Impact of inter-correlated initial binary parameters on double black hole and neutron star mergers

The distributions of the initial main-sequence binary parameters are one of the key ingredients in obtaining evolutionary predictions for compact binary (BH-BH/BH-NS/NS-NS) merger rates. Until now, such calculations were done under the assumption that initial binary parameter distributions were independent. For the first time, we implement empirically derived inter-correlated distributions of initial binary parameters primary mass (M₁), mass ratio (q), orbital period (P), and eccentricity (e). Unexpectedly, the introduction of inter-correlated initial binary parameters leads to only a small decrease in the predicted merger rates by a factor of ≲2-3 relative to the previously used non-correlated initial distributions. The formation of compact object mergers in the isolated classical binary evolution favours initial binaries with stars of comparable masses (q ≈ 0.5-1) at intermediate orbital periods (log P (days) = 2-4). New distributions slightly shift the mass ratios towards lower values with respect to the previously used flat q distribution, which is the dominant effect decreasing the rates. New orbital periods (∼1.3 more initial systems within log P (days) = 2-4), together with new eccentricities (higher), only negligibly increase the number of progenitors of compact binary mergers. Additionally, we discuss the uncertainty of merger rate predictions associated with possible variations of the massive-star initial mass function (IMF). We argue that evolutionary calculations should be normalized to a star formation rate (SFR) that is obtained from the observed amount of UV light at wavelength 1500 Å (an SFR indicator). In this case, contrary to recent reports, the uncertainty of the IMF does not affect the rates by more than a factor of ∼2. Any change to the IMF slope for massive stars requires a change of SFR in a way that counteracts the impact of IMF variations on compact object merger rates. In contrast, we suggest that the uncertainty in cosmic SFR at low metallicity can be a significant factor at play.