In this section we analyse the global completeness of the survey and discuss the statistical accuracy of parameters given in Table 1. We will, unless stated otherwise, assume that errors obey the laws of normal distributions.
Survey completeness
Figure 3: The empirical noise for the different pointing centres. The diameters
of the circles are proportional to the noise levels. The size of the
circle corresonding to the average noise level of 32.2 mJy is shown
in the lower right corner
Figure 3 (click here) shows the empirically determined rms noise level for each of the fields in the Bulge region. For each field, the diameter of the circle is proportional to the rms noise level in the image planes (averaged over all spectral channels in an image cube after the removal of all detected point sources and subtraction of the background continuum level (Sect. 3)).
The empirical noise is lower than the noise expected theoretically (from e.g. system temperature and number of visibilities) by about 10% as a result of the inevitable interpolation in the calculation of velocities from the observed frequency channels.
The 11
-order polynomial fit (see Sect. 3)
causes a decrease in the rms noise levels of 
2%.
The empirical
rms noise level, averaged over all fields, is 32.2 mJy while 90% of
fields have noise levels below 40 mJy. Higher noise levels are
evident in some fields due to higher system temperatures arising
from RFI, or, for fields close to the galactic Centre (GC), from the
proximity of the strong radio emission from Sgr A.
The highest empirical noise level, 106 mJy,
occurs in the field covering the GC.
Figure 4 (click here)a shows the primary beam response
(PBR) of the ATCA antennae at 18cm as a function of radial offset
from the pointing centres (Wieringa & Kesteven 1992). The FWHM of
the response function is at 
.
The offset labelled max corresponds to the offset within which the
flux density of a source is always greater at the true source position
than at a position measured from a ghost image (see Appendix A).
For inner fields, the largest possible offset for a source
is 19
, which coincides with the full width at
0.32 of the global maximum.
For the fields in the outer corners of the survey (4 out of 539),
the largest possible offset is determined entirely by
the image size set in the imaging routines,
which is 42
42
\
(Appendix A). The maximum offset in images is therefore 
, which
corresponds to a PBR of 0.023. As can readily been seen from Fig. 4 (click here)b,
no sources have been detected at such low PBR levels;
the largest offset detected is 21
(PBR 0.25).
This is not surprising; not only is the PBR very low but also the total
area of the survey covered by offsets larger than 21
is only 2%.
Because of primary beam attenuation, the detection level
for OH maser emission in the survey
is not uniform across each field, but increases with
the radial offset of a source position from the field centre.
For the detection of stellar masers, we set an absolute
detection level at 120 mJy, corresponding to approximately three times
the noise level in poor fields. After correcting the OH flux
densities for primary beam attenuation, we would therefore expect to detect
sources with peak flux densities above 0.12 Jy near the pointing centres,
and above (0.32)
120 mJy = 375 mJy at offsets of
19
from the field centres.
In Figs. 4 (click here)b to 4f we investigate the global completeness of the survey.
Figure 4b shows the PBR of each source against the
measured peak flux density,
corrected for primary beam attenuation. The PBR for each source is
directly related to the source offset and is calculated using the curve shown
in Fig. 4 (click here)a. The solid line connects stars with the lowest detected OH
flux densities, determined in PBR bins of width 0.1.
From this diagram it is evident
that nearly all detected sources have PBR values above 0.3, corresponding to
offsets within 19
of the field centres.
Of the total area of the surveyed region, 95% is
within this offset. In addition, a few sources
were detected at larger offsets in the fields at the boundary of the
Bulge region surveyed.
The dashed line in Fig. 4 (click here)b indicates the expected relation between
PBR and flux density cut off for an absolute detection limit of
160 mJy, which is the best fit.
In the final sample, the limiting flux density corrected
for primary beam attenuation is found to be 160 mJy
or 
4
.
The noise levels do not vary (strongly) with offset but
the primary beam attenuation does. This means that the detection
limit is changed for offset smaller than 10
,
where the PBR is more than 0.75. In those regions one could
in principle expect to find sources that have a flux density of 
120 mJy
after correction. However, in the visual inspection the spectra of
those sources, that have a SNR of less than 4, where not found to
be acceptable (Sect. A5).
In Fig. 4 (click here)f the SNR for all objects with SNR < 40 from Table 1 is
plotted against their offset.
Indeed, the limiting SNR is constant at 4 out to 10
\
in offset. Only for larger offsets is the SNR slowly rising with
offset because there the limiting factor is not the 4
detection level in corrected flux density but the 120 mJy detection level
in uncorrected flux density.
