5 Discussion

We discuss in this section possible biases introduced in our sample due to the criteria adopted for the sample selection and to the sensitivity limitations of the NVSS. A detailed discussion about the implications for the radio source population derived from the sample is left for a forthcoming paper (Paper III).

In Fig. 4 we represent the flux density per length unit against the source angular size for all the members of the sample. In this plot we can clearly see the limitations imposed by the selection criteria. The vertical solid line represents the lower limit in angular size ( $4\hbox {$^\prime $ }$). As mentioned in Sect. 3, there are 13 sources with sizes below that limit, which have been kept in the sample. The oblique solid line represents the lower limit in total flux density (100 mJy). There is one source (J0525+718) which lies below that limit (Sect. 3). The horizontal dashed line marks the limit imposed by the NVSS sensitivity ( $1\sigma = 0.45$ mJy/beam), computed considering a rectangular source with a fixed width of $3\hbox{$^\prime$ }$ (an upper limit inferred from the NVSS maps), a variable length l and an uniform brightness distribution at $3\sigma$. The intersection of this line with the flux density limit line (P point) defines the length ( $l \sim 16\hbox{$^\prime$ }$) above which sources with flux densities above 100 mJy could be missed in our sample.

In order to investigate if such very extended sources could be more properly studied using a lower frequency survey, we have cross-checked our sample with a sample of 47 low redshift ($z\leq 0.4$) GRGs with angular sizes larger than $5\hbox{$^\prime$ }$ selected from the WENSS (Schoenmakers 1999). Two radio galaxies, J1047+747 and J1308+619, appear in this sample and are not present in our sample due to their low total flux densities at 1.4 GHz, but not to their too large size. The rest of the sources in Schoenmakers' sample with declination $\ge$ $+60^{\circ}$ are also in our sample. On the other hand, we find 8 low redshift GRGs with angular sizes larger than $5\hbox{$^\prime$ }$ that are missing from Schoenmakers' sample, most possibly due to an underestimation of the true source size induced by the low resolution of the WENSS survey (Schoenmakers priv. comm.). These 8 sources are J0607+612, J0926+653, J1216+674, J1844+653, J1853+800, J1918+742, J1951+706 and J2035+680. We have also checked that all giant radio galaxies larger than $4\hbox {$^\prime $ }$ in the compilation by Ishwara-Chandra & Saikia (1999) are in our sample. Therefore, we have enough confidence that the selection from the NVSS is a good procedure (at least as good as others) to define samples of extended radio sources. In fact, we find in our sample 22 new GRGs (written in boldface in Table 2), increasing to a total of 103 the number of known giants.

Figure 5 shows the number of sources per redshift bin of 0.05. We find that 87% of the sources with known redshift are below z=0.25. In fact, the selection criteria require sources with $z\ge 0.5$to have projected linear sizes larger than 1.7 Mpc (see Fig. 7). Since such huge sources are rare (e.g. Ishwara-Chandra & Saikia 1999), it is not unexpected that our sample is mostly composed by relatively nearby radio galaxies.

Figure 4: Integrated flux density per length unit against the source angular length. The vertical and the oblique solid lines represent the sample limits in angular size ($\ge$ $4\hbox {$^\prime $ }$) and flux density ( $S_{\rm t}^{1.4}\ge$100 mJy), respectively. The dashed horizontal line represents the sensitivity limit of the NVSS (see text). The vertical dotted line marks the angular size of $15.8\hbox {$^\prime $ }$, above which sources with a flux density greater than 100 mJy could be undetected in the NVSS (P point). Sources with uncertain redshift in Table 2 are represented with asterisks

Figure 5: Histogram of the distribution of redshifts in our sample. The redshift bin is 0.05

