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Probing Long Gamma Ray Bursts progenitor mass by Gravitational Waves

In this work we present a procedure to infer the mass of progenitors and remnants of Gamma Ray Bursts (GRB), starting from the observed energy $E_{iso}^{GRB}$ emitted isotropically and considering the associated emission of Gravitational Waves (GW) $ E_{iso}^{GW}$ in the different phases. We assume that the GW energy of the progenitor $E_{PROG}^{GW}$ is emitted partially during a star collapse, and the residual energy is related to the GW energy emitted by the remnant. We take a sample of $237$ Long GRB, and use an hybrid Montecarlo procedure to explore, for each of them, a region of possible solutions of $ E_{iso}^{GW}$ as a function of the masses, radii, oblateness, rotation frequencies of progenitor and remnant and the fraction of energy $k$ emitted as GW by the GRB. We discriminate between a Neutron Star (NS) or Black Hole (BH) for the remnant and obtain interesting values for the GW emitted by the remnant NS or BH, for the conversion factor $k$ of and for the masses and radii of GRB progenitor stars. We also obtain remnant populations with mean masses, mean GW frequencies and GRB frequency of GW emission in agreement with the most accepted models.