Untangling the merger history of massive black holes with LISA

Binary black hole coalescences emit gravitational waves that will be measurable by the space-based detector it LISA to large redshifts. This suggests that LISA may be able to observe black holes grow and evolve as the universe evolves, mapping the distribution of black hole masses as a function of redshift. An immediate difficulty with this idea is that LISA measures certain redshifted combinations of masses with good accuracy: if a system has some mass parameter m, then LISA measures (1+z)m. This mass-redshift degeneracy makes it difficult to follow the mass evolution. In many cases, LISA will also measure the luminosity distance D of a coalescence accurately. Since cosmological parameters (particularly the mean density, the cosmological constant, and the Hubble constant) are now known with moderate precision, we can obtain z from D and break the degeneracy. This makes it possible to untangle the mass and redshift and to study the mass and merger history of black holes. Mapping the black hole mass distribution could open a window onto an early epoch of structure formation.