Galaxy clustering at z similar to 2 and halo radii

The amplitude of the angular two-point galaxy autocorrelation function w(th eta) for galaxies at z similar to 2 is estimated for galaxies in the Hubble Deep Field by using a U < 27 complete subsample. The U-band selection ensu res little contamination from z > 2.5 galaxies, while photometric redshifts minimize the contribution from low redshift galaxies. (i) It is confirmed that the amplitude of the correlation can be corrected for the integral constraint (lack of large-scale variance) without having t o make assumptions about the shape of the correlation function and by avoid ing the introduction of linear error terms. The estimate using this techniq ue is w(theta approximate to 5 arcsec) = 0.10 +/- 0.09. Estimators that ass ume a power law of a given slope and include linear error terms would doubl e this value. (ii) If the biases introduced in faint galaxy selection owing to obscuratio n by large objects are not corrected for by masking areas around them, then the estimate would be w(theta approximate to 5 arcsec) = 0.16 +/- 0.07. (iii) The effective (three-dimensional) galaxy pair separation at 5 arcsec and this redshift range is approximate to 25-250 h(-1) kpc, so the correcti on to the spatial correlation function xi(r) owing to exclusion of overlapp ing galaxy dark matter haloes should be considered. For stable clustering i n proper units in an Omega = i, lambda = 0 universe, our w(5 arcsec) estima te (a) implies a present-day correlation length of r(0) similar to 2.6(-1.7 )(+1.1) h(-1) Mpc if halo overlapping is ignored, but (b) for a present-day correlation length of r(0) = 5.5 h(-1) Mpc implies that a typical halo exc lusion radius is r(halo) = 70(-30)(+420) h(-1) kpc For Omega(0) = 0.1, lamb da(0) = 0.9, the corresponding values are (a) r(0) similar to 5.8(-3.9)(+2. 4) h(-1) Mpc and (b) r(halo) < 210 h(-1) kpc (1 sigma upper limit). (iv) The decreasing correlation period (DCP) of a high initial bias in the spatial correlation function is not detected at this redshift, For an Omega = i, lambda = 0 universe and stable clustering in proper units, possible d etections of the DCP in other work would imply that the values of xi at red shifts greater than z(t) = 1.7 +/- 0.9 would be [(1 + z)/(1 + z(t))](2.1+/- 3.6) times their values at z(t), which is consistent with our lack of detec tion at z similar to 2.