نبذة مختصرة : We calculate the linear e-folding time of pulsation for vibrationally unstable main-sequence supermassive stars (105-3.109M, where M0 is the solar mass), dynamically stabilized by a uniform or differential rotation, using some simplifying assumptions, none of which seems critical. For the most massive stars, stabilized by a differential rotation (108-3.109 M0) which, following Hoyle and Fowler, could represent quasi-stellar objects, the e-folding time of pulsation is of the order of their life time (about 2.106 years) in the main-sequence stage, for a large interval of values of the central angular velocity of rotation. So, the phenomenon of vibrational instability cannot affect significantly the hydrogen burning stage of these stars. Vibrational instability can, however, excite the adiabatic pulsations of some supermassive stars and so explain the optical periodicities observed for certain «quasars », like 3 C 345 and 3 C 273. If it is sufficiently violent, it can give birth to a stellar wind, which can be the source of the clouds of gas moving outward at very high velocities, which seem to be necessary to explain the multiple absorption red-shifts of some «quasars ». Finally, supermassive stars dynamically stabilized by a differential rotation, but vibrationally unstable, could play an important rôle in the formation of the helium observed throughout the universe.
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