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
$z\gtrsim 1$. 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 order $10^4-10^6\, M_\odot$ within some $10^7$ 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 masses BHs in quasar hosts at $z\gtrsim
7$, when the age of the Universe $\lesssim 0.8$ Gyr constitutes a demanding
constraint; moreover, in more common ETG progenitors at redshift $z\sim 2-6$ it
can concur with disk accretion to build such large BH masses even at moderate
Eddington ratios $\lesssim 0.3$ within the short star-formation duration
$\lesssim$ 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 (ET) and
the Laser Interferometer Space Antenna (LISA).
