Shadow bound of black holes with dark matter halo

We investigate the shadow cast of black holes immersed in a dark matter halo. We use the M87* shadow data obtained by the EHT collaboration to constrain two parameters ($M,a$) of dark matter halo surrounding a black hole with mass $M_{\mathrm{b}\mathrm{h}}$. For $a\ge 10.8M$, we find the favored region (shadow bound), while the disfavored region is found for $a<10.8M$ when imposing the EHT results. This shadow bound is much less than the observation bound of galaxies ($a\ge {10}^{4}M$).