Being Careful with the Field Formation Interpretation of GW190412

Abstract: The LIGO/Virgo Scientific Collaboration recently announced the detection of a compact object binary merger, GW190412, as the first asymmetric binary black hole (BBH) merger with mass ratio $q\approx0.25$. Other than the mass ratio, this BBH has shown to have a positive effective spin of around $\chi_{\rm eff}\approx0.28$. Assuming a field formation channel, associating this effective spin to either the primary or the secondary BH each has its implications: If the spin of the BBH comes form the primary BH, it has consequences for the efficiency of angular momentum transport in the formation of the BH. If, on the other hand, the spin is due to the secondary BH through tidal spin-up processes, one has to note that (i) such processes have very short delay-times, and (ii) subsequently, their local merger rate is determined by local star formation rate at assumed formation metallicity of the BBH. We show that the predicted merger rate density from this channel is $\lesssim 0.3~\rm Gpc^{-3} yr^{-1}$ and in tension with the rather high local merger rate of such systems which we estimate from this single event to be $\sim 1.7^{+2.5}_{-1.4}~\rm Gpc^{-3} yr^{-1}$ (90\% confidence interval, and assuming 50 days of observing time). Large natal kicks ($v\gtrsim 500\,{\rm km/s}$) would be required to get such BBHs with an in-plane spin component to account for the marginal detection of precession in GW190412. However, this would only exacerbate the tension as the estimated local merger rate would be further decreased. Similarly, the formation of such systems through the dynamical assembly is exceedingly rare, leaving this system a dilemma hard to account for with the currently accepted paradigms of BBH formation.