At 20
the PBR is 0.28 and we expect a cut off at
120 mJy / 0.28 = 430 mJy or at a SNR of 10 to 11. In Fig. 4 (click here)f this is indeed
found to be the limiting SNR.
Figure 4:
Representation of the completeness of the data.
a) The primary beam response (PBR)
of the ATCA antennae at 18 cm, as a function of
radial offset from the pointing centre, taken from
Wieringa & Kesteven (1992).
The offset labelled max indicates the offset to which the
measured flux density of a genuine source
is always higher than the flux density measured
for a ghost image of that source.
b) The PBR calculated for the detected sources
plotted against the peak OH flux densities, corrected for primary beam
attenuation. The solid line indicates the lowest flux densities detected
for PBR bins of width 0.1. The dashed line indicates the expected inner
boundary calculated from the PBR curve in (a) for a limiting
flux density of 160 mJy (best fit).
c) The cumulative flux density distribution for stars with PBR values
> 0.8 (solid line) and < 0.6 (dashed line). The solid line is taken to
be the intrinsic OH flux density distribution for the sources in the survey.
d) The completeness, relative to the pointing centres,
of the survey as a function of position
offsets from the field centres. An offset of 15
corresponds to
half the distance between nearest fields in a row of constant latitude
(Fig. 1 (click here)); 21
is the largest observed offset in the survey.
e) The completeness of the sample as a function of flux density.
The offset out to which a source with certain flux density can be
observed is determined from the dotted line in (b). Then we integrate
the completeness given in (d) from that offset to zero, normalizing
with surface.
f) The SNR for all sources with SNR lower than 40, plotted
against their radial offset from the pointing centre. The dashed
line shows the lower limit for the SNR at a certain offset
In Fig. 4 (click here)c we plot the cumulative flux density distributions for the detected sources with PBR > 0.8 (solid line) and, for comparison, with PBR < 0.6 (dashed line). Because the minimum detected flux density is almost independent of PBR for high PBR (Fig. 4 (click here)b), we estimate that the survey was essentially complete for PBR > 0.8, given the survey detection limit. The solid line shown in Fig. 4 (click here)c therefore provides a reasonable approximation to the intrinsic cumulative flux density distribution for the OH/IR stars in the present sample.
In Fig. 4 (click here)d we plot the relative completeness of the survey
as a function of
source offset from the pointing centres. For this diagram we have
combined the information given in Figs. 4 (click here)a to 4c, and have assumed that
the solid line shown in Fig. 4 (click here)c is the intrinsic flux density distribution
for the sources in the surveyed region.
A sudden decrease in completeness takes place at 
14
.
The completeness is a function of the value of the PBR at a certain
offset and of the total area where the PBR has that value.
The fields start overlapping at offsets of 15
because
the smallest distance between pointing centres is 30
(on the same latitude row; see Fig. 1 (click here)). Therefore the surface
filled by all points with an offset larger than 15
is no longer
a complete annulus. Whereas for offsets
smaller than 15
the increasing area and decreasing
PBR seem to balance each other into almost constant completeness,
above this offset both PBR and area decrease, and so does the
completeness.
In Fig. 4 (click here)e we plot the completeness of the survey as a function of
flux density, combining Figs. 4 (click here)b and 4d. For the derivation of the
curve in Fig. 4 (click here)e, we have to integrate the completeness given in
Fig. 4 (click here)d from the largest offset possible for a source with a certain
flux density inward to offset 0
, normalizing with area (see above).
For sources of 375 mJy that can, as discussed, be found at all
offsets < 19
, or in other words in 95% of the survey area,
the completeness is 0.95, as found from Fig. 4 (click here)e.
This is a coincidence; for instance,
for sources of 200 mJy (offset < 13
, area 58%)
the survey has a completeness of 0.2.
As expected, the curve levels out
for flux densities above 120 mJy / 0.25 = 480 mJy (offset 21
).
So far, this discussion has been about the global completeness of the
survey. As discussed in Sect. 5.1.1, the noise levels vary from
field to field and therefore the detection level will also vary.
For the fields close to the GC the
degree of completeness is
likely to be lower than elsewhere due to the higher noise levels in the
images (Fig. 3 (click here)). For example, in the central GC field the empirical noise
is 106 mJy. If we assume that the detection limit is
3
(although set to 120 mJy),
we expect the survey to be complete in this field for sources brighter
than 3
106 mJy / 0.32 = 0.99 Jy and to have an absolute flux
density cut off at 318 mJy. Figure 4 (click here)c shows then that
20 to 70% of the intrinsic flux density distribution is unobservable
in this field.
