Extrasolar planet population synthesis IV. Correlations with disk metallicity, mass, and lifetime

Context. This is the fourth paper in a series showing the results of planet population synthesis calculations. In Paper I, we presented our methods. In Paper II, we compared the synthetic and the observed planetary population statistically. Paper III addressed the influences of the stellar mass on the population. Aims. Our goal in this fourth paper is to systematically study the effects of important disk properties, namely disk metallicity, mass, and lifetime on fundamental properties of planets like mass and semimajor axis. Methods. For a large number of protoplanetary disks that have properties following distributions derived from observations, we calculated a population of planets with our formation model. The model is based on the classical core accretion paradigm but self-consistently includes planet migration and disk evolution. Results. We find a very large number of correlations. Regarding the planetary initial mass function, metallicity, M-disk, and tau(disk) play different roles. For high metallicities, giant planets are more frequent. For high M-disk, giant planets are more massive. For long tau(disk), giant planets are both more frequent and massive. At low metallicities, very massive giant planets cannot form, but otherwise giant planet mass and metallicity are nearly uncorrelated. In contrast, (maximum) planet masses and disk gas masses are correlated. The formation of giant planets is possible for initial planetesimal surface densities Sigma(S) of at least 6 g/cm(2) at 5.2 AU. The best spot for giant planet formation is at similar to 5 AU. In-and outside this distance, higher Sigma(S) are necessary. Low metallicities can be compensated for by high M-disk, and vice versa, but not ad infinitum. At low metallicities, giant planets only form outside the ice line, while giant planet formation occurs throughout the disk at high metallicities. The extent of migration increases with M-disk and tau(disk) and usually decreases with metallicity. No clear correlation of metallicity and the semimajor axis distribution of giant planets exists because in low-metallicity disks, planets start farther out, but migrate more, while the contrary applies to high metallicities. The final semimajor axis distribution contains an imprint of the ice line. Close-in low mass planets have a lower mean metallicity than hot Jupiters. The frequency of giant planets varies approximately as M-disk(1.2) and tau(2)(disk). Conclusions. The properties of protoplanetary disks - the initial and boundary conditions for planet formation - are decisive for the properties of planets, and leave many imprints on the population.