The total radio power at 1.4 GHz as a function of the source redshift is represented in Fig. 6. The effect of the total flux density limitation ( $S_{\rm t}^{1.4} \ge 100$ mJy) is easily visible and shown by a solid line. This limitation masks any possible trend of the radio power distribution with the redshift, although we note the small number of nearby ($z \le 0.1$) high power ( $\log P_{\rm t}^{1.4} \ge 25.5$) radio sources in the sample. Similarly, if we represent the source linear sizes against their redshifts (Fig. 7), we find a small number of giant radio galaxies with $z \le 0.1$. We plot in Fig. 7 a dashed line which represents the locus of a 100 mJy $16\hbox{$^\prime$ }$ large radio source in this diagram (P point in Fig. 4), to give an idea of the sensitivity limit of the NVSS. We find that GRGs with $z\le 0.04$ could be below the detection limit. However, the dashed line does not define a stringent limit since the real brightness distribution of radio sources is not rectangular and uniform as we have previously assumed. In consequence, much larger sources could be detected and, in fact, we find a low redshift source in our sample above that limit: J1632+825 (NGC 6251; dominated by a strong narrow jet).

Figure 6: Luminosities of the members of the sample plotted against their redshifts. The solid line represents the flux density limit imposed by our selection criteria ( $S_{\rm t}^{1.4}\ge$100 mJy). Sources with uncertain redshift in Table 2 are represented with asterisks

Figure 7: Projected linear distance against redshift. The solid line indicates the limit imposed by our selection criteria (as in Fig. 4, there are some sources smaller than 4 $\hbox {$^\prime $ }$). The dashed line represents the sensitivity limit of the NVSS for a 16 $\hbox {$^\prime $ }$ extended 100 mJy source (see text). The horizontal dotted line marks the usual definition of giant radio galaxies. Sources with uncertain redshift in Table 2 are represented with asterisks

The lack of small size sources at high redshift is entirely related to our selection limit of 4 $\hbox {$^\prime $ }$ in size (solid line; there are sources below the line, which correspond to sources smaller than 4 $\hbox {$^\prime $ }$ in Table 2). Moreover, we have a few giant radio galaxies at high redshift ($z\ge 0.5$). From previous studies (e.g. Schoenmakers et al. 2000; Lara et al. 2000) it was derived that giant sources are characterized by large spectral ages. The existence of giant radio galaxies at high redshift would then imply that old radio sources are present at $z\ge 0.5$.

Another question raised after a first inspection of the sample is why we do not find radio sources with linear sizes below 200 Kpc. From Fig. 7 we find that intrinsically small sources should have redshifts below 0.03 to fit the size limit of 4 $\hbox {$^\prime $ }$. We have 6 sources below this redshift, but with angular sizes above 7 $\hbox {$^\prime $ }$. The absence of small nearby sources must be related with the radio galaxy population and the small volume enclosed at low redshifts. There exist indeed sources smaller than 100 Kpc which fit our requirements, but must be rare (one example should be Cen A, if it were at declinations above $+60^{\circ}$).

In Fig. 8 we have plotted the source projected linear size versus the source total radio power at 1.4 GHz. The dotted line represents the "limit'' due to sensitivity limitations of the NVSS, as in Fig. 7. We find a striking absence of intrinsically small high power radio galaxies. All sources with sizes below 500 Kpc have $\log P_{\rm t}(1.4)$ below 25.5. Since our criteria require that sources smaller than 500 Kpc be at $z \le 0.1$, this is not a selection effect and must be a consequence of the statistically low number of sources with high radio power enclosed in the limited volume given by z < 0.1. Nearby sources have, in general, low power.

Figure 8: Projected linear sizes of the members of the sample plotted against their luminosities. The dashed line represents the same sensitivity limit shown in Fig. 7. Sources with uncertain redshift in Table 2 are represented with asterisks

Finally, we plot in Fig. 9 a histogram of the core flux density at 4.9 GHz, up to 100 mJy. There are 5 sources with a core flux density above this value and therefore not represented in this plot. We note that our selection criteria do not impose restrictions on the core flux density and in fact, 51 out of 84 radio sources have weak cores, below 10 mJy. This is an expected result, since our sample selection criteria do not favor jets pointing toward the observer and, consequently, we do not expect relativistic Doppler boosting of intrinsically weak cores. However, the study of the parsec scale properties of the members of the sample by means of VLBI observations will require, in most cases, the use of the phase referencing technique in order to achieve enough sensitivity to properly map radio cores with a flux density below 10-20 mJy.

Figure 9: Histogram of the core flux density of the sample sources at 4.9 GHz, up to 100 mJy. The bin size is 5 mJy