  Gravitational instability in the outskirts of Active Galactic Nuclei (AGN)
disks lead to disk fragmentation and formation of super-massive (several
10^2Msun) stars with potentially long lifetimes. Alternatively, stars can be
captured ex-situ and grow from gas accretion in the AGN disk. However, the
number density distribution throughout the disk is limited by thermal feedback
as their luminosities provide the dominant heating source. We derive
equilibrium stellar surface density profiles under two limiting contexts: in
the case where the stellar lifetimes are prolonged due to recycling of hydrogen
rich disk gas, only the fraction of gas converted into heat is removed from the
disk accretion flow. Alternatively, if stellar composition recycling is
inefficient and stars can evolve off the main sequence, the disk accretion rate
is quenched towards smaller radii resembling a classical star-burst disk,
albeit the effective removal rate depends not only on the stellar lifetime, but
also the mass of stellar remnants. For AGNs with central Supermassive Black
Hole (SMBH) masses of \sim 10^6 to 10^8Msun accreting at \sim 0.1 Eddington
efficiency, we estimate a total number of 10^3 to 10^5 coexisting massive stars
and the rate of stellar mergers to be 10^-3 to 1 per year. We motivate the
detailed study of interaction between a swarm of massive stars through hydro
and N body simulations to provide better prescriptions of dynamical processes
in AGN disks, and to constrain more accurate estimates of the stellar
population.
