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5. Data analysis

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

Noise levels

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 11tex2html_wrap_inline1565-order polynomial fit (see Sect. 3) causes a decrease in the rms noise levels of tex2html_wrap_inline15672%. 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.

Detection levels

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 tex2html_wrap_inline1569 . 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 19tex2html_wrap1653 , 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 42tex2html_wrap1655 tex2html_wrap_inline1575 42tex2html_wrap1657\ (Appendix A). The maximum offset in images is therefore tex2html_wrap_inline1579, 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 21tex2html_wrap1661 (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 21tex2html_wrap1663 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)tex2html_wrap_inline1585 tex2html_wrap_inline1587 120 mJy = 375 mJy at offsets of 19tex2html_wrap1665 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 19tex2html_wrap1667 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 tex2html_wrap_inline15934tex2html_wrap_inline1595. 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 10tex2html_wrap1669, 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 tex2html_wrap_inline1599120 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 10tex2html_wrap1671\ in offset. Only for larger offsets is the SNR slowly rising with offset because there the limiting factor is not the 4tex2html_wrap_inline1605 detection level in corrected flux density but the 120 mJy detection level in uncorrected flux density. At 20tex2html_wrap1673 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 15tex2html_wrap1677 corresponds to half the distance between nearest fields in a row of constant latitude (Fig. 1 (click here)); 21tex2html_wrap1679 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 tex2html_wrap_inline162314tex2html_wrap1681. 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 15tex2html_wrap1683 because the smallest distance between pointing centres is 30tex2html_wrap1685 (on the same latitude row; see Fig. 1 (click here)). Therefore the surface filled by all points with an offset larger than 15tex2html_wrap1687 is no longer a complete annulus. Whereas for offsets smaller than 15tex2html_wrap1689 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 0tex2html_wrap1691, normalizing with area (see above). For sources of 375 mJy that can, as discussed, be found at all offsets < 19tex2html_wrap1693 , 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 < 13tex2html_wrap1695, 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 21tex2html_wrap1697 ).

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 3tex2html_wrap_inline1647 (although set to 120 mJy), we expect the survey to be complete in this field for sources brighter than 3tex2html_wrap_inline1649106 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. gif 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.

5.1. Positions

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 tex2html_wrap_inline1699 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 (tex2html_wrap_inline17011 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 tex2html_wrap_inline1703 5tex2html_wrap1741, this translates to a positional error of tex2html_wrap_inline1707, with the largest contribution in declination.

From calibration errors we expect a positional error of less than tex2html_wrap_inline1709 because of fluctuations in the phase gain solutions of about tex2html_wrap_inline1711.

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 tex2html_wrap_inline1713 (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 tex2html_wrap_inline1715 ) and pass of detection. The typical value for tex2html_wrap_inline1717 in Table 1 is tex2html_wrap_inline1719.

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 1tex2html_wrap1755; for most sources, however, the positional error is tex2html_wrap_inline1723 tex2html_wrap_inline1725, 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 10tex2html_wrap1759 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 tex2html_wrap_inline1731, 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 tex2html_wrap_inline1733 (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 tex2html_wrap_inline1735, the OH peak flux densities are systematically too low by tex2html_wrap_inline17375%, with an additional random error of typically 5%.

5.2. Velocities

The velocity resolution (FWHM) of the data, resulting from Hanning smoothing 1024 channels in a 4 MHz bandwidth is 1.46 tex2html_wrap_inline1761, 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 tex2html_wrap_inline1763.

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 tex2html_wrap_inline1765 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 (tex2html_wrap_inline1767 tex2html_wrap_inline1769). 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 tex2html_wrap_inline1773. 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 tex2html_wrap_inline1777 ; only two sources have velocities higher than +320 tex2html_wrap_inline1779.

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 tex2html_wrap_inline178114 tex2html_wrap_inline1783. b) The outflow velocity distribution for all 245 double-peaked objects in Table 1. The average of all outflow velocities is 14 tex2html_wrap_inline1785. 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 tex2html_wrap_inline1787 with a peak in the distribution at velocities near 14 tex2html_wrap_inline1789. 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 tex2html_wrap_inline1791 and 78.8 tex2html_wrap_inline1793 respectively. Although OH/IR sources with outflow velocities up to 90 tex2html_wrap_inline1795 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 tex2html_wrap_inline1797. 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 tex2html_wrap_inline1799.)

Figure 7: The IRAS two-colour diagram for sources with an IRAS identification lying within the IRAS error ellipse (Col. 17 tex2html_wrap_inline1801 1) with well-determined IRAS 12,25 and 60 tex2html_wrap_inline1803 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 tex2html_wrap_inline1805). Features in this diagram will be discussed in future articles

5.3. IRAS identifications

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 30tex2html_wrap1831 tex2html_wrap_inline1815 7tex2html_wrap1833. They define the 2tex2html_wrap_inline1819 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 2tex2html_wrap_inline1825 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 44tex2html_wrap1835; 201 (65%) have an IRAS identification within the error ellipse tex2html_wrap_inline1829. 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).

5.4. OH identifications

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 1tex2html_wrap1849 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 1tex2html_wrap1851 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 11tex2html_wrap1853. 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 tex2html_wrap_inline1847 , 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).

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