Constraining the black hole mass spectrum with gravitational wave observations - II. Direct comparison of detailed models

A number of scenarios have been proposed for the origin of the supermassive black holes (SMBHs) that are found at the centres of most galaxies. Many such scenarios predict a high-redshift population of massive black holes (MBHs), with masses in the range of 102-105 times that of the Sun. When the Laser Interferometer Space Antenna (LISA) is finally operational, it is likely that it will detect on the order of 100 of these MBH binaries as they merge. The differences between proposed population models produce appreciable effects in the portion of the population which is detectable by LISA, so it is likely that the LISA observations will allow us to place constraints on them. However, gravitational wave detectors such as LISA will not be able to detect all such mergers nor assign precise black hole parameters to the merger, due to weak gravitational wave signal strengths. This paper explores LISA's ability to distinguish between several MBH population models. In this way, we go beyond predicting a LISA-observed population and consider the extent to which LISA observations could inform astrophysical modellers. The errors in LISA parameter estimation are applied with a direct method which generates random sample parameters for each source in a population realization. We consider how the distinguishability varies depending on the choice of source parameters (one or two parameters chosen from masses, redshift or spins) used to characterize the model distributions, with confidence levels determined by one- and two-dimensional tests based on the Kolmogorov-Smirnov test.