Growth of Supermassive Black Hole Seeds in ETG Star-forming Progenitors: Multiple Merging of Stellar Compact Remnants via Gaseous Dynamical Friction and Gravitational-wave Emission

We propose a new mechanism for the growth of supermassive black hole (BH) seeds in the star-forming progenitors of local early-type galaxies (ETGs) at z ≳ 1. This envisages the migration and merging of stellar compact remnants (neutron stars and stellar-mass BHs) via gaseous dynamical friction toward the central high-density regions of such galaxies. We show that, under reasonable assumptions and initial conditions, the process can build up central BH masses of the order of 10⁴-10⁶ M_⊙ within some 10⁷ yr, so effectively providing heavy seeds before standard disk (Eddington-like) accretion takes over to become the dominant process for further BH growth. Remarkably, such a mechanism may provide an explanation, alternative to super-Eddington accretion rates, for the buildup of billion-solar-massed BHs in quasar hosts at z ≳ 7, when the age of the universe ≲0.8 Gyr constitutes a demanding constraint; moreover, in more common ETG progenitors at redshift z ∼ 2-6, it can concur with disk accretion to build such large BH masses even at moderate Eddington ratios ≲0.3 within the short star formation duration ≲Gyr of these systems. Finally, we investigate the perspectives to detect the merger events between the migrating stellar remnants and the accumulating central supermassive BH via gravitational-wave emission with future ground- and space-based detectors such as the Einstein Telescope and the Laser Interferometer Space Antenna.