Measures of galaxy environment III: difficulties in identifying protoclusters at z~2

Galaxy environment is frequently discussed, but inconsistently defined. It is especially difficult to measure at high redshift where only photometric redshifts are available. With a focus on early forming protoclusters, we use a semi-analytical model of galaxy formation to show how the environment measurement around high-redshift galaxies is sensitive to both scale and metric, as well as to cluster viewing angle, evolutionary state and the availability of either spectroscopic or photometric data. We use two types of environment metrics (nearestneighbour and fixed aperture) at a range of scales on simulated high-z clusters to see how 'observed' overdensities compare to 'real' overdensities. We also 'observationally' identify z = 2 protocluster candidates in our model and track the growth histories of their parent haloes through time, considering in particular their final state at z = 0. Although the measured environment of early forming clusters is critically dependent on all of the above effects (and in particular the viewing angle), we show that such clusters are very likely (90 per cent) to remain overdense at z = 0, although many will no longer be among the most massive. Object-to-object comparisons using different methodologies and different data, however, require much more caution