The Effect of Merger Boosts on the Luminosity, Temperature, and Inferred Mass Functions of Clusters of Galaxies

In the standard Cold Dark Matter model of structure formation, massive clusters form via the merger of smaller clusters. N-body/hydrodynamical simulations of merging galaxy clusters have shown that mergers can temporarily boost the X-ray luminosity and temperature of the merged cluster above the equilibrium values for the merged system. The cumulative effect of these "merger boosts" will affect the observed X-ray luminosity functions (XLFs) and temperature functions (TFs) of clusters. Merger boosts may bias the values of sigma_8 and Omega_0 inferred from cluster XLFs and TFs if virial equilibrium is assumed. We use a semi-analytic technique to estimate the effect of merger boosts on the X-ray luminosity and temperature functions. The boosts from individual mergers are derived from N-body/hydrodynamical simulations of mergers. The statistics of the merger histories of clusters are determined from extended Press-Schechter (PS) merger trees. We find that merger boosts can increase the apparent number of hot, luminous clusters. For example, in a Universe with Omega_0 = 0.3 and Omega_Lambda = 0.7 at a redshift of z=1, the number of clusters with temperatures T > 10 keV is increased by a factor of 9.5, and the number of clusters with luminosities L_X > 5x10^44 h^-2 erg/s is increased by a factor of 8.9. We have used our merger-boosted TFs and XLFs to derive the cosmological structure parameters sigma_8 and Omega_0 by fitting Press-Schechter equilibrium relations to local (z=0) and distant (either z=0.5 or z=1) cluster samples. Merger boosts cause sigma_8 to be overestimated by about 20%. The matter density parameter Omega_0 may be underestimated by about 20%, although this result is less clear.