What are Protoclusters? -- Defining High Redshift Galaxy Clusters and Protoclusters

We explore the structures of protoclusters and their relationship with high redshift clusters using the Millennium Simulation combined with a semi-analytic model. We find that protoclusters are very extended, with 90 per cent of their mass spread across $\sim35\,h^{-1}{\rm Mpc}$ comoving at $z=2$ ($\sim30\, \rm{arcmin}$). The `main halo', which can manifest as a high redshift cluster or group, is only a minor feature of the protocluster, containing less than 20 per cent of all protocluster galaxies at $z=2$. Furthermore, many protoclusters do not contain a main halo that is massive enough to be identified as a high redshift cluster. Protoclusters exist in a range of evolutionary states at high redshift, independent of the mass they will evolve to at $z=0$. We show that the evolutionary state of a protocluster can be approximated by the mass ratio of the first and second most massive haloes within the protocluster, and the $z=0$ mass of a protocluster can be estimated to within 0.2 dex accuracy if both the mass of the main halo and the evolutionary state is known. We also investigate the biases introduced by only observing star-forming protocluster members within small fields. The star formation rate required for line-emitting galaxies to be detected is typically high, which leads to the artificial loss of low mass galaxies from the protocluster sample. This effect is stronger for observations of the centre of the protocluster, where the quenched galaxy fraction is higher. This loss of low mass galaxies, relative to the field, distorts the size of the galaxy overdensity, which in turn can contribute to errors in predicting the $z=0$ evolved mass.