The equivalent of Fig. 4 (click here)e for individual
fields can be obtained by shifting the curve in the horizontal
direction, shifting to the right for increasing noise levels.
The slope of the curve does not change since we assume
the noise levels are constant over one field or, in other
words, we assume Fig. 4 (click here)d does not change from field to field.
The positions of sources were determined by fitting a parabola (MAXFIT)
to the 3x3 cells centred on the
pixel with the highest value found in a plane (see Appendix A).
The difference between this fitted position and the genuine position
of a source depends upon the size of the image cells relative to the size
of the synthesized beam and upon the shift of the centre of the
central cell with respect to the source position. Naturally, there
is no guarantee that the imaging procedure will put stars exactly in the
centre of an image cell. In Fig. 5 (click here) we plot the error in the fitted
position as a function of cell size for various SNRs
and shifts of the centre cell with respect to the source position.
The errors are found using simulated data by fitting parabolae to
gaussian-shaped peaks with added random noise.
The maximum shift is necessarily half a cell, since we ensure
in the searching method (Appendix A) that
the highest peak value is at the cell that is at the
centre of the 
cells.
When the cells are so small that all
9 cells to be fitted sample the tip of the gaussian, we
are essentially fitting a parabola to a flat line. Therefore, in all
panels we see that the errors increase for cell sizes below 0.2 HWHM.
When, on the other hand, the cell sizes are so large that all cells
except for the central one have a value of essentially zero, we
are essentially trying to fit a parabola to a delta function and again
the errors increase for cell sizes above 3 HWHM.
For the cell sizes (
1 HWHM, both in right ascension and
declination) and SNRs (4 to 4000)
used in the imaging, the positional
errors are typically 0.1 cell size. With cell sizes
of 
5
,
this translates to a positional error of
,
with the largest contribution in declination.
From calibration errors we expect a positional error of less than 
because of fluctuations in the phase gain solutions of about 
.
The positions given in Table 1 are the positions of the star measured
in the channel with the strongest peak. This gives the most accurate
position of the source because the SNR is larger
than in intermediate channels (see Fig. 5 (click here)).
The entry 
(Table 1, Col. 6) is defined as
It gives an indication of the mean scatter in
the position of the star measured in all the channels where it was detected.
It should be carefully interpreted as an upper limit to the individual
positional errors of the sources, because it depends upon various quantities,
such as flux, angular size (for average source properties the angular
size in intermediate channels can be of the order of 
)
and pass of detection.
The typical value for 
in Table 1 is 
.
Figure 5:
The error in the fit as a function of cell size, as found from simulations.
For each of the 100 steps in cell size 100 simulations of the fitting
procedure were done on a perfectly gaussian-shaped
peak with added random noise.
The upper panels show the error in the fitted position for a
SNR of 100, the lower panels for SNR
of 10. From left to right the shift of the gridded
pixel positions with respect to the true source position is increasing
from 0.0 to 0.5.
The cell sizes are given in units of one HWHM of the synthesized
beam; the errors in cell size. A horizontal line in any of the panels
therefore means that the positional error grows linearly with
absolute cell size
In summary, the positional error is at worst a bit
more than 1
; for most sources, however, the positional error
is 
, with the largest contribution in
the declination.
Flux densities
The OH peak flux densities given in Table 1 were
determined directly from the spectra and corrected for
primary beam attenuation.
The absolute calibration of the flux density scale is accurate to
a few per cent while time-dependent flux density variations
were calibrated to give flux densities accurate to < 10%.
The ATCA antennae have rms pointing errors of approximately 10
giving an additional error in the measured flux densities of maximally
3%, varying with offset.
The measured OH peak flux densities are dependent on the velocity
resolution of the measurements.
The spectra have a velocity resolution of 1.46 
, considerably
broader than the natural linewidth of the OH
emission features in OH/IR stars. This leads to a significant
decrease in the measured OH peak flux densities compared to data taken
with higher velocity resolution. This effect is strongest for
the steepest spectral profiles.
For 12 of the sources in the Bulge region, we have compared the ATCA
spectra with single-dish OH 1612 MHz spectra obtained by Chapman et al.
in the same epoch as our data, using the Parkes 64 m radio telescope with a
velocity resolution of 0.36 
(J.M. Chapman, private communication).
