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3 USS samples

\par\includegraphics[width=18cm,clip]{ds1811f5.eps}\end{figure} Figure 5: The density of sources from the high frequency catalog used in the correlation (NVSS or PMN) around sources from the low frequency catalog (WENSS, Texas or MRC) as a function of search radius. The dotted line represents the distribution of confusion sources (see text). The apparent under-density of WENSS-NVSS sources at search radii $\gtrsim 60\hbox {$^{\prime \prime }$ }$ is due to the grouping of multiple component sources in the $\sim $1$^\prime $ resolution WENSS. Note the plateau and secondary peak around the 73 $^{\prime \prime }$ Texas fringe separation in the Texas-NVSS correlation and the much larger uncertainty in the MRC-PMN correlation

Figure 2 shows that the surveys described above have very compatible flux density limits for defining samples of USS sources. At the same time, their sky coverage is larger and more uniform than previous surveys used for USS sample construction (Wieringa & Katgert 1992; Röttgering et al. 1994; Chambers et al. 1996a; Blundell et al. 1998; Rengelink 1998; Pursimo et al. 1999; Pedani & Grueff 1999; Andernach et al. 2000). We selected the deepest low and high frequency survey available at each part of the sky. For a small region $-35\hbox{$^\circ$ }< \delta < -30\hbox{$^\circ$ }$ which is covered by both Texas and MRC, we used both surveys. This resulted in a more complete samples since the lower sensitivity of the PMN survey in the zenith strip (see Sect. 2.6) is partly compensated by the (albeit incomplete) Texas survey. To avoid problems with high Galactic extinction during optical imaging and spectroscopy, all regions at Galactic latitude |b| < 15 $\hbox{$^\circ$ }$ were excluded[*], as well as the area within 7 $\hbox{$^\circ$ }$ of the LMC and SMC. This resulted in three USS samples that cover a total of 9.4 steradians (Fig. 6).

We designate the USS samples by a two-letter name, using the first letter of their low- and high-frequency contributing surveys. Sources from these samples are named with this 2-letter prefix followed by their IAU J2000-names using the positions from the NVSS catalog (WN and TN samples) or the MRC catalog (MP sample). We did not rename the sources after a more accurate position from our radio observations or from the FIRST survey. The sample definitions are summarized in Table 3.

3.1 Survey combination issues

We first discuss the problems that arise when combining radio surveys with different resolutions and positional uncertainties.

3.1.1 Correlation search radius

Due to the positional uncertainties and resolution differences between radio surveys, in general the same source will be listed with slightly different positions in the catalogs.

To empirically determine the search radius within which to accept sources in 2 catalogs to be the same, we compared the density of objects around the position listed in the low-frequency survey (which has lower resolution) with the expected number of random correlations in each sample ($\equiv$ confusion sources). To determine this number as a function of distance from the position in the most accurate catalog, we created a random position catalog by shifting one of the input catalogs by 1 $\hbox{$^\circ$ }$ in declination, and made a correlation with this shifted catalog. The density of sources as a function of distance from the un-shifted catalog then represents the expected number of confusion sources as a function of radial distance. In Fig. 5, we plot for each of our three samples the observed density around these sources with this confusion distribution over-plotted. The correlation search radius should thus be chosen at a distance small enough for the density of confusion sources to be negligible.

We decided to adopt the radius where the density of real sources is at least ten times higher that the density of confusion sources as the search radius for our sample construction, except for the WN sample (would be 15 $^{\prime \prime }$) where we chose the same radius as for the TN sample (10 $^{\prime \prime }$). The later was done for consistency between both samples. Because of the five times lower resolution and source densities in the MRC and PMN surveys, the search radius of the MP sample is eight times larger. Summarized, the search radii we used are 10 $^{\prime \prime }$ for WN and TN, and 80 $^{\prime \prime }$ for MP.


Table 3: USS samples
Sample Sky Area $\qquad\quad$ Density Spectral Index Search Radius Flux Limit Ca Ra # of Sources
    sr-1     mJy      
WN 29 $\hbox{$^\circ$ }< \delta <$ 75 $\hbox{$^\circ$ }$, |b| > 15 $\hbox{$^\circ$ }^b$ 151 $\alpha_{325}^{1400} \le -1.30$ 10 $^{\prime \prime }$ S1400 > 10 96% 90% 343
TN -35 $\hbox{$^\circ$ }< \delta <$ 29 $\hbox{$^\circ$ }$, |b| > 15 $\hbox{$^\circ$ }^b$ 48c $\alpha_{365}^{1400} \le -1.30$ 10 $^{\prime \prime }$ S1400 > 10 97%c 93% 268
MP $\delta < -$30 $\hbox{$^\circ$ }$, |b| > 15 $\hbox{$^\circ$ }$ 26 $\alpha_{408}^{4800} \le -1.20$ 80 $^{\prime \prime }$ S408 > 700; S4850 > 35 100% 100% 58

