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. One expects this effect to be most important for the most luminous and hottest clusters. XLFs and TFs of clusters provide some of the strongest constraints on cosmological and large-scale structure parameters, such as the mean fluctuation parameter sigma(8) and the matter density divided by the critical density Omega(0). 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 semianalytic technique to estimate the effect of merger boosts on the XLFs and TFs. 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 red-shift 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 > 5 x 10(44) h(-2) ergs s(-1) 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 PS 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. If the parameters of the fluctuation spectrum are derived from the observed TF or XLF (e.g., from a low-redshift sample), then this removes most of the boost effect on Omega(0). However, larger merger boost effects may appear when cluster XLFs and TFs are compared to cosmological structure parameters derived by other techniques (e.g., cosmic microwave background fluctuations or the brightness of distant supernovae).