In this paper we investigate how the dark matter halo mass function evolves with redshift, based on a suite of very large (with N p = 3072 3 − 6000 3 particles) cosmological N-body simulations. Our halo catalogue data spans a redshift range of z = 0−30, allowing us to probe the mass function from the Dark Ages to the present. We utilise both the Friends-of-Friends (FOF) and Spherical Overdensity (SO) halofinding methods to directly compare the mass function derived using these commonly used halo definitions. The mass function from SO haloes exhibits a clear evolution with redshift, especially during the recent era of dark energy dominance (z < 1). We provide a redshift-parameterised fit for the SO mass function valid for the entire redshift range to within ∼ 20% as well as a scheme to calculate the mass function for haloes with arbitrary overdensities. The FOF mass function displays a weaker evolution with redshift. We provide a 'universal' fit for the FOF mass function, fitted to data across the entire redshift range simultaneously, and observe redshift evolution in our data versus this fit. The relative evolution of the mass functions derived via the two methods is compared. For an SO halo defined via an overdensity of 178 versus the background matter density and an FOF halo defined via a linking length of 0.2 times the mean inter-particle separation we find that the mass functions most closely match at z = 0. The disparity at z = 0 between the FOF and SO mass functions resides in their high mass tails where the collapsed fraction of mass in SO haloes is ∼ 80% of that in FOF haloes. This difference grows with redshift so that, by z > 20, the SO algorithm finds a ∼ 50 − 80% lower collapsed fraction in high mass haloes than the FOF algorithm.

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The XMM Cluster Survey (XCS) is a serendipitous search for galaxy clusters using all publicly available data in the XMM–Newton Science Archive. Its main aims are to measure cosmological parameters and trace the evolution of X‐ray scaling relations. In this paper we present the first data release from the XMM Cluster Survey (XCS‐DR1). This consists of 503  optically confirmed, serendipitously detected, X‐ray clusters. Of these clusters, 256  are new to the literature and 357  are new X‐ray discoveries. We present 463  clusters with a redshift estimate (0.06 < z < 1.46), including 261  clusters with spectroscopic redshifts. The remainder have photometric redshifts. In addition, we have measured X‐ray temperatures (TX) for 401  clusters (0.4 < TX < 14.7 keV). We highlight seven interesting subsamples of XCS‐DR1 clusters: (i) 10  clusters at high redshift (z > 1.0, including a new spectroscopically confirmed cluster at z= 1.01); (ii) 66  clusters with high TX (>5 keV); (iii) 130  clusters/groups with low TX (<2 keV); (iv) 27  clusters with measured TX values in the Sloan Digital Sky Survey (SDSS) ‘Stripe 82’ co‐add region; (v) 77  clusters with measured TX values in the Dark Energy Survey region; (vi) 40  clusters detected with sufficient counts to permit mass measurements (under the assumption of hydrostatic equilibrium); (vii) 104  clusters that can be used for applications such as the derivation of cosmological parameters and the measurement of cluster scaling relations. The X‐ray analysis methodology used to construct and analyse the XCS‐DR1 cluster sample has been presented in a companion paper, Lloyd‐Davies et al.