The peak flux densities for the
12 sources are a factor of 1.3 to 1.8 smaller in our data than in the
single-dish spectra, but the fluxes are comparable when the
single-dish spectra are smoothed to the same velocity resolution.
Apart from this undersampling error that depends only on the
intrinsic profile, the flux densities inevitably
decrease when interpolating linearly to find the
velocities from the observed frequency channels. This effect
causes an underestimate in the flux density of as much
as 25% at worst, but typically of 5%.
(The rms noise level in the spectra is
decreased by about 10% by the same effect (Sect. 5.1.1)).
We conclude that, for the velocity resolution of 1.46 
,
the OH peak flux densities are systematically too low by 
5%,
with an additional random error of typically 5%.
The velocity resolution (FWHM) of the data, resulting from Hanning
smoothing 1024 channels in a 4 MHz bandwidth is 1.46 
, which
equals the channel separation after we discard every second channel.
Spectral gridding and interpolation causes errors of typically
half a FWHM in the peak velocity determination, from arguments
similar to those used in Sect. 5.2.
When the flux density difference between neighbouring channels
for a detected source are of the order of the amplitude of the noise then
the detected peak can easily shift one channel if the noise adds to the
flux density in the channel with the intrinsically second strongest signal.
This is enhanced by the fact that neighbouring channels are correlated
by about 16% after the Hanning smoothing.
Therefore the typical error in all velocities
given in Table 1 (Cols. 8 to 11) is 1 
.
Because the intrinsic shape of the (double-peaked) spectra is such that peaks are, in general, steeper at the outer edge than at the inner, smoothing will cause the outflow velocity to decrease slightly, rather than changing it in a random way.
A few effects relating to velocity coverage need to be considered.
Firstly, owing to the changing Doppler shift
the velocity band shifted by about 12 
over the observing
period of two months.
Secondly, when fitting the continuum with UVLIN the polynomial
can roam freely and increase the noise
at the outer 5% of the band.
Thirdly, there may be double-peaked sources that have only one
peak in the observed velocity band; these appear to be single-peaked
sources and are therefore less likely to be detected (Sect. A4).
These three factors limit the homogeneously covered
velocity range to (
).
Ten sources where detected with one or more peaks outside this range,
six at negative and four at positive extreme velocities.
Four are identified as single-peaked sources, indicating that
the second peak may be outside the velocity range searched. In fact,
one, source #179,
is a famous double-peaked source, Baud's star (Baud et al. 1975),
which has a second peak at -356 
.
These numbers suggest that there is no need for concern about missing
sources as a result of velocity-dependent effects.
The fact that the band extends to more
extreme positive velocities than negative velocities does not introduce
a large bias either, as already implied by the numbers of extreme
velocity sources mentioned above. The negative extreme of
the velocity range covered is at -320 
; only two sources
have velocities higher than +320 
.
Figure 6: a) LSR stellar velocity distribution for all sources in Table 1.
Note that for the single-peaked sources the stellar velocities
are taken to be at the velocity of the emission peak. For these
stars the true stellar velocities may differ by 
14 
.
b)
The outflow velocity distribution for all 245 double-peaked objects
in Table 1. The average of all outflow velocities is 14 
.
Features in these diagrams will be discussed in future articles
Figure 6 (click here)a shows the distribution of the stellar velocities for the
detected sources.
Figure 6 (click here)b shows the distribution of expansion velocities for the
double-peaked
sources. Nearly all double-peaked sources have expansion velocities between
4 and 30 
with a peak in the distribution at velocities near
14 
. Expansion velocity histograms for other
observations invariably show very similar distributions
(Eder et al. 1988; Habing 1993).
However, there are two sources (#008, #200)
with extremely high outflow
velocities, 65.7 
and 78.8 
respectively.
Although OH/IR sources with outflow velocities up to 90 
are known (te Lintel Hekkert et al. 1992),
they are very rare and mostly the outflow velocities are not
derived from the OH 1612 MHz spectrum but from CO or other OH maser
lines. These sources are mostly found to be PPNe.
For the two extreme-outflow-velocity sources in our sample
no counterparts have been found in the literature.
We will not speculate upon their nature in this article.
In summary, the typical error in stated peak velocities in Table 1
is 1.0 
. The errors are independent of velocity.
(For S (and possibly I) sources it should be realised that
the stellar velocities deviate from the real stellar velocities
by one average outflow velocity, of the order 14 
.)
