Cluster mass function in mixed models

We study the cluster mass function in mixed dark matter (MDM) models, using two COBE-normalized simulations with Omega(h) = 0.26, n = 1.2 and Omega(h) = 0.14, n = 1.05, both with two massive neutrinos (models MDM1 and MDM2, respectively). For the sake of comparison, we also simulate a tilted cold dark matter model with spectral index n = 0.8 (TCDM), also COBE normalized. We argue that, in our nonhydrodynamical simulations, where cold dark matter (CDM) particles describe both actual CDM and baryons, the galaxy distribution traces CDM particles. Therefore, we use them to define clusters and their velocities to work out cluster masses. Since CDM particles are more clustered than hot dark matter (HDM) and therefore have, on average, greater velocities, this leads to significant differences from Press & Schechter (PS) predictions. Such predictions agree with simulations if both HDM and CDM are used to define clusters. If this criterion is adopted, however, we see that (1) MDM corresponds to delta(c) values slightly but systematically greater than CDM; and (2) such delta(c) exhibit a scale dependence: on scales similar to 10(14) M., we find delta(c) similar to 1.7 or 1.8 for CDM or MDM, respectively, while at greater scales the required delta(c) decreases, and a substantial cluster excess is found at the large-mass end (M > 10(15) M.). Clusters defined through CDM in MDM models, on the other hand, are less numerous than PS estimates by a factor of similar to 0.3 at the low-mass end; the factor becomes similar to 0.6-0.8, depending on the mix, on intermediate-mass scales (similar to 4-5 h(-1) 10(14) M.), and almost vanishes on the high-mass end. Therefore, (1) MDM models expected to overproduce clusters over intermediate scales are viable; (2) the greater reduction factor at small scales agrees with the observational data dependence on the cluster mass M (which, however, may be partially due to sample incompleteness); (3) the higher spectral normalization is felt at large scales, where MDM models produce more objects (hence, large clusters) than CDM. MDM1 even exceeds the findings of Donahue et al., while MDM2 is consistent with them. Simulations are performed using a parallel algorithm worked out from the Couchman AP3M serial code, but allowing for different particle masses and used with variable time steps. This allowed us to simulate a cubic box with sides of 360 h(-1) Mpc, reaching a Plummer resolution of 40.6 h(-1) kpc, using (3 x)180(3) particles.