$\textstyle \parbox{18cm}{
$^a$\space C~=~completeness and R~=~reliability accou...
... the Texas survey, the effective completness of the
TN sample is $\sim 30\%$ .}$

3.1.2 Angular size

In order to minimize errors in the spectral indices due to different resolutions and missing flux on large angular scales in the composing surveys, we have only considered sources which are not resolved into different components in the composing surveys. Effectively, this imposes an angular size cutoff of $\sim $1$^\prime $ to the WN, $\sim $2$^\prime $ to the TN sample and $\sim $4$^\prime $ to the MP sample. We deliberately did not choose a smaller angular size cutoff (as e.g. Blundell et al. 1998, did for the 6C* sample), because (1) higher resolution angular size information is only available in the area covered by the FIRST survey, and (2) even a 15 $^{\prime \prime }$ cutoff would only reduce the number of sources by 30%, while it would definitely exclude several HzRGs from the sample. For example, in the 4C USS sample (Chambers et al. 1996b), three out of eight z>2 radio galaxies have angular sizes >15 $^{\prime \prime }$.

\par\includegraphics[width=8.8cm,clip]{ds1811f6.eps}\end{figure} Figure 6: Sky coverage of our 3 USS samples. Constant declination lines denote the boundaries between our the WN and TN and between the TN and MP samples, as indicated on the right. Note the difference in source density and the exclusion of the Galactic Plane

We think that our $\sim $1$^\prime $ angular size cutoff will exclude almost no HzRGs, because the largest angular size for z > 2 radio galaxies in the literature is 53 $^{\prime \prime }$ (4C 23.56 at z = 2.479; Chambers et al. 1996a; Carilli et al. 1997), while all 45 z > 2.5 radio galaxies with good radio maps are < 35 $^{\prime \prime }$ (Carilli et al. 1997). Although the sample of known z>2 radio galaxies is affected by angular size selection effects, very few HzRGs larger than 1$^\prime $ would be expected.

The main incompleteness of our USS sample stems from the spectral index cutoff and the flux limit (Sect. 3.2). However, our flux limit ( S1400=10 mJy) is low enough to break most of the redshift-radio power degeneracy at z>2. To achieve this with flux limited samples, multiple samples are needed (e.g. Blundell et al. 1999).

3.2 Sample definition

3.2.1 WENSS-NVSS (WN) sample

A correlation of the WENSS and NVSS catalogs with a search radius of 10 $^{\prime \prime }$ centered on the WENSS position (see Sect. 3.1.1) provides spectral indices for $\sim 143\,000$ sources. Even with a very steep $\alpha_{325}^{1400} \le -1.30$ spectral index criterion, we would still have 768 sources in our sample. To facilitate follow-up radio observations, and to increase the accuracy of the derived spectral indices (see Sect. 3.3.1), we have selected only NVSS sources with S1400 > 10 mJy. Because the space density of the highest redshift galaxies is low, it is important not to limit the sample area (see e.g. Rawlings et al. 1998) to further reduce the number of sources in our sample. Because the NVSS has a slightly higher resolution than the WENSS (45 $^{\prime \prime }$ compared to $54\hbox{$^{\prime\prime}$ }\times 54\hbox{$^{\prime\prime}$ }\
{\rm cosec}\ \delta$), some WENSS sources have more than one associated NVSS source. We have rejected the 11 WN sources that have a second NVSS source within one WENSS beam. Instead of the nominal WENSS beam ( $54\hbox{$^{\prime\prime}$ }\times 54\hbox{$^{\prime\prime}$ }\
{\rm cosec}\ \delta$), we have used a circular 72 $^{\prime \prime }$ WENSS beam, corresponding to the major axis of the beam at $\delta = 48\hbox{$^\circ$ }$, the position that divides the WN sample into equal numbers to the North and South. The final WN sample contains 343 sources.

3.2.2 Texas-NVSS (TN) sample

Because the Texas and NVSS both have a large sky-coverage, the area covered by the TN sample includes 90% of the WN area. In the region $\delta >29\hbox{$^\circ$ }$, we have based our sample on the WENSS, since it does not suffer from lobe-shift problems and reaches ten times lower flux densities than the Texas survey (Sect. 2.2). In the remaining 5.28 steradians South of declination +29 $\hbox{$^\circ$ }$, we have spectral indices for $\sim 25\,200$ sources. Again, we used a 10 $^{\prime \prime }$ search radius (see Sect. 3.1.1), and for the same reason as in the WN sample we selected only NVSS sources with S1400 > 10 mJy. Combined with the $\alpha_{365}^{1400} \le -1.30$ criterion, the number of USS TN sources is 285. As for the WN sample, we further excluded sources with more than one S1400>10 mJy NVSS source within 60 $^{\prime \prime }$ around the TEXAS position, leaving 268 sources in the final TN sample. We remind (see Sect. 2.2) that the selection of the TEXAS survey we used is only $\sim $40% complete with a strong dependence on flux density. Using the values from Table 2, we estimate that the completeness of our TN sample is $\sim $30%.

