluster becomes larger than our image frame
(
), that is, at a cluster red shift of about 0.57, the
gradient of the galaxy number distribution and therefore the exact center of
the galaxy cluster becomes more difficult to be determined.
There should however still be sufficiently many galaxies in the field of view
to detect the presence of a cluster spectroscopically up to an Abel radius
of (
), corresponding to a redshift of 0.17. All closer
clusters should be very well known and can be identified with the help of
literature search using the SIMBAD or NED data base.
A few of the observed galaxies could be
cooling flow galaxies as defined by Stocke et al. (1991).
Some of them are obviously members of clusters.
They show narrow emission of H
, often also [SII ], but no
strong [OIII ].
[OII ] is usually stronger than [OIII ] in this class of objects.
Because candidates are normally at small redshifts the emission lines of
[OII ] are either not in the observed wavelength region or
often not discernible due to the noise in the blue part of the spectra. For
these objects spectra in the blue wavelength region are required to confirm
the tentative classification as cooling flow galaxies. In our catalog these
sources are preliminarily classified as cluster of galaxies.
A necessary criterion for the classification of a candidate as BL Lac object
is a featureless continuum without emission lines.
In order to discriminate BL Lacs against normal elliptical
galaxies Stocke et al.
(1991) defined a criterion to measure the contribution of
stellar light by making use of the CaII break. Since our spectra usually
have a very low S/N in the blue spectral region this criterion cannot be
used for our spectroscopic data. However, the absence of MgIb and of
NaID absorption features which are located further in the red, and
the absence of Balmer absorption lines for blue objects at least allow to
distinguish the visually brighter (
) BL Lac candidates from
stars.
For the identification of fainter BL Lacs, which we cannot classify directly
spectroscopically, we started a
photometric monitoring program of the potential candidates searching for the
intrinsic variability of BL Lacs. For this purpose we obtain deep R images
of the fields around the candidates.
As additional criteria for the fainter candidates found by means of the
optical variability we use
X-ray-to-optical flux ratio and the location in the
diagram. The use
of these parameters for the identification of BL Lacs was recently discussed
by Nass et al. (1996). The 
parameters are
defined as 
, and
, where 
,
, and 
are the monochromatic fluxes per frequency
interval at 2keV, 2500Å, and at 5GHz (cf. e.g. Tananbaum et al.
1979). Radio fluxes were taken from the 4.85GHz
survey of Gregory & Condon (1991). For those objects for
which no radio measurement exists we adopted an upper limit for the flux at
4.85GHz of 20mJy. As mentioned in Sect. 3 (click here)
the photometric calibration is still being improved. At this time we
therefore use photometry from the APM (see Sect. 3 (click here)) catalog
for the calculation of the flux ratios and the continuum slopes. For
classification
purposes the accuracy is acceptable since an error of 
in V
will introduce an uncertainty of the 
ratio of the
order of
0.4. Hence stars and BL Lacs can still be distinguished. Likewise, the
corresponding uncertainties of the 
coefficients are also acceptably
small. Variable candidates without emission lines in their
spectra are very likely BL Lac objects. Sources for which
light curves are not yet available were classified as "possible BL Lacs''
if a) no other "plausible'' counterpart is present and b) objects
without emission lines and suitable 
and 
parameters are present in the error circle.