Impact of star formation inhomogeneities on merger rates and interpretation of LIGO results

Within the next decade, ground based gravitational-wave detectors are in principle capable of determining the compact object merger rate per unit volume of the local universe to better than 20% with more than 30 detections. These measurements will constrain our models of stellar, binary and star cluster evolution in the nearby present-day and ancient universe. We argue that the stellar models are sensitive to heterogeneities (in age and metallicity at least) in such a way that the predicted merger rates are subject to an additional 30–50% systematic errors unless these heterogeneities are taken into account. Without adding new electromagnetic constraints on massive binary evolution or relying on more information from each merger (e.g., binary masses and spins), as few as the ≃ 5 merger detections could exhaust the information available in a naive comparison to merger rate predictions. As a concrete example immediately relevant to analysis of initial and enhanced LIGO results, we use a nearby-universe catalog to demonstrate that no one tracer of stellar content can be consistently used to constrain merger rates without introducing a systematic error of order O(30%) at 90% confidence (depending on the type of binary involved). For example, though binary black holes typically take many Gyr to merge, binary neutron stars often merge rapidly; different tracers of stellar content are required for these two types. More generally, we argue that theoretical binary evolution can depend sufficiently sensitively on star-forming conditions—even assuming no uncertainty in binary evolution model—that the distribution of star-forming conditions must be incorporated to reduce the systematic error in merger rate predictions below roughly 40%. We emphasize that the degree of sensitivity to star-forming conditions depends on the binary evolution model and on the amount of relevant variation in star-forming conditions. For example, if after further comparison with electromagnetic and gravitational-wave observations future population synthesis models suggest all BH-BH binary mergers occur promptly and therefore are associated with well-studied present-day star formation, the associated composition-related systematic uncertainty could be lower than the pessimistic value quoted above. Further, as gravitational-wave detectors will make available many properties of each merger—binary component masses, spins and even short GRB associations and host galaxies could be available—many detections can still be exploited to create high-precision constraints on binary compact object formation models.