3.2.3 MRC-PMN (MP) sample

In the overlapping area, we preferred the TN over the MP sample for the superior positional accuracies and resolutions of both Texas and NVSS compared to MRC or PMN. Because the MRC survey has a low source density, we would have only 13 MP sources with $\alpha_{408}^{4850} \le -1.30$. We therefore relaxed this selection criterion to $\alpha_{408}^{4850} \le -1.20$, yielding a total sample of 58 sources in the deep South ( $\delta < -30\hbox{$^\circ$ }$).

\par\includegraphics[width=15cm,clip]{ds1811f7.eps}\end{figure} Figure 7: Spectral index distributions from the WENSS-NVSS correlation. The left and right panels show the variation with 325 MHz and 1.4 GHz flux density. A low frequency selected sample is more appropriate to study the steep-spectrum population. The parameters of a two-component Gaussian fit (dotted line = steep, dashed line = flat) are shown in each panel. The solid line is the sum of both Gaussians

3.3 Discussion

3.3.1 Spectral index errors

We have listed the errors in the spectral indices due to flux density errors in the catalogs in Tables A.1 to A.3. The WN and TN samples have the most accurate spectral indices: the median spectral index errors are $\Delta\bar{\alpha}_{325}^{1400} = 0.04$ for WN sources and $\Delta\bar{\alpha}_{365}^{1400} = 0.04$( S365 >1 Jy) to 0.07 ( S365>150 mJy) for TN sources. For the MP sample, $\Delta\bar{\alpha}_{408}^{4850} \approx 0.1$, with little dependence on flux density ( S408 > 750 mJy).

Because our sample selects the sources in the steep tail of the spectral index distribution (Figs. 7 and 8), there will be more sources with an intrinsic spectral index flatter than our cutoff spectral index that get scattered into our sample by measurement errors than there will be sources with intrinsic spectral index steeper than the cutoff that get scattered out of our sample.

Following the method of Rengelink (1998), we fitted the steep tail between $-1.60 < \alpha <
-1.0$ with a Gaussian function. For each of our three samples, we generated a mock sample drawn from this distribution, and added measurement errors by convolving this true spectral index distribution with a Gaussian distribution with as standard deviation the mean error of the spectral indices. The WN mock sample predicts that 13 $\alpha_{325}^{1400} < -1.30$ sources get scattered out of the sample while 36 $\alpha_{325}^{1400} > -1.30$ sources get scattered into the USS sample. Thus, the WN sample is 96% complete and 90% reliable. For the TN sample, we expect to loose 7 $\alpha_{365}^{1400} < -1.30$sources[*], and have 18 contaminating $\alpha_{365}^{1400} > -1.30$ sources. The completeness is thus 97% and the reliability 93%. For the MP sample, this spectral index scattering is negligible, because there are too few sources in the steep spectral index tail.

Our reliability and completeness are significantly better than the values of $\sim $75% and $\sim $50% of Rengelink (1998) because (1) our spectral indices are more accurate because they were determined from a wider frequency interval than the 325-610 MHz used by Rengelink (1998), and (2) our sample has a steeper cutoff spectral index, where the spectral index distribution function contains fewer sources and has a shallower slope, leading to fewer sources that can scatter in or out of the sample.

3.3.2 Spectral index distributions

Using the 143000 spectral indices from the WENSS-NVSS correlation, we examined the flux density dependence of the steep and flat spectrum sources. Selecting sources with S325>50 mJy or S1400>100 mJy assures that we will detect all sources with $\alpha_{325}^{1400}>{\frac{\ln(S_{\rm NVSS}^{\rm lim}/50)}{\ln(325/1400)}}=-1.82$ or $\alpha_{325}^{1400}<{\frac{\ln(S_{\rm WENSS}^{\rm lim}/100)}{\ln(325/1400)}}=0.82$ respectively, where $S_{\rm NVSS}^{\rm lim}=3.5$ mJy and $S_{\rm WENSS}^{\rm lim}=30$ mJy are the lowest flux densities where the NVSS and WENSS are complete (Condon et al. 1998; Rengelink et al. 1997). The results shown in Fig. 7 therefore reflect only the effect of a different selection frequency. Two populations are present in both the S325 and S1400 selected distributions. The peaks of the steep and flat populations at $\bar{\alpha}_{325}^{1400} \approx -0.8$ and $\bar{\alpha}_{325}^{1400} \approx -0.4$ do not show significant shifts over three orders of magnitude in flux density. This is consistent with the results that have been found at 4.8 GHz (Witzel et al. 1979; Machalski & Rys 1981; Owen et al. 1983), with the exception that their $\bar{\alpha}_{1400}^{4800} \approx 0.0$ for the flat spectrum component is flatter than the $\bar{\alpha}_{325}^{1400} \approx -0.4$ we found. However, we find that the relative contribution of the flat spectrum component increases from 25% at S1400>0.1 Jy to 50% at S1400>2.5 Jy.

