5. Source counts

The ATCA source list of compact objects can be used to find the sky density of sources at 1.4 GHz in the direction of the LMC. Comparing the source counts with extragalactic source count results allows us to check for incompleteness of the snapshot survey and can be useful in determining the fraction of sources intrinsic to the LMC, which should appear as an excess of counts compared with the extragalactic ones. For this comparison the integrated flux density has to be used, since the peak flux depends on the telescope beam size. The differential source counts (number of sources with a given flux density) of the LMC snapshot survey have been calculated following the method described by Condon & Condon (1982) for their 1.411 GHz VLA snapshot survey.

The ATCA snapshot survey is complete above the uncorrected peak flux density limits given in Table 1 (click here). Corresponding limits to the primary beam corrected peak flux densities vary with location in each map, so that the solid angle in which a source of given peak flux can be detected increases with . Each source counted must therefore be weighted by to give its proper contribution to the areal density of sources. For the calculation of () the overlapping of the fields has been taken into account. The total counting area is sr. The function () is plotted in Fig. 4 (click here).

  
Figure 4: Solid angle in which a source with a given peak flux density has been counted

Since we want to find the sky number density of sources as a function of their integrated flux densities, we must allow for sources which are missing from the survey because they are extended. Such sources have peak flux densities, , below the completeness limit and integrated flux densities, , above this limit. We distinguish the continuum sources which are significantly resolved from those which are not by using the method of Willis et al. (1976). An observed source is defined as extended if

R is the Gaussian fitted area divided by that of the antenna pattern () and is the rms noise in the area of the source after primary beam correction. Assuming that the angular-size distribution of sources as faint as 4 mJy is not significantly different from the angular-size distribution of sources in the range 35 mJy (Downes et al. 1981), then the fraction of extended sources (0.27) in this flux density interval can be used to estimate the fraction of faint extended sources missing from the ATCA survey.

The source counts including all observed sources are listed in Table 5 (click here). The flux density interval (Col. 2) around (Col. 1) is defined as . The number of resolved sources and the number of unresolved sources found in each flux-density interval is shown in Cols. 3 and 4. The fraction of unresolved sources is listed in Col. 5. The mean fraction of unresolved sources in the flux density range 35 mJy is 0.27, so the correction factor K (Col. 6) is the fraction of unresolved sources in each flux density interval divided by 0.27. Column 7 shows the weighted, uncorrected number of sources per steradian

with the 1 rms error (Garwood et al. 1988)

The summation is taken over all sources in the flux density interval. The last column gives the corrected number of sources per flux density interval () per steradian normalized to , meaning:

 

flux density interval [Jy] K

0.0062 0 12 1 7.3 2.3 18.6 9.6

0.0124 2 28 0.93 10.5 1.95 71.5 22.7

0.0247 3 24 0.89 7.7 1.5 139.2 46.8

0.0495 15 9 0.38 6.7 1.4 146.1 60.5

0.0990 11 2 0.15 3.6 1.0 158.6 44.1

0.1980 6 0 0 1.7 0.7 211.8 87.2

0.3960 1 0 0 0.3 0.28 105.7 98.7

0.0062 0 12 1 7.3 2.3 18.6 9.6

0.0124 1 21 0.95 7.4 1.6 50.4 19.3

0.0247 2 16 0.89 5.3 1.2 95.8 31.9

0.0495 14 9 0.39 6.4 1.33 139.6 66.5

0.0990 11 2 0.15 3.6 1.0 158.6 44.1

0.1980 6 0 0 1.7 0.7 211.8 87.2

0.3960 1 0 0 0.3 0.28 105.7 98.7

 

The source counts in the LMC snapshot fields are plotted in Fig. 5 (click here). The line in the figure represents the extragalactic source count distribution of the Westerbork survey at 1.4 GHz (Oosterbaan 1978). The differential source counts of this survey are well approximated by

The comparison of the ATCA snapshot survey to the Westerbork survey is difficult because the latter is sensitive to more extended structures compared to the ATCA survey. For extended sources we expect that the integrated flux densities of the snapshot sources are underestimated, which causes a higher uncertainty in the source count distribution; for more accurate integrated flux densities we would need more observations with shorter baselines. The LMC source count distribution, however, follows the extragalactic distribution of Oosterbaan very closely. This indicates that most of the compact sources of the LMC survey are background objects. At the highest flux density interval 280 mJy there are two sources missing compared to the Westerbork survey. This might be due to the underestimated integral flux densities. An excess of sources above the extragalactic source counts is indicated in the flux density range from 8.8 to 35 mJy. The discrepency between the number of sources predicted and observed in the 8.8 to 35 mJy bin is only weakly significant, given the uncertainties in flux density in this survey. It suggests, that some of the fainter sources are associated with the LMC, a conclusion strongly supported by the positional coincidence with Halpha knots discussed above.

  
Figure 5: Source counts for all sources of our survey (top). The line presents the source count distribution of Oosterbaan (1978). The lower panel shows the source counts after excluding all possible intrinsic sources and the known HII regions

We get the best match to the extragalactic fit of Oosterbaan (see Fig. 5 (click here) lower panel and Table 5 (click here)) by excluding all 15 possible intrinsic sources in the second and third flux density interval for which the position corresponds to a DEM object plus three known HII regions located in the area (Marx et al., in preparation). So we conclude that only a few compact sources in directions toward the LMC are intrinsic objects, and that most of these have flux densities between 8.8 and 35 mJy and are located within extended H emitting regions.