Observational Limits on Einasto Dark Matter Parameters from Event Horizon Telescope Images of Sgr A ∗ and M87 ∗

Résumé

Abstract The Event Horizon Telescope (EHT) has provided images of the supermassive black holes Sgr A* and M87*, enabling direct tests of gravity. Any extended mass distribution, such as a dark matter halo, perturbs null geodesics in the photon-ring regime, making shadow measurements a probe of inner-halo structure. In this work, we investigate static, spherically symmetric black holes surrounded by Einasto-type dark matter halos and derive constraints from EHT shadow data. Starting from the Einasto density profile with parameters ϱ 0 , α ˜ , ν ˜ , we construct a metric function f ( r ) = 1 − 2 M / r + 2 M ∞ g ˜ ( r ) that interpolates between the black hole horizon and the asymptotic halo, following the approach of Xu et al. but adapted specifically to the Einasto scenario. We analyze the photon potential, null geodesics, and shadow radius as functions of black hole mass M in the nonspinning limit. Using the dimensionless shadow diameter d sh ≡ Dθ / M measured by the EHT— d sh M 87 * = 11.0 ± 1.5 and d sh Sgr A * = 9.5 ± 1.4 —we perform Bayesian parameter estimation to identify allowed regions in the Einasto parameter space. Combined with the independently measured black hole masses from stellar dynamics, our results place constraints on the inner dark matter distribution: for Sgr A*, adopting the stellar-orbit mass prior, we find ϱ 0 ≲ 10 −11 M ⊙ pc −3 at 1 σ confidence, while for M87*, the bounds are weaker due to distance uncertainties. The Einasto index ν ˜ is weakly constrained, indicating that EHT precision primarily limits the mass enclosed near the photon sphere rather than the profile slope. These findings demonstrate that horizon-scale imaging can complement galactic-scale dynamics in probing dark matter models, including fuzzy dark matter scenarios with solitonic cores. Future EHT observations will refine these constraints and distinguish between competing dark matter descriptions.

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