Pulsation-driven mass loss from massive stars behind stellar mergers in metal-poor dense clusters

The recent discovery of high-redshift (z > 6) supermassive black holes (SMBH) favors the formation of massive seed BHs in protogalaxies. One possible scenario is formation of massive stars ~ 1e3-1e4 Msun via runaway stellar collisions in a dense cluster, leaving behind massive BHs without significant mass loss. We study the pulsational instability of massive stars with the zero-age main-sequence (ZAMS) mass Mzams/Msun = 300-3000 and metallicity Z/Zsun = 0-0.1, and discuss whether or not pulsation-driven mass loss prevents massive BH formation. In the MS phase, the pulsational instability excited by the epsilon-mechanism grows in ~ 1e3 yrs. As the stellar mass and metallicity increase, the mass-loss rate increases to < 1e-3 Msun/yr. In the red super-giant (RSG) phase, the instability is excited by the kappa-mechanism operating in the hydrogen ionization zone and grows more rapidly in ~ 10 yrs. The RSG mass-loss rate is almost independent of metallicity and distributes in the range of ~ 1e-3-1e-2 Msun/yr. Conducting the stellar structure calculations including feedback due to pulsation-driven winds, we find that the stellar models of Mzams/Msun = 300-3000 can leave behind remnant BHs more massive than ~ 200-1200 Msun. We conclude that massive merger products can seed monster SMBHs observed at z > 6.