Testing General Relativity with the Black Hole Shadow Size and Asymmetry of Sagittarius A*: Limitations from Interstellar Scattering

Abstract

The Event Horizon Telescope, a global 230 GHz very-long-baseline interferometry array, achieves angular resolution of , sufficient to resolve the supermassive black hole Sagittarius A* (Sgr A*). This resolution may soon enable measurements of the black hole “shadow” size and asymmetry, predicted to be ≈50 and ≲3 μ as, respectively. Measurements that depart from these values could indicate a violation of the “no-hair theorem.” However, refractive scattering by the turbulent ionized interstellar medium distorts the image of Sgr A*, affecting its apparent size and asymmetry. In this paper, we present a general analytic approach to quantify the expected image wander, distortion, and asymmetry from refractive scattering. If the turbulence in the scattering material of Sgr A* is close to Kolmogorov, we estimate the mean refractive image wander, distortion, and asymmetry to be 0.53, 0.72, and 0.52 μ as at 230 GHz. However, alternative scattering models with flatter power spectra can yield larger values, up to 2.1, 6.3, and 5.0 μ as, respectively. We demonstrate that these effects can be reduced by averaging images over multiple observations. For a small number of observations, the effects of scattering can be comparable to or greater than those from black hole spin, and they determine a fundamental limit for testing general relativity via images of Sgr A*.