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Self-interacting dark matter is known as one of the most appropriate candidates for dark matter. Due to its excellent success in removing many astrophysical problems, particularly in small scale structure, studying this model has taken on added significance. In this paper, we focus on the results of two previously performed simulations of cluster sized halos with self-interacting dark matter and introduce a new function for the density profile of galaxy clusters, which can perfectly describe the result of these simulations. This density profile helps to find a velocity dispersion profile and also a relation between cluster mass and concentration parameter. Using these relations, we investigate two scaling relations of galaxy clusters, namely massâvelocity dispersion and massâtemperature relations. The scaling relations reveal that in the self-interacting dark matter model, halos are more massive than what the standard non-interacting model predicts for any fixed temperature. We also study the massâtemperature relation for a hybrid interacting model, which is a combination of self-interacting dark matter idea with another model of the dark sector in which dark matter particle mass is determined according to its interaction with dark energy. This super interacting dark sector (SIDS) model can change the massâtemperature relation to a modified form that has the same result as a non-interacting model. Finally, we provide quantitative expressions which can describe the constants of this interacting model with the value of cross-section per unit mass of dark matter particles.
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