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Flat Central Density Profiles from Scalar Field Dark Matter Halo

The scalar field endowed with a cosh scalar field potential, behaves exactly in the same way as cold dark matter (CDM) in the region where the scalar field oscillates around its minimum. Also, in the linear regime, the scalar field dark matter (SFDM) hypothesis predicts the same structure formation as the cold dark matter one. This means that CDM and SFDM are equivalent from the cosmological point of view. The free parameters of the SFDM model can be fixed using cosmological observations. In a previous work, we showed by solving the Einstein Klein Gordon equations, that if we use such parameters, the scalar field collapses forming stable objects with a mass around $10^{12}M_{\odot}$. In the present work we use analytical solutions of the flat and weak field limit of the Einstein- Klein-Gordon equations. With this solutions we show that its scalar field density profile corresponds to a halo with an almost flat central density and that this halo coincides with the CDM model in a large outer region. Such a result could solve the problem of the cusp DM halo in galaxies without extra hypothesis, adding to the viability of the SFDM model. Thus, the SFDM model can be seen as an alternative model to the CDM one, with a self interacting WIMP.