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 the formation of massive stars similar or equal to 10(3)-10(4) M-circle dot 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 M-ZAMS/M-circle dot = 300-3000 and metallicity Z/Z(circle dot) = 0-10(-1), and discuss whether or not pulsation-driven mass loss prevents massive BH formation. In the MS phase, the pulsational instability excited by the o-mechanism grows in similar to 10(3) yr. As the stellar mass and metallicity increase, the mass-loss rate increases to less than or similar to 10(-3) M yr(-1). In the red supergiant.(RSG) phase, the instability is excited by the kappa-mechanism operating in the hydrogen ionization zone and grows more rapidly in similar to 10 yr. The RSG mass-loss rate is almost independent of metallicity and distributes in the range of similar to 10(-3)-10(-2) M-circle dot yr(-1). Conducting stellar structure calculations including feedback due to pulsation-driven winds, we find that the stellar models of M-ZAMS M-circle dot = 300-3000 can leave behind remnant BHs more massive than similar to 200-1200 M-circle dot. We conclude that massive merger products can seed monster SMBHs observed at z > 6.