Figure 7:
The IRAS two-colour diagram for sources with an IRAS identification
lying within the IRAS error ellipse (Col. 17 
1) with
well-determined IRAS 12,25 and 60 
flux densities (i.e. no upper limits).
The regions marked IIIa and IIIb roughly outline the regions where classical
OH/IR stars are expected (van der Veen & Habing 1988).
The colours are defined as
).
Features in this diagram will be discussed in future articles
For each of the sources in Table 1, Col. 16 gives
the nearest IRAS point source identification,
obtained using version 2 of the IRAS Point Source Catalog (PSC).
The parameter N in Col. 7 is defined as the ratio of the
distance to the nearest IRAS point source to the size of the IRAS error
ellipse in the direction towards the source.
In general the IRAS error ellipses
are highly elongated and much larger than the errors in the OH positions;
they are of the order of 30
7
.
They define the 2
errors in the IRAS positions
(i.e. 95% likelihood).
The ratio N is, therefore, contrary to the absolute distance
from the infrared to the OH position, directly related to the
probability of an association between the OH and infrared sources.
For example, for N = 1, the OH position lies on the 2
IRAS error ellipse, and the likelihood of an association between the radio
and infrared sources is 5%.
In the Bulge region, the IRAS observations were highly confused and many
infrared sources could not be identified as point sources. For this reason
we expect the number of associations between the OH and infrared sources
to be small.
For all 307 sources the average distance
to the nearest IRAS PSC position is 44
;
201 (65%) have an IRAS
identification within the error ellipse 
.
Of those 201, we plotted the ones with reliable
IRAS-colour determination (see IRAS Explanatory Supplements)
in Fig. 7 (click here), the two-colour diagram as described
by van der Veen and Habing (1988).
The OH identifications given in Table 1 (Col. 15), with references
in Table 2, were
obtained using the Simbad (Centre de Données de Strasbourg) database,
which was searched
for previous OH 1612 MHz maser detections within 1
for each source. Most detections of stellar OH 1612 MHz
maser emission that were made before 1989 are comprised
in the catalogue by te Lintel Hekkert et al.\
(1989, (02)). For sources in that catalogue we do not give the original
references.
It would not be realistic to claim that all sources without
identification within 1
are new detections, since
some of the known OH masers have positions taken directly from
the (assumed) associated IRAS point source and these can be
wrong. This is the case for, amongst others,
spectrum #258. No reference is given in Col. 15, but the source
has been detected by te Lintel Hekkert et al. (1991, PTL) at
the location of IRAS 17565-2035. However,
we find IRAS 17560-2027 to be closest to #258.
The new position differs from the previous by 11
.
On the other hand, for some of the sources detected by PTL,
better positions were already known and for those the
reference to the detection of the improved position is given
(e.g. #101, #270, van Langevelde et al. 1992, 08).
It is obviously hard to give proper credit to references
to previous detections of OH maser sources. However, the new
positions are so much more accurate that we feel justified in
counting those few sources as new.
The number of sources in Table 1 without a
previous OH detection in Col. 15 is 145 (47%).
The ATCA survey of the Bulge region overlaps considerably with the
earlier single-dish detection experiment by PTL.
The PTL survey used the Parkes 64 m telescope, with a resolution
of 
, to search for
OH 1612 MHz emission from IRAS-selected sources.
In the Bulge region, PTL detected OH 1612 MHz
maser emission from 145 sources, of which we detected
78 sources in the ATCA survey. The sensitivity of their
survey is comparable to that of the ATCA survey.
However, we will have observed most of the PTL sources with considerable
primary beam attenuation. Besides this, OH/IR stars are variable
with typical periods of one or two years. In the 8 years between the
two surveys, a set of stars with similar flux densities in the PTL survey
will have spread over a wide range in flux density.
Taking these two effects into account, we
calculate the fraction of the PTL sources we would expect to redetect
to be around 60%, which is consistent with the actual
number of redetections.
(Of course the reverse is equally
true; sources we detect were not found in the PTL survey.)
Lindqvist et al. (1992) made a very deep survey for OH/IR stars towards the central degree of the Galaxy, with an rms noise level of 20 mJy, and found 134 double-peaked objects. Our data include 19 detections in common.
Some I objects or nonstandard D objects are known to be objects in transition from the AGB to the planetary-nebula phase, e.g. #134 (extreme peak-flux ratio, see Zijlstra et al. 1989) or supergiants, e.g. #299 (irregular peaks, VX Sgr, see Chapman & Cohen 1986).