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We study the merger rate of primordial black holes (PBHs) in self-interacting dark matter (SIDM) halo models. To explore a numerical description of the density profile of SIDM halo models, we use the result of a previously performed simulation for SIDM halo models with Ã?/m=10Ã¢??Ã¢??cm2Ã¢??g-1. We also propose a concentration-mass-time relation that can explain the evolution of the halo density profile related to SIDM models. Furthermore, we investigate the encounter condition of PBHs that may have been randomly distributed in the medium of dark matter halos. Under these assumptions, we calculate the merger rate of PBHs within each halo considering SIDM halo models and compare the results with that obtained for cold dark matter (CDM) halo models. To do this, we employ the definition of the time after halo virialization as a function of halo mass. Also, by unifying the transition time for all halos using a quantity that depends on the halo mass and cross section of SIDM particles, we indicate that SIDM halo models, for fPBH>0.32, can generate sufficient PBH mergers in such a way that their numbers exceed the corresponding results obtained from CDM halo models. By considering the spherical-collapse halo mass function, we obtain similar results for the cumulative merger rate of PBHs, for fPBH=1. Moreover, we calculate the evolution of the PBH total merger rate as a function of redshift. The results show that SIDM models, when considering fPBH>0.32, could have generated more significant PBH mergers than CDM models at higher redshifts. To determine a constraint on the PBH abundance, we study the merger rate of PBHs in terms of their fraction and masses and compare those with the black hole merger rate estimated by the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) detectors during the third observing run. The results demonstrate that within the context of SIDM halo models, the merger rate of 10Ã¢??Ã¢??MÃ¢??-10Ã¢??Ã¢??MÃ¢?? events can potentially fall within the aLIGO window. We also estimate a relation between the fraction of PBHs and their masses, which is well consistent with our findings.
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