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We study, for the first time, the shadow of the supermassive black hole SgrA$^{*}$ at the center of the Milky Way in dark matter halos. For the Cold DarkMatter and Scalar Field Dark Matter models considered in this work, theapparent shape of the shadow depends upon the black hole spin $a$ and the darkmatter parameter $k$. We find that both dark matter models influence the shadowin a similar way. The shadow is a perfect circle in the non-rotating case($a=0$) and a deformed one in the rotating case ($a\neq0$). The size of theshadow increases with increasing $k$ in both non-rotating and rotating cases,while the shadow gets more and more distorted with increasing $a$ in therotating case. We further investigate the black hole emission rate in both darkmatter halos. We find that the emission rate decreases with increasing $k$ andthe peak of the emission shifts to lower frequency. Finally, by calculating theangular radius of the shadow, we estimate that the dark matter halo couldinfluence the shadow of Sgr A$^{*}$ at a level of order of magnitude of$10^{-3}$ $\mu$as and $10^{-5}$ $\mu$as, for CDM and SFDM, respectively. Futureastronomical instruments with high angular resolution would be able to observethis effect and shed light on the nature of Sgr A$^{*}$. More interestingly, itmay be possible to distinguish between CDM and SFDM models given theresolutions required differing by two orders of magnitude from each other.

Black Hole Shadow of Sgr A$^{*}$ in Dark Matter Halo