6 Galaxies or HII regions?

Colley et al. (1996) suggested that galaxies in the HDF-N may suffer from a wrong selection. High redshift galaxies on optical images have a clumpy appearance: first the redshift moves the ultraviolet rest-frame light into the optical, so galaxies are observed in UV rest-frame where star-forming regions are more prominent, second the fraction of irregular galaxies is higher than locally (van den Bergh et al. 1996; Abraham et al. 1996) and a large number of galaxies display asymmetry and multiple structure.

Colley et al. (1996) stressed that compact high-redshift objects may appear more prominently than diffuse objects if their angular size is smaller than the point-spread function (PSF). The cosmological dimming in surface brightness for these sources is less significant, leading to an enhancement of compact sources over diffuse, resolved objects. Since HST images have an excellent seeing, these clumps are not smoothed, so they may confuse detection algorithms (SExtractor, DAOFIND, FOCAS, etc.), and be counted as several distinct faint sources.

As suggested by Colley et al. (1996) in this case strong correlations between sources on scales <10 kpc should be found. A good test is therefore the two-point angular correlation function.

In order to check our sample against this effect, we computed this function on small angular scales: HII regions physical sizes are about 0.5 kpc, so a wrong selection of the catalogue should bring a positive peak in the two-point angular correlation function at 0.25-1arcsec. This scale corresponds to sizes less than 10 kpc for a wide range in redshift ( 0.8 < z < 3.5).

We computed the correlation function by comparing the number of data pairs at given angular separation to the number of data-random simulated pairs at the same separation (Davis & Peebles 1983). At fixed $\theta$ the sum of data pairs is

$$DD(\theta)=\sum_i\sum_j \delta_i\delta_j$$

where $\delta_i$ and $\delta_j$ are delta-functions on i-th and j-th galaxies positions. The sum over i is over all sources in the sample, and the sum over jincludes only objects within a distance $\theta$ from particle i. We then created a random sample and computed the cross count sum

$$DR(\theta)=\sum_i\sum_j \delta_i\delta^R_j$$

where $\delta_i$ is as before, and $\delta^R_j$ is the delta-function for positions of objects in the random sample within a distance $\theta$ from particle i.

The resulting two-point angular correlation function is given by:

$$w(\theta)=\frac{n_R}{n_D}\frac{DD(\theta)}{DR(\theta)}-1$$

where $\frac{n_R}{n_D}$ is the ratio of the mean density of random and data samples respectively.

We analyzed our sample in I₈₁₄ and B₄₅₀ bands. The I₈₁₄-band catalogue should suffer less from the effects described above, being selected in the reddest filter, the vice versa is true for the B₄₅₀-band catalogue.

The two-point angular correlation function is compatible with zero in each band if computed on the whole catalogue. Following Colley et al. (1996) we selected "small galaxies'' as defined by $\mathcal{D}=\sqrt{ab}<0.2$ arcsec, where a, b are the intensity-weighted second moments. At $\theta =0.8$ arcsec it is evident a peak in the function, $w(\theta)=0.67 \pm 0.59$ (Fig. 7). This feature may not be significant due to large errors.

However about $20-30\%$ of sources in the B₄₅₀-band catalogue have separation <1arcsec. We therefore analyzed these sources, by cross-correlating I₈₁₄ and B₄₅₀catalogues. In the B₄₅₀-band catalogue we selected pairs with a separation <1 arcsec which were not included in the I₈₁₄-band catalogue. These objects were single sources splitted in the B₄₅₀-band (with $B_{450} \approx 27-29$), corresponding to a single detection in the I₈₁₄-band. We then used SExtractor on the B₄₅₀ frame, after choosing a higher deblend-mincont = 0.1. 87 sources, with 21<B₄₅₀<26, corresponding to about 7% of the whole sample, were then considered as single galaxies.

Figure 7: The two-point angular correlation function $w(\theta )$ estimated in the B450 band on small angular scales, for "small'' sources, as defined by $\mathcal{D}=\sqrt{ab}<0.2$ arcsec, where a, b are the intensity-weighted second moments. The function is compatible with zero, but, within the error bars, it is possible to notice a peak at $\theta =0.8$ arcsec (corresponding to a physical distance of 4-6 kpc for 0.3<z<5)

This simple analysis shows that a remarkable fraction of sources in the HDF-S has a neighbour at small angular distance. It should be pointed out that the HDF-S is a pencil-beam survey, and projection effects may be sizeable.