Astrophysical constraints on massive black hole binary evolution from pulsar timing arrays

We consider the information that can be derived about massive black hole binary (MBHB) populations and their formation history solely from current and possible future pulsar timing array (PTA) results. We use models of the stochastic gravitational-wave background from circular MBHBs with chirp mass in the range 106-1011 M⊙ evolving solely due to radiation reaction. Our parametrized models for the black hole merger history make only weak assumptions about the properties of the black holes merging over cosmic time. We show that current PTA results place an upper limit on the black hole merger density which does not depend on the choice of a particular merger history model; however, they provide no information about the redshift or mass distribution. We show that even in the case of a detection resulting from a factor of 10 increase in amplitude sensitivity, PTAs will only put weak constraints on the source merger density as a function of mass, and will not provide any additional information on the redshift distribution. Without additional assumptions or information from other observations, a detection cannot meaningfully bound the massive black hole merger rate above zero for any particular mass.