Because the steep- and flat-spectrum populations are best separated in the S1400>2.5 Jy bin, we have searched the literature for identifications of all 58 S1400 > 2.5 Jy sources to determine the nature of both populations. All but one (3C 399, Martel et al. 1998) of the objects outside of the Galactic plane ( $\vert b\vert>15\hbox{$^\circ$ }$) were optically identified. Of the 30 steep spectrum ( $\alpha_{325}^{1400} < -0.6$) sources, two thirds were galaxies, while the rest were quasars. Half of the flat spectrum ( $\alpha_{325}^{1400} > -0.6$) sources were quasars, 20% blazars, and 30% galaxies. Figure 7 therefore confirms that the steep and flat spectral index populations are dominated by radio galaxies and quasars respectively. We also find that while the relative strength between the steep and flat spectrum populations changes due to the selection frequency, the median spectral index and width of the population does not change significantly over three orders in magnitude of flux density. Even fainter studies would eventually start to get contamination from the faint blue galaxy population (see e.g. Windhorst et al. 1985).

\par\includegraphics[width=8.8cm,clip]{ds1811f8.eps}\end{figure} Figure 8: Logarithmic spectral index distribution for WENSS-NVSS (full line), Texas-NVSS (dot-dash line) and MRC-PMN (dotted line). The vertical line indicates the -1.3 cutoff used in our spectral index selection. Note the difference in number density and the sharper fall-off on the flat-end part of the TN and MP compared to the WN


Table 4: Radio observations
UT Date Telescope Config. Frequency Resolution # of sources
1996 October 28 VLA A 4.86 GHz 0 $.\!\!^{\prime\prime}$3 90 WN, 25 TN
1997 January 25 VLA BnA 4.86 GHz 0 $.\!\!^{\prime\prime}$6 29 TN
1997 March 10 VLA BnA 4.885 GHz 0 $.\!\!^{\prime\prime}$6 8 TN
1997 December 15 ATCA 6C 1.420 GHz 6 $^{\prime \prime }$$\times$ 6 $^{\prime \prime }$ cosec $\delta$ 41 MP, 32 TN
1998 August 12+17 VLA B 4.86 GHz 1 $.\!\!^{\prime\prime}$0 151 WN

3.3.3 Consistency of the three USS samples

We compare the spectral index distributions of our three USS samples in logarithmic histograms (Fig. 8). The distributions are different in two ways. First, the WENSS-NVSS correlation contains nine times more sources than the Texas-NVSS, and 14 times more than the MRC-PMN correlation. Second, the shapes of the distributions are different: while the steep side of the TN sample coincides with that of the WN, its flat end part falls off much faster. The effect is so strong that it even shifts the TN peak steep-wards by $\sim0.15$. For the MP sample, the same effect is less pronounced, though still present.

Both effects are due to the different flux density limits of the catalogs. The deeper WENSS catalog obviously contains more sources than the TEXAS or MRC catalogs, shifting the distributions vertically in Fig. 2. The relative "shortage'' of flat spectrum sources in the Texas-NVSS and MRC-PMN correlations can be explained as follows. A source at the flux density limit in both WENSS and NVSS would have a spectral index of $\alpha_{325}^{1400} = -1.3$, while for Texas and NVSS this would be $\alpha_{365}^{1400} = -1.7$ (see Fig. 2). Faint NVSS sources with spectral indices flatter than these limits will thus more often get missed in the TEXAS catalog than in the WENSS catalog. This effect is even strengthened by the lower completeness at low flux densities of the Texas catalog. However, very few USS sources will be missed in either the WENSS-NVSS or Texas-NVSS correlations[*]. The parallel slope also indicates that the USS sources from both the WENSS-NVSS and Texas-NVSS correlations were drawn from the same population of radio sources. We therefore expect a similar efficiency in finding HzRGs from both samples.

The MP sample has been defined using a spectral index with a much wider frequency difference. However, the observed ATCA 1.420 GHz flux densities can be used to construct $\alpha_{408}^{1420}$. An "a posteriori'' selection using $\alpha_{408}^{1420} \le -1.30$ from out ATCA observations (see Sect. 4.2) would keep $\sim $60% of the MP sources in a WN/TN USS sample.

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